Directory of Open Access Journals (Sweden)
ELİF BULUT
2013-06-01
Full Text Available Partial Least Squares Regression (PLSR is a multivariate statistical method that consists of partial least squares and multiple linear regression analysis. Explanatory variables, X, having multicollinearity are reduced to components which explain the great amount of covariance between explanatory and response variable. These components are few in number and they don’t have multicollinearity problem. Then multiple linear regression analysis is applied to those components to model the response variable Y. There are various PLSR algorithms. In this study NIPALS and PLS-Kernel algorithms will be studied and illustrated on a real data set.
The crux of the method: assumptions in ordinary least squares and logistic regression.
Long, Rebecca G
2008-10-01
Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.
International Nuclear Information System (INIS)
Shuke, Noriyuki
1991-01-01
In hepatobiliary scintigraphy, kinetic model analysis, which provides kinetic parameters like hepatic extraction or excretion rate, have been done for quantitative evaluation of liver function. In this analysis, unknown model parameters are usually determined using nonlinear least square regression method (NLS method) where iterative calculation and initial estimate for unknown parameters are required. As a simple alternative to NLS method, direct integral linear least square regression method (DILS method), which can determine model parameters by a simple calculation without initial estimate, is proposed, and tested the applicability to analysis of hepatobiliary scintigraphy. In order to see whether DILS method could determine model parameters as good as NLS method, or to determine appropriate weight for DILS method, simulated theoretical data based on prefixed parameters were fitted to 1 compartment model using both DILS method with various weightings and NLS method. The parameter values obtained were then compared with prefixed values which were used for data generation. The effect of various weights on the error of parameter estimate was examined, and inverse of time was found to be the best weight to make the error minimum. When using this weight, DILS method could give parameter values close to those obtained by NLS method and both parameter values were very close to prefixed values. With appropriate weighting, the DILS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In conclusion, the DILS method could be used as a simple alternative to NLS method, providing reliable parameter estimate. (author)
An improved partial least-squares regression method for Raman spectroscopy
Momenpour Tehran Monfared, Ali; Anis, Hanan
2017-10-01
It is known that the performance of partial least-squares (PLS) regression analysis can be improved using the backward variable selection method (BVSPLS). In this paper, we further improve the BVSPLS based on a novel selection mechanism. The proposed method is based on sorting the weighted regression coefficients, and then the importance of each variable of the sorted list is evaluated using root mean square errors of prediction (RMSEP) criterion in each iteration step. Our Improved BVSPLS (IBVSPLS) method has been applied to leukemia and heparin data sets and led to an improvement in limit of detection of Raman biosensing ranged from 10% to 43% compared to PLS. Our IBVSPLS was also compared to the jack-knifing (simpler) and Genetic Algorithm (more complex) methods. Our method was consistently better than the jack-knifing method and showed either a similar or a better performance compared to the genetic algorithm.
Borodachev, S. M.
2016-06-01
The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.
Efectivity of Additive Spline for Partial Least Square Method in Regression Model Estimation
Directory of Open Access Journals (Sweden)
Ahmad Bilfarsah
2005-04-01
Full Text Available Additive Spline of Partial Least Square method (ASPL as one generalization of Partial Least Square (PLS method. ASPLS method can be acommodation to non linear and multicollinearity case of predictor variables. As a principle, The ASPLS method approach is cahracterized by two idea. The first is to used parametric transformations of predictors by spline function; the second is to make ASPLS components mutually uncorrelated, to preserve properties of the linear PLS components. The performance of ASPLS compared with other PLS method is illustrated with the fisher economic application especially the tuna fish production.
Helmreich, James E.; Krog, K. Peter
2018-01-01
We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…
Group-wise partial least square regression
Camacho, José; Saccenti, Edoardo
2018-01-01
This paper introduces the group-wise partial least squares (GPLS) regression. GPLS is a new sparse PLS technique where the sparsity structure is defined in terms of groups of correlated variables, similarly to what is done in the related group-wise principal component analysis. These groups are
Least square regularized regression in sum space.
Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu
2013-04-01
This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.
Energy Technology Data Exchange (ETDEWEB)
Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)
2006-02-15
This paper presents an implementation of the least absolute value (LAV) power system state estimator based on obtaining a sequence of solutions to the L{sub 1}-regression problem using an iteratively reweighted least squares (IRLS{sub L1}) method. The proposed implementation avoids reformulating the regression problem into standard linear programming (LP) form and consequently does not require the use of common methods of LP, such as those based on the simplex method or interior-point methods. It is shown that the IRLS{sub L1} method is equivalent to solving a sequence of linear weighted least squares (LS) problems. Thus, its implementation presents little additional effort since the sparse LS solver is common to existing LS state estimators. Studies on the termination criteria of the IRLS{sub L1} method have been carried out to determine a procedure for which the proposed estimator is more computationally efficient than a previously proposed non-linear iteratively reweighted least squares (IRLS) estimator. Indeed, it is revealed that the proposed method is a generalization of the previously reported IRLS estimator, but is based on more rigorous theory. (author)
Comparison of Sparse and Jack-knife partial least squares regression methods for variable selection
DEFF Research Database (Denmark)
Karaman, Ibrahim; Qannari, El Mostafa; Martens, Harald
2013-01-01
The objective of this study was to compare two different techniques of variable selection, Sparse PLSR and Jack-knife PLSR, with respect to their predictive ability and their ability to identify relevant variables. Sparse PLSR is a method that is frequently used in genomics, whereas Jack-knife PL...
ANYOLS, Least Square Fit by Stepwise Regression
International Nuclear Information System (INIS)
Atwoods, C.L.; Mathews, S.
1986-01-01
Description of program or function: ANYOLS is a stepwise program which fits data using ordinary or weighted least squares. Variables are selected for the model in a stepwise way based on a user- specified input criterion or a user-written subroutine. The order in which variables are entered can be influenced by user-defined forcing priorities. Instead of stepwise selection, ANYOLS can try all possible combinations of any desired subset of the variables. Automatic output for the final model in a stepwise search includes plots of the residuals, 'studentized' residuals, and leverages; if the model is not too large, the output also includes partial regression and partial leverage plots. A data set may be re-used so that several selection criteria can be tried. Flexibility is increased by allowing the substitution of user-written subroutines for several default subroutines
Time Scale in Least Square Method
Directory of Open Access Journals (Sweden)
Özgür Yeniay
2014-01-01
Full Text Available Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.
Coskuntuncel, Orkun
2013-01-01
The purpose of this study is two-fold; the first aim being to show the effect of outliers on the widely used least squares regression estimator in social sciences. The second aim is to compare the classical method of least squares with the robust M-estimator using the "determination of coefficient" (R[superscript 2]). For this purpose,…
Directory of Open Access Journals (Sweden)
Xiangbing Zhou
2018-04-01
Full Text Available Rapidly growing GPS (Global Positioning System trajectories hide much valuable information, such as city road planning, urban travel demand, and population migration. In order to mine the hidden information and to capture better clustering results, a trajectory regression clustering method (an unsupervised trajectory clustering method is proposed to reduce local information loss of the trajectory and to avoid getting stuck in the local optimum. Using this method, we first define our new concept of trajectory clustering and construct a novel partitioning (angle-based partitioning method of line segments; second, the Lagrange-based method and Hausdorff-based K-means++ are integrated in fuzzy C-means (FCM clustering, which are used to maintain the stability and the robustness of the clustering process; finally, least squares regression model is employed to achieve regression clustering of the trajectory. In our experiment, the performance and effectiveness of our method is validated against real-world taxi GPS data. When comparing our clustering algorithm with the partition-based clustering algorithms (K-means, K-median, and FCM, our experimental results demonstrate that the presented method is more effective and generates a more reasonable trajectory.
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Dae; Lohumi, Santosh; Cho, Byoung Kwan [Dept. of Biosystems Machinery Engineering, Chungnam National University, Daejeon (Korea, Republic of); Kim, Moon Sung [United States Department of Agriculture Agricultural Research Service, Washington (United States); Lee, Soo Hee [Life and Technology Co.,Ltd., Hwasung (Korea, Republic of)
2014-08-15
This study was conducted to develop a non-destructive detection method for adulterated powder products using Raman spectroscopy and partial least squares regression(PLSR). Garlic and ginger powder, which are used as natural seasoning and in health supplement foods, were selected for this experiment. Samples were adulterated with corn starch in concentrations of 5-35%. PLSR models for adulterated garlic and ginger powders were developed and their performances evaluated using cross validation. The R{sup 2}{sub c} and SEC of an optimal PLSR model were 0.99 and 2.16 for the garlic powder samples, and 0.99 and 0.84 for the ginger samples, respectively. The variable importance in projection (VIP) score is a useful and simple tool for the evaluation of the importance of each variable in a PLSR model. After the VIP scores were taken pre-selection, the Raman spectrum data was reduced by one third. New PLSR models, based on a reduced number of wavelengths selected by the VIP scores technique, gave good predictions for the adulterated garlic and ginger powder samples.
International Nuclear Information System (INIS)
Lee, Sang Dae; Lohumi, Santosh; Cho, Byoung Kwan; Kim, Moon Sung; Lee, Soo Hee
2014-01-01
This study was conducted to develop a non-destructive detection method for adulterated powder products using Raman spectroscopy and partial least squares regression(PLSR). Garlic and ginger powder, which are used as natural seasoning and in health supplement foods, were selected for this experiment. Samples were adulterated with corn starch in concentrations of 5-35%. PLSR models for adulterated garlic and ginger powders were developed and their performances evaluated using cross validation. The R 2 c and SEC of an optimal PLSR model were 0.99 and 2.16 for the garlic powder samples, and 0.99 and 0.84 for the ginger samples, respectively. The variable importance in projection (VIP) score is a useful and simple tool for the evaluation of the importance of each variable in a PLSR model. After the VIP scores were taken pre-selection, the Raman spectrum data was reduced by one third. New PLSR models, based on a reduced number of wavelengths selected by the VIP scores technique, gave good predictions for the adulterated garlic and ginger powder samples.
Multispectral colormapping using penalized least square regression
DEFF Research Database (Denmark)
Dissing, Bjørn Skovlund; Carstensen, Jens Michael; Larsen, Rasmus
2010-01-01
The authors propose a novel method to map a multispectral image into the device independent color space CIE-XYZ. This method provides a way to visualize multispectral images by predicting colorvalues from spectral values while maintaining interpretability and is tested on a light emitting diode...... that the interpretability improves significantly but comes at the cost of slightly worse predictability....
Iterative methods for weighted least-squares
Energy Technology Data Exchange (ETDEWEB)
Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.
Least Squares Methods for Equidistant Tree Reconstruction
Fahey, Conor; Hosten, Serkan; Krieger, Nathan; Timpe, Leslie
2008-01-01
UPGMA is a heuristic method identifying the least squares equidistant phylogenetic tree given empirical distance data among $n$ taxa. We study this classic algorithm using the geometry of the space of all equidistant trees with $n$ leaves, also known as the Bergman complex of the graphical matroid for the complete graph $K_n$. We show that UPGMA performs an orthogonal projection of the data onto a maximal cell of the Bergman complex. We also show that the equidistant tree with the least (Eucl...
BRGLM, Interactive Linear Regression Analysis by Least Square Fit
International Nuclear Information System (INIS)
Ringland, J.T.; Bohrer, R.E.; Sherman, M.E.
1985-01-01
1 - Description of program or function: BRGLM is an interactive program written to fit general linear regression models by least squares and to provide a variety of statistical diagnostic information about the fit. Stepwise and all-subsets regression can be carried out also. There are facilities for interactive data management (e.g. setting missing value flags, data transformations) and tools for constructing design matrices for the more commonly-used models such as factorials, cubic Splines, and auto-regressions. 2 - Method of solution: The least squares computations are based on the orthogonal (QR) decomposition of the design matrix obtained using the modified Gram-Schmidt algorithm. 3 - Restrictions on the complexity of the problem: The current release of BRGLM allows maxima of 1000 observations, 99 variables, and 3000 words of main memory workspace. For a problem with N observations and P variables, the number of words of main memory storage required is MAX(N*(P+6), N*P+P*P+3*N, and 3*P*P+6*N). Any linear model may be fit although the in-memory workspace will have to be increased for larger problems
International Nuclear Information System (INIS)
Leng Ling; Zhang Tianyi; Kleinman, Lawrence; Zhu Wei
2007-01-01
Regression analysis, especially the ordinary least squares method which assumes that errors are confined to the dependent variable, has seen a fair share of its applications in aerosol science. The ordinary least squares approach, however, could be problematic due to the fact that atmospheric data often does not lend itself to calling one variable independent and the other dependent. Errors often exist for both measurements. In this work, we examine two regression approaches available to accommodate this situation. They are orthogonal regression and geometric mean regression. Comparisons are made theoretically as well as numerically through an aerosol study examining whether the ratio of organic aerosol to CO would change with age
Intelligent Quality Prediction Using Weighted Least Square Support Vector Regression
Yu, Yaojun
A novel quality prediction method with mobile time window is proposed for small-batch producing process based on weighted least squares support vector regression (LS-SVR). The design steps and learning algorithm are also addressed. In the method, weighted LS-SVR is taken as the intelligent kernel, with which the small-batch learning is solved well and the nearer sample is set a larger weight, while the farther is set the smaller weight in the history data. A typical machining process of cutting bearing outer race is carried out and the real measured data are used to contrast experiment. The experimental results demonstrate that the prediction accuracy of the weighted LS-SVR based model is only 20%-30% that of the standard LS-SVR based one in the same condition. It provides a better candidate for quality prediction of small-batch producing process.
Delwiche, Stephen R; Reeves, James B
2010-01-01
In multivariate regression analysis of spectroscopy data, spectral preprocessing is often performed to reduce unwanted background information (offsets, sloped baselines) or accentuate absorption features in intrinsically overlapping bands. These procedures, also known as pretreatments, are commonly smoothing operations or derivatives. While such operations are often useful in reducing the number of latent variables of the actual decomposition and lowering residual error, they also run the risk of misleading the practitioner into accepting calibration equations that are poorly adapted to samples outside of the calibration. The current study developed a graphical method to examine this effect on partial least squares (PLS) regression calibrations of near-infrared (NIR) reflection spectra of ground wheat meal with two analytes, protein content and sodium dodecyl sulfate sedimentation (SDS) volume (an indicator of the quantity of the gluten proteins that contribute to strong doughs). These two properties were chosen because of their differing abilities to be modeled by NIR spectroscopy: excellent for protein content, fair for SDS sedimentation volume. To further demonstrate the potential pitfalls of preprocessing, an artificial component, a randomly generated value, was included in PLS regression trials. Savitzky-Golay (digital filter) smoothing, first-derivative, and second-derivative preprocess functions (5 to 25 centrally symmetric convolution points, derived from quadratic polynomials) were applied to PLS calibrations of 1 to 15 factors. The results demonstrated the danger of an over reliance on preprocessing when (1) the number of samples used in a multivariate calibration is low (<50), (2) the spectral response of the analyte is weak, and (3) the goodness of the calibration is based on the coefficient of determination (R(2)) rather than a term based on residual error. The graphical method has application to the evaluation of other preprocess functions and various
Analysis of quantile regression as alternative to ordinary least squares
Ibrahim Abdullahi; Abubakar Yahaya
2015-01-01
In this article, an alternative to ordinary least squares (OLS) regression based on analytical solution in the Statgraphics software is considered, and this alternative is no other than quantile regression (QR) model. We also present goodness of fit statistic as well as approximate distributions of the associated test statistics for the parameters. Furthermore, we suggest a goodness of fit statistic called the least absolute deviation (LAD) coefficient of determination. The procedure is well ...
Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.
1976-01-01
A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.
Least Squares Adjustment: Linear and Nonlinear Weighted Regression Analysis
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2007-01-01
This note primarily describes the mathematics of least squares regression analysis as it is often used in geodesy including land surveying and satellite positioning applications. In these fields regression is often termed adjustment. The note also contains a couple of typical land surveying...... and satellite positioning application examples. In these application areas we are typically interested in the parameters in the model typically 2- or 3-D positions and not in predictive modelling which is often the main concern in other regression analysis applications. Adjustment is often used to obtain...... the clock error) and to obtain estimates of the uncertainty with which the position is determined. Regression analysis is used in many other fields of application both in the natural, the technical and the social sciences. Examples may be curve fitting, calibration, establishing relationships between...
Peng, Ying; Li, Su-Ning; Pei, Xuexue; Hao, Kun
2018-03-01
Amultivariate regression statisticstrategy was developed to clarify multi-components content-effect correlation ofpanaxginseng saponins extract and predict the pharmacological effect by components content. In example 1, firstly, we compared pharmacological effects between panax ginseng saponins extract and individual saponin combinations. Secondly, we examined the anti-platelet aggregation effect in seven different saponin combinations of ginsenoside Rb1, Rg1, Rh, Rd, Ra3 and notoginsenoside R1. Finally, the correlation between anti-platelet aggregation and the content of multiple components was analyzed by a partial least squares algorithm. In example 2, firstly, 18 common peaks were identified in ten different batches of panax ginseng saponins extracts from different origins. Then, we investigated the anti-myocardial ischemia reperfusion injury effects of the ten different panax ginseng saponins extracts. Finally, the correlation between the fingerprints and the cardioprotective effects was analyzed by a partial least squares algorithm. Both in example 1 and 2, the relationship between the components content and pharmacological effect was modeled well by the partial least squares regression equations. Importantly, the predicted effect curve was close to the observed data of dot marked on the partial least squares regression model. This study has given evidences that themulti-component content is a promising information for predicting the pharmacological effects of traditional Chinese medicine.
Directory of Open Access Journals (Sweden)
Ying Peng
2018-03-01
Full Text Available Amultivariate regression statisticstrategy was developed to clarify multi-components content-effect correlation ofpanaxginseng saponins extract and predict the pharmacological effect by components content. In example 1, firstly, we compared pharmacological effects between panax ginseng saponins extract and individual saponin combinations. Secondly, we examined the anti-platelet aggregation effect in seven different saponin combinations of ginsenoside Rb1, Rg1, Rh, Rd, Ra3 and notoginsenoside R1. Finally, the correlation between anti-platelet aggregation and the content of multiple components was analyzed by a partial least squares algorithm. In example 2, firstly, 18 common peaks were identified in ten different batches of panax ginseng saponins extracts from different origins. Then, we investigated the anti-myocardial ischemia reperfusion injury effects of the ten different panax ginseng saponins extracts. Finally, the correlation between the fingerprints and the cardioprotective effects was analyzed by a partial least squares algorithm. Both in example 1 and 2, the relationship between the components content and pharmacological effect was modeled well by the partial least squares regression equations. Importantly, the predicted effect curve was close to the observed data of dot marked on the partial least squares regression model. This study has given evidences that themulti-component content is a promising information for predicting the pharmacological effects of traditional Chinese medicine.
Estimating Frequency by Interpolation Using Least Squares Support Vector Regression
Directory of Open Access Journals (Sweden)
Changwei Ma
2015-01-01
Full Text Available Discrete Fourier transform- (DFT- based maximum likelihood (ML algorithm is an important part of single sinusoid frequency estimation. As signal to noise ratio (SNR increases and is above the threshold value, it will lie very close to Cramer-Rao lower bound (CRLB, which is dependent on the number of DFT points. However, its mean square error (MSE performance is directly proportional to its calculation cost. As a modified version of support vector regression (SVR, least squares SVR (LS-SVR can not only still keep excellent capabilities for generalizing and fitting but also exhibit lower computational complexity. In this paper, therefore, LS-SVR is employed to interpolate on Fourier coefficients of received signals and attain high frequency estimation accuracy. Our results show that the proposed algorithm can make a good compromise between calculation cost and MSE performance under the assumption that the sample size, number of DFT points, and resampling points are already known.
Brightness-normalized Partial Least Squares Regression for hyperspectral data
International Nuclear Information System (INIS)
Feilhauer, Hannes; Asner, Gregory P.; Martin, Roberta E.; Schmidtlein, Sebastian
2010-01-01
Developed in the field of chemometrics, Partial Least Squares Regression (PLSR) has become an established technique in vegetation remote sensing. PLSR was primarily designed for laboratory analysis of prepared material samples. Under field conditions in vegetation remote sensing, the performance of the technique may be negatively affected by differences in brightness due to amount and orientation of plant tissues in canopies or the observing conditions. To minimize these effects, we introduced brightness normalization to the PLSR approach and tested whether this modification improves the performance under changing canopy and observing conditions. This test was carried out using high-fidelity spectral data (400-2510 nm) to model observed leaf chemistry. The spectral data was combined with a canopy radiative transfer model to simulate effects of varying canopy structure and viewing geometry. Brightness normalization enhanced the performance of PLSR by dampening the effects of canopy shade, thus providing a significant improvement in predictions of leaf chemistry (up to 3.6% additional explained variance in validation) compared to conventional PLSR. Little improvement was made on effects due to variable leaf area index, while minor improvement (mostly not significant) was observed for effects of variable viewing geometry. In general, brightness normalization increased the stability of model fits and regression coefficients for all canopy scenarios. Brightness-normalized PLSR is thus a promising approach for application on airborne and space-based imaging spectrometer data.
Application of least-squares method to decay heat evaluation
International Nuclear Information System (INIS)
Schmittroth, F.; Schenter, R.E.
1976-01-01
Generalized least-squares methods are applied to decay-heat experiments and summation calculations to arrive at evaluated values and uncertainties for the fission-product decay-heat from the thermal fission of 235 U. Emphasis is placed on a proper treatment of both statistical and correlated uncertainties in the least-squares method
Handbook of Partial Least Squares Concepts, Methods and Applications
Vinzi, Vincenzo Esposito; Henseler, Jörg
2010-01-01
This handbook provides a comprehensive overview of Partial Least Squares (PLS) methods with specific reference to their use in marketing and with a discussion of the directions of current research and perspectives. It covers the broad area of PLS methods, from regression to structural equation modeling applications, software and interpretation of results. The handbook serves both as an introduction for those without prior knowledge of PLS and as a comprehensive reference for researchers and practitioners interested in the most recent advances in PLS methodology.
See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.
2018-04-01
This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.
Spectrum unfolding by the least-squares methods
International Nuclear Information System (INIS)
Perey, F.G.
1977-01-01
The method of least squares is briefly reviewed, and the conditions under which it may be used are stated. From this analysis, a least-squares approach to the solution of the dosimetry neutron spectrum unfolding problem is introduced. The mathematical solution to this least-squares problem is derived from the general solution. The existence of this solution is analyzed in some detail. A chi 2 -test is derived for the consistency of the input data which does not require the solution to be obtained first. The fact that the problem is technically nonlinear, but should be treated in general as a linear one, is argued. Therefore, the solution should not be obtained by iteration. Two interpretations are made for the solution of the code STAY'SL, which solves this least-squares problem. The relationship of the solution to this least-squares problem to those obtained currently by other methods of solving the dosimetry neutron spectrum unfolding problem is extensively discussed. It is shown that the least-squares method does not require more input information than would be needed by current methods in order to estimate the uncertainties in their solutions. From this discussion it is concluded that the proposed least-squares method does provide the best complete solution, with uncertainties, to the problem as it is understood now. Finally, some implications of this method are mentioned regarding future work required in order to exploit its potential fully
A Generalized Autocovariance Least-Squares Method for Covariance Estimation
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad
2007-01-01
A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter.......A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter....
Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS
Directory of Open Access Journals (Sweden)
Ade Widyaningsih
2015-04-01
Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.
Estimasi Model Seemingly Unrelated Regression (SUR dengan Metode Generalized Least Square (GLS
Directory of Open Access Journals (Sweden)
Ade Widyaningsih
2014-06-01
Full Text Available Regression analysis is a statistical tool that is used to determine the relationship between two or more quantitative variables so that one variable can be predicted from the other variables. A method that can used to obtain a good estimation in the regression analysis is ordinary least squares method. The least squares method is used to estimate the parameters of one or more regression but relationships among the errors in the response of other estimators are not allowed. One way to overcome this problem is Seemingly Unrelated Regression model (SUR in which parameters are estimated using Generalized Least Square (GLS. In this study, the author applies SUR model using GLS method on world gasoline demand data. The author obtains that SUR using GLS is better than OLS because SUR produce smaller errors than the OLS.
Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression
Energy Technology Data Exchange (ETDEWEB)
Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels (Belgium); Shabbir, A. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornung, G. [Department of Applied Physics, Ghent University, B-9000 Ghent (Belgium)
2016-11-15
Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standard least squares.
Outlier detection algorithms for least squares time series regression
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator Sat...
RCS Leak Rate Calculation with High Order Least Squares Method
International Nuclear Information System (INIS)
Lee, Jeong Hun; Kang, Young Kyu; Kim, Yang Ki
2010-01-01
As a part of action items for Application of Leak before Break(LBB), RCS Leak Rate Calculation Program is upgraded in Kori unit 3 and 4. For real time monitoring of operators, periodic calculation is needed and corresponding noise reduction scheme is used. This kind of study was issued in Korea, so there have upgraded and used real time RCS Leak Rate Calculation Program in UCN unit 3 and 4 and YGN unit 1 and 2. For reduction of the noise in signals, Linear Regression Method was used in those programs. Linear Regression Method is powerful method for noise reduction. But the system is not static with some alternative flow paths and this makes mixed trend patterns of input signal values. In this condition, the trend of signal and average of Linear Regression are not entirely same pattern. In this study, high order Least squares Method is used to follow the trend of signal and the order of calculation is rearranged. The result of calculation makes reasonable trend and the procedure is physically consistence
Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems
Czech Academy of Sciences Publication Activity Database
Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav
2014-01-01
Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014
Digital Repository Service at National Institute of Oceanography (India)
Tripathy, G.R.; Das, Anirban.
used methods, the Least Square Regression (LSR) and Inverse Modeling (IM), to determine the contributions of (i) solutes from different sources to global river water, and (ii) various rocks to a glacial till. The purpose of this exercise is to compare...
de Peinder, P.; Visser, T.; Wagemans, R.W.P.; Blomberg, J.; Chaabani, H.; Soulimani, F.; Weckhuysen, B.M.
2013-01-01
Research has been carried out to determine the feasibility of partial least-squares regression (PLS) modeling of infrared (IR) spectra of crude oils as a tool for fast sulfur speciation. The study is a continuation of a previously developed method to predict long and short residue properties of
Geodesic least squares regression for scaling studies in magnetic confinement fusion
International Nuclear Information System (INIS)
Verdoolaege, Geert
2015-01-01
In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices
Optimization of sequential decisions by least squares Monte Carlo method
DEFF Research Database (Denmark)
Nishijima, Kazuyoshi; Anders, Annett
change adaptation measures, and evacuation of people and assets in the face of an emerging natural hazard event. Focusing on the last example, an efficient solution scheme is proposed by Anders and Nishijima (2011). The proposed solution scheme takes basis in the least squares Monte Carlo method, which...... is proposed by Longstaff and Schwartz (2001) for pricing of American options. The present paper formulates the decision problem in a more general manner and explains how the solution scheme proposed by Anders and Nishijima (2011) is implemented for the optimization of the formulated decision problem...
Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F
2018-03-26
This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.
Optimization Method of Fusing Model Tree into Partial Least Squares
Directory of Open Access Journals (Sweden)
Yu Fang
2017-01-01
Full Text Available Partial Least Square (PLS can’t adapt to the characteristics of the data of many fields due to its own features multiple independent variables, multi-dependent variables and non-linear. However, Model Tree (MT has a good adaptability to nonlinear function, which is made up of many multiple linear segments. Based on this, a new method combining PLS and MT to analysis and predict the data is proposed, which build MT through the main ingredient and the explanatory variables(the dependent variable extracted from PLS, and extract residual information constantly to build Model Tree until well-pleased accuracy condition is satisfied. Using the data of the maxingshigan decoction of the monarch drug to treat the asthma or cough and two sample sets in the UCI Machine Learning Repository, the experimental results show that, the ability of explanation and predicting get improved in the new method.
8th International Conference on Partial Least Squares and Related Methods
Vinzi, Vincenzo; Russolillo, Giorgio; Saporta, Gilbert; Trinchera, Laura
2016-01-01
This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics ...
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Cognitive assessment in mathematics with the least squares distance method.
Ma, Lin; Çetin, Emre; Green, Kathy E
2012-01-01
This study investigated the validation of comprehensive cognitive attributes of an eighth-grade mathematics test using the least squares distance method and compared performance on attributes by gender and region. A sample of 5,000 students was randomly selected from the data of the 2005 Turkish national mathematics assessment of eighth-grade students. Twenty-five math items were assessed for presence or absence of 20 cognitive attributes (content, cognitive processes, and skill). Four attributes were found to be misspecified or nonpredictive. However, results demonstrated the validity of cognitive attributes in terms of the revised set of 17 attributes. The girls had similar performance on the attributes as the boys. The students from the two eastern regions significantly underperformed on the most attributes.
Li, Jiangtong; Luo, Yongdao; Dai, Honglin
2018-01-01
Water is the source of life and the essential foundation of all life. With the development of industrialization, the phenomenon of water pollution is becoming more and more frequent, which directly affects the survival and development of human. Water quality detection is one of the necessary measures to protect water resources. Ultraviolet (UV) spectral analysis is an important research method in the field of water quality detection, which partial least squares regression (PLSR) analysis method is becoming predominant technology, however, in some special cases, PLSR's analysis produce considerable errors. In order to solve this problem, the traditional principal component regression (PCR) analysis method was improved by using the principle of PLSR in this paper. The experimental results show that for some special experimental data set, improved PCR analysis method performance is better than PLSR. The PCR and PLSR is the focus of this paper. Firstly, the principal component analysis (PCA) is performed by MATLAB to reduce the dimensionality of the spectral data; on the basis of a large number of experiments, the optimized principal component is extracted by using the principle of PLSR, which carries most of the original data information. Secondly, the linear regression analysis of the principal component is carried out with statistic package for social science (SPSS), which the coefficients and relations of principal components can be obtained. Finally, calculating a same water spectral data set by PLSR and improved PCR, analyzing and comparing two results, improved PCR and PLSR is similar for most data, but improved PCR is better than PLSR for data near the detection limit. Both PLSR and improved PCR can be used in Ultraviolet spectral analysis of water, but for data near the detection limit, improved PCR's result better than PLSR.
Application of the Least Squares Method in Axisymmetric Biharmonic Problems
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Vasyl Chekurin
2016-01-01
Full Text Available An approach for solving of the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain was developed in the paper. On the lateral surface of the domain homogeneous Neumann boundary conditions are prescribed. On the remaining part of the domain’s boundary four different biharmonic boundary pieces of data are considered. To solve the formulated biharmonic problems the method of least squares on the boundary combined with the method of homogeneous solutions was used. That enabled reducing the problems to infinite systems of linear algebraic equations which can be solved with the use of reduction method. Convergence of the solution obtained with developed approach was studied numerically on some characteristic examples. The developed approach can be used particularly to solve axisymmetric elasticity problems for cylindrical bodies, the heights of which are equal to or exceed their diameters, when on their lateral surface normal and tangential tractions are prescribed and on the cylinder’s end faces various types of boundary conditions in stresses in displacements or mixed ones are given.
LSL: a logarithmic least-squares adjustment method
International Nuclear Information System (INIS)
Stallmann, F.W.
1982-01-01
To meet regulatory requirements, spectral unfolding codes must not only provide reliable estimates for spectral parameters, but must also be able to determine the uncertainties associated with these parameters. The newer codes, which are more appropriately called adjustment codes, use the least squares principle to determine estimates and uncertainties. The principle is simple and straightforward, but there are several different mathematical models to describe the unfolding problem. In addition to a sound mathematical model, ease of use and range of options are important considerations in the construction of adjustment codes. Based on these considerations, a least squares adjustment code for neutron spectrum unfolding has been constructed some time ago and tentatively named LSL
International Nuclear Information System (INIS)
Herda, Trent J; Ryan, Eric D; Costa, Pablo B; DeFreitas, Jason M; Walter, Ashley A; Stout, Jeffrey R; Beck, Travis W; Cramer, Joel T; Housh, Terry J; Weir, Joseph P
2009-01-01
The primary purpose of this study was to examine the consistency of ordinary least-squares (OLS) and generalized least-squares (GLS) polynomial regression analyses utilizing linear, quadratic and cubic models on either five or ten data points that characterize the mechanomyographic amplitude (MMG RMS ) versus isometric torque relationship. The secondary purpose was to examine the consistency of OLS and GLS polynomial regression utilizing only linear and quadratic models (excluding cubic responses) on either ten or five data points. Eighteen participants (mean ± SD age = 24 ± 4 yr) completed ten randomly ordered isometric step muscle actions from 5% to 95% of the maximal voluntary contraction (MVC) of the right leg extensors during three separate trials. MMG RMS was recorded from the vastus lateralis during the MVCs and each submaximal muscle action. MMG RMS versus torque relationships were analyzed on a subject-by-subject basis using OLS and GLS polynomial regression. When using ten data points, only 33% and 27% of the subjects were fitted with the same model (utilizing linear, quadratic and cubic models) across all three trials for OLS and GLS, respectively. After eliminating the cubic model, there was an increase to 55% of the subjects being fitted with the same model across all trials for both OLS and GLS regression. Using only five data points (instead of ten data points), 55% of the subjects were fitted with the same model across all trials for OLS and GLS regression. Overall, OLS and GLS polynomial regression models were only able to consistently describe the torque-related patterns of response for MMG RMS in 27–55% of the subjects across three trials. Future studies should examine alternative methods for improving the consistency and reliability of the patterns of response for the MMG RMS versus isometric torque relationship
Extreme Learning Machine and Moving Least Square Regression Based Solar Panel Vision Inspection
Directory of Open Access Journals (Sweden)
Heng Liu
2017-01-01
Full Text Available In recent years, learning based machine intelligence has aroused a lot of attention across science and engineering. Particularly in the field of automatic industry inspection, the machine learning based vision inspection plays a more and more important role in defect identification and feature extraction. Through learning from image samples, many features of industry objects, such as shapes, positions, and orientations angles, can be obtained and then can be well utilized to determine whether there is defect or not. However, the robustness and the quickness are not easily achieved in such inspection way. In this work, for solar panel vision inspection, we present an extreme learning machine (ELM and moving least square regression based approach to identify solder joint defect and detect the panel position. Firstly, histogram peaks distribution (HPD and fractional calculus are applied for image preprocessing. Then an ELM-based defective solder joints identification is discussed in detail. Finally, moving least square regression (MLSR algorithm is introduced for solar panel position determination. Experimental results and comparisons show that the proposed ELM and MLSR based inspection method is efficient not only in detection accuracy but also in processing speed.
New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology
International Nuclear Information System (INIS)
Han, Jubong; Lee, K.B.; Lee, Jong-Man; Park, Tae Soon; Oh, J.S.; Oh, Pil-Jei
2016-01-01
We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. - Highlights: • A new method proposed to incorporate Type B uncertainty into least-squares method. • The method constructed from the likelihood function and PDFs of Type B uncertainty. • A case study performed to compare results from the new and the conventional method. • Fitted parameters are consistent but with larger uncertainties in the new method.
Wavelength detection in FBG sensor networks using least squares support vector regression
Chen, Jing; Jiang, Hao; Liu, Tundong; Fu, Xiaoli
2014-04-01
A wavelength detection method for a wavelength division multiplexing (WDM) fiber Bragg grating (FBG) sensor network is proposed based on least squares support vector regression (LS-SVR). As a kind of promising machine learning technique, LS-SVR is employed to approximate the inverse function of the reflection spectrum. The LS-SVR detection model is established from the training samples, and then the Bragg wavelength of each FBG can be directly identified by inputting the measured spectrum into the well-trained model. We also discuss the impact of the sample size and the preprocess of the input spectrum on the performance of the training effectiveness. The results demonstrate that our approach is effective in improving the accuracy for sensor networks with a large number of FBGs.
Francisco, Fabiane Lacerda; Saviano, Alessandro Morais; Almeida, Túlia de Souza Botelho; Lourenço, Felipe Rebello
2016-05-01
Microbiological assays are widely used to estimate the relative potencies of antibiotics in order to guarantee the efficacy, safety, and quality of drug products. Despite of the advantages of turbidimetric bioassays when compared to other methods, it has limitations concerning the linearity and range of the dose-response curve determination. Here, we proposed to use partial least squares (PLS) regression to solve these limitations and to improve the prediction of relative potencies of antibiotics. Kinetic-reading microplate turbidimetric bioassays for apramacyin and vancomycin were performed using Escherichia coli (ATCC 8739) and Bacillus subtilis (ATCC 6633), respectively. Microbial growths were measured as absorbance up to 180 and 300min for apramycin and vancomycin turbidimetric bioassays, respectively. Conventional dose-response curves (absorbances or area under the microbial growth curve vs. log of antibiotic concentration) showed significant regression, however there were significant deviation of linearity. Thus, they could not be used for relative potency estimations. PLS regression allowed us to construct a predictive model for estimating the relative potencies of apramycin and vancomycin without over-fitting and it improved the linear range of turbidimetric bioassay. In addition, PLS regression provided predictions of relative potencies equivalent to those obtained from agar diffusion official methods. Therefore, we conclude that PLS regression may be used to estimate the relative potencies of antibiotics with significant advantages when compared to conventional dose-response curve determination. Copyright © 2016 Elsevier B.V. All rights reserved.
Bulcock, J. W.
The problem of model estimation when the data are collinear was examined. Though the ridge regression (RR) outperforms ordinary least squares (OLS) regression in the presence of acute multicollinearity, it is not a problem free technique for reducing the variance of the estimates. It is a stochastic procedure when it should be nonstochastic and it…
Maggin, Daniel M.; Swaminathan, Hariharan; Rogers, Helen J.; O'Keeffe, Breda V.; Sugai, George; Horner, Robert H.
2011-01-01
A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of…
International Nuclear Information System (INIS)
Haaland, D.M.; Easterling, R.G.
1982-01-01
Improvements have been made in previous least-squares regression analyses of infrared spectra for the quantitative estimation of concentrations of multicomponent mixtures. Spectral baselines are fitted by least-squares methods, and overlapping spectral features are accounted for in the fitting procedure. Selection of peaks above a threshold value reduces computation time and data storage requirements. Four weighted least-squares methods incorporating different baseline assumptions were investigated using FT-IR spectra of the three pure xylene isomers and their mixtures. By fitting only regions of the spectra that follow Beer's Law, accurate results can be obtained using three of the fitting methods even when baselines are not corrected to zero. Accurate results can also be obtained using one of the fits even in the presence of Beer's Law deviations. This is a consequence of pooling the weighted results for each spectral peak such that the greatest weighting is automatically given to those peaks that adhere to Beer's Law. It has been shown with the xylene spectra that semiquantitative results can be obtained even when all the major components are not known or when expected components are not present. This improvement over previous methods greatly expands the utility of quantitative least-squares analyses
International Nuclear Information System (INIS)
Jiang, B.T.; Zhao, F.Y.
2013-01-01
Highlights: ► CHF data are collected from the published literature. ► Less training data are used to train the LSSVR model. ► PSO is adopted to optimize the key parameters to improve the model precision. ► The reliability of LSSVR is proved through parametric trends analysis. - Abstract: In view of practical importance of critical heat flux (CHF) for design and safety of nuclear reactors, accurate prediction of CHF is of utmost significance. This paper presents a novel approach using least squares support vector regression (LSSVR) and particle swarm optimization (PSO) to predict CHF. Two available published datasets are used to train and test the proposed algorithm, in which PSO is employed to search for the best parameters involved in LSSVR model. The CHF values obtained by the LSSVR model are compared with the corresponding experimental values and those of a previous method, adaptive neuro fuzzy inference system (ANFIS). This comparison is also carried out in the investigation of parametric trends of CHF. It is found that the proposed method can achieve the desired performance and yields a more satisfactory fit with experimental results than ANFIS. Therefore, LSSVR method is likely to be suitable for other parameters processing such as CHF
Caimmi, R.
2011-08-01
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both
Fruit fly optimization based least square support vector regression for blind image restoration
Zhang, Jiao; Wang, Rui; Li, Junshan; Yang, Yawei
2014-11-01
The goal of image restoration is to reconstruct the original scene from a degraded observation. It is a critical and challenging task in image processing. Classical restorations require explicit knowledge of the point spread function and a description of the noise as priors. However, it is not practical for many real image processing. The recovery processing needs to be a blind image restoration scenario. Since blind deconvolution is an ill-posed problem, many blind restoration methods need to make additional assumptions to construct restrictions. Due to the differences of PSF and noise energy, blurring images can be quite different. It is difficult to achieve a good balance between proper assumption and high restoration quality in blind deconvolution. Recently, machine learning techniques have been applied to blind image restoration. The least square support vector regression (LSSVR) has been proven to offer strong potential in estimating and forecasting issues. Therefore, this paper proposes a LSSVR-based image restoration method. However, selecting the optimal parameters for support vector machine is essential to the training result. As a novel meta-heuristic algorithm, the fruit fly optimization algorithm (FOA) can be used to handle optimization problems, and has the advantages of fast convergence to the global optimal solution. In the proposed method, the training samples are created from a neighborhood in the degraded image to the central pixel in the original image. The mapping between the degraded image and the original image is learned by training LSSVR. The two parameters of LSSVR are optimized though FOA. The fitness function of FOA is calculated by the restoration error function. With the acquired mapping, the degraded image can be recovered. Experimental results show the proposed method can obtain satisfactory restoration effect. Compared with BP neural network regression, SVR method and Lucy-Richardson algorithm, it speeds up the restoration rate and
Li, Jie; Sun, Jin; He, Zhonggui
2007-01-26
We aimed to establish quantitative structure-retention relationship (QSRR) with immobilized artificial membrane (IAM) chromatography using easily understood and obtained physicochemical molecular descriptors and to elucidate which descriptors are critical to affect the interaction process between solutes and immobilized phospholipid membranes. The retention indices (logk(IAM)) of 55 structurally diverse drugs were determined on an immobilized artificial membrane column (IAM.PC.DD2) directly or obtained by extrapolation method for highly hydrophobic compounds. Ten simple physicochemical property descriptors (clogP, rings, rotatory bond, hydro-bond counting, etc.) of these drugs were collected and used to establish QSRR and predict the retention data by partial least squares regression (PLSR). Five descriptors, clogP, rotatory bond (RotB), rings, molecular weight (MW) and total surface area (TSA), were reserved by using the Variable Importance for Projection (VIP) values as criterion to build the final PLSR model. An external test set was employed to verify the QSRR based on the training set with the five variables, and QSRR by PLSR exhibited a satisfying predictive ability with R(p)=0.902 and RMSE(p)=0.400. Comparison of coefficients of centered and scaled variables by PLSR demonstrated that, for the descriptors studied, clogP and TSA have the most significant positive effect but the rotatable bond has significant negative effect on drug IAM chromatographic retention.
