interpolating moving least-squares: Topics by WorldWideScience.org

Sample records for interpolating moving least-squares

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)
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 ...
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.
Analysis of a plane stress wave by the moving least squares method

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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
Signal-to-noise ratio enhancement on SEM images using a cubic spline interpolation with Savitzky-Golay filters and weighted least squares error.

Science.gov (United States)

Kiani, M A; Sim, K S; Nia, M E; Tso, C P

2015-05-01

A new technique based on cubic spline interpolation with Savitzky-Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real-time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky-Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal-to-noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation-based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.
Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

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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.
Extreme Learning Machine and Moving Least Square Regression Based Solar Panel Vision Inspection

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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.
Proton Exchange Membrane Fuel Cell Modelling Using Moving Least Squares Technique

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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.
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.
Global Search Strategies for Solving Multilinear Least-Squares Problems

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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.
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
A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Directory of Open Access Journals (Sweden)

Hongyin Yang

2017-01-01

Full Text Available The presented study proposed an improved interpolating boundary node method (IIBNM for 2D potential problems. The improved interpolating moving least-square (IIMLS method was applied to construct the shape functions, of which the delta function properties and boundary conditions were directly implemented. In addition, any weight function used in the moving least-square (MLS method was also applicable in the IIMLS method. Boundary cells were required in the computation of the boundary integrals, and additional discretization error was not avoided if traditional cells were used to approximate the geometry. The present study applied the parametric cells created in the parameter space to preserve the exact geometry, and the geometry was maintained due to the number of cells. Only the number of nodes on the boundary was required as additional information for boundary node construction. Most importantly, the IIMLS method can be applied in the parameter space to construct shape functions without the requirement of additional computations for the curve length.
EXPALS, Least Square Fit of Linear Combination of Exponential Decay Function

International Nuclear Information System (INIS)

Douglas Gardner, C.

1980-01-01

1 - Description of problem or function: This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k)). 2 - Method of solution: The Prony-Householder iteration method is used. For unequally-spaced data, a number of interpolation options are provided. This revision includes an option to call a differential correction subroutine REFINE to improve the approximation to unequally-spaced data when equal-interval interpolation is faulty. If convergence is achieved, the probable errors in the computed parameters are calculated also. 3 - Restrictions on the complexity of the problem: Generally, it is desirable to have at least 10n observations where n equals the number of terms and to input k+n significant figures if k significant figures are expected
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)
Least-squares model-based halftoning

Science.gov (United States)

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
Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

Science.gov (United States)

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.
Least-squares collocation meshless approach for radiative heat transfer in absorbing 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
Partial update least-square adaptive filtering

CERN Document Server

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
Simplified neural networks for solving linear least squares and total least squares problems in real time.

Science.gov (United States)

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.
Interface information transfer between non-matching, nonconforming interfaces using radial basis function interpolation

CSIR Research Space (South Africa)

Bogaers, Alfred EJ

2016-10-01

Full Text Available words, gB = [ φBA PB ] [ MAA PA P TA 0 ]−1 [ gA 0 ] . (15) NAME: DEFINITION C0 compactly supported piecewise polynomial (C0): (1− (||x|| /r))2+ C2 compactly supported piecewise polynomial (C2): (1− (||x|| /r))4+ (4 (||x|| /r) + 1) Thin-plate spline (TPS... a numerical comparison to Kriging and the moving least-squares method, see Krishnamurthy [16]). RBF interpolation is based on fitting a series of splines, or basis functions to interpolate information from one point cloud to another. Let us assume we...

Non-stationary covariance function modelling in 2D least-squares collocation

Science.gov (United States)

Darbeheshti, N.; Featherstone, W. E.

2009-06-01

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.
A Weighted Least Squares Approach To Robustify Least Squares Estimates.

Science.gov (United States)

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,…
Rapid classification of turmeric based on DNA fingerprint by near-infrared spectroscopy combined with moving window partial least squares-discrimination analysis

International Nuclear Information System (INIS)

Kasemsumran, Sumaporn; Suttiwijitpukdee, Nattaporn; Keeratinijakal, Vichein

2017-01-01

In this research, near-infrared (NIR) spectroscopy in combination with moving window partial least squares-discrimination analysis (MWPLS-DA) was utilized to discriminate the variety of turmeric based on DNA markers, which correlated to the quantity of curcuminoid. Curcuminoid was used as a marker compound in variety identification due to the most pharmacological properties of turmeric possessed from it. MWPLS-DA optimized informative NIR spectral regions for the fitting and prediction to {-1/1}-coded turmeric varieties, indicating variables in the development of latent variables in discrimination analysis. Consequently, MWPLS-DA benefited in the selection of combined informative NIR spectral regions of 1100 – 1260, 1300 – 1500 and 1880 – 2500 nm for classification modeling of turmeric variety with 148 calibration samples, and yielded the results better than that obtained from a partial least squares-discrimination analysis (PLS-DA) model built by using the whole NIR spectral region. An effective and rapid strategy of using NIR in combination with MWPLS-DA provided the best variety identification results of 100% in both specificity and total accuracy for 48 test samples. (author)
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
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.
Least-squares reverse time migration of multiples

KAUST Repository

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
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
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

Science.gov (United States)

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
Time Scale in Least Square Method

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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.
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...
An Inverse Function Least Square Fitting Approach of the Buildup Factor for Radiation Shielding Analysis

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.
Plane-wave Least-squares Reverse Time Migration

KAUST Repository

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.
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
Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

Science.gov (United States)

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.
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.
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.
AUTOMATIC EXTRACTION OF ROCK JOINTS FROM LASER SCANNED DATA BY MOVING LEAST SQUARES METHOD AND FUZZY K-MEANS CLUSTERING

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.
Least-squares variance component estimation

NARCIS (Netherlands)

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
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....
Consistency of the least weighted squares under heteroscedasticity

Czech Academy of Sciences Publication Activity Database

Víšek, Jan Ámos

2011-01-01

Roč. 2011, č. 47 (2011), s. 179-206 ISSN 0023-5954 Grant - others:GA UK(CZ) GA402/09/055 Institutional research plan: CEZ:AV0Z10750506 Keywords : Regression * Consistency * The least weighted squares * Heteroscedasticity Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.454, year: 2011 http://library.utia.cas.cz/separaty/2011/SI/visek-consistency of the least weighted squares under heteroscedasticity.pdf

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
note: The least square nucleolus is a general nucleolus

OpenAIRE

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)).
Wave-equation Q tomography and least-squares migration

KAUST Repository

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
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
Multiples least-squares reverse time migration

KAUST Repository

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
Third-order least squares modelling of milling state term for improved computation of stability boundaries

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.
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
New approach to breast cancer CAD using partial least squares and kernel-partial least squares

Science.gov (United States)

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.
Sparse least-squares reverse time migration using seislets

KAUST Repository

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.
Quantized kernel least mean square algorithm.

Science.gov (United States)

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.
Group-wise partial least square regression

NARCIS (Netherlands)

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
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 ...
'AJUSTAR' a interactive processor for to Fit, by means of least squares, one variable polinomials (arbitrary degree) at experimental points

International Nuclear Information System (INIS)

Sanchez Miro, J.J.; Pena, J.

1991-01-01

In this repport is offered, to scientist and technical people, a numeric tool consisting in a FORTRAN program, of interactive use, with destination to make lineal 'least squares', fittings on any set of empirical observations. The method based in the orthogonal functions (for discrete case), instead of direct solving the equations system, is used. The procedure includes also the optionally facilities of: variable change, direct interpolation, correlation non linear factor, 'weights' of the points, confidence intervals (Scheffe, Miller, Student), and plotting results. (Author). 10 refs
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.
Application of Least-Squares Spectral Element Methods to Polynomial Chaos

NARCIS (Netherlands)

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.
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
Multi-source least-squares reverse time migration

KAUST Repository

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

KAUST Repository

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.
Multi-source least-squares migration of marine data

KAUST Repository

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.
Support-Vector-based Least Squares for learning non-linear dynamics

NARCIS (Netherlands)

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

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.
Plane-wave Least-squares Reverse Time Migration

KAUST Repository

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
Regularized plane-wave least-squares Kirchhoff migration

KAUST Repository

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
Least squares reverse time migration of controlled order multiples

Science.gov (United States)

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).
Total least squares for anomalous change detection

Science.gov (United States)

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.
Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

Science.gov (United States)

Olivares, A.; Górriz, J. M.; Ramírez, J.; Olivares, G.

2011-02-01

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed.
Accurate human limb angle measurement: sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering

International Nuclear Information System (INIS)

Olivares, A; Olivares, G; Górriz, J M; Ramírez, J

2011-01-01

Inertial sensors are widely used in human body motion monitoring systems since they permit us to determine the position of the subject's limbs. Limb angle measurement is carried out through the integration of the angular velocity measured by a rate sensor and the decomposition of the components of static gravity acceleration measured by an accelerometer. Different factors derived from the sensors' nature, such as the angle random walk and dynamic bias, lead to erroneous measurements. Dynamic bias effects can be reduced through the use of adaptive filtering based on sensor fusion concepts. Most existing published works use a Kalman filtering sensor fusion approach. Our aim is to perform a comparative study among different adaptive filters. Several least mean squares (LMS), recursive least squares (RLS) and Kalman filtering variations are tested for the purpose of finding the best method leading to a more accurate and robust limb angle measurement. A new angle wander compensation sensor fusion approach based on LMS and RLS filters has been developed
Solution of a Complex Least Squares Problem with Constrained Phase.

Science.gov (United States)

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.
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.
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....
Least Squares Methods for Equidistant Tree Reconstruction

OpenAIRE

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...
Optimally weighted least-squares steganalysis

Science.gov (United States)

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.
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.
The possibilities of least-squares migration of internally scattered seismic energy

KAUST Repository

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

KAUST Repository

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.
Elastic least-squares reverse time migration

KAUST Repository

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

KAUST Repository

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.
8th International Conference on Partial Least Squares and Related Methods

CERN Document Server

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 ...
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
Small-kernel constrained-least-squares restoration of sampled image data

Science.gov (United States)

Hazra, Rajeeb; Park, Stephen K.

1992-10-01

Constrained least-squares image restoration, first proposed by Hunt twenty years ago, is a linear image restoration technique in which the restoration filter is derived by maximizing the smoothness of the restored image while satisfying a fidelity constraint related to how well the restored image matches the actual data. The traditional derivation and implementation of the constrained least-squares restoration filter is based on an incomplete discrete/discrete system model which does not account for the effects of spatial sampling and image reconstruction. For many imaging systems, these effects are significant and should not be ignored. In a recent paper Park demonstrated that a derivation of the Wiener filter based on the incomplete discrete/discrete model can be extended to a more comprehensive end-to-end, continuous/discrete/continuous model. In a similar way, in this paper, we show that a derivation of the constrained least-squares filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model and, by so doing, an improved restoration filter is derived. Building on previous work by Reichenbach and Park for the Wiener filter, we also show that this improved constrained least-squares restoration filter can be efficiently implemented as a small-kernel convolution in the spatial domain.

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.
Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

Science.gov (United States)

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.
Bounded Perturbation Regularization for Linear Least Squares Estimation

KAUST Repository

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
Making the most out of least-squares migration

KAUST Repository

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
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.
Multi-source least-squares migration of marine data

KAUST Repository

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
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
3D plane-wave least-squares Kirchhoff migration

KAUST Repository

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
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.
Bounded Perturbation Regularization for Linear Least Squares Estimation

KAUST Repository

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.
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
Least-squares finite element discretizations of neutron transport equations in 3 dimensions

Energy Technology Data Exchange (ETDEWEB)

Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)

1996-12-31

The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.
Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

Directory of Open Access Journals (Sweden)

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.
Multivariate calibration with least-squares support vector machines.

NARCIS (Netherlands)

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
Multivariate interpolation

Directory of Open Access Journals (Sweden)

Pakhnutov I.A.

2017-04-01

Full Text Available the paper deals with iterative interpolation methods in forms of similar recursive procedures defined by a sort of simple functions (interpolation basis not necessarily real valued. These basic functions are kind of arbitrary type being defined just by wish and considerations of user. The studied interpolant construction shows virtue of versatility: it may be used in a wide range of vector spaces endowed with scalar product, no dimension restrictions, both in Euclidean and Hilbert spaces. The choice of basic interpolation functions is as wide as possible since it is subdued nonessential restrictions. The interpolation method considered in particular coincides with traditional polynomial interpolation (mimic of Lagrange method in real unidimensional case or rational, exponential etc. in other cases. The interpolation as iterative process, in fact, is fairly flexible and allows one procedure to change the type of interpolation, depending on the node number in a given set. Linear interpolation basis options (perhaps some nonlinear ones allow to interpolate in noncommutative spaces, such as spaces of nondegenerate matrices, interpolated data can also be relevant elements of vector spaces over arbitrary numeric field. By way of illustration, the author gives the examples of interpolation on the real plane, in the separable Hilbert space and the space of square matrices with vektorvalued source data.
Linearized least-square imaging of internally scattered data

KAUST Repository

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.
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.
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.
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.

A hybrid least squares support vector machines and GMDH approach for river flow forecasting

Science.gov (United States)

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.
Least-mean-square spatial filter for IR sensors.

Science.gov (United States)

Takken, E H; Friedman, D; Milton, A F; Nitzberg, R

1979-12-15

A new least-mean-square filter is defined for signal-detection problems. The technique is proposed for scanning IR surveillance systems operating in poorly characterized but primarily low-frequency clutter interference. Near-optimal detection of point-source targets is predicted both for continuous-time and sampled-data systems.
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.
The crux of the method: assumptions in ordinary least squares and logistic regression.

Science.gov (United States)

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.
Plane-wave least-squares reverse-time migration

KAUST Repository

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.
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
Least Squares Problems with Absolute Quadratic Constraints

Directory of Open Access Journals (Sweden)

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.
Making the most out of the least (squares migration)

KAUST Repository

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
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.
Regularization Techniques for Linear Least-Squares Problems

KAUST Repository

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
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.
Making the most out of least-squares migration

KAUST Repository

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.
Fast digital zooming system using directionally adaptive image interpolation and restoration.

Science.gov (United States)

Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki

2014-01-01

This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.
Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

Science.gov (United States)

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.
Radial basis function interpolation of unstructured, three-dimensional, volumetric particle tracking velocimetry data

International Nuclear Information System (INIS)

Casa, L D C; Krueger, P S

2013-01-01

Unstructured three-dimensional fluid velocity data were interpolated using Gaussian radial basis function (RBF) interpolation. Data were generated to imitate the spatial resolution and experimental uncertainty of a typical implementation of defocusing digital particle image velocimetry. The velocity field associated with a steadily rotating infinite plate was simulated to provide a bounded, fully three-dimensional analytical solution of the Navier–Stokes equations, allowing for robust analysis of the interpolation accuracy. The spatial resolution of the data (i.e. particle density) and the number of RBFs were varied in order to assess the requirements for accurate interpolation. Interpolation constraints, including boundary conditions and continuity, were included in the error metric used for the least-squares minimization that determines the interpolation parameters to explore methods for improving RBF interpolation results. Even spacing and logarithmic spacing of RBF locations were also investigated. Interpolation accuracy was assessed using the velocity field, divergence of the velocity field, and viscous torque on the rotating boundary. The results suggest that for the present implementation, RBF spacing of 0.28 times the boundary layer thickness is sufficient for accurate interpolation, though theoretical error analysis suggests that improved RBF positioning may yield more accurate results. All RBF interpolation results were compared to standard Gaussian weighting and Taylor expansion interpolation methods. Results showed that RBF interpolation improves interpolation results compared to the Taylor expansion method by 60% to 90% based on the average squared velocity error and provides comparable velocity results to Gaussian weighted interpolation in terms of velocity error. RMS accuracy of the flow field divergence was one to two orders of magnitude better for the RBF interpolation compared to the other two methods. RBF interpolation that was applied to
Angular interpolations and splice options for three-dimensional transport computations

International Nuclear Information System (INIS)

Abu-Shumays, I.K.; Yehnert, C.E.

1996-01-01

New, accurate and mathematically rigorous angular Interpolation strategies are presented. These strategies preserve flow and directionality separately over each octant of the unit sphere, and are based on a combination of spherical harmonics expansions and least squares algorithms. Details of a three-dimensional to three-dimensional (3-D to 3-D) splice method which utilizes the new angular interpolations are summarized. The method has been implemented in a multidimensional discrete ordinates transport computer program. Various features of the splice option are illustrated by several applications to a benchmark Dog-Legged Void Neutron (DLVN) streaming and transport experimental assembly
An information geometric approach to least squares minimization

Science.gov (United States)

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

KAUST Repository

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.
Improved linear least squares estimation using bounded data uncertainty

KAUST Repository

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.
Three Least-Squares Minimization Approaches to Interpret Gravity Data Due to Dipping Faults

Science.gov (United States)

Abdelrahman, E. M.; Essa, K. S.

2015-02-01

We have developed three different least-squares minimization approaches to determine, successively, the depth, dip angle, and amplitude coefficient related to the thickness and density contrast of a buried dipping fault from first moving average residual gravity anomalies. By defining the zero-anomaly distance and the anomaly value at the origin of the moving average residual profile, the problem of depth determination is transformed into a constrained nonlinear gravity inversion. After estimating the depth of the fault, the dip angle is estimated by solving a nonlinear inverse problem. Finally, after estimating the depth and dip angle, the amplitude coefficient is determined using a linear equation. This method can be applied to residuals as well as to measured gravity data because it uses the moving average residual gravity anomalies to estimate the model parameters of the faulted structure. The proposed method was tested on noise-corrupted synthetic and real gravity data. In the case of the synthetic data, good results are obtained when errors are given in the zero-anomaly distance and the anomaly value at the origin, and even when the origin is determined approximately. In the case of practical data (Bouguer anomaly over Gazal fault, south Aswan, Egypt), the fault parameters obtained are in good agreement with the actual ones and with those given in the published literature.

Error propagation of partial least squares for parameters optimization in NIR modeling

Science.gov (United States)

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-01

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models.
Error propagation of partial least squares for parameters optimization in NIR modeling.

Science.gov (United States)

Du, Chenzhao; Dai, Shengyun; Qiao, Yanjiang; Wu, Zhisheng

2018-03-05

A novel methodology is proposed to determine the error propagation of partial least-square (PLS) for parameters optimization in near-infrared (NIR) modeling. The parameters include spectral pretreatment, latent variables and variable selection. In this paper, an open source dataset (corn) and a complicated dataset (Gardenia) were used to establish PLS models under different modeling parameters. And error propagation of modeling parameters for water quantity in corn and geniposide quantity in Gardenia were presented by both type І and type II error. For example, when variable importance in the projection (VIP), interval partial least square (iPLS) and backward interval partial least square (BiPLS) variable selection algorithms were used for geniposide in Gardenia, compared with synergy interval partial least squares (SiPLS), the error weight varied from 5% to 65%, 55% and 15%. The results demonstrated how and what extent the different modeling parameters affect error propagation of PLS for parameters optimization in NIR modeling. The larger the error weight, the worse the model. Finally, our trials finished a powerful process in developing robust PLS models for corn and Gardenia under the optimal modeling parameters. Furthermore, it could provide a significant guidance for the selection of modeling parameters of other multivariate calibration models. Copyright © 2017. Published by Elsevier B.V.
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.
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.
An on-line modified least-mean-square algorithm for training neurofuzzy controllers.

Science.gov (United States)

Tan, Woei Wan

2007-04-01

The problem hindering the use of data-driven modelling methods for training controllers on-line is the lack of control over the amount by which the plant is excited. As the operating schedule determines the information available on-line, the knowledge of the process may degrade if the setpoint remains constant for an extended period. This paper proposes an identification algorithm that alleviates "learning interference" by incorporating fuzzy theory into the normalized least-mean-square update rule. The ability of the proposed methodology to achieve faster learning is examined by employing the algorithm to train a neurofuzzy feedforward controller for controlling a liquid level process. Since the proposed identification strategy has similarities with the normalized least-mean-square update rule and the recursive least-square estimator, the on-line learning rates of these algorithms are also compared.
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 ...
Tensor hypercontraction. II. Least-squares renormalization

Science.gov (United States)

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.
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....
A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

Science.gov (United States)

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.
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.)
Making the most out of the least (squares migration)

KAUST Repository

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.
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
Least-squares reverse time migration of multiples

KAUST Repository

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
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.
The least squares procedure in energy gamma-ray spectroscopy

International Nuclear Information System (INIS)

Helene, O.; Vanin, V.R.; Goldman, I.D.; Pauliquevis, T.M. Jr.; Guimaraes Filho, Z.O.