Directory of Open Access Journals (Sweden)
Vasileios A. Tzanakakis
2014-12-01
Full Text Available Partial Least Squares Regression (PLSR can integrate a great number of variables and overcome collinearity problems, a fact that makes it suitable for intensive agronomical practices such as land application. In the present study a PLSR model was developed to predict important management goals, including biomass production and nutrient recovery (i.e., nitrogen and phosphorus, associated with treatment potential, environmental impacts, and economic benefits. Effluent loading and a considerable number of soil parameters commonly monitored in effluent irrigated lands were considered as potential predictor variables during the model development. All data were derived from a three year field trial including plantations of four different plant species (Acacia cyanophylla, Eucalyptus camaldulensis, Populus nigra, and Arundo donax, irrigated with pre-treated domestic effluent. PLSR method was very effective despite the small sample size and the wide nature of data set (with many highly correlated inputs and several highly correlated responses. Through PLSR method the number of initial predictor variables was reduced and only several variables were remained and included in the final PLSR model. The important input variables maintained were: Effluent loading, electrical conductivity (EC, available phosphorus (Olsen-P, Na+, Ca2+, Mg2+, K2+, SAR, and NO3−-N. Among these variables, effluent loading, EC, and nitrates had the greater contribution to the final PLSR model. PLSR is highly compatible with intensive agronomical practices such as land application, in which a large number of highly collinear and noisy input variables is monitored to assess plant species performance and to detect impacts on the environment.
Aznar, Margarita; López, Ricardo; Cacho, Juan; Ferreira, Vicente
2003-04-23
Partial least squares regression (PLSR) models able to predict some of the wine aroma nuances from its chemical composition have been developed. The aromatic sensory characteristics of 57 Spanish aged red wines were determined by 51 experts from the wine industry. The individual descriptions given by the experts were recorded, and the frequency with which a sensory term was used to define a given wine was taken as a measurement of its intensity. The aromatic chemical composition of the wines was determined by already published gas chromatography (GC)-flame ionization detector and GC-mass spectrometry methods. In the whole, 69 odorants were analyzed. Both matrixes, the sensory and chemical data, were simplified by grouping and rearranging correlated sensory terms or chemical compounds and by the exclusion of secondary aroma terms or of weak aroma chemicals. Finally, models were developed for 18 sensory terms and 27 chemicals or groups of chemicals. Satisfactory models, explaining more than 45% of the original variance, could be found for nine of the most important sensory terms (wood-vanillin-cinnamon, animal-leather-phenolic, toasted-coffee, old wood-reduction, vegetal-pepper, raisin-flowery, sweet-candy-cacao, fruity, and berry fruit). For this set of terms, the correlation coefficients between the measured and predicted Y (determined by cross-validation) ranged from 0.62 to 0.81. Models confirmed the existence of complex multivariate relationships between chemicals and odors. In general, pleasant descriptors were positively correlated to chemicals with pleasant aroma, such as vanillin, beta damascenone, or (E)-beta-methyl-gamma-octalactone, and negatively correlated to compounds showing less favorable odor properties, such as 4-ethyl and vinyl phenols, 3-(methylthio)-1-propanol, or phenylacetaldehyde.
Plata, Maria R.; Koch, Cosima; Wechselberger, Patrick; Herwig, Christoph; Lendl, Bernhard
2013-01-01
A fast and simple method to control variations in carbohydrate composition of Saccharomyces cerevisiae, baker's yeast, during fermentation was developed using mid-infrared (mid-IR) spectroscopy. The method allows for precise and accurate determinations with minimal or no sample preparation and reagent consumption based on mid-IR spectra and partial least squares (PLS) regression. The PLS models were developed employing the results from reference analysis of the yeast cells. The reference anal...
International Nuclear Information System (INIS)
Guo, Yin; Nazarian, Ehsan; Ko, Jeonghan; Rajurkar, Kamlakar
2014-01-01
Highlights: • Developed hourly-indexed ARX models for robust cooling-load forecasting. • Proposed a two-stage weighted least-squares regression approach. • Considered the effect of outliers as well as trend of cooling load and weather patterns. • Included higher order terms and day type patterns in the forecasting models. • Demonstrated better accuracy compared with some ARX and ANN models. - Abstract: This paper presents a robust hourly cooling-load forecasting method based on time-indexed autoregressive with exogenous inputs (ARX) models, in which the coefficients are estimated through a two-stage weighted least squares regression. The prediction method includes a combination of two separate time-indexed ARX models to improve prediction accuracy of the cooling load over different forecasting periods. The two-stage weighted least-squares regression approach in this study is robust to outliers and suitable for fast and adaptive coefficient estimation. The proposed method is tested on a large-scale central cooling system in an academic institution. The numerical case studies show the proposed prediction method performs better than some ANN and ARX forecasting models for the given test data set
Application of Least-Squares Spectral Element Methods to Polynomial Chaos
Vos, P.E.J.; Gerritsma, M.I.
2006-01-01
This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.
Extracting information from two-dimensional electrophoresis gels by partial least squares regression
DEFF Research Database (Denmark)
Jessen, Flemming; Lametsch, R.; Bendixen, E.
2002-01-01
of all proteins/spots in the gels. In the present study it is demonstrated how information can be extracted by multivariate data analysis. The strategy is based on partial least squares regression followed by variable selection to find proteins that individually or in combination with other proteins vary......Two-dimensional gel electrophoresis (2-DE) produces large amounts of data and extraction of relevant information from these data demands a cautious and time consuming process of spot pattern matching between gels. The classical approach of data analysis is to detect protein markers that appear...... or disappear depending on the experimental conditions. Such biomarkers are found by comparing the relative volumes of individual spots in the individual gels. Multivariate statistical analysis and modelling of 2-DE data for comparison and classification is an alternative approach utilising the combination...
Directory of Open Access Journals (Sweden)
Victor Aredo
2017-01-01
Full Text Available The aim of this study was to build a model to predict the beef marbling using HSI and Partial Least Squares Regression (PLSR. Totally 58 samples of longissmus dorsi muscle were scanned by a HSI system (400 - 1000 nm in reflectance mode, using 44 samples to build t he PLSR model and 14 samples to model validation. The Japanese Beef Marbling Standard (BMS was used as reference by 15 middle - trained judges for the samples evaluation. The scores were assigned as continuous values and varied from 1.2 to 5.3 BMS. The PLSR model showed a high correlation coefficient in the prediction (r = 0.95, a low Standard Error of Calibration (SEC of 0.2 BMS score, and a low Standard Error of Prediction (SEP of 0.3 BMS score.
Application of pulse pile-up correction spectrum to the library least-squares method
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Hoon [Kyungpook National Univ., Daegu (Korea, Republic of)
2006-12-15
The Monte Carlo simulation code CEARPPU has been developed and updated to provide pulse pile-up correction spectra for high counting rate cases. For neutron activation analysis, CEARPPU correction spectra were used in library least-squares method to give better isotopic activity results than the convention library least-squares fitting with uncorrected spectra.
Least-squares methods involving the H{sup -1} inner product
Energy Technology Data Exchange (ETDEWEB)
Pasciak, J.
1996-12-31
Least-squares methods are being shown to be an effective technique for the solution of elliptic boundary value problems. However, the methods differ depending on the norms in which they are formulated. For certain problems, it is much more natural to consider least-squares functionals involving the H{sup -1} norm. Such norms give rise to improved convergence estimates and better approximation to problems with low regularity solutions. In addition, fewer new variables need to be added and less stringent boundary conditions need to be imposed. In this talk, I will describe some recent developments involving least-squares methods utilizing the H{sup -1} inner product.
Hecht, Jeffrey B.
The analysis of regression residuals and detection of outliers are discussed, with emphasis on determining how deviant an individual data point must be to be considered an outlier and the impact that multiple suspected outlier data points have on the process of outlier determination and treatment. Only bivariate (one dependent and one independent)…
Directory of Open Access Journals (Sweden)
Gifty E. Acquah
2016-01-01
Full Text Available Fourier transform infrared reflectance (FTIR spectroscopy has been used to predict properties of forest logging residue, a very heterogeneous feedstock material. Properties studied included the chemical composition, thermal reactivity, and energy content. The ability to rapidly determine these properties is vital in the optimization of conversion technologies for the successful commercialization of biobased products. Partial least squares regression of first derivative treated FTIR spectra had good correlations with the conventionally measured properties. For the chemical composition, constructed models generally did a better job of predicting the extractives and lignin content than the carbohydrates. In predicting the thermochemical properties, models for volatile matter and fixed carbon performed very well (i.e., R2 > 0.80, RPD > 2.0. The effect of reducing the wavenumber range to the fingerprint region for PLS modeling and the relationship between the chemical composition and higher heating value of logging residue were also explored. This study is new and different in that it is the first to use FTIR spectroscopy to quantitatively analyze forest logging residue, an abundant resource that can be used as a feedstock in the emerging low carbon economy. Furthermore, it provides a complete and systematic characterization of this heterogeneous raw material.
A least squares calculational method: application to e±-H elastic scattering
International Nuclear Information System (INIS)
Das, J.N.; Chakraborty, S.
1989-01-01
The least squares calcualtional method proposed by Das has been applied for the e ± -H elastic scattering problems for intermediate energies. Some important conclusions are made on the basis of the calculation. (author). 7 refs ., 2 tabs
International Nuclear Information System (INIS)
Comesanna Garcia, Yumirka; Dago Morales, Angel; Talavera Bustamante, Isneri
2010-01-01
The recently introduction of the least squares support vector machines method for regression purposes in the field of Chemometrics has provided several advantages to linear and nonlinear multivariate calibration methods. The objective of the paper was to propose the use of the least squares support vector machine as an alternative multivariate calibration method for the prediction of the percentage of crystallinity of fluidized catalytic cracking catalysts, by means of Fourier transform mid-infrared spectroscopy. A linear kernel was used in the calculations of the regression model. The optimization of its gamma parameter was carried out using the leave-one-out cross-validation procedure. The root mean square error of prediction was used to measure the performance of the model. The accuracy of the results obtained with the application of the method is in accordance with the uncertainty of the X-ray powder diffraction reference method. To compare the generalization capability of the developed method, a comparison study was carried out, taking into account the results achieved with the new model and those reached through the application of linear calibration methods. The developed method can be easily implemented in refinery laboratories
Least square method of estimation of ecological half-lives of radionuclides in sediments
International Nuclear Information System (INIS)
Ranade, A.K.; Pandey, M.; Datta, D.; Ravi, P.M.
2012-01-01
Long term behavior of radionuclides in the environment is an important issue for estimating probable radiological consequences and associated risks. It is also useful for evaluating potential use of contaminated areas and the possible effectiveness of remediation activities. The long term behavior is quantified by means of ecological half life, a parameter that aggregates all processes except radioactive decay which causes a decrease of activity in a specific medium. The process involved in ecological half life depends upon the environmental condition of the medium involved. A fitting model based on least square regression approach was used to evaluate the ecological half life. This least square method has to run several times to evaluate the number of ecological half lives present in the medium for the radionuclide. The case study data considered here is for 137 Cs in Mumbai Harbour Bay. The study shows the trend of 137 Cs over the years at a location in Mumbai Harbour Bay. First iteration model illustrate the ecological half life as 4.94 y and subsequently it passes through a number of runs for more number of ecological half-life present by goodness of fit test. The paper presents a methodology for evaluating ecological half life and exemplifies it with a case study of 137 Cs. (author)
Analysis of a plane stress wave by the moving least squares method
Directory of Open Access Journals (Sweden)
Wojciech Dornowski
2014-08-01
Full Text Available A meshless method based on the moving least squares approximation is applied to stress wave propagation analysis. Two kinds of node meshes, the randomly generated mesh and the regular mesh are used. The nearest neighbours’ problem is developed from a triangulation that satisfies minimum edges length conditions. It is found that this method of neighbours’ choice significantly improves the solution accuracy. The reflection of stress waves from the free edge is modelled using fictitious nodes (outside the plate. The comparison with the finite difference results also demonstrated the accuracy of the proposed approach.[b]Keywords[/b]: civil engineering, meshless method, moving least squares method, elastic waves
Track Circuit Fault Diagnosis Method based on Least Squares Support Vector
Cao, Yan; Sun, Fengru
2018-01-01
In order to improve the troubleshooting efficiency and accuracy of the track circuit, track circuit fault diagnosis method was researched. Firstly, the least squares support vector machine was applied to design the multi-fault classifier of the track circuit, and then the measured track data as training samples was used to verify the feasibility of the methods. Finally, the results based on BP neural network fault diagnosis methods and the methods used in this paper were compared. Results shows that the track fault classifier based on least squares support vector machine can effectively achieve the five track circuit fault diagnosis with less computing time.
DEFF Research Database (Denmark)
Anders, Annett; Nishijima, Kazuyoshi
The present paper aims at enhancing a solution approach proposed by Anders & Nishijima (2011) to real-time decision problems in civil engineering. The approach takes basis in the Least Squares Monte Carlo method (LSM) originally proposed by Longstaff & Schwartz (2001) for computing American option...... prices. In Anders & Nishijima (2011) the LSM is adapted for a real-time operational decision problem; however it is found that further improvement is required in regard to the computational efficiency, in order to facilitate it for practice. This is the focus in the present paper. The idea behind...... the improvement of the computational efficiency is to “best utilize” the least squares method; i.e. least squares method is applied for estimating the expected utility for terminal decisions, conditional on realizations of underlying random phenomena at respective times in a parametric way. The implementation...
Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems
Czech Academy of Sciences Publication Activity Database
Morikuni, Keiichi; Hayami, K.
2015-01-01
Roč. 36, č. 1 (2015), s. 225-250 ISSN 0895-4798 Institutional support: RVO:67985807 Keywords : least squares problem * iterative methods * preconditioner * inner-outer iteration * GMRES method * stationary iterative method * rank-deficient problem Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015
Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport
Directory of Open Access Journals (Sweden)
Rajeev Kumar
2008-01-01
Full Text Available The least-squares finite element method (LSFEM has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM. The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM, is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.
Error analysis of some Galerkin - least squares methods for the elasticity equations
International Nuclear Information System (INIS)
Franca, L.P.; Stenberg, R.
1989-05-01
We consider the recent technique of stabilizing mixed finite element methods by augmenting the Galerkin formulation with least squares terms calculated separately on each element. The error analysis is performed in a unified manner yielding improved results for some methods introduced earlier. In addition, a new formulation is introduced and analyzed [pt
Analysis of neutron and x-ray reflectivity data by constrained least-squares methods
DEFF Research Database (Denmark)
Pedersen, J.S.; Hamley, I.W.
1994-01-01
. The coefficients in the series are determined by constrained nonlinear least-squares methods, in which the smoothest solution that agrees with the data is chosen. In the second approach the profile is expressed as a series of sine and cosine terms. A smoothness constraint is used which reduces the coefficients...
Spectral mimetic least-squares method for div-curl systems
Gerritsma, Marc; Palha, Artur; Lirkov, I.; Margenov, S.
2018-01-01
In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test
Harmonic tidal analysis at a few stations using the least squares method
Digital Repository Service at National Institute of Oceanography (India)
Fernandes, A.A.; Das, V.K.; Bahulayan, N.
Using the least squares method, harmonic analysis has been performed on hourly water level records of 29 days at several stations depicting different types of non-tidal noise. For a tidal record at Mormugao, which was free from storm surges (low...
On the use of a penalized least squares method to process kinematic full-field measurements
International Nuclear Information System (INIS)
Moulart, Raphaël; Rotinat, René
2014-01-01
This work is aimed at exploring the performances of an alternative procedure to smooth and differentiate full-field displacement measurements. After recalling the strategies currently used by the experimental mechanics community, a short overview of the available smoothing algorithms is drawn up and the requirements that such an algorithm has to fulfil to be applicable to process kinematic measurements are listed. A comparative study of the chosen algorithm is performed including the 2D penalized least squares method and two other commonly implemented strategies. The results obtained by penalized least squares are comparable in terms of quality to those produced by the two other algorithms, while the penalized least squares method appears to be the fastest and the most flexible. Unlike both the other considered methods, it is possible with penalized least squares to automatically choose the parameter governing the amount of smoothing to apply. Unfortunately, it appears that this automation is not suitable for the proposed application since it does not lead to optimal strain maps. Finally, it is possible with this technique to perform the derivation to obtain strain maps before smoothing them (while the smoothing is normally applied to displacement maps before the differentiation), which can lead in some cases to a more effective reconstruction of the strain fields. (paper)
Directory of Open Access Journals (Sweden)
Weize Li
2018-01-01
Full Text Available Research on stealthiness has become an important topic in the field of data integrity (DI attacks. To construct stealthy DI attacks, a common assumption in most related studies is that attackers have prior model knowledge of physical systems. In this paper, such assumption is relaxed and a covert agent is proposed based on the least squares support vector regression (LSSVR. By estimating a plant model from control and sensory data, the LSSVR-based covert agent can closely imitate the behavior of the physical plant. Then, the covert agent is used to construct a covert loop, which can keep the controller’s input and output both stealthy over a finite time window. Experiments have been carried out to show the effectiveness of the proposed method.
Strong source heat transfer simulations based on a GalerKin/Gradient - least - squares method
International Nuclear Information System (INIS)
Franca, L.P.; Carmo, E.G.D. do.
1989-05-01
Heat conduction problems with temperature-dependent strong sources are modeled by an equation with a laplacian term, a linear term and a given source distribution term. When the linear-temperature-dependent source term is much larger than the laplacian term, we have a singular perturbation problem. In this case, boundary layers are formed to satisfy the Dirichlet boundary conditions. Although this is an elliptic equation, the standard Galerkin method solution is contaminated by spurious oscillations in the neighborhood of the boundary layers. Herein we employ a Galerkin/Gradient-least-squares method which eliminates all pathological phenomena of the Galerkin method. The method is constructed by adding to the Galerkin method a mesh-dependent term obtained by the least-squares form of the gradient of the Euler-Lagrange equation. Error estimates, numerical simulations in one-and multi-dimensions are given that attest the good stability and accuracy properties of the method [pt
International Nuclear Information System (INIS)
Kim, Jong-Yun; Choi, Yong Suk; Park, Yong Joon; Jung, Sung-Hee
2009-01-01
Neutron spectrometry, based on the scattering of high energy fast neutrons from a radioisotope and slowing-down by the light hydrogen atoms, is a useful technique for non-destructive, quantitative measurement of hydrogen content because it has a large measuring volume, and is not affected by temperature, pressure, pH value and color. The most common choice for radioisotope neutron source is 252 Cf or 241 Am-Be. In this study, 252 Cf with a neutron flux of 6.3x10 6 n/s has been used as an attractive neutron source because of its high flux neutron and weak radioactivity. Pulse-height neutron spectra have been obtained by using in-house built radioisotopic neutron spectrometric system equipped with 3 He detector and multi-channel analyzer, including a neutron shield. As a preliminary study, polyethylene block (density of ∼0.947 g/cc and area of 40 cmx25 cm) was used for the determination of hydrogen content by using multivariate calibration models, depending on the thickness of the block. Compared with the results obtained from a simple linear calibration model, partial least-squares regression (PLSR) method offered a better performance in a quantitative data analysis. It also revealed that the PLSR method in a neutron spectrometric system can be promising in the real-time, online monitoring of the powder process to determine the content of any type of molecules containing hydrogen nuclei.
A weak Galerkin least-squares finite element method for div-curl systems
Li, Jichun; Ye, Xiu; Zhang, Shangyou
2018-06-01
In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.
A Least Square-Based Self-Adaptive Localization Method for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Baoguo Yu
2016-01-01
Full Text Available In the wireless sensor network (WSN localization methods based on Received Signal Strength Indicator (RSSI, it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.
Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem
Directory of Open Access Journals (Sweden)
Baiyu Wang
2014-01-01
Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.
Feasibility study on the least square method for fitting non-Gaussian noise data
Xu, Wei; Chen, Wen; Liang, Yingjie
2018-02-01
This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.
A Generalized Autocovariance Least-Squares Method for Kalman Filter Tuning
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad
2008-01-01
This paper discusses a method for estimating noise covariances from process data. In linear stochastic state-space representations the true noise covariances are generally unknown in practical applications. Using estimated covariances a Kalman filter can be tuned in order to increase the accuracy...... of the state estimates. There is a linear relationship between covariances and autocovariance. Therefore, the covariance estimation problem can be stated as a least-squares problem, which can be solved as a symmetric semidefinite least-squares problem. This problem is convex and can be solved efficiently...... by interior-point methods. A numerical algorithm for solving the symmetric is able to handle systems with mutually correlated process noise and measurement noise. (c) 2007 Elsevier Ltd. All rights reserved....
F. Grigoli; Simone Cesca; Torsten Dahm; L. Krieger
2012-01-01
Determining the relative orientation of the horizontal components of seismic sensors is a common problem that limits data analysis and interpretation for several acquisition setups, including linear arrays of geophones deployed in borehole installations or ocean bottom seismometers deployed at the seafloor. To solve this problem we propose a new inversion method based on a complex linear algebra approach. Relative orientation angles are retrieved by minimizing, in a least-squares sense, the l...
Least-squares methods for identifying biochemical regulatory networks from noisy measurements
Directory of Open Access Journals (Sweden)
Heslop-Harrison Pat
2007-01-01
Full Text Available Abstract Background We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS. The Total Least Squares (TLS technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. Results The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL-6 and (IL-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL-6 and (IL-12b by ATF3. Conclusion The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable
Nonlinear Least Square Based on Control Direction by Dual Method and Its Application
Directory of Open Access Journals (Sweden)
Zhengqing Fu
2016-01-01
Full Text Available A direction controlled nonlinear least square (NLS estimation algorithm using the primal-dual method is proposed. The least square model is transformed into the primal-dual model; then direction of iteration can be controlled by duality. The iterative algorithm is designed. The Hilbert morbid matrix is processed by the new model and the least square estimate and ridge estimate. The main research method is to combine qualitative analysis and quantitative analysis. The deviation between estimated values and the true value and the estimated residuals fluctuation of different methods are used for qualitative analysis. The root mean square error (RMSE is used for quantitative analysis. The results of experiment show that the model has the smallest residual error and the minimum root mean square error. The new estimate model has effectiveness and high precision. The genuine data of Jining area in unwrapping experiments are used and the comparison with other classical unwrapping algorithms is made, so better results in precision aspects can be achieved through the proposed algorithm.
Method for exploiting bias in factor analysis using constrained alternating least squares algorithms
Keenan, Michael R.
2008-12-30
Bias plays an important role in factor analysis and is often implicitly made use of, for example, to constrain solutions to factors that conform to physical reality. However, when components are collinear, a large range of solutions may exist that satisfy the basic constraints and fit the data equally well. In such cases, the introduction of mathematical bias through the application of constraints may select solutions that are less than optimal. The biased alternating least squares algorithm of the present invention can offset mathematical bias introduced by constraints in the standard alternating least squares analysis to achieve factor solutions that are most consistent with physical reality. In addition, these methods can be used to explicitly exploit bias to provide alternative views and provide additional insights into spectral data sets.
International Nuclear Information System (INIS)
Haaland, D.M.; Easterling, R.G.; Vopicka, D.A.
1985-01-01
In an extension of earlier work, weighted multivariate least-squares methods of quantitative FT-IR analysis have been developed. A linear least-squares approximation to nonlinearities in the Beer-Lambert law is made by allowing the reference spectra to be a set of known mixtures, The incorporation of nonzero intercepts in the relation between absorbance and concentration further improves the approximation of nonlinearities while simultaneously accounting for nonzero spectra baselines. Pathlength variations are also accommodated in the analysis, and under certain conditions, unknown sample pathlengths can be determined. All spectral data are used to improve the precision and accuracy of the estimated concentrations. During the calibration phase of the analysis, pure component spectra are estimated from the standard mixture spectra. These can be compared with the measured pure component spectra to determine which vibrations experience nonlinear behavior. In the predictive phase of the analysis, the calculated spectra are used in our previous least-squares analysis to estimate sample component concentrations. These methods were applied to the analysis of the IR spectra of binary mixtures of esters. Even with severely overlapping spectral bands and nonlinearities in the Beer-Lambert law, the average relative error in the estimated concentration was <1%
Lin, Lixin; Wang, Yunjia; Teng, Jiyao; Wang, Xuchen
2016-02-01
Hyperspectral estimation of soil organic matter (SOM) in coal mining regions is an important tool for enhancing fertilization in soil restoration programs. The correlation--partial least squares regression (PLSR) method effectively solves the information loss problem of correlation--multiple linear stepwise regression, but results of the correlation analysis must be optimized to improve precision. This study considers the relationship between spectral reflectance and SOM based on spectral reflectance curves of soil samples collected from coal mining regions. Based on the major absorption troughs in the 400-1006 nm spectral range, PLSR analysis was performed using 289 independent bands of the second derivative (SDR) with three levels and measured SOM values. A wavelet-correlation-PLSR (W-C-PLSR) model was then constructed. By amplifying useful information that was previously obscured by noise, the W-C-PLSR model was optimal for estimating SOM content, with smaller prediction errors in both calibration (R(2) = 0.970, root mean square error (RMSEC) = 3.10, and mean relative error (MREC) = 8.75) and validation (RMSEV = 5.85 and MREV = 14.32) analyses, as compared with other models. Results indicate that W-C-PLSR has great potential to estimate SOM in coal mining regions.
And still, a new beginning: the Galerkin least-squares gradient method
International Nuclear Information System (INIS)
Franca, L.P.; Carmo, E.G.D. do
1988-08-01
A finite element method is proposed to solve a scalar singular diffusion problem. The method is constructed by adding to the standard Galerkin a mesh-dependent term obtained by taking the gradient of the Euler-lagrange equation and multiplying it by its least-squares. For the one-dimensional homogeneous problem the method is designed to develop nodal exact solution. An error estimate shows that the method converges optimaly for any value of the singular parameter. Numerical results demonstrate the good stability and accuracy properties of the method. (author) [pt
Plata, Maria R; Koch, Cosima; Wechselberger, Patrick; Herwig, Christoph; Lendl, Bernhard
2013-10-01
A fast and simple method to control variations in carbohydrate composition of Saccharomyces cerevisiae, baker's yeast, during fermentation was developed using mid-infrared (mid-IR) spectroscopy. The method allows for precise and accurate determinations with minimal or no sample preparation and reagent consumption based on mid-IR spectra and partial least squares (PLS) regression. The PLS models were developed employing the results from reference analysis of the yeast cells. The reference analyses quantify the amount of trehalose, glucose, glycogen, and mannan in S. cerevisiae. The selection and optimization of pretreatment steps of samples such as the disruption of the yeast cells and the hydrolysis of mannan and glycogen to obtain monosaccharides were carried out. Trehalose, glucose, and mannose were determined using high-performance liquid chromatography coupled with a refractive index detector and total carbohydrates were measured using the phenol-sulfuric method. Linear concentration range, accuracy, precision, LOD and LOQ were examined to check the reliability of the chromatographic method for each analyte.
Purpose: The aim of this study was to develop a technique for the non-destructive and rapid prediction of the moisture content in red pepper powder using near-infrared (NIR) spectroscopy and a partial least squares regression (PLSR) model. Methods: Three red pepper powder products were separated in...
International Nuclear Information System (INIS)
Halepoto, I.A.; Uqaili, M.A.
2014-01-01
Nowadays, due to power crisis, electricity demand forecasting is deemed an important area for socioeconomic development and proper anticipation of the load forecasting is considered essential step towards efficient power system operation, scheduling and planning. In this paper, we present STLF (Short Term Load Forecasting) using multiple regression techniques (i.e. linear, multiple linear, quadratic and exponential) by considering hour by hour load model based on specific targeted day approach with temperature variant parameter. The proposed work forecasts the future load demand correlation with linear and non-linear parameters (i.e. considering temperature in our case) through different regression approaches. The overall load forecasting error is 2.98% which is very much acceptable. From proposed regression techniques, Quadratic Regression technique performs better compared to than other techniques because it can optimally fit broad range of functions and data sets. The work proposed in this paper, will pave a path to effectively forecast the specific day load with multiple variance factors in a way that optimal accuracy can be maintained. (author)
Massively-parallel best subset selection for ordinary least-squares regression
DEFF Research Database (Denmark)
Gieseke, Fabian; Polsterer, Kai Lars; Mahabal, Ashish
2017-01-01
Selecting an optimal subset of k out of d features for linear regression models given n training instances is often considered intractable for feature spaces with hundreds or thousands of dimensions. We propose an efficient massively-parallel implementation for selecting such optimal feature...
International Nuclear Information System (INIS)
Gillet, M.
1986-07-01
This thesis presents a study for the surveillance of the Primary circuit water inventory of a pressurized water reactor. A reference model is developed for the development of an automatic system ensuring detection and real-time diagnostic. The methods to our application are statistical tests and adapted a pattern recognition method. The estimation of the detected anomalies is treated by the least square fit method, and by filtering. A new projected optimization method with superlinear convergence is developed in this framework, and a segmented linearization of the model is introduced, in view of a multiple filtering. 46 refs [fr
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Energy Technology Data Exchange (ETDEWEB)
Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)
1996-12-31
Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.
Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems
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Oskar Cahueñas
2013-05-01
Full Text Available We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative schemes that avoid the use of the, usually ill-conditioned, normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method, that are suitable for preconditioning strategies. We present preliminary numerical results to illustrate the advantages of the proposed schemes.
Directory of Open Access Journals (Sweden)
Tianming Yang
2016-01-01
Full Text Available This paper reports a simple, rapid, and effective method for simultaneous detection of cartap (Ca, thiocyclam (Th, and tebufenozide (Te in Chinese herbal medicines including Radix Angelicae Dahuricae and Liquorices using Fourier transform infrared spectroscopy (FT-IR coupled with partial least squares regression (PLSR. The proposed method can handle the intrinsic interferences of herbal samples; satisfactory average recoveries attained from near-infrared (NIR and mid-infrared (MIR PLSR models were 99.0±10.8 and 100.2±1.0% for Ca, 100.2±6.9 and 99.7±2.5% for Th, and 99.1±6.3 and 99.6±1.0% for Te, respectively. Furthermore, some statistical parameters and figures of merit are fully investigated to evaluate the performance of the two models. It was found that both models could give accurate results and only the performance of MIR-PLSR was slightly better than that of NIR-PLSR in the cases suffering from herbal matrix interferences. In conclusion, FT-IR spectroscopy in combination with PLSR has been demonstrated for its application in rapid screening and quantitative analysis of multipesticide residues in Chinese herbal medicines without physical or chemical separation pretreatment step and any spectral processing, which also implies other potential applications such as food and drug safety, herbal plants quality, and environmental evaluation, due to its advantages of nontoxic and nondestructive analysis.
Chen, Jing; Qiu, Xiaojie; Yin, Cunyi; Jiang, Hao
2018-02-01
An efficient method to design the broadband gain-flattened Raman fiber amplifier with multiple pumps is proposed based on least squares support vector regression (LS-SVR). A multi-input multi-output LS-SVR model is introduced to replace the complicated solving process of the nonlinear coupled Raman amplification equation. The proposed approach contains two stages: offline training stage and online optimization stage. During the offline stage, the LS-SVR model is trained. Owing to the good generalization capability of LS-SVR, the net gain spectrum can be directly and accurately obtained when inputting any combination of the pump wavelength and power to the well-trained model. During the online stage, we incorporate the LS-SVR model into the particle swarm optimization algorithm to find the optimal pump configuration. The design results demonstrate that the proposed method greatly shortens the computation time and enhances the efficiency of the pump parameter optimization for Raman fiber amplifier design.
A negative-norm least-squares method for time-harmonic Maxwell equations
Copeland, Dylan M.
2012-04-01
This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.
Obtention of the parameters of the Voigt function using the least square fit method
International Nuclear Information System (INIS)
Flores Ll, H.; Cabral P, A.; Jimenez D, H.
1990-01-01
The fundamental parameters of the Voigt function are determined: lorentzian wide (Γ L ) and gaussian wide (Γ G ) with an error for almost all the cases inferior to 1% in the intervals 0.01 ≤ Γ L / Γ G ≤1 and 0.3 ≤ Γ G / Γ L ≤1. This is achieved using the least square fit method with an algebraic function, being obtained a simple method to obtain the fundamental parameters of the Voigt function used in many spectroscopies. (Author)
Data-adapted moving least squares method for 3-D image interpolation
International Nuclear Information System (INIS)
Jang, Sumi; Lee, Yeon Ju; Jeong, Byeongseon; Nam, Haewon; Lee, Rena; Yoon, Jungho
2013-01-01
In this paper, we present a nonlinear three-dimensional interpolation scheme for gray-level medical images. The scheme is based on the moving least squares method but introduces a fundamental modification. For a given evaluation point, the proposed method finds the local best approximation by reproducing polynomials of a certain degree. In particular, in order to obtain a better match to the local structures of the given image, we employ locally data-adapted least squares methods that can improve the classical one. Some numerical experiments are presented to demonstrate the performance of the proposed method. Five types of data sets are used: MR brain, MR foot, MR abdomen, CT head, and CT foot. From each of the five types, we choose five volumes. The scheme is compared with some well-known linear methods and other recently developed nonlinear methods. For quantitative comparison, we follow the paradigm proposed by Grevera and Udupa (1998). (Each slice is first assumed to be unknown then interpolated by each method. The performance of each interpolation method is assessed statistically.) The PSNR results for the estimated volumes are also provided. We observe that the new method generates better results in both quantitative and visual quality comparisons. (paper)
Directory of Open Access Journals (Sweden)
ZHANG Long
2015-09-01
Full Text Available Near infrared reflectance spectroscopy (NIRS, a non-destructive measurement technique, was combined with partial least squares regression discrimiant analysis (PLS-DA to discriminate the transgenic (TCTP and mi166 and wild type (Zhonghua 11 rice. Furthermore, rice lines transformed with protein gene (OsTCTP and regulation gene (Osmi166 were also discriminated by the NIRS method. The performances of PLS-DA in spectral ranges of 4 000–8 000 cm-1 and 4 000–10 000 cm-1 were compared to obtain the optimal spectral range. As a result, the transgenic and wild type rice were distinguished from each other in the range of 4 000–10 000 cm-1, and the correct classification rate was 100.0% in the validation test. The transgenic rice TCTP and mi166 were also distinguished from each other in the range of 4 000–10 000 cm-1, and the correct classification rate was also 100.0%. In conclusion, NIRS combined with PLS-DA can be used for the discrimination of transgenic rice.
Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems
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Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies
2018-03-29
Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.
Decentralized Gauss-Newton method for nonlinear least squares on wide area network
Liu, Lanchao; Ling, Qing; Han, Zhu
2014-10-01
This paper presents a decentralized approach of Gauss-Newton (GN) method for nonlinear least squares (NLLS) on wide area network (WAN). In a multi-agent system, a centralized GN for NLLS requires the global GN Hessian matrix available at a central computing unit, which may incur large communication overhead. In the proposed decentralized alternative, each agent only needs local GN Hessian matrix to update iterates with the cooperation of neighbors. The detail formulation of decentralized NLLS on WAN is given, and the iteration at each agent is defined. The convergence property of the decentralized approach is analyzed, and numerical results validate the effectiveness of the proposed algorithm.
International Nuclear Information System (INIS)
Ackroyd, R.T.
1987-01-01
A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)
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You, Qiang; Xu, JinXin; Wang, Gang; Zhang, Zhonghua
2016-01-01
The ordinary least-square fitting with polynomial is used in both the dynamic phase of the watt balance method and the weighting phase of joule balance method but few researches have been conducted to evaluate the uncertainty of the fitting data in the electrical balance methods. In this paper, a matrix-calculation method for evaluating the uncertainty of the polynomial fitting data is derived and the properties of this method are studied by simulation. Based on this, another two derived methods are proposed. One is used to find the optimal fitting order for the watt or joule balance methods. Accuracy and effective factors of this method are experimented with simulations. The other is used to evaluate the uncertainty of the integral of the fitting data for joule balance, which is demonstrated with an experiment from the NIM-1 joule balance. (paper)
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Nufang Fang
2015-07-01
Full Text Available Multivariate statistics are commonly used to identify the factors that control the dynamics of runoff or sediment yields during hydrological processes. However, one issue with the use of conventional statistical methods to address relationships between variables and runoff or sediment yield is multicollinearity. The main objectives of this study were to apply a method for effectively identifying runoff and sediment control factors during hydrological processes and apply that method to a case study. The method combines the clustering approach and partial least squares regression (PLSR models. The case study was conducted in a mountainous watershed in the Three Gorges Area. A total of 29 flood events in three hydrological years in areas with different land uses were obtained. In total, fourteen related variables were separated from hydrographs using the classical hydrograph separation method. Twenty-nine rainfall events were classified into two rainfall regimes (heavy Rainfall Regime I and moderate Rainfall Regime II based on rainfall characteristics and K-means clustering. Four separate PLSR models were constructed to identify the main variables that control runoff and sediment yield for the two rainfall regimes. For Rainfall Regime I, the dominant first-order factors affecting the changes in sediment yield in our study were all of the four rainfall-related variables, flood peak discharge, maximum flood suspended sediment concentration, runoff, and the percentages of forest and farmland. For Rainfall Regime II, antecedent condition-related variables have more effects on both runoff and sediment yield than in Rainfall Regime I. The results suggest that the different control factors of the two rainfall regimes are determined by the rainfall characteristics and thus different runoff mechanisms.
Time-domain least-squares migration using the Gaussian beam summation method
Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo
2018-04-01
With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.
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Santosh Kumar Singh
2017-06-01
Full Text Available This paper presents a new hybrid method based on Gravity Search Algorithm (GSA and Recursive Least Square (RLS, known as GSA-RLS, to solve the harmonic estimation problems in the case of time varying power signals in presence of different noises. GSA is based on the Newton’s law of gravity and mass interactions. In the proposed method, the searcher agents are a collection of masses that interact with each other using Newton’s laws of gravity and motion. The basic GSA algorithm strategy is combined with RLS algorithm sequentially in an adaptive way to update the unknown parameters (weights of the harmonic signal. Simulation and practical validation are made with the experimentation of the proposed algorithm with real time data obtained from a heavy paper industry. A comparative performance of the proposed algorithm is evaluated with other recently reported algorithms like, Differential Evolution (DE, Particle Swarm Optimization (PSO, Bacteria Foraging Optimization (BFO, Fuzzy-BFO (F-BFO hybridized with Least Square (LS and BFO hybridized with RLS algorithm, which reveals that the proposed GSA-RLS algorithm is the best in terms of accuracy, convergence and computational time.
Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods
Oza, D. H.; Jones, T. L.; Fabien, S. M.; Mistretta, G. D.; Hart, R. C.; Doll, C. E.
1991-01-01
The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.
Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods
Oza, D. H.; Jones, T. L.; Fabien, S. M.; Mistretta, G. D.; Hart, R. C.; Doll, C. E.
1991-10-01
The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.
Xu, Zheng; Wang, Sheng; Li, Yeqing; Zhu, Feiyun; Huang, Junzhou
2018-02-08
The most recent history of parallel Magnetic Resonance Imaging (pMRI) has in large part been devoted to finding ways to reduce acquisition time. While joint total variation (JTV) regularized model has been demonstrated as a powerful tool in increasing sampling speed for pMRI, however, the major bottleneck is the inefficiency of the optimization method. While all present state-of-the-art optimizations for the JTV model could only reach a sublinear convergence rate, in this paper, we squeeze the performance by proposing a linear-convergent optimization method for the JTV model. The proposed method is based on the Iterative Reweighted Least Squares algorithm. Due to the complexity of the tangled JTV objective, we design a novel preconditioner to further accelerate the proposed method. Extensive experiments demonstrate the superior performance of the proposed algorithm for pMRI regarding both accuracy and efficiency compared with state-of-the-art methods.
Concerning an application of the method of least squares with a variable weight matrix
Sukhanov, A. A.
1979-01-01
An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.