1999-01-01

The report briefly discusses how to calibrate a detector system and how to interpolate data taking into account variances and covariances of the input data, the adjusted parameters, and the interpolated data
Spectral mimetic least-squares method for div-curl systems

NARCIS (Netherlands)

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
Nonnegative least-squares image deblurring: improved gradient projection approaches

Science.gov (United States)

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.
Fishery landing forecasting using EMD-based least square support vector machine models

Science.gov (United States)

Shabri, Ani

2015-05-01

In this paper, the novel hybrid ensemble learning paradigm integrating ensemble empirical mode decomposition (EMD) and least square support machine (LSSVM) is proposed to improve the accuracy of fishery landing forecasting. This hybrid is formulated specifically to address in modeling fishery landing, which has high nonlinear, non-stationary and seasonality time series which can hardly be properly modelled and accurately forecasted by traditional statistical models. In the hybrid model, EMD is used to decompose original data into a finite and often small number of sub-series. The each sub-series is modeled and forecasted by a LSSVM model. Finally the forecast of fishery landing is obtained by aggregating all forecasting results of sub-series. To assess the effectiveness and predictability of EMD-LSSVM, monthly fishery landing record data from East Johor of Peninsular Malaysia, have been used as a case study. The result shows that proposed model yield better forecasts than Autoregressive Integrated Moving Average (ARIMA), LSSVM and EMD-ARIMA models on several criteria..
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.

Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

KAUST Repository

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.
Track Circuit Fault Diagnosis Method based on Least Squares Support Vector

Science.gov (United States)

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.
Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

Science.gov (United States)

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.
A comparison of two least-squared random coefficient autoregressive models: with and without autocorrelated errors

OpenAIRE

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...
Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

Science.gov (United States)

Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang

2016-03-01

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. © The Author(s) 2016.
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
Analysis of quantile regression as alternative to ordinary least squares

OpenAIRE

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 ...
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
On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

Science.gov (United States)

Schaffrin, Burkhard; Felus, Yaron A.

2008-06-01

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model ( Y- E Y = ( X- E X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E Y and E X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler-Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335-342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.
Growth kinetics of borided layers: Artificial neural network and least square approaches

Science.gov (United States)

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.
Unweighted least squares phase unwrapping by means of multigrid techniques

Science.gov (United States)

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.
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.
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
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
Least Squares Magnetic-Field Optimization for Portable Nuclear Magnetic Resonance Magnet Design

International Nuclear Information System (INIS)

Paulsen, Jeffrey L; Franck, John; Demas, Vasiliki; Bouchard, Louis-S.

2008-01-01

Single-sided and mobile nuclear magnetic resonance (NMR) sensors have the advantages of portability, low cost, and low power consumption compared to conventional high-field NMR and magnetic resonance imaging (MRI) systems. We present fast, flexible, and easy-to-implement target field algorithms for mobile NMR and MRI magnet design. The optimization finds a global optimum in a cost function that minimizes the error in the target magnetic field in the sense of least squares. When the technique is tested on a ring array of permanent-magnet elements, the solution matches the classical dipole Halbach solution. For a single-sided handheld NMR sensor, the algorithm yields a 640 G field homogeneous to 16,100 ppm across a 1.9 cc volume located 1.5 cm above the top of the magnets and homogeneous to 32,200 ppm over a 7.6 cc volume. This regime is adequate for MRI applications. We demonstrate that the homogeneous region can be continuously moved away from the sensor by rotating magnet rod elements, opening the way for NMR sensors with adjustable 'sensitive volumes'
A constrained robust least squares approach for contaminant release history identification

Science.gov (United States)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.
PENERAPAN METODE LEAST MEDIAN SQUARE-MINIMUM COVARIANCE DETERMINANT (LMS-MCD DALAM REGRESI KOMPONEN UTAMA

Directory of Open Access Journals (Sweden)

I PUTU EKA IRAWAN

2013-11-01

Full Text Available Principal Component Regression is a method to overcome multicollinearity techniques by combining principal component analysis with regression analysis. The calculation of classical principal component analysis is based on the regular covariance matrix. The covariance matrix is optimal if the data originated from a multivariate normal distribution, but is very sensitive to the presence of outliers. Alternatives are used to overcome this problem the method of Least Median Square-Minimum Covariance Determinant (LMS-MCD. The purpose of this research is to conduct a comparison between Principal Component Regression (RKU and Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD in dealing with outliers. In this study, Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD has a bias and mean square error (MSE is smaller than the parameter RKU. Based on the difference of parameter estimators, still have a test that has a difference of parameter estimators method LMS-MCD greater than RKU method.
Randomized interpolative decomposition of separated representations

Science.gov (United States)

Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory

2015-01-01

We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.
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
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.

Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

KAUST Repository

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 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

Science.gov (United States)

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.
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
Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

Science.gov (United States)

Behnabian, Behzad; Mashhadi Hossainali, Masoud; Malekzadeh, Ahad

2018-02-01

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the
Regularized plane-wave least-squares Kirchhoff migration

KAUST Repository

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.
Multiples least-squares reverse time migration

KAUST Repository

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.
Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

KAUST Repository

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
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

Science.gov (United States)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
Application of new least-squares methods for the quantitative infrared analysis of multicomponent samples

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
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
First-order system least-squares for second-order elliptic problems with discontinuous coefficients: Further results

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.
Feasibility study on the least square method for fitting non-Gaussian noise data

Science.gov (United States)

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%.
An Incremental Weighted Least Squares Approach to Surface Lights Fields

Science.gov (United States)

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.
Non-stationary least-squares complex decomposition for microseismic noise attenuation

Science.gov (United States)

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.
A cross-correlation objective function for least-squares migration and visco-acoustic imaging

KAUST Repository

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

KAUST Repository

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.
Skeletonized Least Squares Wave Equation Migration

KAUST Repository

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

KAUST Repository

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

KAUST Repository

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.

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.
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.
Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

Science.gov (United States)

Samiei-Esfahany, Sami; Hanssen, Ramon F.

2012-01-01

The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.
Adaptive Noise Canceling Menggunakan Algoritma Least Mean Square (Lms)

OpenAIRE

Nardiana, Anita; Sumaryono, Sari Sujoko

2011-01-01

Noise is inevitable in communication system. In some cases, noise can disturb signal. It is veryannoying as the received signal is jumbled with the noise itself. To reduce or remove noise, filter lowpass,highpass or bandpass can solve the problems, but this method cannot reach a maximum standard. One ofthe alternatives to solve the problem is by using adaptive filter. Adaptive algorithm frequently used is LeastMean Square (LMS) Algorithm which is compatible to Finite Impulse Response (FIR). T...
Soft sensor modelling by time difference, recursive partial least squares and adaptive model updating

International Nuclear Information System (INIS)

Fu, Y; Xu, O; Yang, W; Zhou, L; Wang, J

2017-01-01

To investigate time-variant and nonlinear characteristics in industrial processes, a soft sensor modelling method based on time difference, moving-window recursive partial least square (PLS) and adaptive model updating is proposed. In this method, time difference values of input and output variables are used as training samples to construct the model, which can reduce the effects of the nonlinear characteristic on modelling accuracy and retain the advantages of recursive PLS algorithm. To solve the high updating frequency of the model, a confidence value is introduced, which can be updated adaptively according to the results of the model performance assessment. Once the confidence value is updated, the model can be updated. The proposed method has been used to predict the 4-carboxy-benz-aldehyde (CBA) content in the purified terephthalic acid (PTA) oxidation reaction process. The results show that the proposed soft sensor modelling method can reduce computation effectively, improve prediction accuracy by making use of process information and reflect the process characteristics accurately. (paper)
The consistency of ordinary least-squares and generalized least-squares polynomial regression on characterizing the mechanomyographic amplitude versus torque relationship

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
Precision PEP-II optics measurement with an SVD-enhanced Least-Square fitting

Science.gov (United States)

Yan, Y. T.; Cai, Y.

2006-03-01

A singular value decomposition (SVD)-enhanced Least-Square fitting technique is discussed. By automatic identifying, ordering, and selecting dominant SVD modes of the derivative matrix that responds to the variations of the variables, the converging process of the Least-Square fitting is significantly enhanced. Thus the fitting speed can be fast enough for a fairly large system. This technique has been successfully applied to precision PEP-II optics measurement in which we determine all quadrupole strengths (both normal and skew components) and sextupole feed-downs as well as all BPM gains and BPM cross-plane couplings through Least-Square fitting of the phase advances and the Local Green's functions as well as the coupling ellipses among BPMs. The local Green's functions are specified by 4 local transfer matrix components R12, R34, R32, R14. These measurable quantities (the Green's functions, the phase advances and the coupling ellipse tilt angles and axis ratios) are obtained by analyzing turn-by-turn Beam Position Monitor (BPM) data with a high-resolution model-independent analysis (MIA). Once all of the quadrupoles and sextupole feed-downs are determined, we obtain a computer virtual accelerator which matches the real accelerator in linear optics. Thus, beta functions, linear coupling parameters, and interaction point (IP) optics characteristics can be measured and displayed.
Gauss’s, Cholesky’s and Banachiewicz’s Contributions to Least Squares

DEFF Research Database (Denmark)

Gustavson, Fred G.; Wasniewski, Jerzy

This paper describes historically Gauss’s contributions to the area of Least Squares. Also mentioned are Cholesky’s and Banachiewicz’s contributions to linear algebra. The material given is backup information to a Tutorial given at PPAM 2011 to honor Cholesky on the hundred anniversary of his...
Seismic time-lapse imaging using Interferometric least-squares migration

KAUST Repository

Sinha, Mrinal

2016-09-06

One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.
Seismic time-lapse imaging using Interferometric least-squares migration

KAUST Repository

Sinha, Mrinal; Schuster, Gerard T.

2016-01-01

One of the problems with 4D surveys is that the environmental conditions change over time so that the experiment is insufficiently repeatable. To mitigate this problem, we propose the use of interferometric least-squares migration (ILSM) to estimate the migration image for the baseline and monitor surveys. Here, a known reflector is used as the reference reflector for ILSM. Results with synthetic and field data show that ILSM can eliminate artifacts caused by non-repeatability in time-lapse surveys.
Partial least squares path modeling basic concepts, methodological issues and applications

CERN Document Server

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...
Multivariat least-squares methods applied to the quantitative spectral analysis of multicomponent samples

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%
Block Least Mean Squares Algorithm over Distributed Wireless Sensor Network

Directory of Open Access Journals (Sweden)

T. Panigrahi

2012-01-01

Full Text Available In a distributed parameter estimation problem, during each sampling instant, a typical sensor node communicates its estimate either by the diffusion algorithm or by the incremental algorithm. Both these conventional distributed algorithms involve significant communication overheads and, consequently, defeat the basic purpose of wireless sensor networks. In the present paper, we therefore propose two new distributed algorithms, namely, block diffusion least mean square (BDLMS and block incremental least mean square (BILMS by extending the concept of block adaptive filtering techniques to the distributed adaptation scenario. The performance analysis of the proposed BDLMS and BILMS algorithms has been carried out and found to have similar performances to those offered by conventional diffusion LMS and incremental LMS algorithms, respectively. The convergence analyses of the proposed algorithms obtained from the simulation study are also found to be in agreement with the theoretical analysis. The remarkable and interesting aspect of the proposed block-based algorithms is that their communication overheads per node and latencies are less than those of the conventional algorithms by a factor as high as the block size used in the algorithms.
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
Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

Energy Technology Data Exchange (ETDEWEB)

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.
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
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
Least-squares reverse time migration of marine data with frequency-selection encoding

KAUST Repository

Dai, Wei; Huang, Yunsong; Schuster, Gerard T.

2013-01-01

The phase-encoding technique can sometimes increase the efficiency of the least-squares reverse time migration (LSRTM) by more than one order of magnitude. However, traditional random encoding functions require all the encoded shots to share
Handbook of Partial Least Squares Concepts, Methods and Applications

CERN Document Server

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.
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)

Partial Least Square with Savitzky Golay Derivative in Predicting Blood Hemoglobin Using Near Infrared Spectrum

Directory of Open Access Journals (Sweden)

Mohd Idrus Mohd Nazrul Effendy

2018-01-01

Full Text Available Near infrared spectroscopy (NIRS is a reliable technique that widely used in medical fields. Partial least square was developed to predict blood hemoglobin concentration using NIRS. The aims of this paper are (i to develop predictive model for near infrared spectroscopic analysis in blood hemoglobin prediction, (ii to establish relationship between blood hemoglobin and near infrared spectrum using a predictive model, (iii to evaluate the predictive accuracy of a predictive model based on root mean squared error (RMSE and coefficient of determination rp2. Partial least square with first order Savitzky Golay (SG derivative preprocessing (PLS-SGd1 showed the higher performance of predictions with RMSE = 0.7965 and rp2= 0.9206 in K-fold cross validation. Optimum number of latent variable (LV and frame length (f were 32 and 27 nm, respectively. These findings suggest that the relationship between blood hemoglobin and near infrared spectrum is strong, and the partial least square with first order SG derivative is able to predict the blood hemoglobin using near infrared spectral data.
Enhanced least squares Monte Carlo method for real-time decision optimizations for evolving natural hazards

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...
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
Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

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...
Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

Science.gov (United States)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.
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
Regularized Partial Least Squares with an Application to NMR Spectroscopy

OpenAIRE

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...
Multisource Least-squares Reverse Time Migration

KAUST Repository

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
Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

Science.gov (United States)

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…
A new finite element formulation for CFD:VIII. The Galerkin/least-squares method for advective-diffusive equations

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
A Monte Carlo Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative.

OpenAIRE

Showalter, Mark H

1994-01-01

This paper reports a Monte Carlo study of the Box-Cox model and a nonlinear least squares alternative. Key results include the following: the transformation parameter in the Box-Cox model appears to be inconsistently estimated in the presence of conditional heteroskedasticity; the constant term in both the Box-Cox and the nonlinear least squares models is poorly estimated in small samples; conditional mean forecasts tend to underestimate their true value in the Box-Cox model when the transfor...
A rigid-body least-squares program with angular and translation scan facilities

CERN Document Server

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).
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...
A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

Science.gov (United States)

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.
Time-domain least-squares migration using the Gaussian beam summation method

Science.gov (United States)

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.
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.
A Hybrid Least Square Support Vector Machine Model with Parameters Optimization for Stock Forecasting

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.
Updating QR factorization procedure for solution of linear least squares problem with equality constraints.

Science.gov (United States)

Zeb, Salman; Yousaf, Muhammad

2017-01-01

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.
Least square regularized regression in sum space.

Science.gov (United States)

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.
Evaluation of interpolation effects on upsampling and accuracy of cost functions-based optimized automatic image registration.

Science.gov (United States)

Mahmoudzadeh, Amir Pasha; Kashou, Nasser H

2013-01-01

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.

Evaluation of Interpolation Effects on Upsampling and Accuracy of Cost Functions-Based Optimized Automatic Image Registration

Directory of Open Access Journals (Sweden)

Amir Pasha Mahmoudzadeh

2013-01-01

Full Text Available Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order and to compare the effect of cost functions (least squares (LS, normalized mutual information (NMI, normalized cross correlation (NCC, and correlation ratio (CR for optimized automatic image registration (OAIR on 3D spoiled gradient recalled (SPGR magnetic resonance images (MRI of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.
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
The least weighted squares I. The asymptotic linearity of normal equations

Czech Academy of Sciences Publication Activity Database

Víšek, Jan Ámos

2002-01-01

Roč. 9, č. 15 (2002), s. 31-58 ISSN 1212-074X R&D Projects: GA AV ČR KSK1019101 Grant - others:GA UK(CZ) 255/2002/A EK /FSV Institutional research plan: CEZ:AV0Z1075907 Keywords : the least weighted squares * robust regression * asymptotic normality and representation Subject RIV: BA - General Mathematics
Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

Science.gov (United States)

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.
Multilevel weighted least squares polynomial approximation

KAUST Repository

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.
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
Least-squares approximation of an improper correlation matrix by a proper one

NARCIS (Netherlands)

Knol, Dirk L.; ten Berge, Jos M.F.

1989-01-01

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and
Non-linear least squares curve fitting of a simple theoretical model to radioimmunoassay dose-response data using a mini-computer

International Nuclear Information System (INIS)

Wilkins, T.A.; Chadney, D.C.; Bryant, J.; Palmstroem, S.H.; Winder, R.L.

1977-01-01

Using the simple univalent antigen univalent-antibody equilibrium model the dose-response curve of a radioimmunoassay (RIA) may be expressed as a function of Y, X and the four physical parameters of the idealised system. A compact but powerful mini-computer program has been written in BASIC for rapid iterative non-linear least squares curve fitting and dose interpolation with this function. In its simplest form the program can be operated in an 8K byte mini-computer. The program has been extensively tested with data from 10 different assay systems (RIA and CPBA) for measurement of drugs and hormones ranging in molecular size from thyroxine to insulin. For each assay system the results have been analysed in terms of (a) curve fitting biases and (b) direct comparison with manual fitting. In all cases the quality of fitting was remarkably good in spite of the fact that the chemistry of each system departed significantly from one or more of the assumptions implicit in the model used. A mathematical analysis of departures from the model's principal assumption has provided an explanation for this somewhat unexpected observation. The essential features of this analysis are presented in this paper together with the statistical analyses of the performance of the program. From these and the results obtained to date in the routine quality control of these 10 assays, it is concluded that the method of curve fitting and dose interpolation presented in this paper is likely to be of general applicability. (orig.) [de
Robust regularized least-squares beamforming approach to signal estimation

KAUST Repository

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.
Implementation of the Least-Squares Lattice with Order and Forgetting Factor Estimation for FPGA

Czech Academy of Sciences Publication Activity Database

Pohl, Zdeněk; Tichý, Milan; Kadlec, Jiří

2008-01-01

Roč. 2008, č. 2008 (2008), s. 1-11 ISSN 1687-6172 R&D Projects: GA MŠk(CZ) 1M0567 EU Projects: European Commission(XE) 027611 - AETHER Program:FP6 Institutional research plan: CEZ:AV0Z10750506 Keywords : DSP * Least-squares lattice * order estimation * exponential forgetting factor estimation * FPGA implementation * scheduling * dynamic reconfiguration * microblaze Subject RIV: IN - Informatics, Computer Science Impact factor: 1.055, year: 2008 http://library.utia.cas.cz/separaty/2008/ZS/pohl-tichy-kadlec-implementation%20of%20the%20least-squares%20lattice%20with%20order%20and%20forgetting%20factor%20estimation%20for%20fpga.pdf
On Solution of Total Least Squares Problems with Multiple Right-hand Sides

Czech Academy of Sciences Publication Activity Database

Hnětynková, I.; Plešinger, Martin; Strakoš, Zdeněk

2008-01-01

Roč. 8, č. 1 (2008), s. 10815-10816 ISSN 1617-7061 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : total least squares problem * multiple right-hand sides * linear approximation problem Subject RIV: BA - General Mathematics
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.
Method for exploiting bias in factor analysis using constrained alternating least squares algorithms

Science.gov (United States)

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.
Least-squares migration of multisource data with a deblurring filter

KAUST Repository

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

KAUST Repository

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.
Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

Science.gov (United States)

Zhang, Ling; Cai, Yunlong; Li, Chunguang; de Lamare, Rodrigo C.

2017-12-01

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.
Mitigation of defocusing by statics and near-surface velocity errors by interferometric least-squares migration

KAUST Repository

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.
Least-Squares Approximation of an Improper Correlation Matrix by a Proper One.

Science.gov (United States)

Knol, Dirk L.; ten Berge, Jos M. F.

1989-01-01

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…
Radial Basis Function (RBF Interpolation and Investigating its Impact on Rainfall Duration Mapping

Directory of Open Access Journals (Sweden)

Hassan Derakhshan

2012-01-01

Full Text Available The missing data in database must be reproduced primarily by appropriate interpolation techniques. Radial basis function (RBF interpolators can play a significant role in data completion of precipitation mapping. Five RBF techniques were engaged to be employed in compensating the missing data in event-wised dataset of Upper Paramatta River Catchment in the western suburbs of Sydney, Australia. The related shape parameter, C, of RBFs was optimized for first event of database during a cross-validation process. The Normalized mean square error (NMSE, percent average estimation error (PAEE and coefficient of determination (R2 were the statistics used as validation tools. Results showed that the multiquadric RBF technique with the least error, best suits compensation of the related database.
An improved partial least-squares regression method for Raman spectroscopy

Science.gov (United States)

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.