Resolution of the neutron transport equation by a three-dimensional least square method
International Nuclear Information System (INIS)
Varin, Elisabeth
2001-01-01
The knowledge of space and time distribution of neutrons with a certain energy or speed allows the exploitation and control of a nuclear reactor and the assessment of the irradiation dose about an irradiated nuclear fuel storage site. The neutron density is described by a transport equation. The objective of this research thesis is to develop a software for the resolution of this stationary equation in a three-dimensional Cartesian domain by means of a deterministic method. After a presentation of the transport equation, the author gives an overview of the different deterministic resolution approaches, identifies their benefits and drawbacks, and discusses the choice of the Ressel method. The least square method is precisely described and then applied. Numerical benchmarks are reported for validation purposes
A Collocation Method by Moving Least Squares Applicable to European Option Pricing
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M. Amirfakhrian
2016-05-01
Full Text Available The subject matter of the present inquiry is the pricing of European options in the actual form of numbers. To assess the numerical prices of European options, a scheme independent of any kind of mesh but rather powered by moving least squares (MLS estimation is made. In practical terms, first the discretion of time variable is implemented and then, an MLS-powered method is applied for spatial approximation. As, unlike other methods, these courses of action mentioned here don't rely on a mesh, one can firmly claim they are to be categorized under mesh-less methods. And, of course, at the end of the paper, various experiments are offered to prove how efficient and how powerful the introduced approach is.
DEM4-26, Least Square Fit for IBM PC by Deming Method
International Nuclear Information System (INIS)
Rinard, P.M.; Bosler, G.E.
1989-01-01
1 - Description of program or function: DEM4-26 is a generalized least square fitting program based on Deming's method. Functions built into the program for fitting include linear, quadratic, cubic, power, Howard's, exponential, and Gaussian; others can easily be added. The program has the following capabilities: (1) entry, editing, and saving of data; (2) fitting of any of the built-in functions or of a user-supplied function; (3) plotting the data and fitted function on the display screen, with error limits if requested, and with the option of copying the plot to the printer; (4) interpolation of x or y values from the fitted curve with error estimates based on error limits selected by the user; and (5) plotting the residuals between the y data values and the fitted curve, with the option copying the plot to the printer. 2 - Method of solution: Deming's method
A comparative analysis of the EEDF obtained by Regularization and by Least square fit methods
International Nuclear Information System (INIS)
Gutierrez T, C.; Flores Ll, H.
2004-01-01
The second derived of the characteristic curve current-voltage (I - V) of a Langmuir probe (I - V) is numerically calculated using the Tikhonov method for to determine the distribution function of the electrons energy (EEDF). One comparison of the obtained EEDF and a fit by least square are discussed (LS). The I - V experimental curve is obtained in a plasma source in the electron cyclotron resonance (ECR) using a cylindrical probe. The parameters of plasma are determined of the EEDF by means of the Laframboise theory. For the case of the LS fit, the obtained results are similar to those obtained by the Tikhonov method, but in the first case the procedure is slow to achieve the best fit. (Author)
Window least squares method applied to statistical noise smoothing of positron annihilation data
International Nuclear Information System (INIS)
Adam, G.; Adam, S.; Barbiellini, B.; Hoffmann, L.; Manuel, A.A.; Peter, M.
1993-06-01
The paper deals with the off-line processing of experimental data obtained by two-dimensional angular correlation of the electron-positron annihilation radiation (2D-ACAR) technique on high-temperature superconductors. A piecewise continuous window least squares (WLS) method devoted to the statistical noise smoothing of 2D-ACAR data, under close control of the crystal reciprocal lattice periodicity, is derived. Reliability evaluation of the constant local weight WLS smoothing formula (CW-WLSF) shows that consistent processing 2D-ACAR data by CW-WLSF is possible. CW-WLSF analysis of 2D-ACAR data collected on untwinned Y Ba 2 Cu 3 O 7-δ single crystals yields significantly improved signature of the Fermi surface ridge at second Umklapp processes and resolves, for the first time, the ridge signature at third Umklapp processes. (author). 24 refs, 9 figs
Fitting of two and three variate polynomials from experimental data through the least squares method
International Nuclear Information System (INIS)
Sanchez-Miro, J.J.; Sanz-Martin, J.C.
1994-01-01
Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries
International Nuclear Information System (INIS)
Hughes, T.J.R.; Hulbert, G.M.; Franca, L.P.
1988-10-01
Galerkin/least-squares finite element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of SUPG, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. (author) [pt
Linear least-squares method for global luminescent oil film skin friction field analysis
Lee, Taekjin; Nonomura, Taku; Asai, Keisuke; Liu, Tianshu
2018-06-01
A data analysis method based on the linear least-squares (LLS) method was developed for the extraction of high-resolution skin friction fields from global luminescent oil film (GLOF) visualization images of a surface in an aerodynamic flow. In this method, the oil film thickness distribution and its spatiotemporal development are measured by detecting the luminescence intensity of the thin oil film. From the resulting set of GLOF images, the thin oil film equation is solved to obtain an ensemble-averaged (steady) skin friction field as an inverse problem. In this paper, the formulation of a discrete linear system of equations for the LLS method is described, and an error analysis is given to identify the main error sources and the relevant parameters. Simulations were conducted to evaluate the accuracy of the LLS method and the effects of the image patterns, image noise, and sample numbers on the results in comparison with the previous snapshot-solution-averaging (SSA) method. An experimental case is shown to enable the comparison of the results obtained using conventional oil flow visualization and those obtained using both the LLS and SSA methods. The overall results show that the LLS method is more reliable than the SSA method and the LLS method can yield a more detailed skin friction topology in an objective way.
International Nuclear Information System (INIS)
Dyar, M.D.; Carmosino, M.L.; Breves, E.A.; Ozanne, M.V.; Clegg, S.M.; Wiens, R.C.
2012-01-01
A remote laser-induced breakdown spectrometer (LIBS) designed to simulate the ChemCam instrument on the Mars Science Laboratory Rover Curiosity was used to probe 100 geologic samples at a 9-m standoff distance. ChemCam consists of an integrated remote LIBS instrument that will probe samples up to 7 m from the mast of the rover and a remote micro-imager (RMI) that will record context images. The elemental compositions of 100 igneous and highly-metamorphosed rocks are determined with LIBS using three variations of multivariate analysis, with a goal of improving the analytical accuracy. Two forms of partial least squares (PLS) regression are employed with finely-tuned parameters: PLS-1 regresses a single response variable (elemental concentration) against the observation variables (spectra, or intensity at each of 6144 spectrometer channels), while PLS-2 simultaneously regresses multiple response variables (concentrations of the ten major elements in rocks) against the observation predictor variables, taking advantage of natural correlations between elements. Those results are contrasted with those from the multivariate regression technique of the least absolute shrinkage and selection operator (lasso), which is a penalized shrunken regression method that selects the specific channels for each element that explain the most variance in the concentration of that element. To make this comparison, we use results of cross-validation and of held-out testing, and employ unscaled and uncentered spectral intensity data because all of the input variables are already in the same units. Results demonstrate that the lasso, PLS-1, and PLS-2 all yield comparable results in terms of accuracy for this dataset. However, the interpretability of these methods differs greatly in terms of fundamental understanding of LIBS emissions. PLS techniques generate principal components, linear combinations of intensities at any number of spectrometer channels, which explain as much variance in the
Energy Technology Data Exchange (ETDEWEB)
Dyar, M.D., E-mail: mdyar@mtholyoke.edu [Dept. of Astronomy, Mount Holyoke College, 50 College St., South Hadley, MA 01075 (United States); Carmosino, M.L.; Breves, E.A.; Ozanne, M.V. [Dept. of Astronomy, Mount Holyoke College, 50 College St., South Hadley, MA 01075 (United States); Clegg, S.M.; Wiens, R.C. [Los Alamos National Laboratory, P.O. Box 1663, MS J565, Los Alamos, NM 87545 (United States)
2012-04-15
A remote laser-induced breakdown spectrometer (LIBS) designed to simulate the ChemCam instrument on the Mars Science Laboratory Rover Curiosity was used to probe 100 geologic samples at a 9-m standoff distance. ChemCam consists of an integrated remote LIBS instrument that will probe samples up to 7 m from the mast of the rover and a remote micro-imager (RMI) that will record context images. The elemental compositions of 100 igneous and highly-metamorphosed rocks are determined with LIBS using three variations of multivariate analysis, with a goal of improving the analytical accuracy. Two forms of partial least squares (PLS) regression are employed with finely-tuned parameters: PLS-1 regresses a single response variable (elemental concentration) against the observation variables (spectra, or intensity at each of 6144 spectrometer channels), while PLS-2 simultaneously regresses multiple response variables (concentrations of the ten major elements in rocks) against the observation predictor variables, taking advantage of natural correlations between elements. Those results are contrasted with those from the multivariate regression technique of the least absolute shrinkage and selection operator (lasso), which is a penalized shrunken regression method that selects the specific channels for each element that explain the most variance in the concentration of that element. To make this comparison, we use results of cross-validation and of held-out testing, and employ unscaled and uncentered spectral intensity data because all of the input variables are already in the same units. Results demonstrate that the lasso, PLS-1, and PLS-2 all yield comparable results in terms of accuracy for this dataset. However, the interpretability of these methods differs greatly in terms of fundamental understanding of LIBS emissions. PLS techniques generate principal components, linear combinations of intensities at any number of spectrometer channels, which explain as much variance in the
Directory of Open Access Journals (Sweden)
Chi-Cheng Huang
2013-01-01
Full Text Available Multiclass prediction remains an obstacle for high-throughput data analysis such as microarray gene expression profiles. Despite recent advancements in machine learning and bioinformatics, most classification tools were limited to the applications of binary responses. Our aim was to apply partial least square (PLS regression for breast cancer intrinsic taxonomy, of which five distinct molecular subtypes were identified. The PAM50 signature genes were used as predictive variables in PLS analysis, and the latent gene component scores were used in binary logistic regression for each molecular subtype. The 139 prototypical arrays for PAM50 development were used as training dataset, and three independent microarray studies with Han Chinese origin were used for independent validation (n=535. The agreement between PAM50 centroid-based single sample prediction (SSP and PLS-regression was excellent (weighted Kappa: 0.988 within the training samples, but deteriorated substantially in independent samples, which could attribute to much more unclassified samples by PLS-regression. If these unclassified samples were removed, the agreement between PAM50 SSP and PLS-regression improved enormously (weighted Kappa: 0.829 as opposed to 0.541 when unclassified samples were analyzed. Our study ascertained the feasibility of PLS-regression in multi-class prediction, and distinct clinical presentations and prognostic discrepancies were observed across breast cancer molecular subtypes.
A method based on moving least squares for XRII image distortion correction
International Nuclear Information System (INIS)
Yan Shiju; Wang Chengtao; Ye Ming
2007-01-01
This paper presents a novel integrated method to correct geometric distortions of XRII (x-ray image intensifier) images. The method has been compared, in terms of mean-squared residual error measured at control and intermediate points, with two traditional local methods and a traditional global methods. The proposed method is based on the methods of moving least squares (MLS) and polynomial fitting. Extensive experiments were performed on simulated and real XRII images. In simulation, the effect of pincushion distortion, sigmoidal distortion, local distortion, noise, and the number of control points was tested. The traditional local methods were sensitive to pincushion and sigmoidal distortion. The traditional global method was only sensitive to sigmoidal distortion. The proposed method was found neither sensitive to pincushion distortion nor sensitive to sigmoidal distortion. The sensitivity of the proposed method to local distortion was lower than or comparable with that of the traditional global method. The sensitivity of the proposed method to noise was higher than that of all three traditional methods. Nevertheless, provided the standard deviation of noise was not greater than 0.1 pixels, accuracy of the proposed method is still higher than the traditional methods. The sensitivity of the proposed method to the number of control points was greatly lower than that of the traditional methods. Provided that a proper cutoff radius is chosen, accuracy of the proposed method is higher than that of the traditional methods. Experiments on real images, carried out by using a 9 in. XRII, showed that residual error of the proposed method (0.2544±0.2479 pixels) is lower than that of the traditional global method (0.4223±0.3879 pixels) and local methods (0.4555±0.3518 pixels and 0.3696±0.4019 pixels, respectively)
Bukhari, Hassan J.
2017-12-01
In this paper a framework for robust optimization of mechanical design problems and process systems that have parametric uncertainty is presented using three different approaches. Robust optimization problems are formulated so that the optimal solution is robust which means it is minimally sensitive to any perturbations in parameters. The first method uses the price of robustness approach which assumes the uncertain parameters to be symmetric and bounded. The robustness for the design can be controlled by limiting the parameters that can perturb.The second method uses the robust least squares method to determine the optimal parameters when data itself is subjected to perturbations instead of the parameters. The last method manages uncertainty by restricting the perturbation on parameters to improve sensitivity similar to Tikhonov regularization. The methods are implemented on two sets of problems; one linear and the other non-linear. This methodology will be compared with a prior method using multiple Monte Carlo simulation runs which shows that the approach being presented in this paper results in better performance.
A Least Squares Collocation Method for Accuracy Improvement of Mobile LiDAR Systems
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Qingzhou Mao
2015-06-01
Full Text Available In environments that are hostile to Global Navigation Satellites Systems (GNSS, the precision achieved by a mobile light detection and ranging (LiDAR system (MLS can deteriorate into the sub-meter or even the meter range due to errors in the positioning and orientation system (POS. This paper proposes a novel least squares collocation (LSC-based method to improve the accuracy of the MLS in these hostile environments. Through a thorough consideration of the characteristics of POS errors, the proposed LSC-based method effectively corrects these errors using LiDAR control points, thereby improving the accuracy of the MLS. This method is also applied to the calibration of misalignment between the laser scanner and the POS. Several datasets from different scenarios have been adopted in order to evaluate the effectiveness of the proposed method. The results from experiments indicate that this method would represent a significant improvement in terms of the accuracy of the MLS in environments that are essentially hostile to GNSS and is also effective regarding the calibration of misalignment.
Least-squares finite-element method for shallow-water equations with source terms
Institute of Scientific and Technical Information of China (English)
Shin-Jye Liang; Tai-Wen Hsu
2009-01-01
Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
Artificial neural network and classical least-squares methods for neurotransmitter mixture analysis.
Schulze, H G; Greek, L S; Gorzalka, B B; Bree, A V; Blades, M W; Turner, R F
1995-02-01
Identification of individual components in biological mixtures can be a difficult problem regardless of the analytical method employed. In this work, Raman spectroscopy was chosen as a prototype analytical method due to its inherent versatility and applicability to aqueous media, making it useful for the study of biological samples. Artificial neural networks (ANNs) and the classical least-squares (CLS) method were used to identify and quantify the Raman spectra of the small-molecule neurotransmitters and mixtures of such molecules. The transfer functions used by a network, as well as the architecture of a network, played an important role in the ability of the network to identify the Raman spectra of individual neurotransmitters and the Raman spectra of neurotransmitter mixtures. Specifically, networks using sigmoid and hyperbolic tangent transfer functions generalized better from the mixtures in the training data set to those in the testing data sets than networks using sine functions. Networks with connections that permit the local processing of inputs generally performed better than other networks on all the testing data sets. and better than the CLS method of curve fitting, on novel spectra of some neurotransmitters. The CLS method was found to perform well on noisy, shifted, and difference spectra.
Goto, Akifumi; Ishida, Mizuri; Sagawa, Koichi
2010-01-01
The purpose of this study is to derive quantitative assessment indicators of the human postural control ability. An inverted pendulum is applied to standing human body and is controlled by ankle joint torque according to PD control method in sagittal plane. Torque control parameters (KP: proportional gain, KD: derivative gain) and pole placements of postural control system are estimated with time from inclination angle variation using fixed trace method as recursive least square method. Eight young healthy volunteers are participated in the experiment, in which volunteers are asked to incline forward as far as and as fast as possible 10 times over 10 [s] stationary intervals with their neck joint, hip joint and knee joint fixed, and then return to initial upright posture. The inclination angle is measured by an optical motion capture system. Three conditions are introduced to simulate unstable standing posture; 1) eyes-opened posture for healthy condition, 2) eyes-closed posture for visual impaired and 3) one-legged posture for lower-extremity muscle weakness. The estimated parameters Kp, KD and pole placements are applied to multiple comparison test among all stability conditions. The test results indicate that Kp, KD and real pole reflect effect of lower-extremity muscle weakness and KD also represents effect of visual impairment. It is suggested that the proposed method is valid for quantitative assessment of standing postural control ability.
Takahashi, Hisashi; Goto, Taiga; Hirokawa, Koichi; Miyazaki, Osamu
2014-03-01
Statistical iterative reconstruction and post-log data restoration algorithms for CT noise reduction have been widely studied and these techniques have enabled us to reduce irradiation doses while maintaining image qualities. In low dose scanning, electronic noise becomes obvious and it results in some non-positive signals in raw measurements. The nonpositive signal should be converted to positive signal so that it can be log-transformed. Since conventional conversion methods do not consider local variance on the sinogram, they have difficulty of controlling the strength of the filtering. Thus, in this work, we propose a method to convert the non-positive signal to the positive signal by mainly controlling the local variance. The method is implemented in two separate steps. First, an iterative restoration algorithm based on penalized weighted least squares is used to mitigate the effect of electronic noise. The algorithm preserves the local mean and reduces the local variance induced by the electronic noise. Second, smoothed raw measurements by the iterative algorithm are converted to the positive signal according to a function which replaces the non-positive signal with its local mean. In phantom studies, we confirm that the proposed method properly preserves the local mean and reduce the variance induced by the electronic noise. Our technique results in dramatically reduced shading artifacts and can also successfully cooperate with the post-log data filter to reduce streak artifacts.
Calculation of Credit Valuation Adjustment Based on Least Square Monte Carlo Methods
Directory of Open Access Journals (Sweden)
Qian Liu
2015-01-01
Full Text Available Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced mathematically. We examine this issue using interest rate swaps. This largely traded financial product allows us to well identify the risk profiles of both institutions and their counterparties. Concretely, Hull-White model for rate and mean-reverting model for default intensity have proven to be in correspondence with the reality and to be well suited for financial institutions. Besides, we find that least square Monte Carlo method is quite efficient in the calculation of credit valuation adjustment (CVA, for short as it avoids the redundant step to generate inner scenarios. As a result, it accelerates the convergence speed of the CVA estimators. In the second part, we propose a new method to calculate bilateral CVA to avoid double counting in the existing bibliographies, where several copula functions are adopted to describe the dependence of two first to default times.
Least Square NUFFT Methods Applied to 2D and 3D Radially Encoded MR Image Reconstruction
Song, Jiayu; Liu, Qing H.; Gewalt, Sally L.; Cofer, Gary; Johnson, G. Allan
2009-01-01
Radially encoded MR imaging (MRI) has gained increasing attention in applications such as hyperpolarized gas imaging, contrast-enhanced MR angiography, and dynamic imaging, due to its motion insensitivity and improved artifact properties. However, since the technique collects k-space samples nonuniformly, multidimensional (especially 3D) radially sampled MRI image reconstruction is challenging. The balance between reconstruction accuracy and speed becomes critical when a large data set is processed. Kaiser-Bessel gridding reconstruction has been widely used for non-Cartesian reconstruction. The objective of this work is to provide an alternative reconstruction option in high dimensions with on-the-fly kernels calculation. The work develops general multi-dimensional least square nonuniform fast Fourier transform (LS-NUFFT) algorithms and incorporates them into a k-space simulation and image reconstruction framework. The method is then applied to reconstruct the radially encoded k-space, although the method addresses general nonuniformity and is applicable to any non-Cartesian patterns. Performance assessments are made by comparing the LS-NUFFT based method with the conventional Kaiser-Bessel gridding method for 2D and 3D radially encoded computer simulated phantoms and physically scanned phantoms. The results show that the LS-NUFFT reconstruction method has better accuracy-speed efficiency than the Kaiser-Bessel gridding method when the kernel weights are calculated on the fly. The accuracy of the LS-NUFFT method depends on the choice of scaling factor, and it is found that for a particular conventional kernel function, using its corresponding deapodization function as scaling factor and utilizing it into the LS-NUFFT framework has the potential to improve accuracy. When a cosine scaling factor is used, in particular, the LS-NUFFT method is faster than Kaiser-Bessel gridding method because of a quasi closed-form solution. The method is successfully applied to 2D and
Suliman, Mohamed Abdalla Elhag
2016-12-19
This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model matrix. This perturbation is introduced to enhance the singular-value (SV) structure of the matrix and hence to provide a better solution. The proposed approach is derived to select the regularization parameter in a way that minimizes the mean-squared error (MSE) of the estimator. Numerical results demonstrate that the proposed approach outperforms a set of benchmark methods in most cases when applied to different scenarios of discrete ill-posed problems. Jointly, the proposed approach enjoys the lowest run-time and offers the highest level of robustness amongst all the tested methods.
Rebillat, Marc; Schoukens, Maarten
2018-05-01
Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.
Gompertz: A Scilab Program for Estimating Gompertz Curve Using Gauss-Newton Method of Least Squares
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Surajit Ghosh Dastidar
2006-04-01
Full Text Available A computer program for estimating Gompertz curve using Gauss-Newton method of least squares is described in detail. It is based on the estimation technique proposed in Reddy (1985. The program is developed using Scilab (version 3.1.1, a freely available scientific software package that can be downloaded from http://www.scilab.org/. Data is to be fed into the program from an external disk file which should be in Microsoft Excel format. The output will contain sample size, tolerance limit, a list of initial as well as the final estimate of the parameters, standard errors, value of Gauss-Normal equations namely GN1 GN2 and GN3 , No. of iterations, variance(σ2 , Durbin-Watson statistic, goodness of fit measures such as R2 , D value, covariance matrix and residuals. It also displays a graphical output of the estimated curve vis a vis the observed curve. It is an improved version of the program proposed in Dastidar (2005.
Gompertz: A Scilab Program for Estimating Gompertz Curve Using Gauss-Newton Method of Least Squares
Directory of Open Access Journals (Sweden)
Surajit Ghosh Dastidar
2006-04-01
Full Text Available A computer program for estimating Gompertz curve using Gauss-Newton method of least squares is described in detail. It is based on the estimation technique proposed in Reddy (1985. The program is developed using Scilab (version 3.1.1, a freely available scientific software package that can be downloaded from http://www.scilab.org/. Data is to be fed into the program from an external disk file which should be in Microsoft Excel format. The output will contain sample size, tolerance limit, a list of initial as well as the final estimate of the parameters, standard errors, value of Gauss-Normal equations namely GN1 GN2 and GN3, No. of iterations, variance(σ2, Durbin-Watson statistic, goodness of fit measures such as R2, D value, covariance matrix and residuals. It also displays a graphical output of the estimated curve vis a vis the observed curve. It is an improved version of the program proposed in Dastidar (2005.
A scaled Lagrangian method for performing a least squares fit of a model to plant data
International Nuclear Information System (INIS)
Crisp, K.E.
1988-01-01
Due to measurement errors, even a perfect mathematical model will not be able to match all the corresponding plant measurements simultaneously. A further discrepancy may be introduced if an un-modelled change in conditions occurs within the plant which should have required a corresponding change in model parameters - e.g. a gradual deterioration in the performance of some component(s). Taking both these factors into account, what is required is that the overall discrepancy between the model predictions and the plant data is kept to a minimum. This process is known as 'model fitting', A method is presented for minimising any function which consists of the sum of squared terms, subject to any constraints. Its most obvious application is in the process of model fitting, where a weighted sum of squares of the differences between model predictions and plant data is the function to be minimised. When implemented within existing Central Electricity Generating Board computer models, it will perform a least squares fit of a model to plant data within a single job submission. (author)
Amplitude differences least squares method applied to temporal cardiac beat alignment
International Nuclear Information System (INIS)
Correa, R O; Laciar, E; Valentinuzzi, M E
2007-01-01
High resolution averaged ECG is an important diagnostic technique in post-infarcted and/or chagasic patients with high risk of ventricular tachycardia (VT). It calls for precise determination of the synchronism point (fiducial point) in each beat to be averaged. Cross-correlation (CC) between each detected beat and a reference beat is, by and large, the standard alignment procedure. However, the fiducial point determination is not precise in records contaminated with high levels of noise. Herein, we propose an alignment procedure based on the least squares calculation of the amplitude differences (LSAD) between the ECG samples and a reference or template beat. Both techniques, CC and LSAD, were tested in high resolution ECG's corrupted with white noise and 50 Hz line interference of varying amplitudes (RMS range: 0-100μV). Results point out that LSDA produced a lower alignment error in all contaminated records while in those blurred by power line interference better results were found only within the 0-40 μV range. It is concluded that the proposed method represents a valid alignment alternative
Determination of calibration equations by means of the generalized least squares method
International Nuclear Information System (INIS)
Zijp, W.L.
1984-12-01
For the determination of two-dimensional calibration curves (e.g. in tank calibration procedures) or of three dimensional calibration equations (e.g. for the calibration of NDA equipment for enrichment measurements) one performs measurements under well chosen conditions, where all observables of interest (inclusive the values of the standard material) are subject to measurement uncertainties. Moreover correlations in several measurements may occur. This document describes the mathematical-statistical approach to determine the values of the model parameters and their covariance matrix, which fit best to the mathematical model for the calibration equation. The formulae are based on the method of generalized least squares where the term generalized implies that non-linear equations in the unknown parameters and also covariance matrices of the measurement data of the calibration can be taken into account. In the general case an iteration procedure is required. No iteration is required when the model is linear in the parameters and the covariance matrices for the measurements of co-ordinates of the calibration points are proportional to each other
A modified Generalized Least Squares method for large scale nuclear data evaluation
Energy Technology Data Exchange (ETDEWEB)
Schnabel, Georg [Irfu, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette (France); Atominstitut, TU Wien, Vienna (Austria); Leeb, Helmut [Atominstitut, TU Wien, Vienna (Austria)
2017-01-01
Nuclear data evaluation aims to provide estimates and uncertainties in the form of covariance matrices of cross sections and related quantities. Many practitioners use the Generalized Least Squares (GLS) formulas to combine experimental data and results of model calculations in order to determine reliable estimates and covariance matrices. A prerequisite to apply the GLS formulas is the construction of a prior covariance matrix for the observables from a set of model calculations. Modern nuclear model codes are able to provide predictions for a large number of observables. However, the inclusion of all observables may lead to a prior covariance matrix of intractable size. Therefore, we introduce mathematically equivalent versions of the GLS formulas to avoid the construction of the prior covariance matrix. Experimental data can be incrementally incorporated into the evaluation process, hence there is no upper limit on their amount. We demonstrate the modified GLS method in a tentative evaluation involving about three million observables using the code TALYS. The revised scheme is well suited as building block of a database application providing evaluated nuclear data. Updating with new experimental data is feasible and users can query estimates and correlations of arbitrary subsets of the observables stored in the database.
Bayesian inference for data assimilation using Least-Squares Finite Element methods
International Nuclear Information System (INIS)
Dwight, Richard P
2010-01-01
It has recently been observed that Least-Squares Finite Element methods (LS-FEMs) can be used to assimilate experimental data into approximations of PDEs in a natural way, as shown by Heyes et al. in the case of incompressible Navier-Stokes flow. The approach was shown to be effective without regularization terms, and can handle substantial noise in the experimental data without filtering. Of great practical importance is that - unlike other data assimilation techniques - it is not significantly more expensive than a single physical simulation. However the method as presented so far in the literature is not set in the context of an inverse problem framework, so that for example the meaning of the final result is unclear. In this paper it is shown that the method can be interpreted as finding a maximum a posteriori (MAP) estimator in a Bayesian approach to data assimilation, with normally distributed observational noise, and a Bayesian prior based on an appropriate norm of the governing equations. In this setting the method may be seen to have several desirable properties: most importantly discretization and modelling error in the simulation code does not affect the solution in limit of complete experimental information, so these errors do not have to be modelled statistically. Also the Bayesian interpretation better justifies the choice of the method, and some useful generalizations become apparent. The technique is applied to incompressible Navier-Stokes flow in a pipe with added velocity data, where its effectiveness, robustness to noise, and application to inverse problems is demonstrated.
Directory of Open Access Journals (Sweden)
Man Zhu
2017-03-01
Full Text Available Determination of ship maneuvering models is a tough task of ship maneuverability prediction. Among several prime approaches of estimating ship maneuvering models, system identification combined with the full-scale or free- running model test is preferred. In this contribution, real-time system identification programs using recursive identification method, such as the recursive least square method (RLS, are exerted for on-line identification of ship maneuvering models. However, this method seriously depends on the objects of study and initial values of identified parameters. To overcome this, an intelligent technology, i.e., support vector machines (SVM, is firstly used to estimate initial values of the identified parameters with finite samples. As real measured motion data of the Mariner class ship always involve noise from sensors and external disturbances, the zigzag simulation test data include a substantial quantity of Gaussian white noise. Wavelet method and empirical mode decomposition (EMD are used to filter the data corrupted by noise, respectively. The choice of the sample number for SVM to decide initial values of identified parameters is extensively discussed and analyzed. With de-noised motion data as input-output training samples, parameters of ship maneuvering models are estimated using RLS and SVM-RLS, respectively. The comparison between identification results and true values of parameters demonstrates that both the identified ship maneuvering models from RLS and SVM-RLS have reasonable agreements with simulated motions of the ship, and the increment of the sample for SVM positively affects the identification results. Furthermore, SVM-RLS using data de-noised by EMD shows the highest accuracy and best convergence.
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Danilo A. López-Sarmiento
2013-11-01
Full Text Available In this paper is compared the performance of a multi-class least squares support vector machine (LSSVM mc versus a multi-class logistic regression classifier to problem of recognizing the numeric digits (0-9 handwritten. To develop the comparison was used a data set consisting of 5000 images of handwritten numeric digits (500 images for each number from 0-9, each image of 20 x 20 pixels. The inputs to each of the systems were vectors of 400 dimensions corresponding to each image (not done feature extraction. Both classifiers used OneVsAll strategy to enable multi-classification and a random cross-validation function for the process of minimizing the cost function. The metrics of comparison were precision and training time under the same computational conditions. Both techniques evaluated showed a precision above 95 %, with LS-SVM slightly more accurate. However the computational cost if we found a marked difference: LS-SVM training requires time 16.42 % less than that required by the logistic regression model based on the same low computational conditions.
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Abdi Sukmono
2015-02-01
Full Text Available Klorofil merupakan pigmen yang paling penting dalam proses fotosintesis. Tanaman sehat yang mampu tumbuh maksimum umumnya memiliki jumlah klorofil yang lebih besar daripada tanaman yang tidak sehat. Dalam Estimasi kandungan klorofil tanaman padi dengan airborne hiperspektral dibutuhkan model khusus untuk mendaaptkan akurasi yang baik. Citra Hhiperspektral mempunyai ratusan band dan julat yang sempit pada setiap bandnya, sehingga mempunyai kemampuan yang cukup baik untuk estimasi klorofil. Akan tetapi karena julat yang cukup sempit ini menyebabkan adanya efek multikolinearitas. Objek dari penelitian ini mengembangkan reflektan in situ menjadi model estimasi kandungan klorofil tanaman padi untuk citra airborne hiperspektral dengan menggunakan metode partial least square regression untuk menghilangkan efek multikolinearitas. Dalam penelitian ini dengan menggunakan teknik hubungan reflektan dan klorofil dipilih band-band yang berhungan dan efektif untuk estimasi klorofil. Dari hasil seleksi tersebut terpilih 44 band yang efektif untuk estimasi kandungan klorofil daun tanaman padi. Hasil dari penelitian ini menunjukkan mertode PLSR dapat menghasilkan model yang cukup baik untuk estimasi kandungan klorofil tanaman padi dengan nilai Koefisien determinasi (R2 mencapai 0.75 pada PC no 11 dan mempunyai RMSE sebesar 1.44 SPAD unit. Validasi menggunakan data citra airborne hiperspektral menghasilkan RMSE sebesar 1.07 SPAD Unit.
Heddam, Salim; Kisi, Ozgur
2018-04-01
In the present study, three types of artificial intelligence techniques, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5T) are applied for modeling daily dissolved oxygen (DO) concentration using several water quality variables as inputs. The DO concentration and water quality variables data from three stations operated by the United States Geological Survey (USGS) were used for developing the three models. The water quality data selected consisted of daily measured of water temperature (TE, °C), pH (std. unit), specific conductance (SC, μS/cm) and discharge (DI cfs), are used as inputs to the LSSVM, MARS and M5T models. The three models were applied for each station separately and compared to each other. According to the results obtained, it was found that: (i) the DO concentration could be successfully estimated using the three models and (ii) the best model among all others differs from one station to another.
Açikgöz, Güneş; Hamamci, Berna; Yildiz, Abdulkadir
2018-04-01
Alcohol consumption triggers toxic effect to organs and tissues in the human body. The risks are essentially thought to be related to ethanol content in alcoholic beverages. The identification of ethanol in blood samples requires rapid, minimal sample handling, and non-destructive analysis, such as Raman Spectroscopy. This study aims to apply Raman Spectroscopy for identification of ethanol in blood samples. Silver nanoparticles were synthesized to obtain Surface Enhanced Raman Spectroscopy (SERS) spectra of blood samples. The SERS spectra were used for Partial Least Square (PLS) for determining ethanol quantitatively. To apply PLS method, 920~820 cm -1 band interval was chosen and the spectral changes of the observed concentrations statistically associated with each other. The blood samples were examined according to this model and the quantity of ethanol was determined as that: first a calibration method was established. A strong relationship was observed between known concentration values and the values obtained by PLS method (R 2 = 1). Second instead of then, quantities of ethanol in 40 blood samples were predicted according to the calibration method. Quantitative analysis of the ethanol in the blood was done by analyzing the data obtained by Raman spectroscopy and the PLS method.
Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.
2016-01-01
This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model
Joint 2D-DOA and Frequency Estimation for L-Shaped Array Using Iterative Least Squares Method
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Ling-yun Xu
2012-01-01
Full Text Available We introduce an iterative least squares method (ILS for estimating the 2D-DOA and frequency based on L-shaped array. The ILS iteratively finds direction matrix and delay matrix, then 2D-DOA and frequency can be obtained by the least squares method. Without spectral peak searching and pairing, this algorithm works well and pairs the parameters automatically. Moreover, our algorithm has better performance than conventional ESPRIT algorithm and propagator method. The useful behavior of the proposed algorithm is verified by simulations.
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Reza Ezzati
2014-08-01
Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.
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Kosuke Yoshida
Full Text Available In diagnostic applications of statistical machine learning methods to brain imaging data, common problems include data high-dimensionality and co-linearity, which often cause over-fitting and instability. To overcome these problems, we applied partial least squares (PLS regression to resting-state functional magnetic resonance imaging (rs-fMRI data, creating a low-dimensional representation that relates symptoms to brain activity and that predicts clinical measures. Our experimental results, based upon data from clinically depressed patients and healthy controls, demonstrated that PLS and its kernel variants provided significantly better prediction of clinical measures than ordinary linear regression. Subsequent classification using predicted clinical scores distinguished depressed patients from healthy controls with 80% accuracy. Moreover, loading vectors for latent variables enabled us to identify brain regions relevant to depression, including the default mode network, the right superior frontal gyrus, and the superior motor area.
Taipe, Donny
2017-01-01
This article sustains the transfer of the national standard of mass (KP1) of INACAL to two reference standards ‘Weight 1’, ‘Weight 2’ and also KP2 (as witnessed mass standard and with known error). The dissemination was done using the Gauss Markov method by Generalized Least Squares. The uncertainty calculation was performed using Univariate Gaussian Distribution and Multivariate Gaussian Distribution; the latter was developed with the Monte Carlo method using a programming language called 'R...
International Nuclear Information System (INIS)
Geraldo, L.P.; Smith, D.L.
1989-01-01
The methodology of covariance matrix and square methods have been applied in the relative efficiency calibration for a Ge(Li) detector apllied in the relative efficiency calibration for a Ge(Li) detector. Procedures employed to generate, manipulate and test covariance matrices which serve to properly represent uncertainties of experimental data are discussed. Calibration data fitting using least square methods has been performed for a particular experimental data set. (author) [pt
Adib, Arash; Poorveis, Davood; Mehraban, Farid
2018-03-01
In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.
de Peinder, P.; Visser, T.; Petrauskas, D.D.; Salvatori, F.; Soulimani, F.; Weckhuysen, B.M.
2009-01-01
Research has been carried out to determine the feasibility of partial least-squares (PLS) regression models to predict the long-residue (LR) properties of potential blends from infrared (IR) spectra that have been created by linearly co-adding the IR spectra of crude oils. The study is the follow-up
Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald
2011-06-01
Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for
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Omholt Stig W
2011-06-01
Full Text Available Abstract Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs to variation in features of the trajectories of the state variables (outputs throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR, where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR and ordinary least squares (OLS regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback
Two Enhancements of the Logarithmic Least-Squares Method for Analyzing Subjective Comparisons
1989-03-25
error term. 1 For this model, the total sum of squares ( SSTO ), defined as n 2 SSTO = E (yi y) i=1 can be partitioned into error and regression sums...of the regression line around the mean value. Mathematically, for the model given by equation A.4, SSTO = SSE + SSR (A.6) A-4 where SSTO is the total...sum of squares (i.e., the variance of the yi’s), SSE is error sum of squares, and SSR is the regression sum of squares. SSTO , SSE, and SSR are given
Directory of Open Access Journals (Sweden)
Fuqiang Sun
2017-01-01
Full Text Available Rapid and accurate lifetime prediction of critical components in a system is important to maintaining the system’s reliable operation. To this end, many lifetime prediction methods have been developed to handle various failure-related data collected in different situations. Among these methods, machine learning and Bayesian updating are the most popular ones. In this article, a Bayesian least-squares support vector machine method that combines least-squares support vector machine with Bayesian inference is developed for predicting the remaining useful life of a microwave component. A degradation model describing the change in the component’s power gain over time is developed, and the point and interval remaining useful life estimates are obtained considering a predefined failure threshold. In our case study, the radial basis function neural network approach is also implemented for comparison purposes. The results indicate that the Bayesian least-squares support vector machine method is more precise and stable in predicting the remaining useful life of this type of components.
International Nuclear Information System (INIS)
Guseva, E.V.; Peregudov, V.N.
1982-01-01
The FITGAV program for calculation of parameters of the Gauss curve describing experimental data is considered. The calculations are based on the least square fit method. The estimations of errors in the parameter determination as a function of experimental data sample volume and their statistical significance are obtained. The curve fit using 100 points occupies less than 1 s at the SM-4 type computer
A Weighted Least Squares Approach To Robustify Least Squares Estimates.
Lin, Chowhong; Davenport, Ernest C., Jr.
This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…
Yuasa, T.; Akiba, M.; Takeda, T.; Kazama, M.; Hoshino, A.; Watanabe, Y.; Hyodo, K.; Dilmanian, F. A.; Akatsuka, T.; Itai, Y.
1997-02-01
We describe a new attenuation correction method for fluorescent X-ray computed tomography (FXCT) applied to image nonradioactive contrast materials in vivo. The principle of the FXCT imaging is that of computed tomography of the first generation. Using monochromatized synchrotron radiation from the BLNE-5A bending-magnet beam line of Tristan Accumulation Ring in KEK, Japan, we studied phantoms with the FXCT method, and we succeeded in delineating a 4-mm-diameter channel filled with a 500 /spl mu/g I/ml iodine solution in a 20-mm-diameter acrylic cylindrical phantom. However, to detect smaller iodine concentrations, attenuation correction is needed. We present a correction method based on the equation representing the measurement process. The discretized equation system is solved by the least-squares method using the singular value decomposition. The attenuation correction method is applied to the projections by the Monte Carlo simulation and the experiment to confirm its effectiveness.
Directory of Open Access Journals (Sweden)
Minghua Xu
2014-01-01
Full Text Available We consider the problem of seeking a symmetric positive semidefinite matrix in a closed convex set to approximate a given matrix. This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. For solving this class of matrix optimization problems, many methods have been proposed in the literature. The proximal alternating direction method is one of those methods which can be easily applied to solve these matrix optimization problems. Generally, the proximal parameters of the proximal alternating direction method are greater than zero. In this paper, we conclude that the restriction on the proximal parameters can be relaxed for solving this kind of matrix optimization problems. Numerical experiments also show that the proximal alternating direction method with the relaxed proximal parameters is convergent and generally has a better performance than the classical proximal alternating direction method.
Directory of Open Access Journals (Sweden)
Wojciech Rosloniec
2010-01-01
Full Text Available The TLS ESPRIT method is investigated in application to estimation of angular coordinates (angles of arrival of two moving objects at the presence of an external, relatively strong uncorrelated signal. As a radar antenna system, the 32-element uniform linear array (ULA is used. Various computer simulations have been carried out in order to demonstrate good accuracy and high spatial resolution of the TLS ESPRIT method in the scenario outlined above. It is also shown that accuracy and angle resolution can be significantly increased by using the proposed preprocessing (beamforming. The most of simulation results, presented in a graphical form, have been compared to the corresponding equivalent results obtained by using the ESPRIT method and conventional amplitude monopulse method aided by the coherent Doppler filtration.