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
Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2004-01-01

We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. 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 in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least-squares
Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

KAUST Repository

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.
Incoherent dictionary learning for reducing crosstalk noise in least-squares reverse time migration

Science.gov (United States)

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.
Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

KAUST Repository

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.
Small-kernel, constrained least-squares restoration of sampled image data

Science.gov (United States)

Hazra, Rajeeb; Park, Stephen K.

1992-01-01

Following the work of Park (1989), who extended a derivation of the Wiener filter based on the incomplete discrete/discrete model to a more comprehensive end-to-end continuous/discrete/continuous model, it is shown that a derivation of the constrained least-squares (CLS) filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model. This results in an improved CLS restoration filter, which can be efficiently implemented as a small-kernel convolution in the spatial domain.
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
COMPARISON OF PARTIAL LEAST SQUARES REGRESSION METHOD ALGORITHMS: NIPALS AND PLS-KERNEL AND AN APPLICATION

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.
Efficient Algorithms and Design for Interpolation Filters in Digital Receiver

Directory of Open Access Journals (Sweden)

Xiaowei Niu

2014-05-01

Full Text Available Based on polynomial functions this paper introduces a generalized design method for interpolation filters. The polynomial-based interpolation filters can be implemented efficiently by using a modified Farrow structure with an arbitrary frequency response, the filters allow many pass- bands and stop-bands, and for each band the desired amplitude and weight can be set arbitrarily. The optimization coefficients of the interpolation filters in time domain are got by minimizing the weighted mean squared error function, then converting to solve the quadratic programming problem. The optimization coefficients in frequency domain are got by minimizing the maxima (MiniMax of the weighted mean squared error function. The degree of polynomials and the length of interpolation filter can be selected arbitrarily. Numerical examples verified the proposed design method not only can reduce the hardware cost effectively but also guarantee an excellent performance.
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...
Least-squares resolution of gamma-ray spectra in environmental samples

International Nuclear Information System (INIS)

Kanipe, L.G.; Seale, S.K.; Liggett, W.S.

1977-08-01

The use of ALPHA-M, a least squares computer program for analyzing NaI (Tl) gamma spectra of environmental samples, is evaluated. Included is a comprehensive set of program instructions, listings, and flowcharts. Two other programs, GEN4 and SIMSPEC, are also described. GEN4 is used to create standard libraries for ALPHA-M, and SIMSPEC is used to simulate spectra for ALPHA-M analysis. Tests to evaluate the standard libraries selected for use in analyzing environmental samples are provided. An evaluation of the results of sample analyses is discussed
Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

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.
SIOB: a FORTRAN code for least-squares shape fitting several neutron transmission measurements using the Breit--Wigner multilevel formula. [For IBM-360/91

Energy Technology Data Exchange (ETDEWEB)

de Saussure, G.; Olsen, D. K.; Perez, R. B.

1978-05-01

The FORTRAN-IV code SIOB was developed to least-square fit the shape of neutron transmission curves. Any number of measurements on a common energy scale for different sample thicknesses can be simultaneously fitted. The computed transmission curves can be broadened with either a Gaussian or a rectangular resolution function or both, with the resolution width a function of energy. The total cross section is expressed as a sum of single-level or multilevel Breit--Wigner terms and Doppler broadened by using the fast interpolation routine QUICKW. The number of data points, resonance levels, and variables which can be handled simultaneously is only limited by the overall dimensions of two arrays in the program and by the stability of the matrix inversion. In a test problem seven transmissions each with 3750 data points were simultaneously fitted with 74 resonances and 110 variable parameters. The problem took 47 min of CPU time on an IBM-360/91, for 3 iterations. 3 figures, 2 tables.
Weighted least-square approach for simultaneous measurement of multiple reflective surfaces

Science.gov (United States)

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.
Influence of the least-squares phase on optical vortices in strongly scintillated beams

CSIR Research Space (South Africa)

Chen, M

2009-06-01

Full Text Available , the average total number of vortices is reduced further. However, the reduction becomes smaller for each succes- sive step. This indicates that the ability of getting rid of optical vortices by removing the least-squares phase becomes progressively less...
Bayesian model averaging and weighted average least squares : Equivariance, stability, and numerical issues

NARCIS (Netherlands)

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
Expectile smoothing: new perspectives on asymmetric least squares. An application to life expectancy

NARCIS (Netherlands)

Schnabel, S.K.

2011-01-01

While initially motivated from a demographic application, this thesis develops methodology for expectile estimation. To this end first the basic model for expectile curves using least asymmetrically weighted squares (LAWS) was introduced as well as methods for smoothing in this context. The simple
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

Science.gov (United States)

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.
Joint 2D-DOA and Frequency Estimation for L-Shaped Array Using Iterative Least Squares Method

Directory of Open Access Journals (Sweden)

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.

Least median of squares filtering of locally optimal point matches for compressible flow image registration

International Nuclear Information System (INIS)

Castillo, Edward; Guerrero, Thomas; Castillo, Richard; White, Benjamin; Rojo, Javier

2012-01-01

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration. (paper)
Fast Dating Using Least-Squares Criteria and Algorithms.

Science.gov (United States)

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
Ordinary least square regression, orthogonal regression, geometric mean regression and their applications in aerosol science

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
Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

Science.gov (United States)

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.
Shape-based grey-level image interpolation

International Nuclear Information System (INIS)

Keh-Shih Chuang; Chun-Yuan Chen; Ching-Kai Yeh

1999-01-01

The three-dimensional (3D) object data obtained from a CT scanner usually have unequal sampling frequencies in the x-, y- and z-directions. Generally, the 3D data are first interpolated between slices to obtain isotropic resolution, reconstructed, then operated on using object extraction and display algorithms. The traditional grey-level interpolation introduces a layer of intermediate substance and is not suitable for objects that are very different from the opposite background. The shape-based interpolation method transfers a pixel location to a parameter related to the object shape and the interpolation is performed on that parameter. This process is able to achieve a better interpolation but its application is limited to binary images only. In this paper, we present an improved shape-based interpolation method for grey-level images. The new method uses a polygon to approximate the object shape and performs the interpolation using polygon vertices as references. The binary images representing the shape of the object were first generated via image segmentation on the source images. The target object binary image was then created using regular shape-based interpolation. The polygon enclosing the object for each slice can be generated from the shape of that slice. We determined the relative location in the source slices of each pixel inside the target polygon using the vertices of a polygon as the reference. The target slice grey-level was interpolated from the corresponding source image pixels. The image quality of this interpolation method is better and the mean squared difference is smaller than with traditional grey-level interpolation. (author)
Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

OpenAIRE

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...
Credit Risk Evaluation Using a C-Variable Least Squares Support Vector Classification Model

Science.gov (United States)

Yu, Lean; Wang, Shouyang; Lai, K. K.

Credit risk evaluation is one of the most important issues in financial risk management. In this paper, a C-variable least squares support vector classification (C-VLSSVC) model is proposed for credit risk analysis. The main idea of this model is based on the prior knowledge that different classes may have different importance for modeling and more weights should be given to those classes with more importance. The C-VLSSVC model can be constructed by a simple modification of the regularization parameter in LSSVC, whereby more weights are given to the lease squares classification errors with important classes than the lease squares classification errors with unimportant classes while keeping the regularized terms in its original form. For illustration purpose, a real-world credit dataset is used to test the effectiveness of the C-VLSSVC model.
Non-linear HVAC computations using least square support vector machines

International Nuclear Information System (INIS)

Kumar, Mahendra; Kar, I.N.

2009-01-01

This paper aims to demonstrate application of least square support vector machines (LS-SVM) to model two complex heating, ventilating and air-conditioning (HVAC) relationships. The two applications considered are the estimation of the predicted mean vote (PMV) for thermal comfort and the generation of psychrometric chart. LS-SVM has the potential for quick, exact representations and also possesses a structure that facilitates hardware implementation. The results show very good agreement between function values computed from conventional model and LS-SVM model in real time. The robustness of LS-SVM models against input noises has also been analyzed.
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.
Uncertainty analysis of pollutant build-up modelling based on a Bayesian weighted least squares approach

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
Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

KAUST Repository

Dutta, Gaurav; Lu, Kai; Wang, Xin; Schuster, Gerard T.

2013-01-01

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
Internal displacement and strain measurement using digital volume correlation: a least-squares framework

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)
Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

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.
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
Speed control of induction motor using fuzzy recursive least squares technique

OpenAIRE

Santiago Sánchez; Eduardo Giraldo

2008-01-01

A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the c...
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...
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.
Consistent Partial Least Squares Path Modeling via Regularization.

Science.gov (United States)

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.
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.

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 with radon preconditioning

KAUST Repository

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.
Discrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters

KAUST Repository

Nobile, Fabio

2015-01-01

the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial
Modeling geochemical datasets for source apportionment: Comparison of least square regression and inversion approaches.

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...
Speed control of induction motor using fuzzy recursive least squares technique

Directory of Open Access Journals (Sweden)

Santiago Sánchez

2008-12-01

Full Text Available A simple adaptive controller design is presented in this paper, the control system uses the adaptive fuzzy logic, sliding modes and is trained with the recursive least squares technique. The problem of parameter variation is solved with the adaptive controller; the use of an internal PI regulator produces that the speed control of the induction motor be achieved by the stator currents instead the input voltage. The rotor-flux oriented coordinated system model is used to develop and test the control system.
Power system state estimation using an iteratively reweighted least squares method for sequential L{sub 1}-regression

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)
Study of the convergence behavior of the complex kernel least mean square algorithm.