Monte Carlo Library Least Square (MCLLS) Method for Multiple Radioactive Particle Tracking in BPR
Wang, Zhijian; Lee, Kyoung; Gardner, Robin
2010-03-01
In This work, a new method of radioactive particles tracking is proposed. An accurate Detector Response Functions (DRF's) was developed from MCNP5 to generate library for NaI detectors with a significant speed-up factor of 200. This just make possible for the idea of MCLLS method which is used for locating and tracking the radioactive particle in a modular Pebble Bed Reactor (PBR) by searching minimum Chi-square values. The method was tested to work pretty good in our lab condition with a six 2" X 2" NaI detectors array only. This method was introduced in both forward and inverse ways. A single radioactive particle tracking system with three collimated 2" X 2" NaI detectors is used for benchmark purpose.
Zhang, Linna; Li, Gang; Sun, Meixiu; Li, Hongxiao; Wang, Zhennan; Li, Yingxin; Lin, Ling
2017-11-01
Identifying whole bloods to be either human or nonhuman is an important responsibility for import-export ports and inspection and quarantine departments. Analytical methods and DNA testing methods are usually destructive. Previous studies demonstrated that visible diffuse reflectance spectroscopy method can realize noncontact human and nonhuman blood discrimination. An appropriate method for calibration set selection was very important for a robust quantitative model. In this paper, Random Selection (RS) method and Kennard-Stone (KS) method was applied in selecting samples for calibration set. Moreover, proper stoichiometry method can be greatly beneficial for improving the performance of classification model or quantification model. Partial Least Square Discrimination Analysis (PLSDA) method was commonly used in identification of blood species with spectroscopy methods. Least Square Support Vector Machine (LSSVM) was proved to be perfect for discrimination analysis. In this research, PLSDA method and LSSVM method was used for human blood discrimination. Compared with the results of PLSDA method, this method could enhance the performance of identified models. The overall results convinced that LSSVM method was more feasible for identifying human and animal blood species, and sufficiently demonstrated LSSVM method was a reliable and robust method for human blood identification, and can be more effective and accurate.
Least Squares Data Fitting with Applications
DEFF Research Database (Denmark)
Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data....... In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis...
Jiang, Junjun; Hu, Ruimin; Han, Zhen; Wang, Zhongyuan; Chen, Jun
2013-10-01
Face superresolution (SR), or face hallucination, refers to the technique of generating a high-resolution (HR) face image from a low-resolution (LR) one with the help of a set of training examples. It aims at transcending the limitations of electronic imaging systems. Applications of face SR include video surveillance, in which the individual of interest is often far from cameras. A two-step method is proposed to infer a high-quality and HR face image from a low-quality and LR observation. First, we establish the nonlinear relationship between LR face images and HR ones, according to radial basis function and partial least squares (RBF-PLS) regression, to transform the LR face into the global face space. Then, a locality-induced sparse representation (LiSR) approach is presented to enhance the local facial details once all the global faces for each LR training face are constructed. A comparison of some state-of-the-art SR methods shows the superiority of the proposed two-step approach, RBF-PLS global face regression followed by LiSR-based local patch reconstruction. Experiments also demonstrate the effectiveness under both simulation conditions and some real conditions.
Fragkaki, A G; Farmaki, E; Thomaidis, N; Tsantili-Kakoulidou, A; Angelis, Y S; Koupparis, M; Georgakopoulos, C
2012-09-21
The comparison among different modelling techniques, such as multiple linear regression, partial least squares and artificial neural networks, has been performed in order to construct and evaluate models for prediction of gas chromatographic relative retention times of trimethylsilylated anabolic androgenic steroids. The performance of the quantitative structure-retention relationship study, using the multiple linear regression and partial least squares techniques, has been previously conducted. In the present study, artificial neural networks models were constructed and used for the prediction of relative retention times of anabolic androgenic steroids, while their efficiency is compared with that of the models derived from the multiple linear regression and partial least squares techniques. For overall ranking of the models, a novel procedure [Trends Anal. Chem. 29 (2010) 101-109] based on sum of ranking differences was applied, which permits the best model to be selected. The suggested models are considered useful for the estimation of relative retention times of designer steroids for which no analytical data are available. Copyright © 2012 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Habiboallah Khajehsharifi
2017-05-01
Full Text Available Partial least squares (PLS1 and principal component regression (PCR are two multivariate calibration methods that allow simultaneous determination of several analytes in spite of their overlapping spectra. In this research, a spectrophotometric method using PLS1 is proposed for the simultaneous determination of ascorbic acid (AA, dopamine (DA and uric acid (UA. The linear concentration ranges for AA, DA and UA were 1.76–47.55, 0.57–22.76 and 1.68–28.58 (in μg mL−1, respectively. However, PLS1 and PCR were applied to design calibration set based on absorption spectra in the 250–320 nm range for 36 different mixtures of AA, DA and UA, in all cases, the PLS1 calibration method showed more quantitative prediction ability than PCR method. Cross validation method was used to select the optimum number of principal components (NPC. The NPC for AA, DA and UA was found to be 4 by PLS1 and 5, 12, 8 by PCR. Prediction error sum of squares (PRESS of AA, DA and UA were 1.2461, 1.1144, 2.3104 for PLS1 and 11.0563, 1.3819, 4.0956 for PCR, respectively. Satisfactory results were achieved for the simultaneous determination of AA, DA and UA in some real samples such as human urine, serum and pharmaceutical formulations.
International Nuclear Information System (INIS)
Ren, M J; Cheung, C F; Kong, L B
2012-01-01
In the measurement of ultra-precision freeform surfaces, least-squares-based form characterization methods are widely used to evaluate the form error of the measured surfaces. Although many methodologies have been proposed in recent years to improve the efficiency of the characterization process, relatively little research has been conducted on the analysis of associated uncertainty in the characterization results which may result from those characterization methods being used. As a result, this paper presents a task specific uncertainty analysis method with application in the least-squares-based form characterization of ultra-precision freeform surfaces. That is, the associated uncertainty in the form characterization results is estimated when the measured data are extracted from a specific surface with specific sampling strategy. Three factors are considered in this study which include measurement error, surface form error and sample size. The task specific uncertainty analysis method has been evaluated through a series of experiments. The results show that the task specific uncertainty analysis method can effectively estimate the uncertainty of the form characterization results for a specific freeform surface measurement
Yan, Jun; Huang, Jian-Hua; He, Min; Lu, Hong-Bing; Yang, Rui; Kong, Bo; Xu, Qing-Song; Liang, Yi-Zeng
2013-08-01
Retention indices for frequently reported compounds of plant essential oils on three different stationary phases were investigated. Multivariate linear regression, partial least squares, and support vector machine combined with a new variable selection approach called random-frog recently proposed by our group, were employed to model quantitative structure-retention relationships. Internal and external validations were performed to ensure the stability and predictive ability. All the three methods could obtain an acceptable model, and the optimal results by support vector machine based on a small number of informative descriptors with the square of correlation coefficient for cross validation, values of 0.9726, 0.9759, and 0.9331 on the dimethylsilicone stationary phase, the dimethylsilicone phase with 5% phenyl groups, and the PEG stationary phase, respectively. The performances of two variable selection approaches, random-frog and genetic algorithm, are compared. The importance of the variables was found to be consistent when estimated from correlation coefficients in multivariate linear regression equations and selection probability in model spaces. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Miller, Arthur L; Weakley, Andrew Todd; Griffiths, Peter R; Cauda, Emanuele G; Bayman, Sean
2017-05-01
In order to help reduce silicosis in miners, the National Institute for Occupational Health and Safety (NIOSH) is developing field-portable methods for measuring airborne respirable crystalline silica (RCS), specifically the polymorph α-quartz, in mine dusts. In this study we demonstrate the feasibility of end-of-shift measurement of α-quartz using a direct-on-filter (DoF) method to analyze coal mine dust samples deposited onto polyvinyl chloride filters. The DoF method is potentially amenable for on-site analyses, but deviates from the current regulatory determination of RCS for coal mines by eliminating two sample preparation steps: ashing the sampling filter and redepositing the ash prior to quantification by Fourier transform infrared (FT-IR) spectrometry. In this study, the FT-IR spectra of 66 coal dust samples from active mines were used, and the RCS was quantified by using: (1) an ordinary least squares (OLS) calibration approach that utilizes standard silica material as done in the Mine Safety and Health Administration's P7 method; and (2) a partial least squares (PLS) regression approach. Both were capable of accounting for kaolinite, which can confound the IR analysis of silica. The OLS method utilized analytical standards for silica calibration and kaolin correction, resulting in a good linear correlation with P7 results and minimal bias but with the accuracy limited by the presence of kaolinite. The PLS approach also produced predictions well-correlated to the P7 method, as well as better accuracy in RCS prediction, and no bias due to variable kaolinite mass. Besides decreased sensitivity to mineral or substrate confounders, PLS has the advantage that the analyst is not required to correct for the presence of kaolinite or background interferences related to the substrate, making the method potentially viable for automated RCS prediction in the field. This study demonstrated the efficacy of FT-IR transmission spectrometry for silica determination in
Sciazko, Anna; Komatsu, Yosuke; Brus, Grzegorz; Kimijima, Shinji; Szmyd, Janusz S.
2014-09-01
For a mathematical model based on the result of physical measurements, it becomes possible to determine their influence on the final solution and its accuracy. However, in classical approaches, the influence of different model simplifications on the reliability of the obtained results are usually not comprehensively discussed. This paper presents a novel approach to the study of methane/steam reforming kinetics based on an advanced methodology called the Orthogonal Least Squares method. The kinetics of the reforming process published earlier are divergent among themselves. To obtain the most probable values of kinetic parameters and enable direct and objective model verification, an appropriate calculation procedure needs to be proposed. The applied Generalized Least Squares (GLS) method includes all the experimental results into the mathematical model which becomes internally contradicted, as the number of equations is greater than number of unknown variables. The GLS method is adopted to select the most probable values of results and simultaneously determine the uncertainty coupled with all the variables in the system. In this paper, the evaluation of the reaction rate after the pre-determination of the reaction rate, which was made by preliminary calculation based on the obtained experimental results over a Nickel/Yttria-stabilized Zirconia catalyst, was performed.
Directory of Open Access Journals (Sweden)
Zizhou Lao
2018-05-01
Full Text Available For model-based state of charge (SOC estimation methods, the battery model parameters change with temperature, SOC, and so forth, causing the estimation error to increase. Constantly updating model parameters during battery operation, also known as online parameter identification, can effectively solve this problem. In this paper, a lithium-ion battery is modeled using the Thevenin model. A variable forgetting factor (VFF strategy is introduced to improve forgetting factor recursive least squares (FFRLS to variable forgetting factor recursive least squares (VFF-RLS. A novel method based on VFF-RLS for the online identification of the Thevenin model is proposed. Experiments verified that VFF-RLS gives more stable online parameter identification results than FFRLS. Combined with an unscented Kalman filter (UKF algorithm, a joint algorithm named VFF-RLS-UKF is proposed for SOC estimation. In a variable-temperature environment, a battery SOC estimation experiment was performed using the joint algorithm. The average error of the SOC estimation was as low as 0.595% in some experiments. Experiments showed that VFF-RLS can effectively track the changes in model parameters. The joint algorithm improved the SOC estimation accuracy compared to the method with the fixed forgetting factor.
International Nuclear Information System (INIS)
Pollock, D.; Kim, K.; Gunst, R.; Schucany, W.
1993-05-01
Linear estimation of cold magnetic field quality based on warm multipole measurements is being considered as a quality control method for SSC production magnet acceptance. To investigate prediction uncertainties associated with such an approach, axial-scan (Z-scan) magnetic measurements from SSC Prototype Collider Dipole Magnets (CDM's) have been studied. This paper presents a preliminary evaluation of the explanatory ability of warm measurement multipole variation on the prediction of cold magnet multipoles. Two linear estimation methods are presented: least-squares regression, which uses the assumption of fixed independent variable (xi) observations, and the measurement error model, which includes measurement error in the xi's. The influence of warm multipole measurement errors on predicted cold magnet multipole averages is considered. MSD QA is studying warm/cold correlation to answer several magnet quality control questions. How well do warm measurements predict cold (2kA) multipoles? Does sampling error significantly influence estimates of the linear coefficients (slope, intercept and residual standard error)? Is estimation error for the predicted cold magnet average small compared to typical variation along the Z-Axis? What fraction of the multipole RMS tolerance is accounted for by individual magnet prediction uncertainty?
Niimi, Jun; Tomic, Oliver; Næs, Tormod; Jeffery, David W; Bastian, Susan E P; Boss, Paul K
2018-08-01
The current study determined the applicability of sequential and orthogonalised-partial least squares (SO-PLS) regression to relate Cabernet Sauvignon grape chemical composition to the sensory perception of the corresponding wines. Grape samples (n = 25) were harvested at a similar maturity and vinified identically in 2013. Twelve measures using various (bio)chemical methods were made on grapes. Wines were evaluated using descriptive analysis with a trained panel (n = 10) for sensory profiling. Data was analysed globally using SO-PLS for the entire sensory profiles (SO-PLS2), as well as for single sensory attributes (SO-PLS1). SO-PLS1 models were superior in validated explained variances than SO-PLS2. SO-PLS provided a structured approach in the selection of predictor chemical data sets that best contributed to the correlation of important sensory attributes. This new approach presents great potential for application in other explorative metabolomics studies of food and beverages to address factors such as quality and regional influences. Copyright © 2018 Elsevier Ltd. All rights reserved.
Liu, Xiu-ying; Wang, Li; Chang, Qing-rui; Wang, Xiao-xing; Shang, Yan
2015-07-01
Wuqi County of Shaanxi Province, where the vegetation recovering measures have been carried out for years, was taken as the study area. A total of 100 loess samples from 24 different profiles were collected. Total nitrogen (TN) and alkali hydrolysable nitrogen (AHN) contents of the soil samples were analyzed, and the soil samples were scanned in the visible/near-infrared (VNIR) region of 350-2500 nm in the laboratory. The calibration models were developed between TN and AHN contents and VNIR values based on correlation analysis (CA) and partial least squares regression (PLS). Independent samples validated the calibration models. The results indicated that the optimum model for predicting TN of loess was established by using first derivative of reflectance. The best model for predicting AHN of loess was established by using normal derivative spectra. The optimum TN model could effectively predict TN in loess from 0 to 40 cm, but the optimum AHN model could only roughly predict AHN at the same depth. This study provided a good method for rapidly predicting TN of loess where vegetation recovering measures have been adopted, but prediction of AHN needs to be further studied.
International Nuclear Information System (INIS)
Burns, W.A.; Mankiewicz, P.J.; Bence, A.E.; Page, D.S.; Parker, K.R.
1997-01-01
A method was developed to allocate polycyclic aromatic hydrocarbons (PAHs) in sediment samples to the PAH sources from which they came. The method uses principal-component analysis to identify possible sources and a least-squares model to find the source mix that gives the best fit of 36 PAH analytes in each sample. The method identified 18 possible PAH sources in a large set of field data collected in Prince William Sound, Alaska, USA, after the 1989 Exxon Valdez oil spill, including diesel oil, diesel soot, spilled crude oil in various weathering states, natural background, creosote, and combustion products from human activities and forest fires. Spill oil was generally found to be a small increment of the natural background in subtidal sediments, whereas combustion products were often the predominant sources for subtidal PAHs near sites of past or present human activity. The method appears to be applicable to other situations, including other spills
DEFF Research Database (Denmark)
Madsen, H.; Mikkelsen, Peter Steen; Rosbjerg, Dan
2002-01-01
A general framework for regional analysis and modeling of extreme rainfall characteristics is presented. The model is based on the partial duration series (PDS) method that includes in the analysis all events above a threshold level. In the PDS model the average annual number of exceedances...
International Nuclear Information System (INIS)
Aziz, A.; Bouaziz, M.N.
2011-01-01
Highlights: → Analytical solutions for a rectangular fin with temperature dependent heat generation and thermal conductivity. → Graphs give temperature distributions and fin efficiency. → Comparison of analytical and numerical solutions. → Method of least squares used for the analytical solutions. - Abstract: Approximate but highly accurate solutions for the temperature distribution, fin efficiency, and optimum fin parameter for a constant area longitudinal fin with temperature dependent internal heat generation and thermal conductivity are derived analytically. The method of least squares recently used by the authors is applied to treat the two nonlinearities, one associated with the temperature dependent internal heat generation and the other due to temperature dependent thermal conductivity. The solution is built from the classical solution for a fin with uniform internal heat generation and constant thermal conductivity. The results are presented graphically and compared with the direct numerical solutions. The analytical solutions retain their accuracy (within 1% of the numerical solution) even when there is a 60% increase in thermal conductivity and internal heat generation at the base temperature from their corresponding values at the sink temperature. The present solution is simple (involves hyperbolic functions only) compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method and offers high accuracy. The simple analytical expressions for the temperature distribution, the fin efficiency and the optimum fin parameter are convenient for use by engineers dealing with the design and analysis of heat generating fins operating with a large temperature difference between the base and the environment.
Bestari, T. A. S.; Supian, S.; Purwani, S.
2018-03-01
Cimanuk River, Garut District, West Java which have upper course in Papandayan Mountain have an important purpose in dialy living of Garut people as a water source. But in 2016 flash flood in this river was hitted and there was 26 peple dead and 23 peole gone. Flash flood which hitted last year make the settlement almost align with the ground, soaking school and hospital. BPLHD Jawa Barat saw this condition as a disaster which coused by distroyed upper course of Cimanuk River. Flash Flood which happened on the 2016 had ever made economic sector paralized. Least square method selected to analyze economic condition in residents affected post disaster, after the mathematical equations was determined by Cobb Douglas Method. By searching proportion value of the damage, and the result expected became a view to the stakeholder to know which sector that become a worse and be able to make a priority in development
International Nuclear Information System (INIS)
Loula, A.F.D.; Toledo, E.M.; Franca, L.P.; Garcia, E.L.M.
1989-08-01
A variationaly consistent finite element formulation for constrained problems free from shear or membrane locking is applied to axisymetric shells subjected to arbitrary loading. The governing equations are writen according to Love's classical theory for a problem of bending of axisymetric thin and moderately thick shells accounting for shear deformation. The mixed variational formulation, in terms of stresses and displacements here presented consists of classical Galerkin method plus mesh-dependent least-square type terms employed with equal-order finite element polynomials. The additional terms enhance stability and accuracy of the original Galerkin method, as already proven theoretically and confirmed trough numerical experiments. Numerical results of some examples are presented to demonstrate the good stability and accuracy of the formulation. (author) [pt
Directory of Open Access Journals (Sweden)
André Luis Christoforo
2012-12-01
Full Text Available This paper proposes an alternative method of calculation based on the Least Squares Method to determine the longitudinal modulus of elasticity in structural-sized wooden beams. The developed equations require knowledge of three points of displacements, allowing greater reliability on the dependent variable when using the static four-point bending test. Using the Jatobá (Hymenaea sp wood in the study, the methodology proposed here was used in combination with a simplified one, requiring knowledge of displacement only at the midpoint of the beam in order to compare the results among them. Results show statistical equivalence between the models, indicating a good approximation of the simplified model for calculating the modulus of elasticity in wooden structural bending here evaluated.
International Nuclear Information System (INIS)
Wen, Yongfu; Cheng, Haobo; Gao, Ya; Zhang, Huijing; Feng, Yunpeng; Pan, Baozhu
2011-01-01
In Fourier transform profilometry (FTP), we perform a strict theoretical analysis of the phase–height mapping relationship and give a universal calculation formula in which the constraints on the experimental setup are removed. In that case, the projector and camera can be located arbitrarily to get better information on fringes, which makes the system easy to manipulate and improves the speed of measurement. As the relationship between the phase and height distribution depends on system parameters (such as the relative position of the projector and camera) which are difficult to obtain, we propose a least-squares calibration approach for FTP, which can avoid measuring the system parameters directly. Both the simulation and experimental results prove that the 3D shape of the tested objects can be reconstructed exactly by using the calculation formula and calibration method, and that the system has better universality
Naguib, Ibrahim A.; Abdelaleem, Eglal A.; Draz, Mohammed E.; Zaazaa, Hala E.
2014-09-01
Partial least squares regression (PLSR) and support vector regression (SVR) are two popular chemometric models that are being subjected to a comparative study in the presented work. The comparison shows their characteristics via applying them to analyze Hydrochlorothiazide (HCZ) and Benazepril hydrochloride (BZ) in presence of HCZ impurities; Chlorothiazide (CT) and Salamide (DSA) as a case study. The analysis results prove to be valid for analysis of the two active ingredients in raw materials and pharmaceutical dosage form through handling UV spectral data in range (220-350 nm). For proper analysis a 4 factor 4 level experimental design was established resulting in a training set consisting of 16 mixtures containing different ratios of interfering species. An independent test set consisting of 8 mixtures was used to validate the prediction ability of the suggested models. The results presented indicate the ability of mentioned multivariate calibration models to analyze HCZ and BZ in presence of HCZ impurities CT and DSA with high selectivity and accuracy of mean percentage recoveries of (101.01 ± 0.80) and (100.01 ± 0.87) for HCZ and BZ respectively using PLSR model and of (99.78 ± 0.80) and (99.85 ± 1.08) for HCZ and BZ respectively using SVR model. The analysis results of the dosage form were statistically compared to the reference HPLC method with no significant differences regarding accuracy and precision. SVR model gives more accurate results compared to PLSR model and show high generalization ability, however, PLSR still keeps the advantage of being fast to optimize and implement.
Deconinck, E; Zhang, M H; Petitet, F; Dubus, E; Ijjaali, I; Coomans, D; Vander Heyden, Y
2008-02-18
The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.
Wang, Lu; Xu, Lisheng; Feng, Shuting; Meng, Max Q-H; Wang, Kuanquan
2013-11-01
Analysis of pulse waveform is a low cost, non-invasive method for obtaining vital information related to the conditions of the cardiovascular system. In recent years, different Pulse Decomposition Analysis (PDA) methods have been applied to disclose the pathological mechanisms of the pulse waveform. All these methods decompose single-period pulse waveform into a constant number (such as 3, 4 or 5) of individual waves. Furthermore, those methods do not pay much attention to the estimation error of the key points in the pulse waveform. The estimation of human vascular conditions depends on the key points' positions of pulse wave. In this paper, we propose a Multi-Gaussian (MG) model to fit real pulse waveforms using an adaptive number (4 or 5 in our study) of Gaussian waves. The unknown parameters in the MG model are estimated by the Weighted Least Squares (WLS) method and the optimized weight values corresponding to different sampling points are selected by using the Multi-Criteria Decision Making (MCDM) method. Performance of the MG model and the WLS method has been evaluated by fitting 150 real pulse waveforms of five different types. The resulting Normalized Root Mean Square Error (NRMSE) was less than 2.0% and the estimation accuracy for the key points was satisfactory, demonstrating that our proposed method is effective in compressing, synthesizing and analyzing pulse waveforms. Copyright © 2013 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.
Energy Technology Data Exchange (ETDEWEB)
Nygaard, K
1968-09-15
From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra.
International Nuclear Information System (INIS)
Nygaard, K.
1968-09-01
From the point of view that no mathematical method can ever minimise or alter errors already made in a physical measurement, the classical least squares method has severe limitations which makes it unsuitable for the statistical analysis of many physical measurements. Based on the assumptions that the experimental errors are characteristic for each single experiment and that the errors must be properly estimated rather than minimised, a new method for solving large systems of linear equations is developed. The new method exposes the entire range of possible solutions before the decision is taken which of the possible solutions should be chosen as a representative one. The choice is based on physical considerations which (in two examples, curve fitting and unfolding of a spectrum) are presented in such a form that a computer is able to make the decision, A description of the computation is given. The method described is a tool for removing uncertainties due to conventional mathematical formulations (zero determinant, linear dependence) and which are not inherent in the physical problem as such. The method is therefore especially well fitted for unfolding of spectra
Time series modeling with pruned multi-layer perceptron and 2-stage damped least-squares method
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Voyant, Cyril; Tamas, Wani; Paoli, Christophe; Balu, Aurélia; Muselli, Marc; Nivet, Marie-Laure; Notton, Gilles
2014-01-01
A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its ''black box'' aspect, many researchers refuse to use it. Moreover, the optimization (often based on the exhaustive approach where ''all'' configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the 2-stage LMA
Directory of Open Access Journals (Sweden)
S. Oh
2012-09-01
Full Text Available Recent development of laser scanning device increased the capability of representing rock outcrop in a very high resolution. Accurate 3D point cloud model with rock joint information can help geologist to estimate stability of rock slope on-site or off-site. An automatic plane extraction method was developed by computing normal directions and grouping them in similar direction. Point normal was calculated by moving least squares (MLS method considering every point within a given distance to minimize error to the fitting plane. Normal directions were classified into a number of dominating clusters by fuzzy K-means clustering. Region growing approach was exploited to discriminate joints in a point cloud. Overall procedure was applied to point cloud with about 120,000 points, and successfully extracted joints with joint information. The extraction procedure was implemented to minimize number of input parameters and to construct plane information into the existing point cloud for less redundancy and high usability of the point cloud itself.
Mofavvaz, Shirin; Sohrabi, Mahmoud Reza; Nezamzadeh-Ejhieh, Alireza
2017-07-01
In the present study, artificial neural networks (ANNs) and least squares support vector machines (LS-SVM) as intelligent methods based on absorption spectra in the range of 230-300 nm have been used for determination of antihistamine decongestant contents. In the first step, one type of network (feed-forward back-propagation) from the artificial neural network with two different training algorithms, Levenberg-Marquardt (LM) and gradient descent with momentum and adaptive learning rate back-propagation (GDX) algorithm, were employed and their performance was evaluated. The performance of the LM algorithm was better than the GDX algorithm. In the second one, the radial basis network was utilized and results compared with the previous network. In the last one, the other intelligent method named least squares support vector machine was proposed to construct the antihistamine decongestant prediction model and the results were compared with two of the aforementioned networks. The values of the statistical parameters mean square error (MSE), Regression coefficient (R2), correlation coefficient (r) and also mean recovery (%), relative standard deviation (RSD) used for selecting the best model between these methods. Moreover, the proposed methods were compared to the high- performance liquid chromatography (HPLC) as a reference method. One way analysis of variance (ANOVA) test at the 95% confidence level applied to the comparison results of suggested and reference methods that there were no significant differences between them.
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Moehammad Awaluddin
2012-07-01
Full Text Available Continuous Global Positioning System (GPS observations showed significant crustal displacements as a result of the Bengkulu earthquake occurring on September 12, 2007. A maximum horizontal displacement of 2.11 m was observed at PRKB station, while the vertical component at BSAT station was uplifted with a maximum of 0.73 m, and the vertical component at LAIS station was subsided by -0.97 m. The method of adding more constraint on the inversion for the Bengkulu earthquake slip distribution from GPS observations can help solve a least squares inversion with an under-determined condition. Checkerboard tests were performed to help conduct the weighting for constraining the inversion. The inversion calculation of the Bengkulu earthquake slip distribution yielded in an optimum value of slip distribution by giving a weight of smoothing constraint of 0.001 and a weight of slip value constraint = 0 at the edge of the earthquake rupture area. A maximum coseismic slip of the optimal inversion calculation was 5.12 m at the lower area of PRKB and BSAT stations. The seismic moment calculated from the optimal slip distribution was 7.14 x 1021 Nm, which is equivalent to a magnitude of 8.5.
International Nuclear Information System (INIS)
Fiorito, L.; Diez, C.; Cabellos, O.; Stankovskiy, A.; Van den Eynde, G.; Labeau, P.E.
2014-01-01
Fission product yields are fundamental parameters for several nuclear engineering calculations and in particular for burn-up/activation problems. The impact of their uncertainties was widely studied in the past and evaluations were released, although still incomplete. Recently, the nuclear community expressed the need for full fission yield covariance matrices to produce inventory calculation results that take into account the complete uncertainty data. In this work, we studied and applied a Bayesian/generalised least-squares method for covariance generation, and compared the generated uncertainties to the original data stored in the JEFF-3.1.2 library. Then, we focused on the effect of fission yield covariance information on fission pulse decay heat results for thermal fission of 235 U. Calculations were carried out using different codes (ACAB and ALEPH-2) after introducing the new covariance values. Results were compared with those obtained with the uncertainty data currently provided by the library. The uncertainty quantification was performed with the Monte Carlo sampling technique. Indeed, correlations between fission yields strongly affect the statistics of decay heat. (authors)
Directory of Open Access Journals (Sweden)
Roberto Romaniello
2015-12-01
Full Text Available The aim of this work is to evaluate the potential of least squares support vector machine (LS-SVM regression to develop an efficient method to measure the colour of food materials in L*a*b* units by means of a computer vision systems (CVS. A laboratory CVS, based on colour digital camera (CDC, was implemented and three LS-SVM models were trained and validated, one for each output variables (L*, a*, and b* required by this problem, using the RGB signals generated by the CDC as input variables to these models. The colour target-based approach was used to camera characterization and a standard reference target of 242 colour samples was acquired using the CVS and a colorimeter. This data set was split in two sets of equal sizes, for training and validating the LS-SVM models. An effective two-stage grid search process on the parameters space was performed in MATLAB to tune the regularization parameters γ and the kernel parameters σ2 of the three LS-SVM models. A 3-8-3 multilayer feed-forward neural network (MFNN, according to the research conducted by León et al. (2006, was also trained in order to compare its performance with those of LS-SVM models. The LS-SVM models developed in this research have been shown better generalization capability then the MFNN, allowed to obtain high correlations between L*a*b* data acquired using the colorimeter and the corresponding data obtained by transformation of the RGB data acquired by the CVS. In particular, for the validation set, R2 values equal to 0.9989, 0.9987, and 0.9994 for L*, a* and b* parameters were obtained. The root mean square error values were 0.6443, 0.3226, and 0.2702 for L*, a*, and b* respectively, and the average of colour differences ΔEab was 0.8232±0.5033 units. Thus, LS-SVM regression seems to be a useful tool to measurement of food colour using a low cost CVS.
Tang, Kunkun; Massa, Luca; Wang, Jonathan; Freund, Jonathan B.
2018-05-01
We introduce an efficient non-intrusive surrogate-based methodology for global sensitivity analysis and uncertainty quantification. Modified covariance-based sensitivity indices (mCov-SI) are defined for outputs that reflect correlated effects. The overall approach is applied to simulations of a complex plasma-coupled combustion system with disparate uncertain parameters in sub-models for chemical kinetics and a laser-induced breakdown ignition seed. The surrogate is based on an Analysis of Variance (ANOVA) expansion, such as widely used in statistics, with orthogonal polynomials representing the ANOVA subspaces and a polynomial dimensional decomposition (PDD) representing its multi-dimensional components. The coefficients of the PDD expansion are obtained using a least-squares regression, which both avoids the direct computation of high-dimensional integrals and affords an attractive flexibility in choosing sampling points. This facilitates importance sampling using a Bayesian calibrated posterior distribution, which is fast and thus particularly advantageous in common practical cases, such as our large-scale demonstration, for which the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense. Effort, instead, is focused on efficient finite-resolution sampling. Standard covariance-based sensitivity indices (Cov-SI) are employed to account for correlation of the uncertain parameters. Magnitude of Cov-SI is unfortunately unbounded, which can produce extremely large indices that limit their utility. Alternatively, mCov-SI are then proposed in order to bound this magnitude ∈ [ 0 , 1 ]. The polynomial expansion is coupled with an adaptive ANOVA strategy to provide an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational cost of a high-dimensional expansion. It is also adaptively simplified according to the relative contribution of the different polynomials to the total
Cheng, Jian; Zhang, Fan; Liu, Tiegang
2018-06-01
In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.
Talebpour, Zahra; Tavallaie, Roya; Ahmadi, Seyyed Hamid; Abdollahpour, Assem
2010-09-01
In this study, a new method for the simultaneous determination of penicillin G salts in pharmaceutical mixture via FT-IR spectroscopy combined with chemometrics was investigated. The mixture of penicillin G salts is a complex system due to similar analytical characteristics of components. Partial least squares (PLS) and radial basis function-partial least squares (RBF-PLS) were used to develop the linear and nonlinear relation between spectra and components, respectively. The orthogonal signal correction (OSC) preprocessing method was used to correct unexpected information, such as spectral overlapping and scattering effects. In order to compare the influence of OSC on PLS and RBF-PLS models, the optimal linear (PLS) and nonlinear (RBF-PLS) models based on conventional and OSC preprocessed spectra were established and compared. The obtained results demonstrated that OSC clearly enhanced the performance of both RBF-PLS and PLS calibration models. Also in the case of some nonlinear relation between spectra and component, OSC-RBF-PLS gave satisfactory results than OSC-PLS model which indicated that the OSC was helpful to remove extrinsic deviations from linearity without elimination of nonlinear information related to component. The chemometric models were tested on an external dataset and finally applied to the analysis commercialized injection product of penicillin G salts.
Elsohaby, Ibrahim; Windeyer, M Claire; Haines, Deborah M; Homerosky, Elizabeth R; Pearson, Jennifer M; McClure, J Trenton; Keefe, Greg P
2018-03-06
The objective of this study was to explore the potential of transmission infrared (TIR) spectroscopy in combination with partial least squares regression (PLSR) for quantification of dairy and beef cow colostral immunoglobulin G (IgG) concentration and assessment of colostrum quality. A total of 430 colostrum samples were collected from dairy (n = 235) and beef (n = 195) cows and tested by a radial immunodiffusion (RID) assay and TIR spectroscopy. Colostral IgG concentrations obtained by the RID assay were linked to the preprocessed spectra and divided into combined and prediction data sets. Three PLSR calibration models were built: one for the dairy cow colostrum only, the second for beef cow colostrum only, and the third for the merged dairy and beef cow colostrum. The predictive performance of each model was evaluated separately using the independent prediction data set. The Pearson correlation coefficients between IgG concentrations as determined by the TIR-based assay and the RID assay were 0.84 for dairy cow colostrum, 0.88 for beef cow colostrum, and 0.92 for the merged set of dairy and beef cow colostrum. The average of the differences between colostral IgG concentrations obtained by the RID- and TIR-based assays were -3.5, 2.7, and 1.4 g/L for dairy, beef, and merged colostrum samples, respectively. Further, the average relative error of the colostral IgG predicted by the TIR spectroscopy from the RID assay was 5% for dairy cow, 1.2% for beef cow, and 0.8% for the merged data set. The average intra-assay CV% of the IgG concentration predicted by the TIR-based method were 3.2%, 2.5%, and 6.9% for dairy cow, beef cow, and merged data set, respectively.The utility of TIR method for assessment of colostrum quality was evaluated using the entire data set and showed that TIR spectroscopy accurately identified the quality status of 91% of dairy cow colostrum, 95% of beef cow colostrum, and 89% and 93% of the merged dairy and beef cow colostrum samples
Terra, Luciana A; Filgueiras, Paulo R; Tose, Lílian V; Romão, Wanderson; de Souza, Douglas D; de Castro, Eustáquio V R; de Oliveira, Mirela S L; Dias, Júlio C M; Poppi, Ronei J
2014-10-07
Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.
Esteves, José; Pastor Collado, Juan Antonio; Casanovas Garcia, Josep
2002-01-01
This technical research report proposes the usage of a statistical approach named Partial Least squares (PLS) to define the relationships between critical success factors for ERP implementation projects. In previous research work, we developed a unified model of critical success factors for ERP implementation projects. Some researchers have evidenced the relationships between these critical success factors, however no one has defined in a form...
Wu, Jie; Yu, Sheng-Tao; Jiang, Bo-nan
1996-01-01
In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.
Nazeer, Majid; Bilal, Muhammad
2018-04-01
Landsat-5 Thematic Mapper (TM) dataset have been used to estimate salinity in the coastal area of Hong Kong. Four adjacent Landsat TM images were used in this study, which was atmospherically corrected using the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative transfer code. The atmospherically corrected images were further used to develop models for salinity using Ordinary Least Square (OLS) regression and Geographically Weighted Regression (GWR) based on in situ data of October 2009. Results show that the coefficient of determination ( R 2) of 0.42 between the OLS estimated and in situ measured salinity is much lower than that of the GWR model, which is two times higher ( R 2 = 0.86). It indicates that the GWR model has more ability than the OLS regression model to predict salinity and show its spatial heterogeneity better. It was observed that the salinity was high in Deep Bay (north-western part of Hong Kong) which might be due to the industrial waste disposal, whereas the salinity was estimated to be constant (32 practical salinity units) towards the open sea.
Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza
2018-03-01
In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.
Passos, Cláudia P; Cardoso, Susana M; Barros, António S; Silva, Carlos M; Coimbra, Manuel A
2010-02-28
Fourier transform infrared (FTIR) spectroscopy has being emphasised as a widespread technique in the quick assess of food components. In this work, procyanidins were extracted with methanol and acetone/water from the seeds of white and red grape varieties. A fractionation by graded methanol/chloroform precipitations allowed to obtain 26 samples that were characterised using thiolysis as pre-treatment followed by HPLC-UV and MS detection. The average degree of polymerisation (DPn) of the procyanidins in the samples ranged from 2 to 11 flavan-3-ol residues. FTIR spectroscopy within the wavenumbers region of 1800-700 cm(-1) allowed to build a partial least squares (PLS1) regression model with 8 latent variables (LVs) for the estimation of the DPn, giving a RMSECV of 11.7%, with a R(2) of 0.91 and a RMSEP of 2.58. The application of orthogonal projection to latent structures (O-PLS1) clarifies the interpretation of the regression model vectors. Moreover, the O-PLS procedure has removed 88% of non-correlated variations with the DPn, allowing to relate the increase of the absorbance peaks at 1203 and 1099 cm(-1) with the increase of the DPn due to the higher proportion of substitutions in the aromatic ring of the polymerised procyanidin molecules. Copyright 2009 Elsevier B.V. All rights reserved.
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Arlinah Abd Rashid
2016-06-01
Full Text Available The good and service tax (GST in Malaysia was implemented in 2015 as a tax reform program to generate a stable source of revenue. This study explores the respondents’ behaviour towards GST, a week post-implementation. The partial least square (PLS modelling was used to establish the relationship between acceptance, knowledge and feelings towards GST as well as the household quality of life. There is a positive relationship between the antecedents and the quality of life. Acceptance of GST exerts a significant relationship towards feelings and quality of life. The study concludes that Malaysians, in general, accept GST that ensures a better quality of life in the future.
Sarkar, Arnab; Karki, Vijay; Aggarwal, Suresh K.; Maurya, Gulab S.; Kumar, Rohit; Rai, Awadhesh K.; Mao, Xianglei; Russo, Richard E.
2015-06-01
Laser induced breakdown spectroscopy (LIBS) was applied for elemental characterization of high alloy steel using partial least squares regression (PLSR) with an objective to evaluate the analytical performance of this multivariate approach. The optimization of the number of principle components for minimizing error in PLSR algorithm was investigated. The effect of different pre-treatment procedures on the raw spectral data before PLSR analysis was evaluated based on several statistical (standard error of prediction, percentage relative error of prediction etc.) parameters. The pre-treatment with "NORM" parameter gave the optimum statistical results. The analytical performance of PLSR model improved by increasing the number of laser pulses accumulated per spectrum as well as by truncating the spectrum to appropriate wavelength region. It was found that the statistical benefit of truncating the spectrum can also be accomplished by increasing the number of laser pulses per accumulation without spectral truncation. The constituents (Co and Mo) present in hundreds of ppm were determined with relative precision of 4-9% (2σ), whereas the major constituents Cr and Ni (present at a few percent levels) were determined with a relative precision of ~ 2%(2σ).
Kisi, Ozgur; Parmar, Kulwinder Singh
2016-03-01
This study investigates the accuracy of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5Tree) in modeling river water pollution. Various combinations of water quality parameters, Free Ammonia (AMM), Total Kjeldahl Nitrogen (TKN), Water Temperature (WT), Total Coliform (TC), Fecal Coliform (FC) and Potential of Hydrogen (pH) monitored at Nizamuddin, Delhi Yamuna River in India were used as inputs to the applied models. Results indicated that the LSSVM and MARS models had almost same accuracy and they performed better than the M5Tree model in modeling monthly chemical oxygen demand (COD). The average root mean square error (RMSE) of the LSSVM and M5Tree models was decreased by 1.47% and 19.1% using MARS model, respectively. Adding TC input to the models did not increase their accuracy in modeling COD while adding FC and pH inputs to the models generally decreased the accuracy. The overall results indicated that the MARS and LSSVM models could be successfully used in estimating monthly river water pollution level by using AMM, TKN and WT parameters as inputs.
Golmohammadi, Hassan
2009-11-30
A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structure of 141 organic compounds to their octanol-water partition coefficients (log P(o/w)). A genetic algorithm was applied as a variable selection tool. Modeling of log P(o/w) of these compounds as a function of theoretically derived descriptors was established by multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN). The best selected descriptors that appear in the models are: atomic charge weighted partial positively charged surface area (PPSA-3), fractional atomic charge weighted partial positive surface area (FPSA-3), minimum atomic partial charge (Qmin), molecular volume (MV), total dipole moment of molecule (mu), maximum antibonding contribution of a molecule orbital in the molecule (MAC), and maximum free valency of a C atom in the molecule (MFV). The result obtained showed the ability of developed artificial neural network to prediction of partition coefficients of organic compounds. Also, the results revealed the superiority of ANN over the MLR and PLS models. Copyright 2009 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Johnson, K.; Bittorf, K.J.