Science.gov (United States)

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.
A weak Galerkin least-squares finite element method for div-curl systems

Science.gov (United States)

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.
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...
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.
Spatial and temporal interpolation of satellite-based aerosol optical depth measurements over North America using B-splines

Science.gov (United States)

Pfister, Nicolas; O'Neill, Norman T.; Aube, Martin; Nguyen, Minh-Nghia; Bechamp-Laganiere, Xavier; Besnier, Albert; Corriveau, Louis; Gasse, Geremie; Levert, Etienne; Plante, Danick

2005-08-01

Satellite-based measurements of aerosol optical depth (AOD) over land are obtained from an inversion procedure applied to dense dark vegetation pixels of remotely sensed images. The limited number of pixels over which the inversion procedure can be applied leaves many areas with little or no AOD data. Moreover, satellite coverage by sensors such as MODIS yields only daily images of a given region with four sequential overpasses required to straddle mid-latitude North America. Ground based AOD data from AERONET sun photometers are available on a more continuous basis but only at approximately fifty locations throughout North America. The object of this work is to produce a complete and coherent mapping of AOD over North America with a spatial resolution of 0.1 degree and a frequency of three hours by interpolating MODIS satellite-based data together with available AERONET ground based measurements. Before being interpolated, the MODIS AOD data extracted from different passes are synchronized to the mapping time using analyzed wind fields from the Global Multiscale Model (Meteorological Service of Canada). This approach amounts to a trajectory type of simplified atmospheric dynamics correction method. The spatial interpolation is performed using a weighted least squares method applied to bicubic B-spline functions defined on a rectangular grid. The least squares method enables one to weight the data accordingly to the measurement errors while the B-splines properties of local support and C2 continuity offer a good approximation of AOD behaviour viewed as a function of time and space.
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.
Hourly cooling load forecasting using time-indexed ARX models with two-stage weighted least squares regression

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
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
Parameter Estimation of Permanent Magnet Synchronous Motor Using Orthogonal Projection and Recursive Least Squares Combinatorial Algorithm

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.
From least squares to multilevel modeling: A graphical introduction to Bayesian inference

Science.gov (United States)

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.
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....
Estimasi Kanal Akustik Bawah Air Untuk Perairan Dangkal Menggunakan Metode Least Square (LS dan Minimum Mean Square Error (MMSE

Directory of Open Access Journals (Sweden)

Mardawia M Panrereng

2015-06-01

Full Text Available Dalam beberapa tahun terakhir, sistem komunikasi akustik bawah air banyak dikembangkan oleh beberapa peneliti. Besarnya tantangan yang dihadapi membuat para peneliti semakin tertarik untuk mengembangkan penelitian dibidang ini. Kanal bawah air merupakan media komunikasi yang sulit karena adanya attenuasi, absorption, dan multipath yang disebabkan oleh gerakan gelombang air setiap saat. Untuk perairan dangkal, multipath disebabkan adanya pantulan dari permukaan dan dasar laut. Kebutuhan pengiriman data cepat dengan bandwidth terbatas menjadikan Ortogonal Frequency Division Multiplexing (OFDM sebagai solusi untuk komunikasi transmisi tinggi dengan modulasi menggunakan Binary Phase-Shift Keying (BPSK. Estimasi kanal bertujuan untuk mengetahui karakteristik respon impuls kanal propagasi dengan mengirimkan pilot simbol. Pada estimasi kanal menggunakan metode Least Square (LS nilai Mean Square Error (MSE yang diperoleh cenderung lebih besar dari metode estimasi kanal menggunakan metode Minimum Mean Square (MMSE. Hasil kinerja estimasi kanal berdasarkan perhitungan Bit Error Rate (BER untuk estimasi kanal menggunakan metode LS dan metode MMSE tidak menunjukkan perbedaan yang signifikan yaitu berselisih satu SNR untuk setiap metode estimasi kanal yang digunakan.
A negative-norm least-squares method for time-harmonic Maxwell equations

KAUST Repository

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.
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

Comment on "Fringe projection profilometry with nonparallel illumination: a least-squares approach"

Science.gov (United States)

Wang, Zhaoyang; Bi, Hongbo

2006-07-01

We comment on the recent Letter by Chen and Quan [Opt. Lett.30, 2101 (2005)] in which a least-squares approach was proposed to cope with the nonparallel illumination in fringe projection profilometry. It is noted that the previous mathematical derivations of the fringe pitch and carrier phase functions on the reference plane were incorrect. In addition, we suggest that the variation of carrier phase along the vertical direction should be considered.
Phase-unwrapping algorithm by a rounding-least-squares approach

Science.gov (United States)

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.
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.
3D plane-wave least-squares Kirchhoff migration

KAUST Repository

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.
Modeling and forecasting monthly movement of annual average solar insolation based on the least-squares Fourier-model

International Nuclear Information System (INIS)

Yang, Zong-Chang

2014-01-01

Highlights: • Introduce a finite Fourier-series model for evaluating monthly movement of annual average solar insolation. • Present a forecast method for predicting its movement based on the extended Fourier-series model in the least-squares. • Shown its movement is well described by a low numbers of harmonics with approximately 6-term Fourier series. • Predict its movement most fitting with less than 6-term Fourier series. - Abstract: Solar insolation is one of the most important measurement parameters in many fields. Modeling and forecasting monthly movement of annual average solar insolation is of increasingly importance in areas of engineering, science and economics. In this study, Fourier-analysis employing finite Fourier-series is proposed for evaluating monthly movement of annual average solar insolation and extended in the least-squares for forecasting. The conventional Fourier analysis, which is the most common analysis method in the frequency domain, cannot be directly applied for prediction. Incorporated with the least-square method, the introduced Fourier-series model is extended to predict its movement. The extended Fourier-series forecasting model obtains its optimums Fourier coefficients in the least-square sense based on its previous monthly movements. The proposed method is applied to experiments and yields satisfying results in the different cities (states). It is indicated that monthly movement of annual average solar insolation is well described by a low numbers of harmonics with approximately 6-term Fourier series. The extended Fourier forecasting model predicts the monthly movement of annual average solar insolation most fitting with less than 6-term Fourier series
Linear, Transﬁnite and Weighted Method for Interpolation from Grid Lines Applied to OCT Images

DEFF Research Database (Denmark)

Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen

2018-01-01

of a square grid, but are unknown inside each square. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid lines: linear, transfinite and weighted. The linear method does not preserve...... and the stability of the linear method further away. An important parameter influencing the performance of the interpolation methods is the upsampling rate. We perform an extensive evaluation of the three interpolation methods across a range of upsampling rates. Our statistical analysis shows significant difference...... in the performance of the three methods. We find that the transfinite interpolation works well for small upsampling rates and the proposed weighted interpolation method performs very well for all upsampling rates typically used in practice. On the basis of these findings we propose an approach for combining two OCT...
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....
New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

Science.gov (United States)

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.
Ajustar: A interactive processor for to fit, by means of least squares, one variable polynomials (arbitrary degree) at experimental points

International Nuclear Information System (INIS)

Sanchez Miro, J. J.; Pena Gutierrez, J.

1991-01-01

In this report is offered, to scientist and technical people, a numeric tool consisting in a FORTRAN program, of interactive use, with destination to make lineal l east squares , fittings on any set of empirical observations. The method based in the orthogonal functions (for discrete case), instead of direct solving the equations system, is used. The procedure includes also the optionally facilities of: variable change, direct interpolation, correlation non linear factor, w eights o f the points, confidence intervals (Schelle, Miller, Student), and plotting results. (Author) 10 refs
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 ℓ²-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.
A Bayesian least-squares support vector machine method for predicting the remaining useful life of a microwave component

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.
PERBANDINGAN ANALISIS LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR DAN PARTIAL LEAST SQUARES (Studi Kasus: Data Microarray

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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.
Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

Science.gov (United States)

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.
Gravity Search Algorithm hybridized Recursive Least Square method for power system harmonic estimation

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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.
Locally Linear Embedding of Local Orthogonal Least Squares Images for Face Recognition

Science.gov (United States)

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.
Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

Science.gov (United States)

Van Benthem, Mark H.; Keenan, Michael R.

2008-11-11

A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.
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
Cognitive assessment in mathematics with the least squares distance method.

Science.gov (United States)

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.
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.
Medium Band Least Squares Estimation of Fractional Cointegration in the Presence of Low-Frequency Contamination

DEFF Research Database (Denmark)

Christensen, Bent Jesper; Varneskov, Rasmus T.

band least squares (MBLS) estimator uses sample dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing...

Multisource least-squares migration of marine streamer and land data with frequency-division encoding

KAUST Repository

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.
Multisource least-squares migration of marine streamer and land data with frequency-division encoding

KAUST Repository

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 fit of a linear combination of functions

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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.
Robust Homography Estimation Based on Nonlinear Least Squares Optimization

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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.
Commutative discrete filtering on unstructured grids based on least-squares techniques

International Nuclear Information System (INIS)

Haselbacher, Andreas; Vasilyev, Oleg V.

2003-01-01

The present work is concerned with the development of commutative discrete filters for unstructured grids and contains two main contributions. First, building on the work of Marsden et al. [J. Comp. Phys. 175 (2002) 584], a new commutative discrete filter based on least-squares techniques is constructed. Second, a new analysis of the discrete commutation error is carried out. The analysis indicates that the discrete commutation error is not only dependent on the number of vanishing moments of the filter weights, but also on the order of accuracy of the discrete gradient operator. The results of the analysis are confirmed by grid-refinement studies
Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

Science.gov (United States)

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.
Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

Science.gov (United States)

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.
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)
Short-term traffic flow prediction model using particle swarm optimization–based combined kernel function-least squares support vector machine combined with chaos theory

Directory of Open Access Journals (Sweden)

Qiang Shang

2016-08-01

Full Text Available Short-term traffic flow prediction is an important part of intelligent transportation systems research and applications. For further improving the accuracy of short-time traffic flow prediction, a novel hybrid prediction model (multivariate phase space reconstruction–combined kernel function-least squares support vector machine based on multivariate phase space reconstruction and combined kernel function-least squares support vector machine is proposed. The C-C method is used to determine the optimal time delay and the optimal embedding dimension of traffic variables’ (flow, speed, and occupancy time series for phase space reconstruction. The G-P method is selected to calculate the correlation dimension of attractor which is an important index for judging chaotic characteristics of the traffic variables’ series. The optimal input form of combined kernel function-least squares support vector machine model is determined by multivariate phase space reconstruction, and the model’s parameters are optimized by particle swarm optimization algorithm. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. The experimental results suggest that the new proposed model yields better predictions compared with similar models (combined kernel function-least squares support vector machine, multivariate phase space reconstruction–generalized kernel function-least squares support vector machine, and phase space reconstruction–combined kernel function-least squares support vector machine, which indicates that the new proposed model exhibits stronger prediction ability and robustness.
Multisource least-squares reverse-time migration with structure-oriented filtering

Science.gov (United States)

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.
An improved conjugate gradient scheme to the solution of least squares SVM.

Science.gov (United States)

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.
Multivariate fault isolation of batch processes via variable selection in partial least squares discriminant analysis.

Science.gov (United States)

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.
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

2015-01-01

Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Electric Load Forecasting Based on a Least Squares Support Vector Machine with Fuzzy Time Series and Global Harmony Search Algorithm

Directory of Open Access Journals (Sweden)

Yan Hong Chen

2016-01-01

Full Text Available This paper proposes a new electric load forecasting model by hybridizing the fuzzy time series (FTS and global harmony search algorithm (GHSA with least squares support vector machines (LSSVM, namely GHSA-FTS-LSSVM model. Firstly, the fuzzy c-means clustering (FCS algorithm is used to calculate the clustering center of each cluster. Secondly, the LSSVM is applied to model the resultant series, which is optimized by GHSA. Finally, a real-world example is adopted to test the performance of the proposed model. In this investigation, the proposed model is verified using experimental datasets from the Guangdong Province Industrial Development Database, and results are compared against autoregressive integrated moving average (ARIMA model and other algorithms hybridized with LSSVM including genetic algorithm (GA, particle swarm optimization (PSO, harmony search, and so on. The forecasting results indicate that the proposed GHSA-FTS-LSSVM model effectively generates more accurate predictive results.
Positivity Preserving Interpolation Using Rational Bicubic Spline

Directory of Open Access Journals (Sweden)

Samsul Ariffin Abdul Karim

2015-01-01

Full Text Available This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE, our partially blended rational bicubic spline is on a par with the established methods.
Sulfur Speciation of Crude Oils by Partial Least Squares Regression Modeling of Their Infrared Spectra

NARCIS (Netherlands)

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
Ajustar: A interactive processor for to fit, by means of least squares, one variable polynomials (arbitrary degree) at experimental points; Ajustar: Un procesador interactivo para ajuste por minimos cuadrados de polinomios algebraicos (en una sola variable y grado arbitrario) a conjuntos de datos experimentales

Energy Technology Data Exchange (ETDEWEB)

Sanchez Miro, J J; Pena Gutierrez, J

1991-07-01

In this report is offered, to scientist and technical people, a numeric tool consisting in a FORTRAN program, of interactive use, with destination to make lineal {sup l}east squares{sup ,} fittings on any set of empirical observations. The method based in the orthogonal functions (for discrete case), instead of direct solving the equations system, is used. The procedure includes also the optionally facilities of: variable change, direct interpolation, correlation non linear factor, {sup w}eights{sup o}f the points, confidence intervals (Schelle, Miller, Student), and plotting results. (Author) 10 refs.
The current strain distribution in the North China Basin of eastern China by least-squares collocation

Science.gov (United States)

Wu, J. C.; Tang, H. W.; Chen, Y. Q.; Li, Y. X.

2006-07-01

In this paper, the velocities of 154 stations obtained in 2001 and 2003 GPS survey campaigns are applied to formulate a continuous velocity field by the least-squares collocation method. The strain rate field obtained by the least-squares collocation method shows more clear deformation patterns than that of the conventional discrete triangle method. The significant deformation zones obtained are mainly located in three places, to the north of Tangshan, between Tianjing and Shijiazhuang, and to the north of Datong, which agree with the places of the Holocene active deformation zones obtained by geological investigations. The maximum shear strain rate is located at latitude 38.6°N and longitude 116.8°E, with a magnitude of 0.13 ppm/a. The strain rate field obtained can be used for earthquake prediction research in the North China Basin.
Least square methods and covariance matrix applied to the relative efficiency calibration of a Ge(Li) detector

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
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.

Intelligent Quality Prediction Using Weighted Least Square Support Vector Regression

Science.gov (United States)

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.
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.
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.
Geometric Least Square Models for Deriving [0,1]-Valued Interval Weights from Interval Fuzzy Preference Relations Based on Multiplicative Transitivity

Directory of Open Access Journals (Sweden)

Xuan Yang

2015-01-01

Full Text Available This paper presents a geometric least square framework for deriving [0,1]-valued interval weights from interval fuzzy preference relations. By analyzing the relationship among [0,1]-valued interval weights, multiplicatively consistent interval judgments, and planes, a geometric least square model is developed to derive a normalized [0,1]-valued interval weight vector from an interval fuzzy preference relation. Based on the difference ratio between two interval fuzzy preference relations, a geometric average difference ratio between one interval fuzzy preference relation and the others is defined and employed to determine the relative importance weights for individual interval fuzzy preference relations. A geometric least square based approach is further put forward for solving group decision making problems. An individual decision numerical example and a group decision making problem with the selection of enterprise resource planning software products are furnished to illustrate the effectiveness and applicability of the proposed models.
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.
Battery state-of-charge estimation using approximate least squares

Science.gov (United States)

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.
Application of partial least squares near-infrared spectral classification in diabetic identification

Science.gov (United States)

Yan, Wen-juan; Yang, Ming; He, Guo-quan; Qin, Lin; Li, Gang

2014-11-01

In order to identify the diabetic patients by using tongue near-infrared (NIR) spectrum - a spectral classification model of the NIR reflectivity of the tongue tip is proposed, based on the partial least square (PLS) method. 39sample data of tongue tip's NIR spectra are harvested from healthy people and diabetic patients , respectively. After pretreatment of the reflectivity, the spectral data are set as the independent variable matrix, and information of classification as the dependent variables matrix, Samples were divided into two groups - i.e. 53 samples as calibration set and 25 as prediction set - then the PLS is used to build the classification model The constructed modelfrom the 53 samples has the correlation of 0.9614 and the root mean square error of cross-validation (RMSECV) of 0.1387.The predictions for the 25 samples have the correlation of 0.9146 and the RMSECV of 0.2122.The experimental result shows that the PLS method can achieve good classification on features of healthy people and diabetic patients.
Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl

Science.gov (United States)

De Beuckeleer, Liene I.; Herrebout, Wouter A.

2016-02-01

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before.
Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

Science.gov (United States)

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.
A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

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)
Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

KAUST Repository

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
SU-E-I-08: An Inpaint-Based Interpolation Technique to Recover Blocked Information for Cone Beam CT with a Synchronized Moving Grid (SMOG)

International Nuclear Information System (INIS)

Kong, V; Zhang, H; Jin, J; Ren, L

2014-01-01

Purpose: Synchronized moving grid (SMOG) is a promising technique to reduce scatter and ghost artifacts in cone beam computed tomography (CBCT). However, the grid blocks part of image information in each projection, and multiple projections at the same gantry angle have to been taken to obtain full information. Because of the continuity of a patient's anatomy in the projection, the blocked information may be estimated by interpolation. This study aims to evaluate an inpainting-based interpolation approach to recover the missing information for CBCT reconstruction. Method: We used a simple region-based inpainting approach to interpolate the missing information. For a pixel to be interpolated, we divided the nearby regions having image information into 6 sub-regions: up-left, up-middle, up-right, down-left, down-middle, and down-right, each with 9 pixels. The average pixel value of each sub-region was calculated. These average values, along with the pixel location, were used to determine the interpolated pixel value. We compared our approach with the Criminisi Exemplar (CE) and total variation (TV) based inpainting techniques. Projection images of Catphan and a head phantom were used for the comparison. The SMOG was simulated by erasing the information (filling with “0”) of the areas in each projection corresponding to the grid. Results: For the Catphan, the processing time was 178, 45 and 0.98 minutes for CE, TV and our approach, respectively. The signal to noise ratio (SNR) was 19.4, 18.5 and 26.4 db, correspondingly. For the head phantom, the processing time was 222, 45 and 0.93 minutes for CE, TV and our approach, respectively. The SNR was 24.6, 20.2 and 26.2db correspondingly. Conclusion: We have developed a simple inpainting based interpolation approach, which can recover some of the image information for the SMOG-based CBCT imaging. This study is supported by NIH/NCI grant 1R01CA166948-01
Emulating facial biomechanics using multivariate partial least squares surrogate models.

Science.gov (United States)

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.
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...
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.
Facial Expression Recognition using Multiclass Ensemble Least-Square Support Vector Machine

Science.gov (United States)

Lawi, Armin; Sya'Rani Machrizzandi, M.

2018-03-01

Facial expression is one of behavior characteristics of human-being. The use of biometrics technology system with facial expression characteristics makes it possible to recognize a person’s mood or emotion. The basic components of facial expression analysis system are face detection, face image extraction, facial classification and facial expressions recognition. This paper uses Principal Component Analysis (PCA) algorithm to extract facial features with expression parameters, i.e., happy, sad, neutral, angry, fear, and disgusted. Then Multiclass Ensemble Least-Squares Support Vector Machine (MELS-SVM) is used for the classification process of facial expression. The result of MELS-SVM model obtained from our 185 different expression images of 10 persons showed high accuracy level of 99.998% using RBF kernel.
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)
Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

KAUST Repository

Migliorati, Giovanni; Nobile, Fabio; Tempone, Raul

2015-01-01

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability
Discrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters

KAUST Repository

Nobile, Fabio

2015-01-07

We consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality
Polynomial curve fitting for control rod worth using least square numerical analysis

International Nuclear Information System (INIS)

Muhammad Husamuddin Abdul Khalil; Mark Dennis Usang; Julia Abdul Karim; Mohd Amin Sharifuldin Salleh

2012-01-01

RTP must have sufficient excess reactivity to compensate the negative reactivity feedback effects such as those caused by the fuel temperature and power defects of reactivity, fuel burn-up and to allow full power operation for predetermined period of time. To compensate this excess reactivity, it is necessary to introduce an amount of negative reactivity by adjusting or controlling the control rods at will. Control rod worth depends largely upon the value of the neutron flux at the location of the rod and reflected by a polynomial curve. Purpose of this paper is to rule out the polynomial curve fitting using least square numerical techniques via MATLAB compatible language. (author)

Decentralized Gauss-Newton method for nonlinear least squares on wide area network

Science.gov (United States)

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.
Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

Directory of Open Access Journals (Sweden)

Sun Zhangzhen

2012-08-01

Full Text Available In this paper, an improved weighted least squares (WLS, together with autoregressive (AR model, is proposed to improve prediction accuracy of earth rotation parameters(ERP. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.
Fault Estimation for Fuzzy Delay Systems: A Minimum Norm Least Squares Solution Approach.