2002-01-01
A novel approach for computer aided modeling and optimizing mixing process has been developed using Galerkin least-squares finite element technology. Computer aided mixing modeling and analysis involves Lagrangian and Eulerian analysis for relative fluid stretching, and energy dissipation concepts for laminar and turbulent flows. High quality, conservative, accurate, fluid velocity, and continuity solutions are required for determining mixing quality. The ORCA Computational Fluid Dynamics (CFD) package, based on a finite element formulation, solves the incompressible Reynolds Averaged Navier Stokes (RANS) equations. Although finite element technology has been well used in areas of heat transfer, solid mechanics, and aerodynamics for years, it has only recently been applied to the area of fluid mixing. ORCA, developed using the Galerkin Least-Squares (GLS) finite element technology, provides another formulation for numerically solving the RANS based and LES based fluid mechanics equations. The ORCA CFD package is validated against two case studies. The first, a free round jet, demonstrates that the CFD code predicts the theoretical velocity decay rate, linear expansion rate, and similarity profile. From proper prediction of fundamental free jet characteristics, confidence can be derived when predicting flows in a stirred tank, as a stirred tank reactor can be considered a series of free jets and wall jets. (author)
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Ali Izadi
2015-10-01
Full Text Available In this study, substrates concentration profile has been studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis has been performed by using of an analytical method called Least Square Method and results have been compared with numerical solution. Effects of effective diffusivity (, Michael's constant (, maximum reaction rate ( and initial substrate concentration ( are studied on Soluble Starch and Dextrin concentration in the spherical support. Outcomes reveal that Least Square Method has an excellent agreement with numerical solution and in the center of support, substrate concentration is minimum and increasing of effective diffusivity and Michael's constant reduce the Soluble Starch and Dextrin profile gradient.
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Lanfa Liu
2017-12-01
Full Text Available Soil spectroscopy has experienced a tremendous increase in soil property characterisation, and can be used not only in the laboratory but also from the space (imaging spectroscopy. Partial least squares (PLS regression is one of the most common approaches for the calibration of soil properties using soil spectra. Besides functioning as a calibration method, PLS can also be used as a dimension reduction tool, which has scarcely been studied in soil spectroscopy. PLS components retained from high-dimensional spectral data can further be explored with the gradient-boosted decision tree (GBDT method. Three soil sample categories were extracted from the Land Use/Land Cover Area Frame Survey (LUCAS soil library according to the type of land cover (woodland, grassland, and cropland. First, PLS regression and GBDT were separately applied to build the spectroscopic models for soil organic carbon (OC, total nitrogen content (N, and clay for each soil category. Then, PLS-derived components were used as input variables for the GBDT model. The results demonstrate that the combined PLS-GBDT approach has better performance than PLS or GBDT alone. The relative important variables for soil property estimation revealed by the proposed method demonstrated that the PLS method is a useful dimension reduction tool for soil spectra to retain target-related information.
He, Qiaolin; Glowinski, Roland; Wang, Xiao Ping
2011-01-01
element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property
Weighted conditional least-squares estimation
International Nuclear Information System (INIS)
Booth, J.G.
1987-01-01
A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered
Niedzielski, Tomasz; Kosek, Wiesław
2008-02-01
This article presents the application of a multivariate prediction technique for predicting universal time (UT1-UTC), length of day (LOD) and the axial component of atmospheric angular momentum (AAM χ 3). The multivariate predictions of LOD and UT1-UTC are generated by means of the combination of (1) least-squares (LS) extrapolation of models for annual, semiannual, 18.6-year, 9.3-year oscillations and for the linear trend, and (2) multivariate autoregressive (MAR) stochastic prediction of LS residuals (LS + MAR). The MAR technique enables the use of the AAM χ 3 time-series as the explanatory variable for the computation of LOD or UT1-UTC predictions. In order to evaluate the performance of this approach, two other prediction schemes are also applied: (1) LS extrapolation, (2) combination of LS extrapolation and univariate autoregressive (AR) prediction of LS residuals (LS + AR). The multivariate predictions of AAM χ 3 data, however, are computed as a combination of the extrapolation of the LS model for annual and semiannual oscillations and the LS + MAR. The AAM χ 3 predictions are also compared with LS extrapolation and LS + AR prediction. It is shown that the predictions of LOD and UT1-UTC based on LS + MAR taking into account the axial component of AAM are more accurate than the predictions of LOD and UT1-UTC based on LS extrapolation or on LS + AR. In particular, the UT1-UTC predictions based on LS + MAR during El Niño/La Niña events exhibit considerably smaller prediction errors than those calculated by means of LS or LS + AR. The AAM χ 3 time-series is predicted using LS + MAR with higher accuracy than applying LS extrapolation itself in the case of medium-term predictions (up to 100 days in the future). However, the predictions of AAM χ 3 reveal the best accuracy for LS + AR.
Directory of Open Access Journals (Sweden)
Jyuo-Min Shyu
2010-11-01
Full Text Available A great deal of work has been done to develop techniques for odor analysis by electronic nose systems. These analyses mostly focus on identifying a particular odor by comparing with a known odor dataset. However, in many situations, it would be more practical if each individual odorant could be determined directly. This paper proposes two methods for such odor components analysis for electronic nose systems. First, a K-nearest neighbor (KNN-based local weighted nearest neighbor (LWNN algorithm is proposed to determine the components of an odor. According to the component analysis, the odor training data is firstly categorized into several groups, each of which is represented by its centroid. The examined odor is then classified as the class of the nearest centroid. The distance between the examined odor and the centroid is calculated based on a weighting scheme, which captures the local structure of each predefined group. To further determine the concentration of each component, odor models are built by regressions. Then, a weighted and constrained least-squares (WCLS method is proposed to estimate the component concentrations. Experiments were carried out to assess the effectiveness of the proposed methods. The LWNN algorithm is able to classify mixed odors with different mixing ratios, while the WCLS method can provide good estimates on component concentrations.
Khoshmanesh, Aazam; Cook, Perran L M; Wood, Bayden R
2012-08-21
Phosphorus (P) is a major cause of eutrophication and subsequent loss of water quality in freshwater ecosystems. A major part of the flux of P to eutrophic lake sediments is organically bound or of biogenic origin. Despite the broad relevance of polyphosphate (Poly-P) in bioremediation and P release processes in the environment, its quantification is not yet well developed for sediment samples. Current methods possess significant disadvantages because of the difficulties associated with using a single extractant to extract a specific P compound without altering others. A fast and reliable method to estimate the quantitative contribution of microorganisms to sediment P release processes is needed, especially when an excessive P accumulation in the form of polyphosphate (Poly-P) occurs. Development of novel approaches for application of emerging spectroscopic techniques to complex environmental matrices such as sediments significantly contributes to the speciation models of P mobilization, biogeochemical nutrient cycling and development of nutrient models. In this study, for the first time Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopy in combination with partial least squares (PLS) was used to quantify Poly-P in sediments. To reduce the high absorption matrix components in sediments such as silica, a physical extraction method was developed to separate sediment biological materials from abiotic particles. The aim was to achieve optimal separation of the biological materials from sediment abiotic particles with minimum chemical change in the sample matrix prior to ATR-FTIR analysis. Using a calibration set of 60 samples for the PLS prediction models in the Poly-P concentration range of 0-1 mg g(-1) d.w. (dry weight of sediment) (R(2) = 0.984 and root mean square error of prediction RMSEP = 0.041 at Factor-1) Poly-P could be detected at less than 50 μg g(-l) d.w. Using this technique, there is no solvent extraction or chemical
Li, Lin
2008-12-01
Partial least squares (PLS) regressions were applied to lunar highland and mare soil data characterized by the Lunar Soil Characterization Consortium (LSCC) for spectral estimation of the abundance of lunar soil chemical constituents FeO and Al2O3. The LSCC data set was split into a number of subsets including the total highland, Apollo 16, Apollo 14, and total mare soils, and then PLS was applied to each to investigate the effect of nonlinearity on the performance of the PLS method. The weight-loading vectors resulting from PLS were analyzed to identify mineral species responsible for spectral estimation of the soil chemicals. The results from PLS modeling indicate that the PLS performance depends on the correlation of constituents of interest to their major mineral carriers, and the Apollo 16 soils are responsible for the large errors of FeO and Al2O3 estimates when the soils were modeled along with other types of soils. These large errors are primarily attributed to the degraded correlation FeO to pyroxene for the relatively mature Apollo 16 soils as a result of space weathering and secondary to the interference of olivine. PLS consistently yields very accurate fits to the two soil chemicals when applied to mare soils. Although Al2O3 has no spectrally diagnostic characteristics, this chemical can be predicted for all subset data by PLS modeling at high accuracies because of its correlation to FeO. This correlation is reflected in the symmetry of the PLS weight-loading vectors for FeO and Al2O3, which prove to be very useful for qualitative interpretation of the PLS results. However, this qualitative interpretation of PLS modeling cannot be achieved using principal component regression loading vectors.
Least-square NUFFT methods applied to 2-D and 3-D radially encoded MR image reconstruction.
Song, Jiayu; Liu, Yanhui; Gewalt, Sally L; Cofer, Gary; Johnson, G Allan; Liu, Qing Huo
2009-04-01
Radially encoded MRI has gained increasing attention due to its motion insensitivity and reduced artifacts. However, because its samples are collected nonuniformly in the k-space, multidimensional (especially 3-D) radially sampled MRI image reconstruction is challenging. The objective of this paper is to develop a reconstruction technique in high dimensions with on-the-fly kernel calculation. It implements general multidimensional nonuniform fast Fourier transform (NUFFT) algorithms and incorporates them into a k-space image reconstruction framework. The method is then applied to reconstruct from the radially encoded k-space data, although the method is applicable to any non-Cartesian patterns. Performance comparisons are made against the conventional Kaiser-Bessel (KB) gridding method for 2-D and 3-D radially encoded computer-simulated phantoms and physically scanned phantoms. The results show that the NUFFT reconstruction method has better accuracy-efficiency tradeoff than the KB gridding method when the kernel weights are calculated on the fly. It is found that for a particular conventional kernel function, using its corresponding deapodization function as a scaling factor in the NUFFT framework has the potential to improve accuracy. In particular, when a cosine scaling factor is used, the NUFFT method is faster than KB gridding method since a closed-form solution is available and is less computationally expensive than the KB kernel (KB griding requires computation of Bessel functions). The NUFFT method has been successfully applied to 2-D and 3-D in vivo studies on small animals.
He, Qiaolin
2011-06-01
In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
Latief, Yusuf; Machfudiyanto, Rossy A.; Arifuddin, Rosmariani; Yogiswara, Yoko
2017-03-01
Based on the data, 32% of accidental cases in Indonesia occurs on constructional sectors. It is supported by the data from Public Work and Housing Department that 27.43% of the implementation level of Safety Management System policy at construction companies in Indonesia remains unsafe categories. Moreover, there are dimensions of occupational safety culture formed including leadership, behavior, strategy, policy, process, people, safety cost, value and contract system. The aim of this study is to determine the model of an effective safety culture and know the relationship between dimensions in construction industry. The method used in this research was questionnaire survey which was distributed to the sample of construction companies either in a national private one in Indonesia. The result of this research is supposed to be able to illustrate the development of the relationship among occupational safety culture dimensions which have influences to the performances of constructional companies in Indonesia.
Energy Technology Data Exchange (ETDEWEB)
Flores Ll, H.; Cabral P, A.; Jimenez D, H
1990-01-15
The fundamental parameters of the Voigt function are determined: lorentzian wide ({gamma}{sub L}) and gaussian wide ({gamma}{sub G}) with an error for almost all the cases inferior to 1% in the intervals 0.01 {<=} {gamma}{sub L} / {gamma}{sub G} {<=}1 and 0.3 {<=} {gamma}{sub G} / {gamma}{sub L} {<=}1. This is achieved using the least square fit method with an algebraic function, being obtained a simple method to obtain the fundamental parameters of the Voigt function used in many spectroscopies. (Author)
Mohammadi Moghaddam, Toktam; Razavi, Seyed M A; Taghizadeh, Masoud; Sazgarnia, Ameneh
2016-01-01
Roasting is an important step in the processing of pistachio nuts. The effect of hot air roasting temperature (90, 120 and 150 °C), time (20, 35 and 50 min) and air velocity (0.5, 1.5 and 2.5 m/s) on textural and sensory characteristics of pistachio nuts and kernels were investigated. The results showed that increasing the roasting temperature decreased the fracture force (82-25.54 N), instrumental hardness (82.76-37.59 N), apparent modulus of elasticity (47-21.22 N/s), compressive energy (280.73-101.18 N.s) and increased amount of bitterness (1-2.5) and the hardness score (6-8.40) of pistachio kernels. Higher roasting time improved the flavor of samples. The results of the consumer test showed that the roasted pistachio kernels have good acceptability for flavor (score 5.83-8.40), color (score 7.20-8.40) and hardness (score 6-8.40) acceptance. Moreover, Partial Least Square (PLS) analysis of instrumental and sensory data provided important information for the correlation of objective and subjective properties. The univariate analysis showed that over 93.87 % of the variation in sensory hardness and almost 87 % of the variation in sensory acceptability could be explained by instrumental texture properties.
Pralle, R S; Weigel, K W; White, H M
2018-05-01
Prediction of postpartum hyperketonemia (HYK) using Fourier transform infrared (FTIR) spectrometry analysis could be a practical diagnostic option for farms because these data are now available from routine milk analysis during Dairy Herd Improvement testing. The objectives of this study were to (1) develop and evaluate blood β-hydroxybutyrate (BHB) prediction models using multivariate linear regression (MLR), partial least squares regression (PLS), and artificial neural network (ANN) methods and (2) evaluate whether milk FTIR spectrum (mFTIR)-based models are improved with the inclusion of test-day variables (mTest; milk composition and producer-reported data). Paired blood and milk samples were collected from multiparous cows 5 to 18 d postpartum at 3 Wisconsin farms (3,629 observations from 1,013 cows). Blood BHB concentration was determined by a Precision Xtra meter (Abbot Diabetes Care, Alameda, CA), and milk samples were analyzed by a privately owned laboratory (AgSource, Menomonie, WI) for components and FTIR spectrum absorbance. Producer-recorded variables were extracted from farm management software. A blood BHB ≥1.2 mmol/L was considered HYK. The data set was divided into a training set (n = 3,020) and an external testing set (n = 609). Model fitting was implemented with JMP 12 (SAS Institute, Cary, NC). A 5-fold cross-validation was performed on the training data set for the MLR, PLS, and ANN prediction methods, with square root of blood BHB as the dependent variable. Each method was fitted using 3 combinations of variables: mFTIR, mTest, or mTest + mFTIR variables. Models were evaluated based on coefficient of determination, root mean squared error, and area under the receiver operating characteristic curve. Four models (PLS-mTest + mFTIR, ANN-mFTIR, ANN-mTest, and ANN-mTest + mFTIR) were chosen for further evaluation in the testing set after fitting to the full training set. In the cross-validation analysis, model fit was greatest for ANN, followed
Directory of Open Access Journals (Sweden)
Yu-Kang Tu
2011-04-01
Full Text Available Due to a problem of identification, how to estimate the distinct effects of age, time period and cohort has been a controversial issue in the analysis of trends in health outcomes in epidemiology. In this study, we propose a novel approach, partial least squares (PLS analysis, to separate the effects of age, period, and cohort. Our example for illustration is taken from the Glasgow Alumni cohort. A total of 15,322 students (11,755 men and 3,567 women received medical screening at the Glasgow University between 1948 and 1968. The aim is to investigate the secular trends in blood pressure over 1925 and 1950 while taking into account the year of examination and age at examination. We excluded students born before 1925 or aged over 25 years at examination and those with missing values in confounders from the analyses, resulting in 12,546 and 12,516 students for analysis of systolic and diastolic blood pressure, respectively. PLS analysis shows that both systolic and diastolic blood pressure increased with students' age, and students born later had on average lower blood pressure (SBP: -0.17 mmHg/per year [95% confidence intervals: -0.19 to -0.15] for men and -0.25 [-0.28 to -0.22] for women; DBP: -0.14 [-0.15 to -0.13] for men; -0.09 [-0.11 to -0.07] for women. PLS also shows a decreasing trend in blood pressure over the examination period. As identification is not a problem for PLS, it provides a flexible modelling strategy for age-period-cohort analysis. More emphasis is then required to clarify the substantive and conceptual issues surrounding the definitions and interpretations of age, period and cohort effects.
Least-squares variance component estimation
Teunissen, P.J.G.; Amiri-Simkooei, A.R.
2007-01-01
Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight
Total least squares for anomalous change detection
Theiler, James; Matsekh, Anna M.
2010-04-01
A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.
DEFF Research Database (Denmark)
Peng, Yi; Knadel, Maria; Gislum, René
2014-01-01
A total of 125 soil samples were collected from a Danish field varying in soil texture from sandy to loamy. Visible near-infrared reflectance (Vis-NIR) and mid-infrared reflectance (MIR) spectroscopy combined with chemometric methods were used to predict soil organic carbon (SOC) and clay content...
Regularization by truncated total least squares
DEFF Research Database (Denmark)
Hansen, Per Christian; Fierro, R.D; Golub, G.H
1997-01-01
The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use...... schemes for relativistic hydrodynamical equations. Such an approximate Riemann solver is presented in this paper which treats all waves emanating from an initial discontinuity as themselves discontinuous. Therefore, jump conditions for shocks are approximately used for rarefaction waves. The solver...... is easy to implement in a Godunov scheme and converges rapidly for relativistic hydrodynamics. The fast convergence of the solver indicates the potential of a higher performance of a Godunov scheme in which the solver is used....
Cichocki, A; Unbehauen, R
1994-01-01
In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.
Least-squares model-based halftoning
Pappas, Thrasyvoulos N.; Neuhoff, David L.
1992-08-01
A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach
International Nuclear Information System (INIS)
Sun Bin; Zhou Yunlong; Zhao Peng; Guan Yuebo
2007-01-01
Aiming at the non-stationary characteristics of differential pressure fluctuation signals of gas-liquid two-phase flow, and the slow convergence of learning and liability of dropping into local minima for BP neural networks, flow regime identification method based on Singular Value Decomposition (SVD) and Least Square Support Vector Machine (LS-SVM) is presented. First of all, the Empirical Mode Decomposition (EMD) method is used to decompose the differential pressure fluctuation signals of gas-liquid two-phase flow into a number of stationary Intrinsic Mode Functions (IMFs) components from which the initial feature vector matrix is formed. By applying the singular vale decomposition technique to the initial feature vector matrixes, the singular values are obtained. Finally, the singular values serve as the flow regime characteristic vector to be LS-SVM classifier and flow regimes are identified by the output of the classifier. The identification result of four typical flow regimes of air-water two-phase flow in horizontal pipe has shown that this method achieves a higher identification rate. (authors)
Razi-Asrami, Mahboobeh; Ghasemi, Jahan B; Amiri, Nayereh; Sadeghi, Seyed Jamal
2017-04-01
In this paper, a simple, fast, and inexpensive method is introduced for the simultaneous spectrophotometric determination of crystal violet (CV) and malachite green (MG) contents in aquatic samples using partial least squares regression (PLS) as a multivariate calibration technique after preconcentration by graphene oxide (GO). The method was based on the sorption and desorption of analytes onto GO and direct determination by ultraviolet-visible spectrophotometric techniques. GO was synthesized according to Hummers method. To characterize the shape and structure of GO, FT-IR, SEM, and XRD were used. The effective factors on the extraction efficiency such as pH, extraction time, and the amount of adsorbent were optimized using central composite design. The optimum values of these factors were 6, 15 min, and 12 mg, respectively. The maximum capacity of GO for the adsorption of CV and MG was 63.17 and 77.02 mg g -1 , respectively. Preconcentration factors and extraction recoveries were obtained and were 19.6, 98% for CV and 20, 100% for MG, respectively. LOD and linear dynamic ranges for CV and MG were 0.009, 0.03-0.3, 0.015, and 0.05-0.5 (μg mL -1 ), respectively. The intra-day and inter-day relative standard deviations were 1.99 and 0.58 for CV and 1.69 and 3.13 for MG at the concentration level of 50 ng mL -1 , respectively. Finally, the proposed DSPE/PLS method was successfully applied for the simultaneous determination of the trace amount of CV and MG in the real water samples.
Zhang, George Z.; Myers, Kyle J.; Park, Subok
2013-03-01
Digital breast tomosynthesis (DBT) has shown promise for improving the detection of breast cancer, but it has not yet been fully optimized due to a large space of system parameters to explore. A task-based statistical approach1 is a rigorous method for evaluating and optimizing this promising imaging technique with the use of optimal observers such as the Hotelling observer (HO). However, the high data dimensionality found in DBT has been the bottleneck for the use of a task-based approach in DBT evaluation. To reduce data dimensionality while extracting salient information for performing a given task, efficient channels have to be used for the HO. In the past few years, 2D Laguerre-Gauss (LG) channels, which are a complete basis for stationary backgrounds and rotationally symmetric signals, have been utilized for DBT evaluation2, 3 . But since background and signal statistics from DBT data are neither stationary nor rotationally symmetric, LG channels may not be efficient in providing reliable performance trends as a function of system parameters. Recently, partial least squares (PLS) has been shown to generate efficient channels for the Hotelling observer in detection tasks involving random backgrounds and signals.4 In this study, we investigate the use of PLS as a method for extracting salient information from DBT in order to better evaluate such systems.
Ghaedi, M; Rahimi, Mahmoud Reza; Ghaedi, A M; Tyagi, Inderjeet; Agarwal, Shilpi; Gupta, Vinod Kumar
2016-01-01
Two novel and eco friendly adsorbents namely tin oxide nanoparticles loaded on activated carbon (SnO2-NP-AC) and activated carbon prepared from wood tree Pistacia atlantica (AC-PAW) were used for the rapid removal and fast adsorption of methyl orange (MO) from the aqueous phase. The dependency of MO removal with various adsorption influential parameters was well modeled and optimized using multiple linear regressions (MLR) and least squares support vector regression (LSSVR). The optimal parameters for the LSSVR model were found based on γ value of 0.76 and σ(2) of 0.15. For testing the data set, the mean square error (MSE) values of 0.0010 and the coefficient of determination (R(2)) values of 0.976 were obtained for LSSVR model, and the MSE value of 0.0037 and the R(2) value of 0.897 were obtained for the MLR model. The adsorption equilibrium and kinetic data was found to be well fitted and in good agreement with Langmuir isotherm model and second-order equation and intra-particle diffusion models respectively. The small amount of the proposed SnO2-NP-AC and AC-PAW (0.015 g and 0.08 g) is applicable for successful rapid removal of methyl orange (>95%). The maximum adsorption capacity for SnO2-NP-AC and AC-PAW was 250 mg g(-1) and 125 mg g(-1) respectively. Copyright © 2015 Elsevier Inc. All rights reserved.
New approach to breast cancer CAD using partial least squares and kernel-partial least squares
Land, Walker H., Jr.; Heine, John; Embrechts, Mark; Smith, Tom; Choma, Robert; Wong, Lut
2005-04-01
Breast cancer is second only to lung cancer as a tumor-related cause of death in women. Currently, the method of choice for the early detection of breast cancer is mammography. While sensitive to the detection of breast cancer, its positive predictive value (PPV) is low, resulting in biopsies that are only 15-34% likely to reveal malignancy. This paper explores the use of two novel approaches called Partial Least Squares (PLS) and Kernel-PLS (K-PLS) to the diagnosis of breast cancer. The approach is based on optimization for the partial least squares (PLS) algorithm for linear regression and the K-PLS algorithm for non-linear regression. Preliminary results show that both the PLS and K-PLS paradigms achieved comparable results with three separate support vector learning machines (SVLMs), where these SVLMs were known to have been trained to a global minimum. That is, the average performance of the three separate SVLMs were Az = 0.9167927, with an average partial Az (Az90) = 0.5684283. These results compare favorably with the K-PLS paradigm, which obtained an Az = 0.907 and partial Az = 0.6123. The PLS paradigm provided comparable results. Secondly, both the K-PLS and PLS paradigms out performed the ANN in that the Az index improved by about 14% (Az ~ 0.907 compared to the ANN Az of ~ 0.8). The "Press R squared" value for the PLS and K-PLS machine learning algorithms were 0.89 and 0.9, respectively, which is in good agreement with the other MOP values.
Directory of Open Access Journals (Sweden)
Xiangwei Guo
2016-02-01
Full Text Available An estimation of the power battery state of charge (SOC is related to the energy management, the battery cycle life and the use cost of electric vehicles. When a lithium-ion power battery is used in an electric vehicle, the SOC displays a very strong time-dependent nonlinearity under the influence of random factors, such as the working conditions and the environment. Hence, research on estimating the SOC of a power battery for an electric vehicle is of great theoretical significance and application value. In this paper, according to the dynamic response of the power battery terminal voltage during a discharging process, the second-order RC circuit is first used as the equivalent model of the power battery. Subsequently, on the basis of this model, the least squares method (LS with a forgetting factor and the adaptive unscented Kalman filter (AUKF algorithm are used jointly in the estimation of the power battery SOC. Simulation experiments show that the joint estimation algorithm proposed in this paper has higher precision and convergence of the initial value error than a single AUKF algorithm.
A least-squares computational ''tool kit''
International Nuclear Information System (INIS)
Smith, D.L.
1993-04-01
The information assembled in this report is intended to offer a useful computational ''tool kit'' to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications
Energy Technology Data Exchange (ETDEWEB)
Hashim, Yusof bin [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Gambang 26300 Kuantan, Pahang (Malaysia); Taha, Zahari bin [Faculty of Manufacturing Engineering, Malaysia Pahang, 26600 Pekan, Pahang (Malaysia)
2015-02-03
Public, stake holders and authorities in Malaysian government show great concern towards high numbers of passenger’s injuries and passengers fatalities in express bus accident. This paper studies the underlying factors involved in determining ergonomics risk factors towards human error as the reasons in express bus accidents in order to develop an integrated analytical framework. Reliable information about drivers towards bus accident should lead to the design of strategies intended to make the public feel safe in public transport services. In addition there is an analysis of ergonomics risk factors to determine highly ergonomic risk factors which led to accidents. The research was performed in east coast of peninsular Malaysia using variance-based structural equation modeling namely the Partial Least Squares (PLS) regression techniques. A questionnaire survey was carried out at random among 65 express bus drivers operating from the city of Kuantan in Pahang and among 49 express bus drivers operating from the city of Kuala Terengganu in Terengganu to all towns in the east coast of peninsular west Malaysia. The ergonomic risks factors questionnaire is based on demographic information, occupational information, organizational safety climate, ergonomic workplace, physiological factors, stress at workplace, physical fatigue and near miss accidents. The correlation and significant values between latent constructs (near miss accident) were analyzed using SEM SmartPLS, 3M. The finding shows that the correlated ergonomic risks factors (occupational information, t=2.04, stress at workplace, t = 2.81, physiological factor, t=2.08) are significant to physical fatigue and as the mediator to near miss accident at t = 2.14 at p<0.05and T-statistics, t>1.96. The results shows that the effects of physical fatigue due to ergonomic risks factors influence the human error as the reasons in express bus accidents.
International Nuclear Information System (INIS)
Hashim, Yusof bin; Taha, Zahari bin
2015-01-01
Public, stake holders and authorities in Malaysian government show great concern towards high numbers of passenger’s injuries and passengers fatalities in express bus accident. This paper studies the underlying factors involved in determining ergonomics risk factors towards human error as the reasons in express bus accidents in order to develop an integrated analytical framework. Reliable information about drivers towards bus accident should lead to the design of strategies intended to make the public feel safe in public transport services. In addition there is an analysis of ergonomics risk factors to determine highly ergonomic risk factors which led to accidents. The research was performed in east coast of peninsular Malaysia using variance-based structural equation modeling namely the Partial Least Squares (PLS) regression techniques. A questionnaire survey was carried out at random among 65 express bus drivers operating from the city of Kuantan in Pahang and among 49 express bus drivers operating from the city of Kuala Terengganu in Terengganu to all towns in the east coast of peninsular west Malaysia. The ergonomic risks factors questionnaire is based on demographic information, occupational information, organizational safety climate, ergonomic workplace, physiological factors, stress at workplace, physical fatigue and near miss accidents. The correlation and significant values between latent constructs (near miss accident) were analyzed using SEM SmartPLS, 3M. The finding shows that the correlated ergonomic risks factors (occupational information, t=2.04, stress at workplace, t = 2.81, physiological factor, t=2.08) are significant to physical fatigue and as the mediator to near miss accident at t = 2.14 at p<0.05and T-statistics, t>1.96. The results shows that the effects of physical fatigue due to ergonomic risks factors influence the human error as the reasons in express bus accidents
Hashim, Yusof bin; Taha, Zahari bin
2015-02-01
Public, stake holders and authorities in Malaysian government show great concern towards high numbers of passenger's injuries and passengers fatalities in express bus accident. This paper studies the underlying factors involved in determining ergonomics risk factors towards human error as the reasons in express bus accidents in order to develop an integrated analytical framework. Reliable information about drivers towards bus accident should lead to the design of strategies intended to make the public feel safe in public transport services. In addition there is an analysis of ergonomics risk factors to determine highly ergonomic risk factors which led to accidents. The research was performed in east coast of peninsular Malaysia using variance-based structural equation modeling namely the Partial Least Squares (PLS) regression techniques. A questionnaire survey was carried out at random among 65 express bus drivers operating from the city of Kuantan in Pahang and among 49 express bus drivers operating from the city of Kuala Terengganu in Terengganu to all towns in the east coast of peninsular west Malaysia. The ergonomic risks factors questionnaire is based on demographic information, occupational information, organizational safety climate, ergonomic workplace, physiological factors, stress at workplace, physical fatigue and near miss accidents. The correlation and significant values between latent constructs (near miss accident) were analyzed using SEM SmartPLS, 3M. The finding shows that the correlated ergonomic risks factors (occupational information, t=2.04, stress at workplace, t = 2.81, physiological factor, t=2.08) are significant to physical fatigue and as the mediator to near miss accident at t = 2.14 at p1.96. The results shows that the effects of physical fatigue due to ergonomic risks factors influence the human error as the reasons in express bus accidents.
Gu, Huidong; Liu, Guowen; Wang, Jian; Aubry, Anne-Françoise; Arnold, Mark E
2014-09-16
A simple procedure for selecting the correct weighting factors for linear and quadratic calibration curves with least-squares regression algorithm in bioanalytical LC-MS/MS assays is reported. The correct weighting factor is determined by the relationship between the standard deviation of instrument responses (σ) and the concentrations (x). The weighting factor of 1, 1/x, or 1/x(2) should be selected if, over the entire concentration range, σ is a constant, σ(2) is proportional to x, or σ is proportional to x, respectively. For the first time, we demonstrated with detailed scientific reasoning, solid historical data, and convincing justification that 1/x(2) should always be used as the weighting factor for all bioanalytical LC-MS/MS assays. The impacts of using incorrect weighting factors on curve stability, data quality, and assay performance were thoroughly investigated. It was found that the most stable curve could be obtained when the correct weighting factor was used, whereas other curves using incorrect weighting factors were unstable. It was also found that there was a very insignificant impact on the concentrations reported with calibration curves using incorrect weighting factors as the concentrations were always reported with the passing curves which actually overlapped with or were very close to the curves using the correct weighting factor. However, the use of incorrect weighting factors did impact the assay performance significantly. Finally, the difference between the weighting factors of 1/x(2) and 1/y(2) was discussed. All of the findings can be generalized and applied into other quantitative analysis techniques using calibration curves with weighted least-squares regression algorithm.
Least-squares reverse time migration of multiples
Zhang, Dongliang; Schuster, Gerard T.
2013-01-01
The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual
Solution of a Complex Least Squares Problem with Constrained Phase.
Bydder, Mark
2010-12-30
The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.
de Oliveira, Rodrigo Rocha; de Lima, Kássio Michell Gomes; Tauler, Romà; de Juan, Anna
2014-07-01
This study describes two applications of a variant of the multivariate curve resolution alternating least squares (MCR-ALS) method with a correlation constraint. The first application describes the use of MCR-ALS for the determination of biodiesel concentrations in biodiesel blends using near infrared (NIR) spectroscopic data. In the second application, the proposed method allowed the determination of the synthetic antioxidant N,N'-Di-sec-butyl-p-phenylenediamine (PDA) present in biodiesel mixtures from different vegetable sources using UV-visible spectroscopy. Well established multivariate regression algorithm, partial least squares (PLS), were calculated for comparison of the quantification performance in the models developed in both applications. The correlation constraint has been adapted to handle the presence of batch-to-batch matrix effects due to ageing effects, which might occur when different groups of samples were used to build a calibration model in the first application. Different data set configurations and diverse modes of application of the correlation constraint are explored and guidelines are given to cope with different type of analytical problems, such as the correction of matrix effects among biodiesel samples, where MCR-ALS outperformed PLS reducing the relative error of prediction RE (%) from 9.82% to 4.85% in the first application, or the determination of minor compound with overlapped weak spectroscopic signals, where MCR-ALS gave higher (RE (%)=3.16%) for prediction of PDA compared to PLS (RE (%)=1.99%), but with the advantage of recovering the related pure spectral profile of analytes and interferences. The obtained results show the potential of the MCR-ALS method with correlation constraint to be adapted to diverse data set configurations and analytical problems related to the determination of biodiesel mixtures and added compounds therein. Copyright © 2014 Elsevier B.V. All rights reserved.
Constrained least squares regularization in PET
International Nuclear Information System (INIS)
Choudhury, K.R.; O'Sullivan, F.O.
1996-01-01
Standard reconstruction methods used in tomography produce images with undesirable negative artifacts in background and in areas of high local contrast. While sophisticated statistical reconstruction methods can be devised to correct for these artifacts, their computational implementation is excessive for routine operational use. This work describes a technique for rapid computation of approximate constrained least squares regularization estimates. The unique feature of the approach is that it involves no iterative projection or backprojection steps. This contrasts with the familiar computationally intensive algorithms based on algebraic reconstruction (ART) or expectation-maximization (EM) methods. Experimentation with the new approach for deconvolution and mixture analysis shows that the root mean square error quality of estimators based on the proposed algorithm matches and usually dominates that of more elaborate maximum likelihood, at a fraction of the computational effort
Optimally weighted least-squares steganalysis
Ker, Andrew D.
2007-02-01
Quantitative steganalysis aims to estimate the amount of payload in a stego object, and such estimators seem to arise naturally in steganalysis of Least Significant Bit (LSB) replacement in digital images. However, as with all steganalysis, the estimators are subject to errors, and their magnitude seems heavily dependent on properties of the cover. In very recent work we have given the first derivation of estimation error, for a certain method of steganalysis (the Least-Squares variant of Sample Pairs Analysis) of LSB replacement steganography in digital images. In this paper we make use of our theoretical results to find an improved estimator and detector. We also extend the theoretical analysis to another (more accurate) steganalysis estimator (Triples Analysis) and hence derive an improved version of that estimator too. Experimental results show that the new steganalyzers have improved accuracy, particularly in the difficult case of never-compressed covers.
Multiples least-squares reverse time migration
Zhang, Dongliang
2013-01-01
To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated as a virtual source, knowledge of the source wavelet is not required. Numerical tests on synthetic data for the Sigsbee2B model and field data from Gulf of Mexico show that MLSRTM can improve the image quality by removing artifacts, balancing amplitudes, and suppressing crosstalk compared to standard migration of the free-surface multiples. The potential liability of this method is that multiples require several roundtrips between the reflector and the free surface, so that high frequencies in the multiples are attenuated compared to the primary reflections. This can lead to lower resolution in the migration image compared to that computed from primaries.
Tensor hypercontraction. II. Least-squares renormalization
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2012-12-01
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.
Directory of Open Access Journals (Sweden)
Iman Yousefi
2015-01-01
Full Text Available This paper presents parameter estimation of Permanent Magnet Synchronous Motor (PMSM using a combinatorial algorithm. Nonlinear fourth-order space state model of PMSM is selected. This model is rewritten to the linear regression form without linearization. Noise is imposed to the system in order to provide a real condition, and then combinatorial Orthogonal Projection Algorithm and Recursive Least Squares (OPA&RLS method is applied in the linear regression form to the system. Results of this method are compared to the Orthogonal Projection Algorithm (OPA and Recursive Least Squares (RLS methods to validate the feasibility of the proposed method. Simulation results validate the efficacy of the proposed algorithm.
Multisource Least-squares Reverse Time Migration
Dai, Wei
2012-12-01
Least-squares migration has been shown to be able to produce high quality migration images, but its computational cost is considered to be too high for practical imaging. In this dissertation, a multisource least-squares reverse time migration algorithm (LSRTM) is proposed to increase by up to 10 times the computational efficiency by utilizing the blended sources processing technique. There are three main chapters in this dissertation. In Chapter 2, the multisource LSRTM algorithm is implemented with random time-shift and random source polarity encoding functions. Numerical tests on the 2D HESS VTI data show that the multisource LSRTM algorithm suppresses migration artifacts, balances the amplitudes, improves image resolution, and reduces crosstalk noise associated with the blended shot gathers. For this example, multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution, and fewer migration artifacts compared to conventional RTM. The empirical results suggest that the multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with similar or less computational cost. The caveat is that LSRTM image is sensitive to large errors in the migration velocity model. In Chapter 3, the multisource LSRTM algorithm is implemented with frequency selection encoding strategy and applied to marine streamer data, for which traditional random encoding functions are not applicable. The frequency-selection encoding functions are delta functions in the frequency domain, so that all the encoded shots have unique non-overlapping frequency content. Therefore, the receivers can distinguish the wavefield from each shot according to the frequencies. With the frequency-selection encoding method, the computational efficiency of LSRTM is increased so that its cost is
Bounded Perturbation Regularization for Linear Least Squares Estimation
Ballal, Tarig; Suliman, Mohamed Abdalla Elhag; Al-Naffouri, Tareq Y.
2017-01-01
This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef
2017-06-30
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.
A Newton Algorithm for Multivariate Total Least Squares Problems
Directory of Open Access Journals (Sweden)
WANG Leyang
2016-04-01
Full Text Available In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.
Kehimkar, Benjamin; Hoggard, Jamin C; Marney, Luke C; Billingsley, Matthew C; Fraga, Carlos G; Bruno, Thomas J; Synovec, Robert E
2014-01-31
There is an increased need to more fully assess and control the composition of kerosene-based rocket propulsion fuels such as RP-1. In particular, it is critical to make better quantitative connections among the following three attributes: fuel performance (thermal stability, sooting propensity, engine specific impulse, etc.), fuel properties (such as flash point, density, kinematic viscosity, net heat of combustion, and hydrogen content), and the chemical composition of a given fuel, i.e., amounts of specific chemical compounds and compound classes present in a fuel as a result of feedstock blending and/or processing. Recent efforts in predicting fuel chemical and physical behavior through modeling put greater emphasis on attaining detailed and accurate fuel properties and fuel composition information. Often, one-dimensional gas chromatography (GC) combined with mass spectrometry (MS) is employed to provide chemical composition information. Building on approaches that used GC-MS, but to glean substantially more chemical information from these complex fuels, we recently studied the use of comprehensive two dimensional (2D) gas chromatography combined with time-of-flight mass spectrometry (GC×GC-TOFMS) using a "reversed column" format: RTX-wax column for the first dimension, and a RTX-1 column for the second dimension. In this report, by applying chemometric data analysis, specifically partial least-squares (PLS) regression analysis, we are able to readily model (and correlate) the chemical compositional information provided by use of GC×GC-TOFMS to RP-1 fuel property information such as density, kinematic viscosity, net heat of combustion, and so on. Furthermore, we readily identified compounds that contribute significantly to measured differences in fuel properties based on results from the PLS models. We anticipate this new chemical analysis strategy will have broad implications for the development of high fidelity composition-property models, leading to an
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Partial update least-square adaptive filtering
Xie, Bei
2014-01-01
Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity (O(N)) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster a
Multiples least-squares reverse time migration
Zhang, Dongliang; Zhan, Ge; Dai, Wei; Schuster, Gerard T.
2013-01-01
To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated
Deformation analysis with Total Least Squares
Directory of Open Access Journals (Sweden)
M. Acar
2006-01-01
Full Text Available Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS and the Total Least Squares (TLS, respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.
Optimistic semi-supervised least squares classification
DEFF Research Database (Denmark)
Krijthe, Jesse H.; Loog, Marco
2017-01-01
The goal of semi-supervised learning is to improve supervised classifiers by using additional unlabeled training examples. In this work we study a simple self-learning approach to semi-supervised learning applied to the least squares classifier. We show that a soft-label and a hard-label variant ...
Partial Least Squares tutorial for analyzing neuroimaging data
Directory of Open Access Journals (Sweden)
Patricia Van Roon
2014-09-01
Full Text Available Partial least squares (PLS has become a respected and meaningful soft modeling analysis technique that can be applied to very large datasets where the number of factors or variables is greater than the number of observations. Current biometric studies (e.g., eye movements, EKG, body movements, EEG are often of this nature. PLS eliminates the multiple linear regression issues of over-fitting data by finding a few underlying or latent variables (factors that account for most of the variation in the data. In real-world applications, where linear models do not always apply, PLS can model the non-linear relationship well. This tutorial introduces two PLS methods, PLS Correlation (PLSC and PLS Regression (PLSR and their applications in data analysis which are illustrated with neuroimaging examples. Both methods provide straightforward and comprehensible techniques for determining and modeling relationships between two multivariate data blocks by finding latent variables that best describes the relationships. In the examples, the PLSC will analyze the relationship between neuroimaging data such as Event-Related Potential (ERP amplitude averages from different locations on the scalp with their corresponding behavioural data. Using the same data, the PLSR will be used to model the relationship between neuroimaging and behavioural data. This model will be able to predict future behaviour solely from available neuroimaging data. To find latent variables, Singular Value Decomposition (SVD for PLSC and Non-linear Iterative PArtial Least Squares (NIPALS for PLSR are implemented in this tutorial. SVD decomposes the large data block into three manageable matrices containing a diagonal set of singular values, as well as left and right singular vectors. For PLSR, NIPALS algorithms are used because it provides amore precise estimation of the latent variables. Mathematica notebooks are provided for each PLS method with clearly labeled sections and subsections. The
Elastic least-squares reverse time migration
Feng, Zongcai; Schuster, Gerard T.
2016-01-01
Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.
Elastic least-squares reverse time migration
Feng, Zongcai
2016-09-06
Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.
Least Squares Problems with Absolute Quadratic Constraints
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R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
International Nuclear Information System (INIS)
Dousseau, F.; Pezolet, M.
1990-01-01
A method for estimating protein secondary structure from infrared spectra has been developed. The infrared spectra of H 2 O solutions of 13 proteins of known crystal structure have been recorded and corrected for the spectral contribution of water in the amide I and II region by using the algorithm of Dousseau et al. This calibration set of proteins has been analyzed by using either a classical least-squares (CLS) method or the partial least-squares (PLS) method. The pure-structure spectra calculated by the classical least-squares method are in good agreement with spectra of poly(L-lysine) in the α-helix, β-sheet, and undefined conformations. The results show that the best agreement between the secondary structure determined by X-ray crystal-lography and that predicted by infrared spectroscopy is obtained when both the amide I and II bands are used to generate the calibration set, when the PLS method is used, and when it is assumed that the secondary structure of proteins is composed of only four types of structure: ordered and disordered α-helices, β-sheet, and undefined conformation. Attempts to include turns in the secondary structure estimation have led to a loss of accuracy. The spectra of the calibration proteins were also recorded in 2 H 2 O solution. After correction for the contribution of the combination band of 2 H 2 O in the amide I' band region, the spectra were analyzed with PLS, but the results were not as good as for the spectra obtained in H 2 O, especially for the α-helical conformation
Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach
Ulbrich, N.; Volden, T.
2017-01-01
A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.
Least squares reverse time migration of controlled order multiples
Liu, Y.
2016-12-01
Imaging using the reverse time migration of multiples generates inherent crosstalk artifacts due to the interference among different order multiples. Traditionally, least-square fitting has been used to address this issue by seeking the best objective function to measure the amplitude differences between the predicted and observed data. We have developed an alternative objective function by decomposing multiples into different orders to minimize the difference between Born modeling predicted multiples and specific-order multiples from observational data in order to attenuate the crosstalk. This method is denoted as the least-squares reverse time migration of controlled order multiples (LSRTM-CM). Our numerical examples demonstrated that the LSRTM-CM can significantly improve image quality compared with reverse time migration of multiples and least-square reverse time migration of multiples. Acknowledgments This research was funded by the National Nature Science Foundation of China (Grant Nos. 41430321 and 41374138).
Sparse least-squares reverse time migration using seislets
Dutta, Gaurav
2015-08-19
We propose sparse least-squares reverse time migration (LSRTM) using seislets as a basis for the reflectivity distribution. This basis is used along with a dip-constrained preconditioner that emphasizes image updates only along prominent dips during the iterations. These dips can be estimated from the standard migration image or from the gradient using plane-wave destruction filters or structural tensors. Numerical tests on synthetic datasets demonstrate the benefits of this method for mitigation of aliasing artifacts and crosstalk noise in multisource least-squares migration.
Moving least squares simulation of free surface flows
DEFF Research Database (Denmark)
Felter, C. L.; Walther, Jens Honore; Henriksen, Christian
2014-01-01
In this paper a Moving Least Squares method (MLS) for the simulation of 2D free surface flows is presented. The emphasis is on the governing equations, the boundary conditions, and the numerical implementation. The compressible viscous isothermal Navier–Stokes equations are taken as the starting ...
Multivariate calibration with least-squares support vector machines.
Thissen, U.M.J.; Ustun, B.; Melssen, W.J.; Buydens, L.M.C.
2004-01-01
This paper proposes the use of least-squares support vector machines (LS-SVMs) as a relatively new nonlinear multivariate calibration method, capable of dealing with ill-posed problems. LS-SVMs are an extension of "traditional" SVMs that have been introduced recently in the field of chemistry and
Plane-wave Least-squares Reverse Time Migration
Dai, Wei
2012-11-04
Least-squares reverse time migration is formulated with a new parameterization, where the migration image of each shot is updated separately and a prestack image is produced with common image gathers. The advantage is that it can offer stable convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A regularization term which penalizes the image difference between nearby angles are used to keep the prestack image consistent through all the angles. Numerical tests on a marine dataset is performed to illustrate the advantages of least-squares reverse time migration in the plane-wave domain. Through iterations of least-squares migration, the migration artifacts are reduced and the image resolution is improved. Empirical results suggest that the LSRTM in plane wave domain is an efficient method to improve the image quality and produce common image gathers.
Skeletonized Least Squares Wave Equation Migration
Zhan, Ge
2010-10-17
The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).
Elastic least-squares reverse time migration
Feng, Zongcai
2017-03-08
We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.
Elastic least-squares reverse time migration
Feng, Zongcai; Schuster, Gerard T.
2017-01-01
We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTMsolves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional leastsquares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTMwill produce migration noise stronger than that seen in the RTM images.
Energy Technology Data Exchange (ETDEWEB)
Gutierrez T, C.; Flores Ll, H. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)
2004-07-01
The second derived of the characteristic curve current-voltage (I - V) of a Langmuir probe (I - V) is numerically calculated using the Tikhonov method for to determine the distribution function of the electrons energy (EEDF). One comparison of the obtained EEDF and a fit by least square are discussed (LS). The I - V experimental curve is obtained in a plasma source in the electron cyclotron resonance (ECR) using a cylindrical probe. The parameters of plasma are determined of the EEDF by means of the Laframboise theory. For the case of the LS fit, the obtained results are similar to those obtained by the Tikhonov method, but in the first case the procedure is slow to achieve the best fit. (Author)
Directory of Open Access Journals (Sweden)
F. S. Zhang
2016-01-01
Full Text Available The spatial mapping of losses attributable to such disasters is now well established as a means of describing the spatial patterns of disaster risk, and it has been shown to be suitable for many types of major meteorological disasters. However, few studies have been carried out by developing a regression model to estimate the effects of the spatial distribution of meteorological factors on losses associated with meteorological disasters. In this study, the proposed approach is capable of the following: (a estimating the spatial distributions of seven meteorological factors using Bayesian maximum entropy, (b identifying the four mapping methods used in this research with the best performance based on the cross validation, and (c establishing a fitted model between the PLS components and disaster losses information using partial least squares regression within a specific research area. The results showed the following: (a best mapping results were produced by multivariate Bayesian maximum entropy with probabilistic soft data; (b the regression model using three PLS components, extracted from seven meteorological factors by PLS method, was the most predictive by means of PRESS/SS test; (c northern Hunan Province sustains the most damage, and southeastern Gansu Province and western Guizhou Province sustained the least.
International Nuclear Information System (INIS)
Sanchez Miro, J. J.; Sanz Martin, J. C.
1994-01-01
Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries. (Author) 10 refs
Multisplitting for linear, least squares and nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
Least-squares fit of a linear combination of functions
Directory of Open Access Journals (Sweden)
Niraj Upadhyay
2013-12-01
Full Text Available We propose that given a data-set $S=\\{(x_i,y_i/i=1,2,{\\dots}n\\}$ and real-valued functions $\\{f_\\alpha(x/\\alpha=1,2,{\\dots}m\\},$ the least-squares fit vector $A=\\{a_\\alpha\\}$ for $y=\\sum_\\alpha a_{\\alpha}f_\\alpha(x$ is $A = (F^TF^{-1}F^TY$ where $[F_{i\\alpha}]=[f_\\alpha(x_i].$ We test this formalism by deriving the algebraic expressions of the regression coefficients in $y = ax + b$ and in $y = ax^2 + bx + c.$ As a practical application, we successfully arrive at the coefficients in the semi-empirical mass formula of nuclear physics. The formalism is {\\it generic} - it has the potential of being applicable to any {\\it type} of $\\{x_i\\}$ as long as there exist appropriate $\\{f_\\alpha\\}.$ The method can be exploited with a CAS or an object-oriented language and is excellently suitable for parallel-processing.
Wave-equation Q tomography and least-squares migration
Dutta, Gaurav
2016-03-01
This thesis designs new methods for Q tomography and Q-compensated prestack depth migration when the recorded seismic data suffer from strong attenuation. A motivation of this work is that the presence of gas clouds or mud channels in overburden structures leads to the distortion of amplitudes and phases in seismic waves propagating inside the earth. If the attenuation parameter Q is very strong, i.e., Q<30, ignoring the anelastic effects in imaging can lead to dimming of migration amplitudes and loss of resolution. This, in turn, adversely affects the ability to accurately predict reservoir properties below such layers. To mitigate this problem, I first develop an anelastic least-squares reverse time migration (Q-LSRTM) technique. I reformulate the conventional acoustic least-squares migration problem as a viscoacoustic linearized inversion problem. Using linearized viscoacoustic modeling and adjoint operators during the least-squares iterations, I show with numerical tests that Q-LSRTM can compensate for the amplitude loss and produce images with better balanced amplitudes than conventional migration. To estimate the background Q model that can be used for any Q-compensating migration algorithm, I then develop a wave-equation based optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through numerical tests on synthetic and field data, I show that noticeable improvements in the migration image quality can be obtained from Q models inverted using wave-equation Q tomography. A key feature of skeletonized inversion is that it is much less likely to get stuck in a local minimum than a standard waveform inversion method. Finally, I develop a preconditioning technique for least-squares migration using a directional Gabor-based preconditioning approach for isotropic
Kim, Sanghong; Kano, Manabu; Nakagawa, Hiroshi; Hasebe, Shinji
2011-01-01
Development of quality estimation models using near infrared spectroscopy (NIRS) and multivariate analysis has been accelerated as a process analytical technology (PAT) tool in the pharmaceutical industry. Although linear regression methods such as partial least squares (PLS) are widely used, they cannot always achieve high estimation accuracy because physical and chemical properties of a measuring object have a complex effect on NIR spectra. In this research, locally weighted PLS (LW-PLS) wh...
Regularized Partial Least Squares with an Application to NMR Spectroscopy
Allen, Genevera I.; Peterson, Christine; Vannucci, Marina; Maletic-Savatic, Mirjana
2012-01-01
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexi...
A FORTRAN program for a least-square fitting
International Nuclear Information System (INIS)
Yamazaki, Tetsuo
1978-01-01
A practical FORTRAN program for a least-squares fitting is presented. Although the method is quite usual, the program calculates not only the most satisfactory set of values of unknowns but also the plausible errors associated with them. As an example, a measured lateral absorbed-dose distribution in water for a narrow 25-MeV electron beam is fitted to a Gaussian distribution. (auth.)
Multi-source least-squares reverse time migration
Dai, Wei
2012-06-15
Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.
Multi-source least-squares reverse time migration
Dai, Wei; Fowler, Paul J.; Schuster, Gerard T.
2012-01-01
Least-squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least-squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase-encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least-squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model. © 2012 European Association of Geoscientists & Engineers.
Unweighted least squares phase unwrapping by means of multigrid techniques
Pritt, Mark D.
1995-11-01
We present a multigrid algorithm for unweighted least squares phase unwrapping. This algorithm applies Gauss-Seidel relaxation schemes to solve the Poisson equation on smaller, coarser grids and transfers the intermediate results to the finer grids. This approach forms the basis of our multigrid algorithm for weighted least squares phase unwrapping, which is described in a separate paper. The key idea of our multigrid approach is to maintain the partial derivatives of the phase data in separate arrays and to correct these derivatives at the boundaries of the coarser grids. This maintains the boundary conditions necessary for rapid convergence to the correct solution. Although the multigrid algorithm is an iterative algorithm, we demonstrate that it is nearly as fast as the direct Fourier-based method. We also describe how to parallelize the algorithm for execution on a distributed-memory parallel processor computer or a network-cluster of workstations.
Source allocation by least-squares hydrocarbon fingerprint matching
Energy Technology Data Exchange (ETDEWEB)
William A. Burns; Stephen M. Mudge; A. Edward Bence; Paul D. Boehm; John S. Brown; David S. Page; Keith R. Parker [W.A. Burns Consulting Services LLC, Houston, TX (United States)
2006-11-01
There has been much controversy regarding the origins of the natural polycyclic aromatic hydrocarbon (PAH) and chemical biomarker background in Prince William Sound (PWS), Alaska, site of the 1989 Exxon Valdez oil spill. Different authors have attributed the sources to various proportions of coal, natural seep oil, shales, and stream sediments. The different probable bioavailabilities of hydrocarbons from these various sources can affect environmental damage assessments from the spill. This study compares two different approaches to source apportionment with the same data (136 PAHs and biomarkers) and investigate whether increasing the number of coal source samples from one to six increases coal attributions. The constrained least-squares (CLS) source allocation method that fits concentrations meets geologic and chemical constraints better than partial least-squares (PLS) which predicts variance. The field data set was expanded to include coal samples reported by others, and CLS fits confirm earlier findings of low coal contributions to PWS. 15 refs., 5 figs.
Least-Square Prediction for Backward Adaptive Video Coding
Directory of Open Access Journals (Sweden)
Li Xin
2006-01-01
Full Text Available Almost all existing approaches towards video coding exploit the temporal redundancy by block-matching-based motion estimation and compensation. Regardless of its popularity, block matching still reflects an ad hoc understanding of the relationship between motion and intensity uncertainty models. In this paper, we present a novel backward adaptive approach, named "least-square prediction" (LSP, and demonstrate its potential in video coding. Motivated by the duality between edge contour in images and motion trajectory in video, we propose to derive the best prediction of the current frame from its causal past using least-square method. It is demonstrated that LSP is particularly effective for modeling video material with slow motion and can be extended to handle fast motion by temporal warping and forward adaptation. For typical QCIF test sequences, LSP often achieves smaller MSE than , full-search, quarter-pel block matching algorithm (BMA without the need of transmitting any overhead.
Liu, Ying-Pei; Liang, Hai-Ping; Gao, Zhong-Ke
2015-01-01
In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane.
Directory of Open Access Journals (Sweden)
Ying-Pei Liu
Full Text Available In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC system, we propose an improved auto-disturbance rejection control (ADRC method based on least squares support vector machines (LSSVM in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD and adaptive optimal kernel (AOK time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane.
Single Directional SMO Algorithm for Least Squares Support Vector Machines
Directory of Open Access Journals (Sweden)
Xigao Shao
2013-01-01
Full Text Available Working set selection is a major step in decomposition methods for training least squares support vector machines (LS-SVMs. In this paper, a new technique for the selection of working set in sequential minimal optimization- (SMO- type decomposition methods is proposed. By the new method, we can select a single direction to achieve the convergence of the optimality condition. A simple asymptotic convergence proof for the new algorithm is given. Experimental comparisons demonstrate that the classification accuracy of the new method is not largely different from the existing methods, but the training speed is faster than existing ones.
Positive Scattering Cross Sections using Constrained Least Squares
International Nuclear Information System (INIS)
Dahl, J.A.; Ganapol, B.D.; Morel, J.E.
1999-01-01
A method which creates a positive Legendre expansion from truncated Legendre cross section libraries is presented. The cross section moments of order two and greater are modified by a constrained least squares algorithm, subject to the constraints that the zeroth and first moments remain constant, and that the standard discrete ordinate scattering matrix is positive. A method using the maximum entropy representation of the cross section which reduces the error of these modified moments is also presented. These methods are implemented in PARTISN, and numerical results from a transport calculation using highly anisotropic scattering cross sections with the exponential discontinuous spatial scheme is presented
Nonnegative least-squares image deblurring: improved gradient projection approaches
Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.
2010-02-01
The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.
Regression modeling methods, theory, and computation with SAS
Panik, Michael
2009-01-01
Regression Modeling: Methods, Theory, and Computation with SAS provides an introduction to a diverse assortment of regression techniques using SAS to solve a wide variety of regression problems. The author fully documents the SAS programs and thoroughly explains the output produced by the programs.The text presents the popular ordinary least squares (OLS) approach before introducing many alternative regression methods. It covers nonparametric regression, logistic regression (including Poisson regression), Bayesian regression, robust regression, fuzzy regression, random coefficients regression,
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren
2017-01-01
, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose
Directory of Open Access Journals (Sweden)
Taimoor Zahid
2016-09-01
Full Text Available Battery energy storage management for electric vehicles (EV and hybrid EV is the most critical and enabling technology since the dawn of electric vehicle commercialization. A battery system is a complex electrochemical phenomenon whose performance degrades with age and the existence of varying material design. Moreover, it is very tedious and computationally very complex to monitor and control the internal state of a battery’s electrochemical systems. For Thevenin battery model we established a state-space model which had the advantage of simplicity and could be easily implemented and then applied the least square method to identify the battery model parameters. However, accurate state of charge (SoC estimation of a battery, which depends not only on the battery model but also on highly accurate and efficient algorithms, is considered one of the most vital and critical issue for the energy management and power distribution control of EV. In this paper three different estimation methods, i.e., extended Kalman filter (EKF, particle filter (PF and unscented Kalman Filter (UKF, are presented to estimate the SoC of LiFePO4 batteries for an electric vehicle. Battery’s experimental data, current and voltage, are analyzed to identify the Thevenin equivalent model parameters. Using different open circuit voltages the SoC is estimated and compared with respect to the estimation accuracy and initialization error recovery. The experimental results showed that these online SoC estimation methods in combination with different open circuit voltage-state of charge (OCV-SoC curves can effectively limit the error, thus guaranteeing the accuracy and robustness.
Bounded Perturbation Regularization for Linear Least Squares Estimation
Ballal, Tarig
2017-10-18
This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.
Weighted-Average Least Squares Prediction
Magnus, Jan R.; Wang, Wendun; Zhang, Xinyu
2016-01-01
Prediction under model uncertainty is an important and difficult issue. Traditional prediction methods (such as pretesting) are based on model selection followed by prediction in the selected model, but the reported prediction and the reported prediction variance ignore the uncertainty from the
Weighted least squares phase unwrapping based on the wavelet transform
Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia
2007-01-01
The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.
Emulating facial biomechanics using multivariate partial least squares surrogate models.
Wu, Tim; Martens, Harald; Hunter, Peter; Mithraratne, Kumar
2014-11-01
A detailed biomechanical model of the human face driven by a network of muscles is a useful tool in relating the muscle activities to facial deformations. However, lengthy computational times often hinder its applications in practical settings. The objective of this study is to replace precise but computationally demanding biomechanical model by a much faster multivariate meta-model (surrogate model), such that a significant speedup (to real-time interactive speed) can be achieved. Using a multilevel fractional factorial design, the parameter space of the biomechanical system was probed from a set of sample points chosen to satisfy maximal rank optimality and volume filling. The input-output relationship at these sampled points was then statistically emulated using linear and nonlinear, cross-validated, partial least squares regression models. It was demonstrated that these surrogate models can mimic facial biomechanics efficiently and reliably in real-time. Copyright © 2014 John Wiley & Sons, Ltd.
Feature extraction through least squares fit to a simple model
International Nuclear Information System (INIS)
Demuth, H.B.
1976-01-01
The Oak Ridge National Laboratory (ORNL) presented the Los Alamos Scientific Laboratory (LASL) with 18 radiographs of fuel rod test bundles. The problem is to estimate the thickness of the gap between some cylindrical rods and a flat wall surface. The edges of the gaps are poorly defined due to finite source size, x-ray scatter, parallax, film grain noise, and other degrading effects. The radiographs were scanned and the scan-line data were averaged to reduce noise and to convert the problem to one dimension. A model of the ideal gap, convolved with an appropriate point-spread function, was fit to the averaged data with a least squares program; and the gap width was determined from the final fitted-model parameters. The least squares routine did converge and the gaps obtained are of reasonable size. The method is remarkably insensitive to noise. This report describes the problem, the techniques used to solve it, and the results and conclusions. Suggestions for future work are also given
International Nuclear Information System (INIS)
Wang, Jianzhou; Hu, Jianming
2015-01-01
With the increasing importance of wind power as a component of power systems, the problems induced by the stochastic and intermittent nature of wind speed have compelled system operators and researchers to search for more reliable techniques to forecast wind speed. This paper proposes a combination model for probabilistic short-term wind speed forecasting. In this proposed hybrid approach, EWT (Empirical Wavelet Transform) is employed to extract meaningful information from a wind speed series by designing an appropriate wavelet filter bank. The GPR (Gaussian Process Regression) model is utilized to combine independent forecasts generated by various forecasting engines (ARIMA (Autoregressive Integrated Moving Average), ELM (Extreme Learning Machine), SVM (Support Vector Machine) and LSSVM (Least Square SVM)) in a nonlinear way rather than the commonly used linear way. The proposed approach provides more probabilistic information for wind speed predictions besides improving the forecasting accuracy for single-value predictions. The effectiveness of the proposed approach is demonstrated with wind speed data from two wind farms in China. The results indicate that the individual forecasting engines do not consistently forecast short-term wind speed for the two sites, and the proposed combination method can generate a more reliable and accurate forecast. - Highlights: • The proposed approach can make probabilistic modeling for wind speed series. • The proposed approach adapts to the time-varying characteristic of the wind speed. • The hybrid approach can extract the meaningful components from the wind speed series. • The proposed method can generate adaptive, reliable and more accurate forecasting results. • The proposed model combines four independent forecasting engines in a nonlinear way.
Support-Vector-based Least Squares for learning non-linear dynamics
de Kruif, B.J.; de Vries, Theodorus J.A.
2002-01-01
A function approximator is introduced that is based on least squares support vector machines (LSSVM) and on least squares (LS). The potential indicators for the LS method are chosen as the kernel functions of all the training samples similar to LSSVM. By selecting these as indicator functions the
Regularization Techniques for Linear Least-Squares Problems
Suliman, Mohamed
2016-04-01
Linear estimation is a fundamental branch of signal processing that deals with estimating the values of parameters from a corrupted measured data. Throughout the years, several optimization criteria have been used to achieve this task. The most astonishing attempt among theses is the linear least-squares. Although this criterion enjoyed a wide popularity in many areas due to its attractive properties, it appeared to suffer from some shortcomings. Alternative optimization criteria, as a result, have been proposed. These new criteria allowed, in one way or another, the incorporation of further prior information to the desired problem. Among theses alternative criteria is the regularized least-squares (RLS). In this thesis, we propose two new algorithms to find the regularization parameter for linear least-squares problems. In the constrained perturbation regularization algorithm (COPRA) for random matrices and COPRA for linear discrete ill-posed problems, an artificial perturbation matrix with a bounded norm is forced into the model matrix. This perturbation is introduced to enhance the singular value structure of the matrix. As a result, the new modified model is expected to provide a better stabilize substantial solution when used to estimate the original signal through minimizing the worst-case residual error function. Unlike many other regularization algorithms that go in search of minimizing the estimated data error, the two new proposed algorithms are developed mainly to select the artifcial perturbation bound and the regularization parameter in a way that approximately minimizes the mean-squared error (MSE) between the original signal and its estimate under various conditions. The first proposed COPRA method is developed mainly to estimate the regularization parameter when the measurement matrix is complex Gaussian, with centered unit variance (standard), and independent and identically distributed (i.i.d.) entries. Furthermore, the second proposed COPRA
Linear least squares compartmental-model-independent parameter identification in PET
International Nuclear Information System (INIS)
Thie, J.A.; Smith, G.T.; Hubner, K.F.
1997-01-01
A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals -- all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible
Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations
Energy Technology Data Exchange (ETDEWEB)
Wang, Qiqi, E-mail: qiqi@mit.edu; Hu, Rui, E-mail: hurui@mit.edu; Blonigan, Patrick, E-mail: blonigan@mit.edu
2014-06-15
The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.
note: The least square nucleolus is a general nucleolus
Elisenda Molina; Juan Tejada
2000-01-01
This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the least square nucleolus is a general nucleolus (Maschler et al. (1992)).
DEFF Research Database (Denmark)
Madsen, Henrik; Rosbjerg, Dan
1997-01-01
parameters is inferred from regional data using generalized least squares (GLS) regression. Two different Bayesian T-year event estimators are introduced: a linear estimator that requires only some moments of the prior distributions to be specified and a parametric estimator that is based on specified......A regional estimation procedure that combines the index-flood concept with an empirical Bayes method for inferring regional information is introduced. The model is based on the partial duration series approach with generalized Pareto (GP) distributed exceedances. The prior information of the model...
SECOND ORDER LEAST SQUARE ESTIMATION ON ARCH(1 MODEL WITH BOX-COX TRANSFORMED DEPENDENT VARIABLE
Directory of Open Access Journals (Sweden)
Herni Utami
2014-03-01
Full Text Available Box-Cox transformation is often used to reduce heterogeneity and to achieve a symmetric distribution of response variable. In this paper, we estimate the parameters of Box-Cox transformed ARCH(1 model using second-order leastsquare method and then we study the consistency and asymptotic normality for second-order least square (SLS estimators. The SLS estimation was introduced byWang (2003, 2004 to estimate the parameters of nonlinear regression models with independent and identically distributed errors
A Galerkin least squares approach to viscoelastic flow.
Energy Technology Data Exchange (ETDEWEB)
Rao, Rekha R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schunk, Peter Randall [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-10-01
A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.
Least-squares reverse time migration of multiples
Zhang, Dongliang
2013-12-06
The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. For a single source, the entire free-surface becomes an extended virtual source where the downgoing free-surface multiples more fully illuminate the subsurface compared to the primaries. Since each recorded trace is treated as the time history of a virtual source, knowledge of the source wavelet is not required and the ringy time series for each source is automatically deconvolved. If the multiples can be perfectly separated from the primaries, numerical tests on synthetic data for the Sigsbee2B and Marmousi2 models show that least-squares reverse time migration of multiples (LSRTMM) can significantly improve the image quality compared to RTMM or standard reverse time migration (RTM) of primaries. However, if there is imperfect separation and the multiples are strongly interfering with the primaries then LSRTMM images show no significant advantage over the primary migration images. In some cases, they can be of worse quality. Applying LSRTMM to Gulf of Mexico data shows higher signal-to-noise imaging of the salt bottom and top compared to standard RTM images. This is likely attributed to the fact that the target body is just below the sea bed so that the deep water multiples do not have strong interference with the primaries. Migrating a sparsely sampled version of the Marmousi2 ocean bottom seismic data shows that LSM of primaries and LSRTMM provides significantly better imaging than standard RTM. A potential liability of LSRTMM is that multiples require several round trips between the reflector and the free surface, so that high frequencies in the multiples suffer greater attenuation compared to the primary reflections. This can lead to lower
semPLS: Structural Equation Modeling Using Partial Least Squares
Directory of Open Access Journals (Sweden)
Armin Monecke
2012-05-01
Full Text Available Structural equation models (SEM are very popular in many disciplines. The partial least squares (PLS approach to SEM offers an alternative to covariance-based SEM, which is especially suited for situations when data is not normally distributed. PLS path modelling is referred to as soft-modeling-technique with minimum demands regarding mea- surement scales, sample sizes and residual distributions. The semPLS package provides the capability to estimate PLS path models within the R programming environment. Different setups for the estimation of factor scores can be used. Furthermore it contains modular methods for computation of bootstrap confidence intervals, model parameters and several quality indices. Various plot functions help to evaluate the model. The well known mobile phone dataset from marketing research is used to demonstrate the features of the package.
Least-squares reverse time migration with radon preconditioning
Dutta, Gaurav
2016-09-06
We present a least-squares reverse time migration (LSRTM) method using Radon preconditioning to regularize noisy or severely undersampled data. A high resolution local radon transform is used as a change of basis for the reflectivity and sparseness constraints are applied to the inverted reflectivity in the transform domain. This reflects the prior that for each location of the subsurface the number of geological dips is limited. The forward and the adjoint mapping of the reflectivity to the local Radon domain and back are done through 3D Fourier-based discrete Radon transform operators. The sparseness is enforced by applying weights to the Radon domain components which either vary with the amplitudes of the local dips or are thresholded at given quantiles. Numerical tests on synthetic and field data validate the effectiveness of the proposed approach in producing images with improved SNR and reduced aliasing artifacts when compared with standard RTM or LSRTM.
Robust Homography Estimation Based on Nonlinear Least Squares Optimization
Directory of Open Access Journals (Sweden)
Wei Mou
2014-01-01
Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.
Multilevel solvers of first-order system least-squares for Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
Multi-source least-squares migration of marine data
Wang, Xin; Schuster, Gerard T.
2012-01-01
Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes
Regularized plane-wave least-squares Kirchhoff migration
Wang, Xin; Dai, Wei; Schuster, Gerard T.
2013-01-01
A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity
Plane-wave Least-squares Reverse Time Migration
Dai, Wei; Schuster, Gerard T.
2012-01-01
convergence for least-squares migration even when the migration velocity is not completely accurate. To significantly reduce computation cost, linear phase shift encoding is applied to hundreds of shot gathers to produce dozens of planes waves. A
3D plane-wave least-squares Kirchhoff migration
Wang, Xin; Dai, Wei; Huang, Yunsong; Schuster, Gerard T.
2014-01-01
A three dimensional least-squares Kirchhoff migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images and the computational efficiency. Due to the limitation of current 3D marine acquisition
Making the most out of least-squares migration
Huang, Yunsong; Dutta, Gaurav; Dai, Wei; Wang, Xin; Schuster, Gerard T.; Yu, Jianhua
2014-01-01
) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly
Making the most out of the least (squares migration)
Dutta, Gaurav; Huang, Yunsong; Dai, Wei; Wang, Xin; Schuster, Gerard T.
2014-01-01
) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution
Least squares analysis of fission neutron standard fields
International Nuclear Information System (INIS)
Griffin, P.J.; Williams, J.G.
1997-01-01
A least squares analysis of fission neutron standard fields has been performed using the latest dosimetry cross sections. Discrepant nuclear data are identified and adjusted spectra for 252 Cf spontaneous fission and 235 U thermal fission fields are presented
A new stabilized least-squares imaging condition
International Nuclear Information System (INIS)
Vivas, Flor A; Pestana, Reynam C; Ursin, Bjørn
2009-01-01
The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions
Iterative least-squares solvers for the Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Bochev, P. [Univ. of Texas, Arlington, TX (United States)
1996-12-31
In the recent years finite element methods of least-squares type have attracted considerable attention from both mathematicians and engineers. This interest has been motivated, to a large extent, by several valuable analytic and computational properties of least-squares variational principles. In particular, finite element methods based on such principles circumvent Ladyzhenskaya-Babuska-Brezzi condition and lead to symmetric and positive definite algebraic systems. Thus, it is not surprising that numerical solution of fluid flow problems has been among the most promising and successful applications of least-squares methods. In this context least-squares methods offer significant theoretical and practical advantages in the algorithmic design, which makes resulting methods suitable, among other things, for large-scale numerical simulations.
Autcha Araveeporn
2013-01-01
This paper compares a Least-Squared Random Coefficient Autoregressive (RCA) model with a Least-Squared RCA model based on Autocorrelated Errors (RCA-AR). We looked at only the first order models, denoted RCA(1) and RCA(1)-AR(1). The efficiency of the Least-Squared method was checked by applying the models to Brownian motion and Wiener process, and the efficiency followed closely the asymptotic properties of a normal distribution. In a simulation study, we compared the performance of RCA(1) an...
Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs
Energy Technology Data Exchange (ETDEWEB)
Chater, Mario, E-mail: chaterm@mit.edu; Ni, Angxiu, E-mail: niangxiu@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu
2017-01-15
This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be more efficient and simpler to implement, especially for PDEs.
Locally Linear Embedding of Local Orthogonal Least Squares Images for Face Recognition
Hafizhelmi Kamaru Zaman, Fadhlan
2018-03-01
Dimensionality reduction is very important in face recognition since it ensures that high-dimensionality data can be mapped to lower dimensional space without losing salient and integral facial information. Locally Linear Embedding (LLE) has been previously used to serve this purpose, however, the process of acquiring LLE features requires high computation and resources. To overcome this limitation, we propose a locally-applied Local Orthogonal Least Squares (LOLS) model can be used as initial feature extraction before the application of LLE. By construction of least squares regression under orthogonal constraints we can preserve more discriminant information in the local subspace of facial features while reducing the overall features into a more compact form that we called LOLS images. LLE can then be applied on the LOLS images to maps its representation into a global coordinate system of much lower dimensionality. Several experiments carried out using publicly available face datasets such as AR, ORL, YaleB, and FERET under Single Sample Per Person (SSPP) constraint demonstrates that our proposed method can reduce the time required to compute LLE features while delivering better accuracy when compared to when either LLE or OLS alone is used. Comparison against several other feature extraction methods and more recent feature-learning method such as state-of-the-art Convolutional Neural Networks (CNN) also reveal the superiority of the proposed method under SSPP constraint.
Li, Guoqiang; Niu, Peifeng; Wang, Huaibao; Liu, Yongchao
2014-03-01
This paper presents a novel artificial neural network with a very fast learning speed, all of whose weights and biases are determined by the twice Least Square method, so it is called Least Square Fast Learning Network (LSFLN). In addition, there is another difference from conventional neural networks, which is that the output neurons of LSFLN not only receive the information from the hidden layer neurons, but also receive the external information itself directly from the input neurons. In order to test the validity of LSFLN, it is applied to 6 classical regression applications, and also employed to build the functional relation between the combustion efficiency and operating parameters of a 300WM coal-fired boiler. Experimental results show that, compared with other methods, LSFLN with very less hidden neurons could achieve much better regression precision and generalization ability at a much faster learning speed. Copyright © 2013 Elsevier Ltd. All rights reserved.
Battery state-of-charge estimation using approximate least squares
Unterrieder, C.; Zhang, C.; Lunglmayr, M.; Priewasser, R.; Marsili, S.; Huemer, M.
2015-03-01
In recent years, much effort has been spent to extend the runtime of battery-powered electronic applications. In order to improve the utilization of the available cell capacity, high precision estimation approaches for battery-specific parameters are needed. In this work, an approximate least squares estimation scheme is proposed for the estimation of the battery state-of-charge (SoC). The SoC is determined based on the prediction of the battery's electromotive force. The proposed approach allows for an improved re-initialization of the Coulomb counting (CC) based SoC estimation method. Experimental results for an implementation of the estimation scheme on a fuel gauge system on chip are illustrated. Implementation details and design guidelines are presented. The performance of the presented concept is evaluated for realistic operating conditions (temperature effects, aging, standby current, etc.). For the considered test case of a GSM/UMTS load current pattern of a mobile phone, the proposed method is able to re-initialize the CC-method with a high accuracy, while state-of-the-art methods fail to perform a re-initialization.
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares
Orr, Jeb S.
2012-01-01
A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed
Dual stacked partial least squares for analysis of near-infrared spectra
Energy Technology Data Exchange (ETDEWEB)
Bi, Yiming [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Xie, Qiong, E-mail: yimbi@163.com [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Peng, Silong; Tang, Liang; Hu, Yong; Tan, Jie [Institute of Automation, Chinese Academy of Sciences, 100190 Beijing (China); Zhao, Yuhui [School of Economics and Business, Northeastern University at Qinhuangdao, 066000 Qinhuangdao City (China); Li, Changwen [Food Research Institute of Tianjin Tasly Group, 300410 Tianjin (China)
2013-08-20
Graphical abstract: -- Highlights: •Dual stacking steps are used for multivariate calibration of near-infrared spectra. •A selective weighting strategy is introduced that only a subset of all available sub-models is used for model fusion. •Using two public near-infrared datasets, the proposed method achieved competitive results. •The method can be widely applied in many fields, such as Mid-infrared spectra data and Raman spectra data. -- Abstract: A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications.
Dual stacked partial least squares for analysis of near-infrared spectra
International Nuclear Information System (INIS)
Bi, Yiming; Xie, Qiong; Peng, Silong; Tang, Liang; Hu, Yong; Tan, Jie; Zhao, Yuhui; Li, Changwen
2013-01-01
Graphical abstract: -- Highlights: •Dual stacking steps are used for multivariate calibration of near-infrared spectra. •A selective weighting strategy is introduced that only a subset of all available sub-models is used for model fusion. •Using two public near-infrared datasets, the proposed method achieved competitive results. •The method can be widely applied in many fields, such as Mid-infrared spectra data and Raman spectra data. -- Abstract: A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications
Recursive N-way partial least squares for brain-computer interface.
Directory of Open Access Journals (Sweden)
Andrey Eliseyev
Full Text Available In the article tensor-input/tensor-output blockwise Recursive N-way Partial Least Squares (RNPLS regression is considered. It combines the multi-way tensors decomposition with a consecutive calculation scheme and allows blockwise treatment of tensor data arrays with huge dimensions, as well as the adaptive modeling of time-dependent processes with tensor variables. In the article the numerical study of the algorithm is undertaken. The RNPLS algorithm demonstrates fast and stable convergence of regression coefficients. Applied to Brain Computer Interface system calibration, the algorithm provides an efficient adjustment of the decoding model. Combining the online adaptation with easy interpretation of results, the method can be effectively applied in a variety of multi-modal neural activity flow modeling tasks.
Directory of Open Access Journals (Sweden)
Marco Flôres Ferrão
2004-09-01
Full Text Available As técnicas de espectroscopia por reflexão no infravermelho próximo (NIRRS e por reflexão difusa no infravermelho médio com transformada de Fourier (DRIFTS foram empregadas com o método de regressão multivariado por mínimos quadrados parciais (PLS para a determinação simultânea dos teores de proteína e cinza em amostras de farinha de trigo da variedade Triticum aestivum L. Foram coletados espectros no infravermelho em duplicata de 100 amostras, empregando-se acessórios de reflexão difusa. Os teores de proteína (8,85-13,23% e cinza (0,330-1,287%, empregados como referência, foram determinados pelo método Kjeldhal e método gravimétrico, respectivamente. Os dados espectrais foram utilizados no formato log(1/R, bem como suas derivadas de primeira e segunda ordem, sendo pré-processados usando-se os dados centrados na média (MC ou escalados pela variância (VS ou ambos. Cinqüenta e cinco amostras foram usadas para calibração e 45 para validação dos modelos, adotando-se como critério de construção os valores mínimos do erro padrão de calibração (SEC e do erro padrão de validação (SEV. Estes valores foram inferiores a 0,33% para proteína e a 0,07% para cinza. Os métodos desenvolvidos apresentam como vantagens a não agressão ao ambiente, bem como permitem uma determinação direta, simultânea, rápida e não destrutiva dos teores de proteína e cinza em amostras de farinha de trigo.Partial Least Square (PLS multivariate calibration associated to Near Infrared Reflection Spectroscopy (NIRRS or Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS were used to establish methods for simultaneous determination of protein and ash content on commercial wheat flour samples of Triticum aestivum L. Duplicate spectra of 100 samples with protein content between 8.85-13.23% (Kjeldahl method and ash content between 0.330-1.287% (gravimetric method were employed to build calibration methods. The spectra were used
Weighted least-squares criteria for electrical impedance tomography
International Nuclear Information System (INIS)
Kallman, J.S.; Berryman, J.G.
1992-01-01
Methods are developed for design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found: (1) the optimum constant for the starting model is determined automatically; (2) the weighted least-squares error between the predicted and measured power dissipation data is as small as possible; (3) the variance of the reconstructed conductivity from the starting model is minimized; (4) potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized; (5) cells that dissipate the most power during the current injection tests tend to deviate least from the background value. The resulting algorithm maps the reconstruction problem into a vector space where the contribution to the inversion from the background conductivity remains invariant, while the optimum contributions in orthogonal directions are found. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties
Classification of Hyperspectral Images Using Kernel Fully Constrained Least Squares
Directory of Open Access Journals (Sweden)
Jianjun Liu
2017-11-01
Full Text Available As a widely used classifier, sparse representation classification (SRC has shown its good performance for hyperspectral image classification. Recent works have highlighted that it is the collaborative representation mechanism under SRC that makes SRC a highly effective technique for classification purposes. If the dimensionality and the discrimination capacity of a test pixel is high, other norms (e.g., ℓ 2 -norm can be used to regularize the coding coefficients, except for the sparsity ℓ 1 -norm. In this paper, we show that in the kernel space the nonnegative constraint can also play the same role, and thus suggest the investigation of kernel fully constrained least squares (KFCLS for hyperspectral image classification. Furthermore, in order to improve the classification performance of KFCLS by incorporating spatial-spectral information, we investigate two kinds of spatial-spectral methods using two regularization strategies: (1 the coefficient-level regularization strategy, and (2 the class-level regularization strategy. Experimental results conducted on four real hyperspectral images demonstrate the effectiveness of the proposed KFCLS, and show which way to incorporate spatial-spectral information efficiently in the regularization framework.
Multi-source least-squares migration of marine data
Wang, Xin
2012-11-04
Kirchhoff based multi-source least-squares migration (MSLSM) is applied to marine streamer data. To suppress the crosstalk noise from the excitation of multiple sources, a dynamic encoding function (including both time-shifts and polarity changes) is applied to the receiver side traces. Results show that the MSLSM images are of better quality than the standard Kirchhoff migration and reverse time migration images; moreover, the migration artifacts are reduced and image resolution is significantly improved. The computational cost of MSLSM is about the same as conventional least-squares migration, but its IO cost is significantly decreased.
Global Search Strategies for Solving Multilinear Least-Squares Problems
Directory of Open Access Journals (Sweden)
Mats Andersson
2012-04-01
Full Text Available The multilinear least-squares (MLLS problem is an extension of the linear least-squares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by the results of numerical experiments performed for some problems related to the design of filter networks.
Performance Evaluation of the Ordinary Least Square (OLS) and ...
African Journals Online (AJOL)
Nana Kwasi Peprah
1Deparment of Geomatic Engineering, University of Mines and Technology, ... precise, accurate and can be used to execute any engineering works due to ..... and Ordinary Least Squares Methods”, Journal of Geomatics and Planning, Vol ... Technology”, Unpublished BSc Project Report, University of Mines and Technology ...
Non linear-least-squares fitting for pixe spectra
International Nuclear Information System (INIS)
Benamar, M.A.; Tchantchane, A.; Benouali, N.; Azbouche, A.; Tobbeche, S.
1992-10-01
An interactive computer program for the analysis of Pixe spectra is described. The fitting procedure consists of computing a function which approximates the experimental data. A nonlinear least-squares fitting is used to determine the parameters of the fit. The program takes into account the low energy tail and the escape peaks
Fast Dating Using Least-Squares Criteria and Algorithms.
To, Thu-Hien; Jung, Matthieu; Lycett, Samantha; Gascuel, Olivier
2016-01-01
Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses (e.g., human immunodeficiency virus (HIV)). Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley-Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes. When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint). Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint (i.e., an ancestral node must be older that its daughter nodes) is accounted for. With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time. With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa). In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees. We compare these algorithms to standard methods (root-to-tip, r8s version of Langley-Fitch method, and BEAST). Using simulated data, we show that their estimation accuracy is similar to that
Yuniarto, Budi; Kurniawan, Robert
2017-03-01
PLS Path Modeling (PLS-PM) is different from covariance based SEM, where PLS-PM use an approach based on variance or component, therefore, PLS-PM is also known as a component based SEM. Multiblock Partial Least Squares (MBPLS) is a method in PLS regression which can be used in PLS Path Modeling which known as Multiblock PLS Path Modeling (MBPLS-PM). This method uses an iterative procedure in its algorithm. This research aims to modify MBPLS-PM with Back Propagation Neural Network approach. The result is MBPLS-PM algorithm can be modified using the Back Propagation Neural Network approach to replace the iterative process in backward and forward step to get the matrix t and the matrix u in the algorithm. By modifying the MBPLS-PM algorithm using Back Propagation Neural Network approach, the model parameters obtained are relatively not significantly different compared to model parameters obtained by original MBPLS-PM algorithm.
Finding A Minimally Informative Dirichlet Prior Using Least Squares
International Nuclear Information System (INIS)
Kelly, Dana
2011-01-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson λ, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Finding a minimally informative Dirichlet prior distribution using least squares
International Nuclear Information System (INIS)
Kelly, Dana; Atwood, Corwin
2011-01-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson λ, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Finding a Minimally Informative Dirichlet Prior Distribution Using Least Squares
International Nuclear Information System (INIS)
Kelly, Dana; Atwood, Corwin
2011-01-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straight-forward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in closed form, and so an approximate beta distribution is used in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial aleatory model for common-cause failure, must be estimated from data that is often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
DEFF Research Database (Denmark)
Nolte, Ingmar; Voev, Valeri
The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise...
De Luca, G.; Magnus, J.R.
2011-01-01
In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares
Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim
2018-01-01
The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.
Linearized least-square imaging of internally scattered data
Aldawood, Ali; Hoteit, Ibrahim; Turkiyyah, George M.; Zuberi, M. A H; Alkhalifah, Tariq Ali
2014-01-01
Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single-scattering energy such as nearly vertical faults. Standard migration of these multiples provide subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. Hence, we apply a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. Application to synthetic data demonstrated the effectiveness of the proposed inversion in imaging a reflector that is poorly illuminated by single-scattering energy. The least-square inversion of doublescattered data helped delineate that reflector with minimal acquisition fingerprint.
Least squares orthogonal polynomial approximation in several independent variables
International Nuclear Information System (INIS)
Caprari, R.S.
1992-06-01
This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab
Liu, L. H.; Tan, J. Y.
2007-02-01
A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.
International Nuclear Information System (INIS)
Liu, L.H.; Tan, J.Y.
2007-01-01
A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media
Solving linear inequalities in a least squares sense
Energy Technology Data Exchange (ETDEWEB)
Bramley, R.; Winnicka, B. [Indiana Univ., Bloomington, IN (United States)
1994-12-31
Let A {element_of} {Re}{sup mxn} be an arbitrary real matrix, and let b {element_of} {Re}{sup m} a given vector. A familiar problem in computational linear algebra is to solve the system Ax = b in a least squares sense; that is, to find an x* minimizing {parallel}Ax {minus} b{parallel}, where {parallel} {center_dot} {parallel} refers to the vector two-norm. Such an x* solves the normal equations A{sup T}(Ax {minus} b) = 0, and the optimal residual r* = b {minus} Ax* is unique (although x* need not be). The least squares problem is usually interpreted as corresponding to multiple observations, represented by the rows of A and b, on a vector of data x. The observations may be inconsistent, and in this case a solution is sought that minimizes the norm of the residuals. A less familiar problem to numerical linear algebraists is the solution of systems of linear inequalities Ax {le} b in a least squares sense, but the motivation is similar: if a set of observations places upper or lower bounds on linear combinations of variables, the authors want to find x* minimizing {parallel} (Ax {minus} b){sub +} {parallel}, where the i{sup th} component of the vector v{sub +} is the maximum of zero and the i{sup th} component of v.
Comparing implementations of penalized weighted least-squares sinogram restoration
International Nuclear Information System (INIS)
Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick
2010-01-01
Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix
Analysis of total least squares in estimating the parameters of a mortar trajectory
Energy Technology Data Exchange (ETDEWEB)
Lau, D.L.; Ng, L.C.
1994-12-01
Least Squares (LS) is a method of curve fitting used with the assumption that error exists in the observation vector. The method of Total Least Squares (TLS) is more useful in cases where there is error in the data matrix as well as the observation vector. This paper describes work done in comparing the LS and TLS results for parameter estimation of a mortar trajectory based on a time series of angular observations. To improve the results, we investigated several derivations of the LS and TLS methods, and early findings show TLS provided slightly, 10%, improved results over the LS method.
A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment
Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong
Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.
Stable Galerkin versus equal-order Galerkin least-squares elements for the stokes flow problem
International Nuclear Information System (INIS)
Franca, L.P.; Frey, S.L.; Sampaio, R.
1989-11-01
Numerical experiments are performed for the stokes flow problem employing a stable Galerkin method and a Galerkin/Least-squares method with equal-order elements. Error estimates for the methods tested herein are reviewed. The numerical results presented attest the good stability properties of all methods examined herein. (A.C.A.S.) [pt
FC LSEI WNNLS, Least-Square Fitting Algorithms Using B Splines
International Nuclear Information System (INIS)
Hanson, R.J.; Haskell, K.H.
1989-01-01
1 - Description of problem or function: FC allows a user to fit dis- crete data, in a weighted least-squares sense, using piece-wise polynomial functions represented by B-Splines on a given set of knots. In addition to the least-squares fitting of the data, equality, inequality, and periodic constraints at a discrete, user-specified set of points can be imposed on the fitted curve or its derivatives. The subprograms LSEI and WNNLS solve the linearly-constrained least-squares problem. LSEI solves the class of problem with general inequality constraints, and, if requested, obtains a covariance matrix of the solution parameters. WNNLS solves the class of problem with non-negativity constraints. It is anticipated that most users will find LSEI suitable for their needs; however, users with inequalities that are single bounds on variables may wish to use WNNLS. 2 - Method of solution: The discrete data are fit by a linear combination of piece-wise polynomial curves which leads to a linear least-squares system of algebraic equations. Additional information is expressed as a discrete set of linear inequality and equality constraints on the fitted curve which leads to a linearly-constrained least-squares system of algebraic equations. The solution of this system is the main computational problem solved
The possibilities of least-squares migration of internally scattered seismic energy
Aldawood, Ali
2015-05-26
Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.
The possibilities of least-squares migration of internally scattered seismic energy
Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad; Turkiyyah, George; Alkhalifah, Tariq Ali
2015-01-01
Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.
Energy Technology Data Exchange (ETDEWEB)
Park, Chang Je [Sejong Univ., Seoul (Korea, Republic of); Alkhatee, Sari; Roh, Gyuhong; Lee, Byungchul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-05-15
Dose absorption and energy absorption buildup factors are widely used in the shielding analysis. The dose rate of the medium is main concern in the dose buildup factor, however energy absorption is an important parameter in the energy buildup factors. ANSI/ANS-6.4.3-1991 standard data is widely used based on interpolation and extrapolation by means of an approximation method. Recently, Yoshida's geometric progression (GP) formulae are also popular and it is already implemented in QAD code. In the QAD code, two buildup factors are notated as DOSE for standard air exposure response and ENG for the response of the energy absorbed in the material itself. In this paper, a new least square fitting method is suggested to obtain a reliable buildup factors proposed since 1991. Total 4 datasets of air exposure buildup factors are used for evaluation including ANSI/ANS-6.4.3-1991, Taylor, Berger, and GP data. The standard deviation of the fitted data are analyzed based on the results. A new reverse least square fitting method is proposed in this study in order to reduce the fitting uncertainties. It adapts an inverse function rather than the original function by the distribution slope of dataset. Some quantitative comparisons are provided for concrete and lead in this paper, too. This study is focused on the least square fitting of existing buildup factors to be utilized in the point-kernel code for radiation shielding analysis. The inverse least square fitting method is suggested to obtain more reliable results of concave shaped dataset such as concrete. In the concrete case, the variance and residue are decreased significantly, too. However, the convex shaped case of lead can be applied to the usual least square fitting method. In the future, more datasets will be tested by using the least square fitting. And the fitted data could be implemented to the existing point-kernel codes.
Directory of Open Access Journals (Sweden)
Jian Chai
2015-01-01
Full Text Available This paper proposes an EMD-LSSVM (empirical mode decomposition least squares support vector machine model to analyze the CSI 300 index. A WD-LSSVM (wavelet denoising least squares support machine is also proposed as a benchmark to compare with the performance of EMD-LSSVM. Since parameters selection is vital to the performance of the model, different optimization methods are used, including simplex, GS (grid search, PSO (particle swarm optimization, and GA (genetic algorithm. Experimental results show that the EMD-LSSVM model with GS algorithm outperforms other methods in predicting stock market movement direction.
Nolte, Ingmar; Voev, Valeri
2009-01-01
The expected value of sums of squared intraday returns (realized variance)gives rise to a least squares regression which adapts itself to the assumptions ofthe noise process and allows for a joint inference on integrated volatility (IV),noise moments and price-noise relations. In the iid noise case we derive theasymptotic variance of the regression parameter estimating the IV, show thatit is consistent and compare its asymptotic efficiency against alternative consistentIV measures. In case of...
Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions
International Nuclear Information System (INIS)
Zhu Menghua; Liu Lianggang; Qi Dongxu; You Zhong; Xu Aoao
2009-01-01
In this paper, the least square fitting method with the cubic B-spline basis functions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation. (authors)
An Incremental Weighted Least Squares Approach to Surface Lights Fields
Coombe, Greg; Lastra, Anselmo
An Image-Based Rendering (IBR) approach to appearance modelling enables the capture of a wide variety of real physical surfaces with complex reflectance behaviour. The challenges with this approach are handling the large amount of data, rendering the data efficiently, and previewing the model as it is being constructed. In this paper, we introduce the Incremental Weighted Least Squares approach to the representation and rendering of spatially and directionally varying illumination. Each surface patch consists of a set of Weighted Least Squares (WLS) node centers, which are low-degree polynomial representations of the anisotropic exitant radiance. During rendering, the representations are combined in a non-linear fashion to generate a full reconstruction of the exitant radiance. The rendering algorithm is fast, efficient, and implemented entirely on the GPU. The construction algorithm is incremental, which means that images are processed as they arrive instead of in the traditional batch fashion. This human-in-the-loop process enables the user to preview the model as it is being constructed and to adapt to over-sampling and under-sampling of the surface appearance.
Decision-Directed Recursive Least Squares MIMO Channels Tracking
Directory of Open Access Journals (Sweden)
Karami Ebrahim
2006-01-01
Full Text Available A new approach for joint data estimation and channel tracking for multiple-input multiple-output (MIMO channels is proposed based on the decision-directed recursive least squares (DD-RLS algorithm. RLS algorithm is commonly used for equalization and its application in channel estimation is a novel idea. In this paper, after defining the weighted least squares cost function it is minimized and eventually the RLS MIMO channel estimation algorithm is derived. The proposed algorithm combined with the decision-directed algorithm (DDA is then extended for the blind mode operation. From the computational complexity point of view being versus the number of transmitter and receiver antennas, the proposed algorithm is very efficient. Through various simulations, the mean square error (MSE of the tracking of the proposed algorithm for different joint detection algorithms is compared with Kalman filtering approach which is one of the most well-known channel tracking algorithms. It is shown that the performance of the proposed algorithm is very close to Kalman estimator and that in the blind mode operation it presents a better performance with much lower complexity irrespective of the need to know the channel model.
Plane-wave least-squares reverse-time migration
Dai, Wei
2013-06-03
A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reversetime migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors. © 2013 Society of Exploration Geophysicists.
Making the most out of least-squares migration
Huang, Yunsong
2014-09-01
Standard migration images can suffer from (1) migration artifacts caused by an undersampled acquisition geometry, (2) poor resolution resulting from a limited recording aperture, (3) ringing artifacts caused by ripples in the source wavelet, and (4) weak amplitudes resulting from geometric spreading, attenuation, and defocusing. These problems can be remedied in part by least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), which aims to linearly invert seismic data for the reflectivity distribution. Given a sufficiently accurate migration velocity model, LSM can mitigate many of the above problems and can produce more resolved migration images, sometimes with more than twice the spatial resolution of standard migration. However, LSM faces two challenges: The computational cost can be an order of magnitude higher than that of standard migration, and the resulting image quality can fail to improve for migration velocity errors of about 5% or more. It is possible to obtain the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.
Making the most out of the least (squares migration)
Dutta, Gaurav
2014-08-05
Standard migration images can suffer from migration artifacts due to 1) poor source-receiver sampling, 2) weak amplitudes caused by geometric spreading, 3) attenuation, 4) defocusing, 5) poor resolution due to limited source-receiver aperture, and 6) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution. If the migration velocity model is sufficiently accurate, then LSM can mitigate many of the above problems and lead to a more resolved migration image, sometimes with twice the spatial resolution. However, there are two problems with LSM: the cost can be an order of magnitude more than standard migration and the quality of the LSM image is no better than the standard image for velocity errors of 5% or more. We now show how to get the most from least-squares migration by reducing the cost and velocity sensitivity of LSM.
Efficient Model Selection for Sparse Least-Square SVMs
Directory of Open Access Journals (Sweden)
Xiao-Lei Xia
2013-01-01
Full Text Available The Forward Least-Squares Approximation (FLSA SVM is a newly-emerged Least-Square SVM (LS-SVM whose solution is extremely sparse. The algorithm uses the number of support vectors as the regularization parameter and ensures the linear independency of the support vectors which span the solution. This paper proposed a variant of the FLSA-SVM, namely, Reduced FLSA-SVM which is of reduced computational complexity and memory requirements. The strategy of “contexts inheritance” is introduced to improve the efficiency of tuning the regularization parameter for both the FLSA-SVM and the RFLSA-SVM algorithms. Experimental results on benchmark datasets showed that, compared to the SVM and a number of its variants, the RFLSA-SVM solutions contain a reduced number of support vectors, while maintaining competitive generalization abilities. With respect to the time cost for tuning of the regularize parameter, the RFLSA-SVM algorithm was empirically demonstrated fastest compared to FLSA-SVM, the LS-SVM, and the SVM algorithms.
Directory of Open Access Journals (Sweden)
KADEK DWI FARMANI
2012-09-01
Full Text Available Linear regression analysis is one of the parametric statistical methods which utilize the relationship between two or more quantitative variables. In linear regression analysis, there are several assumptions that must be met that is normal distribution of errors, there is no correlation between the error and error variance is constant and homogent. There are some constraints that caused the assumption can not be met, for example, the correlation between independent variables (multicollinearity, constraints on the number of data and independent variables are obtained. When the number of samples obtained less than the number of independent variables, then the data is called the microarray data. Least Absolute shrinkage and Selection Operator (LASSO and Partial Least Squares (PLS is a statistical method that can be used to overcome the microarray, overfitting, and multicollinearity. From the above description, it is necessary to study with the intention of comparing LASSO and PLS method. This study uses coronary heart and stroke patients data which is a microarray data and contain multicollinearity. With these two characteristics of the data that most have a weak correlation between independent variables, LASSO method produces a better model than PLS seen from the large RMSEP.
Directory of Open Access Journals (Sweden)
Margaretha Ohyver
2014-12-01
Full Text Available Multicollinearity and outliers are the common problems when estimating regression model. Multicollinearitiy occurs when there are high correlations among predictor variables, leading to difficulties in separating the effects of each independent variable on the response variable. While, if outliers are present in the data to be analyzed, then the assumption of normality in the regression will be violated and the results of the analysis may be incorrect or misleading. Both of these cases occurred in the data on room occupancy rate of hotels in Kendari. The purpose of this study is to find a model for the data that is free of multicollinearity and outliers and to determine the factors that affect the level of room occupancy hotels in Kendari. The method used is Continuous Wavelet Transformation and Partial Least Squares. The result of this research is a regression model that is free of multicollinearity and a pattern of data that resolved the present of outliers.
International Nuclear Information System (INIS)
Haddad, Khaled; Egodawatta, Prasanna; Rahman, Ataur; Goonetilleke, Ashantha
2013-01-01
Reliable pollutant build-up prediction plays a critical role in the accuracy of urban stormwater quality modelling outcomes. However, water quality data collection is resource demanding compared to streamflow data monitoring, where a greater quantity of data is generally available. Consequently, available water quality datasets span only relatively short time scales unlike water quantity data. Therefore, the ability to take due consideration of the variability associated with pollutant processes and natural phenomena is constrained. This in turn gives rise to uncertainty in the modelling outcomes as research has shown that pollutant loadings on catchment surfaces and rainfall within an area can vary considerably over space and time scales. Therefore, the assessment of model uncertainty is an essential element of informed decision making in urban stormwater management. This paper presents the application of a range of regression approaches such as ordinary least squares regression, weighted least squares regression and Bayesian weighted least squares regression for the estimation of uncertainty associated with pollutant build-up prediction using limited datasets. The study outcomes confirmed that the use of ordinary least squares regression with fixed model inputs and limited observational data may not provide realistic estimates. The stochastic nature of the dependent and independent variables need to be taken into consideration in pollutant build-up prediction. It was found that the use of the Bayesian approach along with the Monte Carlo simulation technique provides a powerful tool, which attempts to make the best use of the available knowledge in prediction and thereby presents a practical solution to counteract the limitations which are otherwise imposed on water quality modelling. - Highlights: ► Water quality data spans short time scales leading to significant model uncertainty. ► Assessment of uncertainty essential for informed decision making in water
Chkifa, Abdellah; Cohen, Albert; Migliorati, Giovanni; Nobile, Fabio; Tempone, Raul
2015-01-01
shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R. Tempone
A rigid-body least-squares program with angular and translation scan facilities
Kutschabsky, L
1981-01-01
The described computer program, written in CERN Fortran, is designed to enlarge the convergence radius of the rigid-body least-squares method by allowing a stepwise change of the angular and/or translational parameters within a chosen range. (6 refs).
Risk and Management Control: A Partial Least Square Modelling Approach
DEFF Research Database (Denmark)
Nielsen, Steen; Pontoppidan, Iens Christian
Risk and economic theory goes many year back (e.g. to Keynes & Knight 1921) and risk/uncertainty belong to one of the explanations for the existence of the firm (Coarse, 1937). The present financial crisis going on in the past years have re-accentuated risk and the need of coherence...... and interrelations between risk and areas within management accounting. The idea is that management accounting should be able to conduct a valid feed forward but also predictions for decision making including risk. This study reports the test of a theoretical model using partial least squares (PLS) on survey data...... and a external attitude dimension. The results have important implications for both management control research and for the management control systems design for the way accountants consider the element of risk in their different tasks, both operational and strategic. Specifically, it seems that different risk...
Consistent Partial Least Squares Path Modeling via Regularization.
Jung, Sunho; Park, JaeHong
2018-01-01
Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.
An information geometric approach to least squares minimization
Transtrum, Mark; Machta, Benjamin; Sethna, James
2009-03-01
Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.
Improved linear least squares estimation using bounded data uncertainty
Ballal, Tarig
2015-04-01
This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.
Regularized plane-wave least-squares Kirchhoff migration
Wang, Xin
2013-09-22
A Kirchhoff least-squares migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images. A regularization term is included that accounts for mispositioning of reflectors due to errors in the velocity model. Both synthetic and field results show that: 1) LSM with a reflectivity model common for all the plane-wave gathers provides the best image when the migration velocity model is accurate, but it is more sensitive to the velocity errors, 2) the regularized plane-wave LSM is more robust in the presence of velocity errors, and 3) LSM achieves both computational and IO saving by plane-wave encoding compared to shot-domain LSM for the models tested.
Improved linear least squares estimation using bounded data uncertainty
Ballal, Tarig; Al-Naffouri, Tareq Y.
2015-01-01
This paper addresses the problemof linear least squares (LS) estimation of a vector x from linearly related observations. In spite of being unbiased, the original LS estimator suffers from high mean squared error, especially at low signal-to-noise ratios. The mean squared error (MSE) of the LS estimator can be improved by introducing some form of regularization based on certain constraints. We propose an improved LS (ILS) estimator that approximately minimizes the MSE, without imposing any constraints. To achieve this, we allow for perturbation in the measurement matrix. Then we utilize a bounded data uncertainty (BDU) framework to derive a simple iterative procedure to estimate the regularization parameter. Numerical results demonstrate that the proposed BDU-ILS estimator is superior to the original LS estimator, and it converges to the best linear estimator, the linear-minimum-mean-squared error estimator (LMMSE), when the elements of x are statistically white.
Using the Linear Least Square Method in determining the ...
African Journals Online (AJOL)
This study was aimed at generating a mathematical relationship connecting four quality parameters of water, namely salinity, electrical conductivity, density and pH. Samples of surface water and ground water were collected from eight major towns in Delta State, Nigeria. Measurements of the parameters were carried out ...
Andries, Jan P M; Vander Heyden, Yvan; Buydens, Lutgarde M C
2011-10-31
The calibration performance of partial least squares for one response variable (PLS1) can be improved by elimination of uninformative variables. Many methods are based on so-called predictive variable properties, which are functions of various PLS-model parameters, and which may change during the variable reduction process. In these methods variable reduction is made on the variables ranked in descending order for a given variable property. The methods start with full spectrum modelling. Iteratively, until a specified number of remaining variables is reached, the variable with the smallest property value is eliminated; a new PLS model is calculated, followed by a renewed ranking of the variables. The Stepwise Variable Reduction methods using Predictive-Property-Ranked Variables are denoted as SVR-PPRV. In the existing SVR-PPRV methods the PLS model complexity is kept constant during the variable reduction process. In this study, three new SVR-PPRV methods are proposed, in which a possibility for decreasing the PLS model complexity during the variable reduction process is build in. Therefore we denote our methods as PPRVR-CAM methods (Predictive-Property-Ranked Variable Reduction with Complexity Adapted Models). The selective and predictive abilities of the new methods are investigated and tested, using the absolute PLS regression coefficients as predictive property. They were compared with two modifications of existing SVR-PPRV methods (with constant PLS model complexity) and with two reference methods: uninformative variable elimination followed by either a genetic algorithm for PLS (UVE-GA-PLS) or an interval PLS (UVE-iPLS). The performance of the methods is investigated in conjunction with two data sets from near-infrared sources (NIR) and one simulated set. The selective and predictive performances of the variable reduction methods are compared statistically using the Wilcoxon signed rank test. The three newly developed PPRVR-CAM methods were able to retain
Chkifa, Abdellah
2015-04-08
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R. Tempone, Found. Comput. Math. 14 (2014) 419–456], under suitable conditions that relate the number of samples with respect to the dimension of the polynomial space. Here “quasi-optimal” means that the accuracy of the least-squares approximation is comparable with that of the best approximation in the given polynomial space. In this paper, we discuss the quasi-optimality of the polynomial least-squares method in arbitrary dimension. Our analysis applies to any arbitrary multivariate polynomial space (including tensor product, total degree or hyperbolic crosses), under the minimal requirement that its associated index set is downward closed. The optimality criterion only involves the relation between the number of samples and the dimension of the polynomial space, independently of the anisotropic shape and of the number of variables. We extend our results to the approximation of Hilbert space-valued functions in order to apply them to the approximation of parametric and stochastic elliptic PDEs. As a particular case, we discuss “inclusion type” elliptic PDE models, and derive an exponential convergence estimate for the least-squares method. Numerical results confirm our estimate, yet pointing out a gap between the condition necessary to achieve optimality in the theory, and the condition that in practice yields the optimal convergence rate.
Directory of Open Access Journals (Sweden)
Margaretha Ohyver
2016-12-01
Full Text Available Partial Least Squares (PLS method was developed in 1960 by Herman Wold. The method particularly suits with construct a regression model when the number of independent variables is many and highly collinear. The PLS can be combined with other methods, one of which is a Continuous Wavelet Transformation (CWT. By considering that the presence of outliers can lead to a less reliable model, and this kind of transformation may be required at a stage of pre-processing, the data is free of noise or outliers. Based on the previous study, Kendari hotel room occupancy rate was affected by the outlier, and it had a low value of R2. Therefore, this research aimed to obtain a good model by combining the PLS method and CWT transformation using the Mexican Hats them other wavelet of CWT. The research concludes that merging the PLS and the Mexican Hat transformation has resulted in a better model compared to the model that combined the PLS and the Haar wavelet transformation as shown in the previous study. The research shows that by changing the mother of the wavelet, the value of R2 can be improved significantly. The result provides information on how to increase the value of R2. The other advantage is the information for hotel managements to notice the age of the hotel, the maximum rates, the facilities, and the number of rooms to increase the number of visitors.
Prediction of toxicity of nitrobenzenes using ab initio and least squares support vector machines
International Nuclear Information System (INIS)
Niazi, Ali; Jameh-Bozorghi, Saeed; Nori-Shargh, Davood
2008-01-01
A quantitative structure-property relationship (QSPR) study is suggested for the prediction of toxicity (IGC 50 ) of nitrobenzenes. Ab initio theory was used to calculate some quantum chemical descriptors including electrostatic potentials and local charges at each atom, HOMO and LUMO energies, etc. Modeling of the IGC 50 of nitrobenzenes as a function of molecular structures was established by means of the least squares support vector machines (LS-SVM). This model was applied for the prediction of the toxicity (IGC 50 ) of nitrobenzenes, which were not in the modeling procedure. The resulted model showed high prediction ability with root mean square error of prediction of 0.0049 for LS-SVM. Results have shown that the introduction of LS-SVM for quantum chemical descriptors drastically enhances the ability of prediction in QSAR studies superior to multiple linear regression and partial least squares
Kim, Sanghong; Kano, Manabu; Nakagawa, Hiroshi; Hasebe, Shinji
2011-12-15
Development of quality estimation models using near infrared spectroscopy (NIRS) and multivariate analysis has been accelerated as a process analytical technology (PAT) tool in the pharmaceutical industry. Although linear regression methods such as partial least squares (PLS) are widely used, they cannot always achieve high estimation accuracy because physical and chemical properties of a measuring object have a complex effect on NIR spectra. In this research, locally weighted PLS (LW-PLS) which utilizes a newly defined similarity between samples is proposed to estimate active pharmaceutical ingredient (API) content in granules for tableting. In addition, a statistical wavelength selection method which quantifies the effect of API content and other factors on NIR spectra is proposed. LW-PLS and the proposed wavelength selection method were applied to real process data provided by Daiichi Sankyo Co., Ltd., and the estimation accuracy was improved by 38.6% in root mean square error of prediction (RMSEP) compared to the conventional PLS using wavelengths selected on the basis of variable importance on the projection (VIP). The results clearly show that the proposed calibration modeling technique is useful for API content estimation and is superior to the conventional one. Copyright © 2011 Elsevier B.V. All rights reserved.
Consistent Partial Least Squares Path Modeling via Regularization
Directory of Open Access Journals (Sweden)
Sunho Jung
2018-02-01
Full Text Available Partial least squares (PLS path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc, designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.
BER analysis of regularized least squares for BPSK recovery
Ben Atitallah, Ismail; Thrampoulidis, Christos; Kammoun, Abla; Al-Naffouri, Tareq Y.; Hassibi, Babak; Alouini, Mohamed-Slim
2017-01-01
This paper investigates the problem of recovering an n-dimensional BPSK signal x
BER analysis of regularized least squares for BPSK recovery
Ben Atitallah, Ismail
2017-06-20
This paper investigates the problem of recovering an n-dimensional BPSK signal x
Robust regularized least-squares beamforming approach to signal estimation
Suliman, Mohamed Abdalla Elhag
2017-05-12
In this paper, we address the problem of robust adaptive beamforming of signals received by a linear array. The challenge associated with the beamforming problem is twofold. Firstly, the process requires the inversion of the usually ill-conditioned covariance matrix of the received signals. Secondly, the steering vector pertaining to the direction of arrival of the signal of interest is not known precisely. To tackle these two challenges, the standard capon beamformer is manipulated to a form where the beamformer output is obtained as a scaled version of the inner product of two vectors. The two vectors are linearly related to the steering vector and the received signal snapshot, respectively. The linear operator, in both cases, is the square root of the covariance matrix. A regularized least-squares (RLS) approach is proposed to estimate these two vectors and to provide robustness without exploiting prior information. Simulation results show that the RLS beamformer using the proposed regularization algorithm outperforms state-of-the-art beamforming algorithms, as well as another RLS beamformers using a standard regularization approaches.
3D plane-wave least-squares Kirchhoff migration
Wang, Xin
2014-08-05
A three dimensional least-squares Kirchhoff migration (LSM) is developed in the prestack plane-wave domain to increase the quality of migration images and the computational efficiency. Due to the limitation of current 3D marine acquisition geometries, a cylindrical-wave encoding is adopted for the narrow azimuth streamer data. To account for the mispositioning of reflectors due to errors in the velocity model, a regularized LSM is devised so that each plane-wave or cylindrical-wave gather gives rise to an individual migration image, and a regularization term is included to encourage the similarities between the migration images of similar encoding schemes. Both synthetic and field results show that: 1) plane-wave or cylindrical-wave encoding LSM can achieve both computational and IO saving, compared to shot-domain LSM, however, plane-wave LSM is still about 5 times more expensive than plane-wave migration; 2) the regularized LSM is more robust compared to LSM with one reflectivity model common for all the plane-wave or cylindrical-wave gathers.
Least squares shadowing sensitivity analysis of a modified Kuramoto–Sivashinsky equation
International Nuclear Information System (INIS)
Blonigan, Patrick J.; Wang, Qiqi
2014-01-01
Highlights: •Modifying the Kuramoto–Sivashinsky equation and changing its boundary conditions make it an ergodic dynamical system. •The modified Kuramoto–Sivashinsky equation exhibits distinct dynamics for three different ranges of system parameters. •Least squares shadowing sensitivity analysis computes accurate gradients for a wide range of system parameters. - Abstract: Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters
Directory of Open Access Journals (Sweden)
Xisheng Yu
2014-01-01
Full Text Available The paper by Liu (2010 introduces a method termed the canonical least-squares Monte Carlo (CLM which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.
Constrained Balancing of Two Industrial Rotor Systems: Least Squares and Min-Max Approaches
Directory of Open Access Journals (Sweden)
Bin Huang
2009-01-01
Full Text Available Rotor vibrations caused by rotor mass unbalance distributions are a major source of maintenance problems in high-speed rotating machinery. Minimizing this vibration by balancing under practical constraints is quite important to industry. This paper considers balancing of two large industrial rotor systems by constrained least squares and min-max balancing methods. In current industrial practice, the weighted least squares method has been utilized to minimize rotor vibrations for many years. One of its disadvantages is that it cannot guarantee that the maximum value of vibration is below a specified value. To achieve better balancing performance, the min-max balancing method utilizing the Second Order Cone Programming (SOCP with the maximum correction weight constraint, the maximum residual response constraint as well as the weight splitting constraint has been utilized for effective balancing. The min-max balancing method can guarantee a maximum residual vibration value below an optimum value and is shown by simulation to significantly outperform the weighted least squares method.
Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres
Abdelrahman, E. M.; El-Araby, T. M.; Soliman, K. S.; Essa, K. S.; Abo-Ezz, E. R.
2007-05-01
We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.
Least squares methodology applied to LWR-PV damage dosimetry, experience and expectations
International Nuclear Information System (INIS)
Wagschal, J.J.; Broadhead, B.L.; Maerker, R.E.
1979-01-01
The development of an advanced methodology for Light Water Reactors (LWR) Pressure Vessel (PV) damage dosimetry applications is the subject of an ongoing EPRI-sponsored research project at ORNL. This methodology includes a generalized least squares approach to a combination of data. The data include measured foil activations, evaluated cross sections and calculated fluxes. The uncertainties associated with the data as well as with the calculational methods are an essential component of this methodology. Activation measurements in two NBS benchmark neutron fields ( 252 Cf ISNF) and in a prototypic reactor field (Oak Ridge Pool Critical Assembly - PCA) are being analyzed using a generalized least squares method. The sensitivity of the results to the representation of the uncertainties (covariances) was carefully checked. Cross element covariances were found to be of utmost importance
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2003-01-01
We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation
Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine
International Nuclear Information System (INIS)
Xu Ruirui; Bian Guoxing; Gao Chenfeng; Chen Tianlun
2005-01-01
The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.
Use of correspondence analysis partial least squares on linear and unimodal data
DEFF Research Database (Denmark)
Frisvad, Jens Christian; Norsker, Merete
1996-01-01
Correspondence analysis partial least squares (CA-PLS) has been compared with PLS conceming classification and prediction of unimodal growth temperature data and an example using infrared (IR) spectroscopy for predicting amounts of chemicals in mixtures. CA-PLS was very effective for ordinating...... that could only be seen in two-dimensional plots, and also less effective predictions. PLS was the best method in the linear case treated, with fewer components and a better prediction than CA-PLS....
Incoherent dictionary learning for reducing crosstalk noise in least-squares reverse time migration
Wu, Juan; Bai, Min
2018-05-01
We propose to apply a novel incoherent dictionary learning (IDL) algorithm for regularizing the least-squares inversion in seismic imaging. The IDL is proposed to overcome the drawback of traditional dictionary learning algorithm in losing partial texture information. Firstly, the noisy image is divided into overlapped image patches, and some random patches are extracted for dictionary learning. Then, we apply the IDL technology to minimize the coherency between atoms during dictionary learning. Finally, the sparse representation problem is solved by a sparse coding algorithm, and image is restored by those sparse coefficients. By reducing the correlation among atoms, it is possible to preserve most of the small-scale features in the image while removing much of the long-wavelength noise. The application of the IDL method to regularization of seismic images from least-squares reverse time migration shows successful performance.
Doppler-shift estimation of flat underwater channel using data-aided least-square approach
Directory of Open Access Journals (Sweden)
Weiqiang Pan
2015-03-01
Full Text Available In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.
Doppler-shift estimation of flat underwater channel using data-aided least-square approach
Pan, Weiqiang; Liu, Ping; Chen, Fangjiong; Ji, Fei; Feng, Jing
2015-06-01
In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB) of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.
Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model
Directory of Open Access Journals (Sweden)
WANG Bin
2015-06-01
Full Text Available Based on the Newton-Gauss iterative algorithm of weighted total least squares (WTLS, a robust WTLS (RWTLS model is presented. The model utilizes the standardized residuals to construct the weight factor function and the square root of the variance component estimator with robustness is obtained by introducing the median method. Therefore, the robustness in both the observation and structure spaces can be simultaneously achieved. To obtain standardized residuals, the linearly approximate cofactor propagation law is employed to derive the expression of the cofactor matrix of WTLS residuals. The iterative calculation steps for RWTLS are also described. The experiment indicates that the model proposed in this paper exhibits satisfactory robustness for gross errors handling problem of WTLS, the obtained parameters have no significant difference with the results of WTLS without gross errors. Therefore, it is superior to the robust weighted total least squares model directly constructed with residuals.
International Nuclear Information System (INIS)
Chen Qiang; Ren Xuemei; Na Jing
2011-01-01
Highlights: Model uncertainty of the system is approximated by multiple-kernel LSSVM. Approximation errors and disturbances are compensated in the controller design. Asymptotical anti-synchronization is achieved with model uncertainty and disturbances. Abstract: In this paper, we propose a robust anti-synchronization scheme based on multiple-kernel least squares support vector machine (MK-LSSVM) modeling for two uncertain chaotic systems. The multiple-kernel regression, which is a linear combination of basic kernels, is designed to approximate system uncertainties by constructing a multiple-kernel Lagrangian function and computing the corresponding regression parameters. Then, a robust feedback control based on MK-LSSVM modeling is presented and an improved update law is employed to estimate the unknown bound of the approximation error. The proposed control scheme can guarantee the asymptotic convergence of the anti-synchronization errors in the presence of system uncertainties and external disturbances. Numerical examples are provided to show the effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Sanchez Miro, J J; Sanz Martin, J C
1994-07-01
Obtaining polynomial fittings from observational data in two and three dimensions is an interesting and practical task. Such an arduous problem suggests the development of an automatic code. The main novelty we provide lies in the generalization of the classical least squares method in three FORTRAN 77 programs usable in any sampling problem. Furthermore, we introduce the orthogonal 2D-Legendre function in the fitting process. These FORTRAN 77 programs are equipped with the options to calculate the approximation quality standard indicators, obviously generalized to two and three dimensions (correlation nonlinear factor, confidence intervals, cuadratic mean error, and so on). The aim of this paper is to rectify the absence of fitting algorithms for more than one independent variable in mathematical libraries. (Author) 10 refs.
A least-squares computational ``tool kit``. Nuclear data and measurements series
Energy Technology Data Exchange (ETDEWEB)
Smith, D.L.
1993-04-01
The information assembled in this report is intended to offer a useful computational ``tool kit`` to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications.
Growth kinetics of borided layers: Artificial neural network and least square approaches
Campos, I.; Islas, M.; Ramírez, G.; VillaVelázquez, C.; Mota, C.
2007-05-01
The present study evaluates the growth kinetics of the boride layer Fe 2B in AISI 1045 steel, by means of neural networks and the least square techniques. The Fe 2B phase was formed at the material surface using the paste boriding process. The surface boron potential was modified considering different boron paste thicknesses, with exposure times of 2, 4 and 6 h, and treatment temperatures of 1193, 1223 and 1273 K. The neural network and the least square models were set by the layer thickness of Fe 2B phase, and assuming that the growth of the boride layer follows a parabolic law. The reliability of the techniques used is compared with a set of experiments at a temperature of 1223 K with 5 h of treatment time and boron potentials of 2, 3, 4 and 5 mm. The results of the Fe 2B layer thicknesses show a mean error of 5.31% for the neural network and 3.42% for the least square method.
A cross-correlation objective function for least-squares migration and visco-acoustic imaging
Dutta, Gaurav
2014-08-05
Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.
A cross-correlation objective function for least-squares migration and visco-acoustic imaging
Dutta, Gaurav; Sinha, Mrinal; Schuster, Gerard T.
2014-01-01
Conventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the visco-elastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Qp-LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Qp is insufficiently accurate.
Linear regression methods a ccording to objective functions
Yasemin Sisman; Sebahattin Bektas
2012-01-01
The aim of the study is to explain the parameter estimation methods and the regression analysis. The simple linear regressionmethods grouped according to the objective function are introduced. The numerical solution is achieved for the simple linear regressionmethods according to objective function of Least Squares and theLeast Absolute Value adjustment methods. The success of the appliedmethods is analyzed using their objective function values.
A hybrid partial least squares and random forest approach to ...
African Journals Online (AJOL)
Nicole Reddy
GLCM describes the texture features by the stochastic ... The linear regression model is then fit to the latent variables known as the PLS factors in an .... The hyper-parameter optimization results for all the E. grandis and E.dunnii models ...
Alternative Methods of Regression
Birkes, David
2011-01-01
Of related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts ".an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models.highly recommend[ed].for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." --Technometrics This book provides a balance between theory and practice supported by extensive displays of instructive geometrical constructs. Numerous in-depth case studies illustrate the use of nonlinear regression analysis--with all data s
Proton Exchange Membrane Fuel Cell Modelling Using Moving Least Squares Technique
Directory of Open Access Journals (Sweden)
Radu Tirnovan
2009-07-01
Full Text Available Proton exchange membrane fuel cell, with low polluting emissions, is a great alternative to replace the traditional electrical power sources for automotive applications or for small stationary consumers. This paper presents a numerical method, for the fuel cell modelling, based on moving least squares (MLS. Experimental data have been used for developing an approximated model of the PEMFC function of the current density, air inlet pressure and operating temperature of the fuel cell. The method can be applied for modelling others fuel cell sub-systems, such as the compressor. The method can be used for off-line or on-line identification of the PEMFC stack.
Fault Estimation for Fuzzy Delay Systems: A Minimum Norm Least Squares Solution Approach.
Huang, Sheng-Juan; Yang, Guang-Hong
2017-09-01
This paper mainly focuses on the problem of fault estimation for a class of Takagi-Sugeno fuzzy systems with state delays. A minimum norm least squares solution (MNLSS) approach is first introduced to establish a fault estimation compensator, which is able to optimize the fault estimator. Compared with most of the existing fault estimation methods, the MNLSS-based fault estimation method can effectively decrease the effect of state errors on the accuracy of fault estimation. Finally, three examples are given to illustrate the effectiveness and merits of the proposed method.
Huang, Yunsong; Schuster, Gerard T.
2012-01-01
Multisource migration of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. The accompanying crosstalk noise, in addition to the migration footprint, can be reduced by least-squares inversion. But the application of this approach to marine streamer data is hampered by the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modelling method. This leads to a strong mismatch in the misfit function and results in strong artefacts (crosstalk) in the multisource least-squares migration image. To eliminate this noise, we present a frequency-division multiplexing (FDM) strategy with iterative least-squares migration (ILSM) of supergathers. The key idea is, at each ILSM iteration, to assign a unique frequency band to each shot gather. In this case there is no overlap in the crosstalk spectrum of each migrated shot gather m(x, ω i), so the spectral crosstalk product m(x, ω i)m(x, ω j) =δ i, j is zero, unless i=j. Our results in applying this method to 2D marine data for a SEG/EAGE salt model show better resolved images than standard migration computed at about 1/10 th of the cost. Similar results are achieved after applying this method to synthetic data for a 3D SEG/EAGE salt model, except the acquisition geometry is similar to that of a marine OBS survey. Here, the speedup of this method over conventional migration is more than 10. We conclude that multisource migration for a marine geometry can be successfully achieved by a frequency-division encoding strategy, as long as crosstalk-prone sources are segregated in their spectral content. This is both the strength and the potential limitation of this method. © 2012 European Association of Geoscientists & Engineers.
Huang, Yunsong
2012-05-22
Multisource migration of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. The accompanying crosstalk noise, in addition to the migration footprint, can be reduced by least-squares inversion. But the application of this approach to marine streamer data is hampered by the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modelling method. This leads to a strong mismatch in the misfit function and results in strong artefacts (crosstalk) in the multisource least-squares migration image. To eliminate this noise, we present a frequency-division multiplexing (FDM) strategy with iterative least-squares migration (ILSM) of supergathers. The key idea is, at each ILSM iteration, to assign a unique frequency band to each shot gather. In this case there is no overlap in the crosstalk spectrum of each migrated shot gather m(x, ω i), so the spectral crosstalk product m(x, ω i)m(x, ω j) =δ i, j is zero, unless i=j. Our results in applying this method to 2D marine data for a SEG/EAGE salt model show better resolved images than standard migration computed at about 1/10 th of the cost. Similar results are achieved after applying this method to synthetic data for a 3D SEG/EAGE salt model, except the acquisition geometry is similar to that of a marine OBS survey. Here, the speedup of this method over conventional migration is more than 10. We conclude that multisource migration for a marine geometry can be successfully achieved by a frequency-division encoding strategy, as long as crosstalk-prone sources are segregated in their spectral content. This is both the strength and the potential limitation of this method. © 2012 European Association of Geoscientists & Engineers.
Least Squares Approach to the Alignment of the Generic High Precision Tracking System
de Renstrom, Pawel Brückman; Haywood, Stephen
2006-04-01
A least squares method to solve a generic alignment problem of a high granularity tracking system is presented. The algorithm is based on an analytical linear expansion and allows for multiple nested fits, e.g. imposing a common vertex for groups of particle tracks is of particular interest. We present a consistent and complete recipe to impose constraints on either implicit or explicit parameters. The method has been applied to the full simulation of a subset of the ATLAS silicon tracking system. The ultimate goal is to determine ≈35,000 degrees of freedom (DoF's). We present a limited scale exercise exploring various aspects of the solution.
Combining Approach in Stages with Least Squares for fits of data in hyperelasticity
Beda, Tibi
2006-10-01
The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).
An improved conjugate gradient scheme to the solution of least squares SVM.
Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya
2005-03-01
The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.
Energy Technology Data Exchange (ETDEWEB)
Bloechle, B.; Manteuffel, T.; McCormick, S.; Starke, G.
1996-12-31
Many physical phenomena are modeled as scalar second-order elliptic boundary value problems with discontinuous coefficients. The first-order system least-squares (FOSLS) methodology is an alternative to standard mixed finite element methods for such problems. The occurrence of singularities at interface corners and cross-points requires that care be taken when implementing the least-squares finite element method in the FOSLS context. We introduce two methods of handling the challenges resulting from singularities. The first method is based on a weighted least-squares functional and results in non-conforming finite elements. The second method is based on the use of singular basis functions and results in conforming finite elements. We also share numerical results comparing the two approaches.
Method for nonlinear exponential regression analysis
Junkin, B. G.
1972-01-01
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Discrete Wavelet Transform-Partial Least Squares Versus Derivative ...
African Journals Online (AJOL)
DWT-PLS method was successfully applied for the analysis of raw materials and the dosage form. For. DD1 method ... from each stock standard solutions separately in. 250 mL ..... good agreement with the data indicated in the formulations ...
Performance improvement of shunt active power filter based on non-linear least-square approach
DEFF Research Database (Denmark)
Terriche, Yacine
2018-01-01
. This paper proposes an improved open loop strategy which is unconditionally stable and flexible. The proposed method which is based on non-linear least square (NLS) approach can extract the fundamental voltage and estimates its phase within only half cycle, even in the presence of odd harmonics and dc offset......). The synchronous reference frame (SRF) approach is widely used for generating the RCC due to its simplicity and computation efficiency. However, the SRF approach needs precise information of the voltage phase which becomes a challenge under adverse grid conditions. A typical solution to answer this need...
Sparse least-squares reverse time migration using seislets
Dutta, Gaurav; Schuster, Gerard T.
2015-01-01
the iterations. These dips can be estimated from the standard migration image or from the gradient using plane-wave destruction filters or structural tensors. Numerical tests on synthetic datasets demonstrate the benefits of this method for mitigation of aliasing
Testing measurement invariance of composites using partial least squares
Henseler, Jörg; Ringle, Christian M.; Sarstedt, Marko
2016-01-01
Purpose Research on international marketing usually involves comparing different groups of respondents. When using structural equation modeling (SEM), group comparisons can be misleading unless researchers establish the invariance of their measures. While methods have been proposed to analyze
Ridge regression estimator: combining unbiased and ordinary ridge regression methods of estimation
Directory of Open Access Journals (Sweden)
Sharad Damodar Gore
2009-10-01
Full Text Available Statistical literature has several methods for coping with multicollinearity. This paper introduces a new shrinkage estimator, called modified unbiased ridge (MUR. This estimator is obtained from unbiased ridge regression (URR in the same way that ordinary ridge regression (ORR is obtained from ordinary least squares (OLS. Properties of MUR are derived. Results on its matrix mean squared error (MMSE are obtained. MUR is compared with ORR and URR in terms of MMSE. These results are illustrated with an example based on data generated by Hoerl and Kennard (1975.
Anderson, R. B.; Clegg, S. M.; Frydenvang, J.
2015-12-01
One of the primary challenges faced by the ChemCam instrument on the Curiosity Mars rover is developing a regression model that can accurately predict the composition of the wide range of target types encountered (basalts, calcium sulfate, feldspar, oxides, etc.). The original calibration used 69 rock standards to train a partial least squares (PLS) model for each major element. By expanding the suite of calibration samples to >400 targets spanning a wider range of compositions, the accuracy of the model was improved, but some targets with "extreme" compositions (e.g. pure minerals) were still poorly predicted. We have therefore developed a simple method, referred to as "submodel PLS", to improve the performance of PLS across a wide range of target compositions. In addition to generating a "full" (0-100 wt.%) PLS model for the element of interest, we also generate several overlapping submodels (e.g. for SiO2, we generate "low" (0-50 wt.%), "mid" (30-70 wt.%), and "high" (60-100 wt.%) models). The submodels are generally more accurate than the "full" model for samples within their range because they are able to adjust for matrix effects that are specific to that range. To predict the composition of an unknown target, we first predict the composition with the submodels and the "full" model. Then, based on the predicted composition from the "full" model, the appropriate submodel prediction can be used (e.g. if the full model predicts a low composition, use the "low" model result, which is likely to be more accurate). For samples with "full" predictions that occur in a region of overlap between submodels, the submodel predictions are "blended" using a simple linear weighted sum. The submodel PLS method shows improvements in most of the major elements predicted by ChemCam and reduces the occurrence of negative predictions for low wt.% targets. Submodel PLS is currently being used in conjunction with ICA regression for the major element compositions of ChemCam data.
Wave-equation Q tomography and least-squares migration
Dutta, Gaurav
2016-01-01
optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through
Partial least squares path modeling basic concepts, methodological issues and applications
Noonan, Richard
2017-01-01
This edited book presents the recent developments in partial least squares-path modeling (PLS-PM) and provides a comprehensive overview of the current state of the most advanced research related to PLS-PM. The first section of this book emphasizes the basic concepts and extensions of the PLS-PM method. The second section discusses the methodological issues that are the focus of the recent development of the PLS-PM method. The third part discusses the real world application of the PLS-PM method in various disciplines. The contributions from expert authors in the field of PLS focus on topics such as the factor-based PLS-PM, the perfect match between a model and a mode, quantile composite-based path modeling (QC-PM), ordinal consistent partial least squares (OrdPLSc), non-symmetrical composite-based path modeling (NSCPM), modern view for mediation analysis in PLS-PM, a multi-method approach for identifying and treating unobserved heterogeneity, multigroup analysis (PLS-MGA), the assessment of the common method b...
International Nuclear Information System (INIS)
Pan, Bing; Wu, Dafang; Wang, Zhaoyang
2012-01-01
As a novel tool for quantitative 3D internal deformation measurement throughout the interior of a material or tissue, digital volume correlation (DVC) has increasingly gained attention and application in the fields of experimental mechanics, material research and biomedical engineering. However, the practical implementation of DVC involves important challenges such as implementation complexity, calculation accuracy and computational efficiency. In this paper, a least-squares framework is presented for 3D internal displacement and strain field measurement using DVC. The proposed DVC combines a practical linear-intensity-change model with an easy-to-implement iterative least-squares (ILS) algorithm to retrieve 3D internal displacement vector field with sub-voxel accuracy. Because the linear-intensity-change model is capable of accounting for both the possible intensity changes and the relative geometric transform of the target subvolume, the presented DVC thus provides the highest sub-voxel registration accuracy and widest applicability. Furthermore, as the ILS algorithm uses only first-order spatial derivatives of the deformed volumetric image, the developed DVC thus significantly reduces computational complexity. To further extract 3D strain distributions from the 3D discrete displacement vectors obtained by the ILS algorithm, the presented DVC employs a pointwise least-squares algorithm to estimate the strain components for each measurement point. Computer-simulated volume images with controlled displacements are employed to investigate the performance of the proposed DVC method in terms of mean bias error and standard deviation error. Results reveal that the present technique is capable of providing accurate measurements in an easy-to-implement manner, and can be applied to practical 3D internal displacement and strain calculation. (paper)
Yan, Zhengbing; Kuang, Te-Hui; Yao, Yuan
2017-09-01
In recent years, multivariate statistical monitoring of batch processes has become a popular research topic, wherein multivariate fault isolation is an important step aiming at the identification of the faulty variables contributing most to the detected process abnormality. Although contribution plots have been commonly used in statistical fault isolation, such methods suffer from the smearing effect between correlated variables. In particular, in batch process monitoring, the high autocorrelations and cross-correlations that exist in variable trajectories make the smearing effect unavoidable. To address such a problem, a variable selection-based fault isolation method is proposed in this research, which transforms the fault isolation problem into a variable selection problem in partial least squares discriminant analysis and solves it by calculating a sparse partial least squares model. As different from the traditional methods, the proposed method emphasizes the relative importance of each process variable. Such information may help process engineers in conducting root-cause diagnosis. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Weighted least-square approach for simultaneous measurement of multiple reflective surfaces
Tang, Shouhong; Bills, Richard E.; Freischlad, Klaus
2007-09-01
Phase shifting interferometry (PSI) is a highly accurate method for measuring the nanometer-scale relative surface height of a semi-reflective test surface. PSI is effectively used in conjunction with Fizeau interferometers for optical testing, hard disk inspection, and semiconductor wafer flatness. However, commonly-used PSI algorithms are unable to produce an accurate phase measurement if more than one reflective surface is present in the Fizeau interferometer test cavity. Examples of test parts that fall into this category include lithography mask blanks and their protective pellicles, and plane parallel optical beam splitters. The plane parallel surfaces of these parts generate multiple interferograms that are superimposed in the recording plane of the Fizeau interferometer. When using wavelength shifting in PSI the phase shifting speed of each interferogram is proportional to the optical path difference (OPD) between the two reflective surfaces. The proposed method is able to differentiate each underlying interferogram from each other in an optimal manner. In this paper, we present a method for simultaneously measuring the multiple test surfaces of all underlying interferograms from these superimposed interferograms through the use of a weighted least-square fitting technique. The theoretical analysis of weighted least-square technique and the measurement results will be described in this paper.
Least-squares migration of multisource data with a deblurring filter
Dai, Wei; Wang, Xin; Schuster, Gerard T.
2011-01-01
Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.
Least-squares migration of multisource data with a deblurring filter
Dai, Wei
2011-09-01
Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method. © 2011 Society of Exploration Geophysicists.
Directory of Open Access Journals (Sweden)
C.G. Ozoegwu
2016-01-01
Full Text Available The general least squares model for milling process state term is presented. A discrete map for milling stability analysis that is based on the third-order case of the presented general least squares milling state term model is first studied and compared with its third-order counterpart that is based on the interpolation theory. Both numerical rate of convergence and chatter stability results of the two maps are compared using the single degree of freedom (1DOF milling model. The numerical rate of convergence of the presented third-order model is also studied using the two degree of freedom (2DOF milling process model. Comparison gave that stability results from the two maps agree closely but the presented map demonstrated reduction in number of needed calculations leading to about 30% savings in computational time (CT. It is seen in earlier works that accuracy of milling stability analysis using the full-discretization method rises from first-order theory to second-order theory and continues to rise to the third-order theory. The present work confirms this trend. In conclusion, the method presented in this work will enable fast and accurate computation of stability diagrams for use by machinists.
Ma, W; Zhang, T-F; Lu, P; Lu, S H
2014-01-01
Breast cancer is categorized into two broad groups: estrogen receptor positive (ER+) and ER negative (ER-) groups. Previous study proposed that under trastuzumab-based neoadjuvant chemotherapy, tumor initiating cell (TIC) featured ER- tumors response better than ER+ tumors. Exploration of the molecular difference of these two groups may help developing new therapeutic strategies, especially for ER- patients. With gene expression profile from the Gene Expression Omnibus (GEO) database, we performed partial least squares (PLS) based analysis, which is more sensitive than common variance/regression analysis. We acquired 512 differentially expressed genes. Four pathways were found to be enriched with differentially expressed genes, involving immune system, metabolism and genetic information processing process. Network analysis identified five hub genes with degrees higher than 10, including APP, ESR1, SMAD3, HDAC2, and PRKAA1. Our findings provide new understanding for the molecular difference between TIC featured ER- and ER+ breast tumors with the hope offer supports for therapeutic studies.
Non-stationary least-squares complex decomposition for microseismic noise attenuation
Chen, Yangkang
2018-06-01
Microseismic data processing and imaging are crucial for subsurface real-time monitoring during hydraulic fracturing process. Unlike the active-source seismic events or large-scale earthquake events, the microseismic event is usually of very small magnitude, which makes its detection challenging. The biggest trouble of microseismic data is the low signal-to-noise ratio issue. Because of the small energy difference between effective microseismic signal and ambient noise, the effective signals are usually buried in strong random noise. I propose a useful microseismic denoising algorithm that is based on decomposing a microseismic trace into an ensemble of components using least-squares inversion. Based on the predictive property of useful microseismic event along the time direction, the random noise can be filtered out via least-squares fitting of multiple damping exponential components. The method is flexible and almost automated since the only parameter needed to be defined is a decomposition number. I use some synthetic and real data examples to demonstrate the potential of the algorithm in processing complicated microseismic data sets.
Online Least Squares One-Class Support Vector Machines-Based Abnormal Visual Event Detection
Directory of Open Access Journals (Sweden)
Tian Wang
2013-12-01
Full Text Available The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM, combined with its sparsified version (sparse online LS-OC-SVM. LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method.
Equalization of Loudspeaker and Room Responses Using Kautz Filters: Direct Least Squares Design
Directory of Open Access Journals (Sweden)
Karjalainen Matti
2007-01-01
Full Text Available DSP-based correction of loudspeaker and room responses is becoming an important part of improving sound reproduction. Such response equalization (EQ is based on using a digital filter in cascade with the reproduction channel to counteract the response errors introduced by loudspeakers and room acoustics. Several FIR and IIR filter design techniques have been proposed for equalization purposes. In this paper we investigate Kautz filters, an interesting class of IIR filters, from the point of view of direct least squares EQ design. Kautz filters can be seen as generalizations of FIR filters and their frequency-warped counterparts. They provide a flexible means to obtain desired frequency resolution behavior, which allows low filter orders even for complex corrections. Kautz filters have also the desirable property to avoid inverting dips in transfer function to sharp and long-ringing resonances in the equalizer. Furthermore, the direct least squares design is applicable to nonminimum-phase EQ design and allows using a desired target response. The proposed method is demonstrated by case examples with measured and synthetic loudspeaker and room responses.
Sinha, Mrinal
2015-08-19
We propose an interferometric least-squares migration method that can significantly reduce migration artifacts due to statics and errors in the near-surface velocity model. We first choose a reference reflector whose topography is well known from the, e.g., well logs. Reflections from this reference layer are correlated with the traces associated with reflections from deeper interfaces to get crosscorrelograms. These crosscorrelograms are then migrated using interferometric least-squares migration (ILSM). In this way statics and velocity errors at the near surface are largely eliminated for the examples in our paper.
Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding
Directory of Open Access Journals (Sweden)
Ying Chen
2014-05-01
Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.
Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.
1987-01-01
The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.
Gogu, C.; Haftka, R.; LeRiche, R.; Molimard, J.; Vautrin, A.; Sankar, B.
2008-11-01
The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.
Khawaja, Taimoor Saleem
A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior
Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.
Energy Technology Data Exchange (ETDEWEB)
Choi, Youngsoo [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carlberg, Kevin Thomas [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.
2017-09-01
Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ^{2}-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.
Multisource least-squares reverse-time migration with structure-oriented filtering
Fan, Jing-Wen; Li, Zhen-Chun; Zhang, Kai; Zhang, Min; Liu, Xue-Tong
2016-09-01
The technology of simultaneous-source acquisition of seismic data excited by several sources can significantly improve the data collection efficiency. However, direct imaging of simultaneous-source data or blended data may introduce crosstalk noise and affect the imaging quality. To address this problem, we introduce a structure-oriented filtering operator as preconditioner into the multisource least-squares reverse-time migration (LSRTM). The structure-oriented filtering operator is a nonstationary filter along structural trends that suppresses crosstalk noise while maintaining structural information. The proposed method uses the conjugate-gradient method to minimize the mismatch between predicted and observed data, while effectively attenuating the interference noise caused by exciting several sources simultaneously. Numerical experiments using synthetic data suggest that the proposed method can suppress the crosstalk noise and produce highly accurate images.
Phase-unwrapping algorithm by a rounding-least-squares approach
Juarez-Salazar, Rigoberto; Robledo-Sanchez, Carlos; Guerrero-Sanchez, Fermin
2014-02-01
A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm's performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.
Kazemi, Mahdi; Arefi, Mohammad Mehdi
2017-03-01
In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Saïda Bedoui
2013-01-01
Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.
First-order system least squares for the pure traction problem in planar linear elasticity
Energy Technology Data Exchange (ETDEWEB)
Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.
1996-12-31
This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.
A technique is presented for finding the least squares estimates for the ultimate biochemical oxygen demand (BOD) and rate coefficient for the BOD reaction without resorting to complicated computer algorithms or subjective graphical methods. This may be used in stream water quali...
A library least-squares approach for scatter correction in gamma-ray tomography
Meric, Ilker; Anton Johansen, Geir; Valgueiro Malta Moreira, Icaro
2015-03-01
Scattered radiation is known to lead to distortion in reconstructed images in Computed Tomography (CT). The effects of scattered radiation are especially more pronounced in non-scanning, multiple source systems which are preferred for flow imaging where the instantaneous density distribution of the flow components is of interest. In this work, a new method based on a library least-squares (LLS) approach is proposed as a means of estimating the scatter contribution and correcting for this. The validity of the proposed method is tested using the 85-channel industrial gamma-ray tomograph previously developed at the University of Bergen (UoB). The results presented here confirm that the LLS approach can effectively estimate the amounts of transmission and scatter components in any given detector in the UoB gamma-ray tomography system.
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
Analysis of Shift and Deformation of Planar Surfaces Using the Least Squares Plane
Directory of Open Access Journals (Sweden)
Hrvoje Matijević
2006-12-01
Full Text Available Modern methods of measurement developed on the basis of advanced reflectorless distance measurement have paved the way for easier detection and analysis of shift and deformation. A large quantity of collected data points will often require a mathematical model of the surface that fits best into these. Although this can be a complex task, in the case of planar surfaces it is easily done, enabling further processing and analysis of measurement results. The paper describes the fitting of a plane to a set of collected points using the least squares distance, with previously excluded outliers via the RANSAC algorithm. Based on that, a method for analysis of the deformation and shift of planar surfaces is also described.
Distributed weighted least-squares estimation with fast convergence for large-scale systems.
Marelli, Damián Edgardo; Fu, Minyue
2015-01-01
In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.
An Improved Generalized Predictive Control in a Robust Dynamic Partial Least Square Framework
Directory of Open Access Journals (Sweden)
Jin Xin
2015-01-01
Full Text Available To tackle the sensitivity to outliers in system identification, a new robust dynamic partial least squares (PLS model based on an outliers detection method is proposed in this paper. An improved radial basis function network (RBFN is adopted to construct the predictive model from inputs and outputs dataset, and a hidden Markov model (HMM is applied to detect the outliers. After outliers are removed away, a more robust dynamic PLS model is obtained. In addition, an improved generalized predictive control (GPC with the tuning weights under dynamic PLS framework is proposed to deal with the interaction which is caused by the model mismatch. The results of two simulations demonstrate the effectiveness of proposed method.
Directory of Open Access Journals (Sweden)
Byambaa Dorj
2016-01-01
Full Text Available The next promising key issue of the automobile development is a self-driving technique. One of the challenges for intelligent self-driving includes a lane-detecting and lane-keeping capability for advanced driver assistance systems. This paper introduces an efficient and lane detection method designed based on top view image transformation that converts an image from a front view to a top view space. After the top view image transformation, a Hough transformation technique is integrated by using a parabolic model of a curved lane in order to estimate a parametric model of the lane in the top view space. The parameters of the parabolic model are estimated by utilizing a least-square approach. The experimental results show that the newly proposed lane detection method with the top view transformation is very effective in estimating a sharp and curved lane leading to a precise self-driving capability.
A least squares approach for efficient and reliable short-term versus long-term optimization
DEFF Research Database (Denmark)
Christiansen, Lasse Hjuler; Capolei, Andrea; Jørgensen, John Bagterp
2017-01-01
The uncertainties related to long-term forecasts of oil prices impose significant financial risk on ventures of oil production. To minimize risk, oil companies are inclined to maximize profit over short-term horizons ranging from months to a few years. In contrast, conventional production...... optimization maximizes long-term profits over horizons that span more than a decade. To address this challenge, the oil literature has introduced short-term versus long-term optimization. Ideally, this problem is solved by a posteriori multi-objective optimization methods that generate an approximation...... the balance between the objectives, leaving an unfulfilled potential to increase profits. To promote efficient and reliable short-term versus long-term optimization, this paper introduces a natural way to characterize desirable Pareto points and proposes a novel least squares (LS) method. Unlike hierarchical...
Least-squares dual characterization for ROI assessment in emission tomography
International Nuclear Information System (INIS)
Ben Bouallègue, F; Mariano-Goulart, D; Crouzet, J F; Dubois, A; Buvat, I
2013-01-01
Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff. (paper)
Least-squares dual characterization for ROI assessment in emission tomography
Ben Bouallègue, F.; Crouzet, J. F.; Dubois, A.; Buvat, I.; Mariano-Goulart, D.
2013-06-01
Our aim is to describe an original method for estimating the statistical properties of regions of interest (ROIs) in emission tomography. Drawn upon the works of Louis on the approximate inverse, we propose a dual formulation of the ROI estimation problem to derive the ROI activity and variance directly from the measured data without any image reconstruction. The method requires the definition of an ROI characteristic function that can be extracted from a co-registered morphological image. This characteristic function can be smoothed to optimize the resolution-variance tradeoff. An iterative procedure is detailed for the solution of the dual problem in the least-squares sense (least-squares dual (LSD) characterization), and a linear extrapolation scheme is described to compensate for sampling partial volume effect and reduce the estimation bias (LSD-ex). LSD and LSD-ex are compared with classical ROI estimation using pixel summation after image reconstruction and with Huesman's method. For this comparison, we used Monte Carlo simulations (GATE simulation tool) of 2D PET data of a Hoffman brain phantom containing three small uniform high-contrast ROIs and a large non-uniform low-contrast ROI. Our results show that the performances of LSD characterization are at least as good as those of the classical methods in terms of root mean square (RMS) error. For the three small tumor regions, LSD-ex allows a reduction in the estimation bias by up to 14%, resulting in a reduction in the RMS error of up to 8.5%, compared with the optimal classical estimation. For the large non-specific region, LSD using appropriate smoothing could intuitively and efficiently handle the resolution-variance tradeoff.
Temporal gravity field modeling based on least square collocation with short-arc approach
ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet
2014-05-01
After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.
Cao, Hongliang; Xin, Ya; Yuan, Qiaoxia
2016-02-01
To predict conveniently the biochar yield from cattle manure pyrolysis, intelligent modeling approach was introduced in this research. A traditional artificial neural networks (ANN) model and a novel least squares support vector machine (LS-SVM) model were developed. For the identification and prediction evaluation of the models, a data set with 33 experimental data was used, which were obtained using a laboratory-scale fixed bed reaction system. The results demonstrated that the intelligent modeling approach is greatly convenient and effective for the prediction of the biochar yield. In particular, the novel LS-SVM model has a more satisfying predicting performance and its robustness is better than the traditional ANN model. The introduction and application of the LS-SVM modeling method gives a successful example, which is a good reference for the modeling study of cattle manure pyrolysis process, even other similar processes. Copyright © 2015 Elsevier Ltd. All rights reserved.
Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil
Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris
2016-01-01
Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.
A hybrid least squares support vector machines and GMDH approach for river flow forecasting
Samsudin, R.; Saad, P.; Shabri, A.
2010-06-01
This paper proposes a novel hybrid forecasting model, which combines the group method of data handling (GMDH) and the least squares support vector machine (LSSVM), known as GLSSVM. The GMDH is used to determine the useful input variables for LSSVM model and the LSSVM model which works as time series forecasting. In this study the application of GLSSVM for monthly river flow forecasting of Selangor and Bernam River are investigated. The results of the proposed GLSSVM approach are compared with the conventional artificial neural network (ANN) models, Autoregressive Integrated Moving Average (ARIMA) model, GMDH and LSSVM models using the long term observations of monthly river flow discharge. The standard statistical, the root mean square error (RMSE) and coefficient of correlation (R) are employed to evaluate the performance of various models developed. Experiment result indicates that the hybrid model was powerful tools to model discharge time series and can be applied successfully in complex hydrological modeling.
Waller, Niels
2018-01-01
Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.
Song, Xiaoying; Huang, Qijun; Chang, Sheng; He, Jin; Wang, Hao
2018-06-01
To improve the compression rates for lossless compression of medical images, an efficient algorithm, based on irregular segmentation and region-based prediction, is proposed in this paper. Considering that the first step of a region-based compression algorithm is segmentation, this paper proposes a hybrid method by combining geometry-adaptive partitioning and quadtree partitioning to achieve adaptive irregular segmentation for medical images. Then, least square (LS)-based predictors are adaptively designed for each region (regular subblock or irregular subregion). The proposed adaptive algorithm not only exploits spatial correlation between pixels but it utilizes local structure similarity, resulting in efficient compression performance. Experimental results show that the average compression performance of the proposed algorithm is 10.48, 4.86, 3.58, and 0.10% better than that of JPEG 2000, CALIC, EDP, and JPEG-LS, respectively. Graphical abstract ᅟ.
Least Squares Estimate of the Initial Phases in STFT based Speech Enhancement
DEFF Research Database (Denmark)
Nørholm, Sidsel Marie; Krawczyk-Becker, Martin; Gerkmann, Timo
2015-01-01
In this paper, we consider single-channel speech enhancement in the short time Fourier transform (STFT) domain. We suggest to improve an STFT phase estimate by estimating the initial phases. The method is based on the harmonic model and a model for the phase evolution over time. The initial phases...... are estimated by setting up a least squares problem between the noisy phase and the model for phase evolution. Simulations on synthetic and speech signals show a decreased error on the phase when an estimate of the initial phase is included compared to using the noisy phase as an initialisation. The error...... on the phase is decreased at input SNRs from -10 to 10 dB. Reconstructing the signal using the clean amplitude, the mean squared error is decreased and the PESQ score is increased....
A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants
Cooper, Paul D.
2010-01-01
A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…
A wavelet and least square filter based spatial-spectral denoising approach of hyperspectral imagery
Li, Ting; Chen, Xiao-Mei; Chen, Gang; Xue, Bo; Ni, Guo-Qiang
2009-11-01
Noise reduction is a crucial step in hyperspectral imagery pre-processing. Based on sensor characteristics, the noise of hyperspectral imagery represents in both spatial and spectral domain. However, most prevailing denosing techniques process the imagery in only one specific domain, which have not utilized multi-domain nature of hyperspectral imagery. In this paper, a new spatial-spectral noise reduction algorithm is proposed, which is based on wavelet analysis and least squares filtering techniques. First, in the spatial domain, a new stationary wavelet shrinking algorithm with improved threshold function is utilized to adjust the noise level band-by-band. This new algorithm uses BayesShrink for threshold estimation, and amends the traditional soft-threshold function by adding shape tuning parameters. Comparing with soft or hard threshold function, the improved one, which is first-order derivable and has a smooth transitional region between noise and signal, could save more details of image edge and weaken Pseudo-Gibbs. Then, in the spectral domain, cubic Savitzky-Golay filter based on least squares method is used to remove spectral noise and artificial noise that may have been introduced in during the spatial denoising. Appropriately selecting the filter window width according to prior knowledge, this algorithm has effective performance in smoothing the spectral curve. The performance of the new algorithm is experimented on a set of Hyperion imageries acquired in 2007. The result shows that the new spatial-spectral denoising algorithm provides more significant signal-to-noise-ratio improvement than traditional spatial or spectral method, while saves the local spectral absorption features better.
Directory of Open Access Journals (Sweden)
Bao Wang
2012-11-01
Full Text Available The accuracy of annual electric load forecasting plays an important role in the economic and social benefits of electric power systems. The least squares support vector machine (LSSVM has been proven to offer strong potential in forecasting issues, particularly by employing an appropriate meta-heuristic algorithm to determine the values of its two parameters. However, these meta-heuristic algorithms have the drawbacks of being hard to understand and reaching the global optimal solution slowly. As a novel meta-heuristic and evolutionary algorithm, the fruit fly optimization algorithm (FOA has the advantages of being easy to understand and fast convergence to the global optimal solution. Therefore, to improve the forecasting performance, this paper proposes a LSSVM-based annual electric load forecasting model that uses FOA to automatically determine the appropriate values of the two parameters for the LSSVM model. By taking the annual electricity consumption of China as an instance, the computational result shows that the LSSVM combined with FOA (LSSVM-FOA outperforms other alternative methods, namely single LSSVM, LSSVM combined with coupled simulated annealing algorithm (LSSVM-CSA, generalized regression neural network (GRNN and regression model.
Smith, Tony E.; Lee, Ka Lok
2012-01-01
There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce "spurious correlation" that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.
Yang, J-J; Yoon, U; Yun, H J; Im, K; Choi, Y Y; Lee, K H; Park, H; Hough, M G; Lee, J-M
2013-08-29
A number of imaging studies have reported neuroanatomical correlates of human intelligence with various morphological characteristics of the cerebral cortex. However, it is not yet clear whether these morphological properties of the cerebral cortex account for human intelligence. We assumed that the complex structure of the cerebral cortex could be explained effectively considering cortical thickness, surface area, sulcal depth and absolute mean curvature together. In 78 young healthy adults (age range: 17-27, male/female: 39/39), we used the full-scale intelligence quotient (FSIQ) and the cortical measurements calculated in native space from each subject to determine how much combining various cortical measures explained human intelligence. Since each cortical measure is thought to be not independent but highly inter-related, we applied partial least square (PLS) regression, which is one of the most promising multivariate analysis approaches, to overcome multicollinearity among cortical measures. Our results showed that 30% of FSIQ was explained by the first latent variable extracted from PLS regression analysis. Although it is difficult to relate the first derived latent variable with specific anatomy, we found that cortical thickness measures had a substantial impact on the PLS model supporting the most significant factor accounting for FSIQ. Our results presented here strongly suggest that the new predictor combining different morphometric properties of complex cortical structure is well suited for predicting human intelligence. Copyright © 2013 IBRO. Published by Elsevier Ltd. All rights reserved.
Extension of least squares spectral resolution algorithm to high-resolution lipidomics data
International Nuclear Information System (INIS)
Zeng, Ying-Xu; Mjøs, Svein Are; David, Fabrice P.A.; Schmid, Adrien W.
2016-01-01
Lipidomics, which focuses on the global study of molecular lipids in biological systems, has been driven tremendously by technical advances in mass spectrometry (MS) instrumentation, particularly high-resolution MS. This requires powerful computational tools that handle the high-throughput lipidomics data analysis. To address this issue, a novel computational tool has been developed for the analysis of high-resolution MS data, including the data pretreatment, visualization, automated identification, deconvolution and quantification of lipid species. The algorithm features the customized generation of a lipid compound library and mass spectral library, which covers the major lipid classes such as glycerolipids, glycerophospholipids and sphingolipids. Next, the algorithm performs least squares resolution of spectra and chromatograms based on the theoretical isotope distribution of molecular ions, which enables automated identification and quantification of molecular lipid species. Currently, this methodology supports analysis of both high and low resolution MS as well as liquid chromatography-MS (LC-MS) lipidomics data. The flexibility of the methodology allows it to be expanded to support more lipid classes and more data interpretation functions, making it a promising tool in lipidomic data analysis. - Highlights: • A flexible strategy for analyzing MS and LC-MS data of lipid molecules is proposed. • Isotope distribution spectra of theoretically possible compounds were generated. • High resolution MS and LC-MS data were resolved by least squares spectral resolution. • The method proposed compounds that are likely to occur in the analyzed samples. • The proposed compounds matched results from manual interpretation of fragment spectra.
Extension of least squares spectral resolution algorithm to high-resolution lipidomics data
Energy Technology Data Exchange (ETDEWEB)
Zeng, Ying-Xu [Department of Chemistry, University of Bergen, PO Box 7803, N-5020 Bergen (Norway); Mjøs, Svein Are, E-mail: svein.mjos@kj.uib.no [Department of Chemistry, University of Bergen, PO Box 7803, N-5020 Bergen (Norway); David, Fabrice P.A. [Bioinformatics and Biostatistics Core Facility, School of Life Sciences, Ecole Polytechnique Fédérale de Lausanne (EPFL) and Swiss Institute of Bioinformatics (SIB), Lausanne (Switzerland); Schmid, Adrien W. [Proteomics Core Facility, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland)
2016-03-31
Lipidomics, which focuses on the global study of molecular lipids in biological systems, has been driven tremendously by technical advances in mass spectrometry (MS) instrumentation, particularly high-resolution MS. This requires powerful computational tools that handle the high-throughput lipidomics data analysis. To address this issue, a novel computational tool has been developed for the analysis of high-resolution MS data, including the data pretreatment, visualization, automated identification, deconvolution and quantification of lipid species. The algorithm features the customized generation of a lipid compound library and mass spectral library, which covers the major lipid classes such as glycerolipids, glycerophospholipids and sphingolipids. Next, the algorithm performs least squares resolution of spectra and chromatograms based on the theoretical isotope distribution of molecular ions, which enables automated identification and quantification of molecular lipid species. Currently, this methodology supports analysis of both high and low resolution MS as well as liquid chromatography-MS (LC-MS) lipidomics data. The flexibility of the methodology allows it to be expanded to support more lipid classes and more data interpretation functions, making it a promising tool in lipidomic data analysis. - Highlights: • A flexible strategy for analyzing MS and LC-MS data of lipid molecules is proposed. • Isotope distribution spectra of theoretically possible compounds were generated. • High resolution MS and LC-MS data were resolved by least squares spectral resolution. • The method proposed compounds that are likely to occur in the analyzed samples. • The proposed compounds matched results from manual interpretation of fragment spectra.
Directory of Open Access Journals (Sweden)
T. Kim
2012-09-01
Full Text Available Automated generation of digital elevation models (DEMs from high resolution satellite images (HRSIs has been an active research topic for many years. However, stereo matching of HRSIs, in particular based on image-space search, is still difficult due to occlusions and building facades within them. Object-space matching schemes, proposed to overcome these problem, often are very time consuming and critical to the dimensions of voxels. In this paper, we tried a new least square matching (LSM algorithm that works in a 3D object space. The algorithm starts with an initial height value on one location of the object space. From this 3D point, the left and right image points are projected. The true height is calculated by iterative least squares estimation based on the grey level differences between the left and right patches centred on the projected left and right points. We tested the 3D LSM to the Worldview images over 'Terrassa Sud' provided by the ISPRS WG I/4. We also compared the performance of the 3D LSM with the correlation matching based on 2D image space and the correlation matching based on 3D object space. The accuracy of the DEM from each method was analysed against the ground truth. Test results showed that 3D LSM offers more accurate DEMs over the conventional matching algorithms. Results also showed that 3D LSM is sensitive to the accuracy of initial height value to start the estimation. We combined the 3D COM and 3D LSM for accurate and robust DEM generation from HRSIs. The major contribution of this paper is that we proposed and validated that LSM can be applied to object space and that the combination of 3D correlation and 3D LSM can be a good solution for automated DEM generation from HRSIs.
DEFF Research Database (Denmark)
Fitzenberger, Bernd; Wilke, Ralf Andreas
2015-01-01
if the mean regression model does not. We provide a short informal introduction into the principle of quantile regression which includes an illustrative application from empirical labor market research. This is followed by briefly sketching the underlying statistical model for linear quantile regression based......Quantile regression is emerging as a popular statistical approach, which complements the estimation of conditional mean models. While the latter only focuses on one aspect of the conditional distribution of the dependent variable, the mean, quantile regression provides more detailed insights...... by modeling conditional quantiles. Quantile regression can therefore detect whether the partial effect of a regressor on the conditional quantiles is the same for all quantiles or differs across quantiles. Quantile regression can provide evidence for a statistical relationship between two variables even...
Dutta, Gaurav
2013-08-20
Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.
Optimization of wood flour acetylation by factorial design and partial least squares regression
Directory of Open Access Journals (Sweden)
Lisandra M. K. Nadal
2012-01-01
Full Text Available Acetylation was performed to reduce the polarity of wood and increase its compatibility with polymer matrices for the production of composites. These reactions were performed first as a function of acetic acid and anhydride concentration in a mixture catalyzed by sulfuric acid. A concentration of 50%/50% (v/v of acetic acid and anhydride was found to produced the highest conversion rate between the functional groups. After these reactions, the kinetics were investigated by varying times and temperatures using a 3² factorial design, and showed time was the most relevant parameter in determining the conversion of hydroxyl into carbonyl groups.
Albaqshi, Amani Mohammed H.
2017-01-01
Functional Data Analysis (FDA) has attracted substantial attention for the last two decades. Within FDA, classifying curves into two or more categories is consistently of interest to scientists, but multi-class prediction within FDA is challenged in that most classification tools have been limited to binary response applications. The functional…
Hecker, Christoph; Dilles, John H.; van der Meijde, Mark; van der Meer, Freek D.
2012-01-01
In this paper, we present an approach to extracting mineralogic information from thermal infrared (TIR) spectra that is not based on an input library of pure mineral spectra nor tries to extract spectral end‐members from the data. Instead, existing modal mineralogy for a number of samples are used