Science.gov (United States)

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.
Weighted least squares phase unwrapping based on the wavelet transform

Science.gov (United States)

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.
Improvement of image quality using interpolated projection data estimation method in SPECT

International Nuclear Information System (INIS)

Takaki, Akihiro; Soma, Tsutomu; Murase, Kenya; Kojima, Akihiro; Asao, Kimie; Kamada, Shinya; Matsumoto, Masanori

2009-01-01

General data acquisition for single photon emission computed tomography (SPECT) is performed in 90 or 60 directions, with a coarse pitch of approximately 4-6 deg for a rotation of 360 deg or 180 deg, using a gamma camera. No data between adjacent projections will be sampled under these circumstances. The aim of the study was to develop a method to improve SPECT image quality by generating lacking projection data through interpolation of data obtained with a coarse pitch such as 6 deg. The projection data set at each individual degree in 360 directions was generated by a weighted average interpolation method from the projection data acquired with a coarse sampling angle (interpolated projection data estimation processing method, IPDE method). The IPDE method was applied to the numerical digital phantom data, actual phantom data and clinical brain data with Tc-99m ethyle cysteinate dimer (ECD). All SPECT images were reconstructed by the filtered back-projection method and compared with the original SPECT images. The results confirmed that streak artifacts decreased by apparently increasing a sampling number in SPECT after interpolation and also improved signal-to-noise (S/N) ratio of the root mean square uncertainty value. Furthermore, the normalized mean square error values, compared with standard images, had similar ones after interpolation. Moreover, the contrast and concentration ratios increased their effects after interpolation. These results indicate that effective improvement of image quality can be expected with interpolation. Thus, image quality and the ability to depict images can be improved while maintaining the present acquisition time and image quality. In addition, this can be achieved more effectively than at present even if the acquisition time is reduced. (author)
BER analysis of regularized least squares for BPSK recovery

KAUST Repository

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 x0 ∈ {−1, 1}ⁿ from m-dimensional measurement vector y = Ax+z, where A and z are assumed to be Gaussian with iid entries. We consider two variants of decoders based on the regularized least squares followed by hard-thresholding: the case where the convex relaxation is from {−1, 1}ⁿ to ℝⁿ and the box constrained case where the relaxation is to [−1, 1]ⁿ. For both cases, we derive an exact expression of the bit error probability when n and m grow simultaneously large at a fixed ratio. For the box constrained case, we show that there exists a critical value of the SNR, above which the optimal regularizer is zero. On the other side, the regularization can further improve the performance of the box relaxation at low to moderate SNR regimes. We also prove that the optimal regularizer in the bit error rate sense for the unboxed case is nothing but the MMSE detector.
BER analysis of regularized least squares for BPSK recovery

KAUST Repository

Ben Atitallah, Ismail

2017-06-20

This paper investigates the problem of recovering an n-dimensional BPSK signal x0 ∈ {−1, 1}ⁿ from m-dimensional measurement vector y = Ax+z, where A and z are assumed to be Gaussian with iid entries. We consider two variants of decoders based on the regularized least squares followed by hard-thresholding: the case where the convex relaxation is from {−1, 1}ⁿ to ℝⁿ and the box constrained case where the relaxation is to [−1, 1]ⁿ. For both cases, we derive an exact expression of the bit error probability when n and m grow simultaneously large at a fixed ratio. For the box constrained case, we show that there exists a critical value of the SNR, above which the optimal regularizer is zero. On the other side, the regularization can further improve the performance of the box relaxation at low to moderate SNR regimes. We also prove that the optimal regularizer in the bit error rate sense for the unboxed case is nothing but the MMSE detector.
New Method for Mesh Moving Based on Radial Basis Function Interpolation

NARCIS (Netherlands)

De Boer, A.; Van der Schoot, M.S.; Bijl, H.

2006-01-01

A new point-by-point mesh movement algorithm is developed for the deformation of unstructured grids. The method is based on using radial basis function, RBFs, to interpolate the displacements of the boundary nodes to the whole flow mesh. A small system of equations has to be solved, only involving
PROPOSED MODIFICATIONS OF K2-TEMPERATURE RELATION AND LEAST SQUARES ESTIMATES OF BOD (BIOCHEMICAL OXYGEN DEMAND) PARAMETERS

Science.gov (United States)

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...
Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

International Nuclear Information System (INIS)

Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo; Martinet, Philippe

2008-01-01

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot
Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

Energy Technology Data Exchange (ETDEWEB)

Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo [Sungkyunkwan University, Suwon (Korea, Republic of); Martinet, Philippe [Blaise Pascal University, Clermont-Ferrand Cedex (France)

2008-07-15

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot
Direct integral linear least square regression method for kinetic evaluation of hepatobiliary scintigraphy

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)
3D Medical Image Interpolation Based on Parametric Cubic Convolution

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.
A Generalized Least Squares Regression Approach for Computing Effect Sizes in Single-Case Research: Application Examples

Science.gov (United States)

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…
Application of the Total Least Square ESPRIT Method to Estimation of Angular Coordinates of Moving Objects

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.
Estimating monthly temperature using point based interpolation techniques

Science.gov (United States)

Saaban, Azizan; Mah Hashim, Noridayu; Murat, Rusdi Indra Zuhdi

2013-04-01

This paper discusses the use of point based interpolation to estimate the value of temperature at an unallocated meteorology stations in Peninsular Malaysia using data of year 2010 collected from the Malaysian Meteorology Department. Two point based interpolation methods which are Inverse Distance Weighted (IDW) and Radial Basis Function (RBF) are considered. The accuracy of the methods is evaluated using Root Mean Square Error (RMSE). The results show that RBF with thin plate spline model is suitable to be used as temperature estimator for the months of January and December, while RBF with multiquadric model is suitable to estimate the temperature for the rest of the months.
A Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

Science.gov (United States)

Cheung, KW; So, HC; Ma, W.-K.; Chan, YT

2006-12-01

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.
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)
Evaluation of unconfined-aquifer parameters from pumping test data by nonlinear least squares

Science.gov (United States)

Heidari, Manoutchehr; Wench, Allen

1997-05-01

Nonlinear least squares (NLS) with automatic differentiation was used to estimate aquifer parameters from drawdown data obtained from published pumping tests conducted in homogeneous, water-table aquifers. The method is based on a technique that seeks to minimize the squares of residuals between observed and calculated drawdown subject to bounds that are placed on the parameter of interest. The analytical model developed by Neuman for flow to a partially penetrating well of infinitesimal diameter situated in an infinite, homogeneous and anisotropic aquifer was used to obtain calculated drawdown. NLS was first applied to synthetic drawdown data from a hypothetical but realistic aquifer to demonstrate that the relevant hydraulic parameters (storativity, specific yield, and horizontal and vertical hydraulic conductivity) can be evaluated accurately. Next the method was used to estimate the parameters at three field sites with widely varying hydraulic properties. NLS produced unbiased estimates of the aquifer parameters that are close to the estimates obtained with the same data using a visual curve-matching approach. Small differences in the estimates are a consequence of subjective interpretation introduced in the visual approach.
First-order system least-squares for the Helmholtz equation

Energy Technology Data Exchange (ETDEWEB)

Lee, B.; Manteuffel, T.; McCormick, S.; Ruge, J.

1996-12-31

We apply the FOSLS methodology to the exterior Helmholtz equation {Delta}p + k{sup 2}p = 0. Several least-squares functionals, some of which include both H{sup -1}({Omega}) and L{sup 2}({Omega}) terms, are examined. We show that in a special subspace of [H(div; {Omega}) {intersection} H(curl; {Omega})] x H{sup 1}({Omega}), each of these functionals are equivalent independent of k to a scaled H{sup 1}({Omega}) norm of p and u = {del}p. This special subspace does not include the oscillatory near-nullspace components ce{sup ik}({sup {alpha}x+{beta}y)}, where c is a complex vector and where {alpha}{sub 2} + {beta}{sup 2} = 1. These components are eliminated by applying a non-standard coarsening scheme. We achieve this scheme by introducing {open_quotes}ray{close_quotes} basis functions which depend on the parameter pair ({alpha}, {beta}), and which approximate ce{sup ik}({sup {alpha}x+{beta}y)} well on the coarser levels where bilinears cannot. We use several pairs of these parameters on each of these coarser levels so that several coarse grid problems are spun off from the finer levels. Some extensions of this theory to the transverse electric wave solution for Maxwell`s equations will also be presented.

Least Square Fast Learning Network for modeling the combustion efficiency of a 300WM coal-fired boiler.

Science.gov (United States)

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.
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.
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
Application of the Least Squares Method in Axisymmetric Biharmonic Problems

Directory of Open Access Journals (Sweden)

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.
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.
A least-squares minimisation approach to depth determination from numerical second horizontal self-potential anomalies

Science.gov (United States)

Abdelrahman, El-Sayed Mohamed; Soliman, Khalid; Essa, Khalid Sayed; Abo-Ezz, Eid Ragab; El-Araby, Tarek Mohamed

2009-06-01

This paper develops a least-squares minimisation approach to determine the depth of a buried structure from numerical second horizontal derivative anomalies obtained from self-potential (SP) data using filters of successive window lengths. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the centre of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination from second derivative SP anomalies has been transformed into the problem of finding a solution to a non-linear equation of the form f(z)=0. Formulas have been derived for horizontal cylinders, spheres, and vertical cylinders. Procedures are also formulated to determine the electric dipole moment and the polarization angle. The proposed method was tested on synthetic noisy and real SP data. In the case of the synthetic data, the least-squares method determined the correct depths of the sources. In the case of practical data (SP anomalies over a sulfide ore deposit, Sariyer, Turkey and over a Malachite Mine, Jefferson County, Colorado, USA), the estimated depths of the buried structures are in good agreement with the results obtained from drilling and surface geology.
Quantification of anaesthetic effects on atrial fibrillation rate by partial least-squares

International Nuclear Information System (INIS)

Cervigón, R; Moreno, J; Pérez-Villacastín, J; Reilly, R B; Castells, F

2012-01-01

The mechanism underlying atrial fibrillation (AF) remains poorly understood. Multiple wandering propagation wavelets drifting through both atria under hierarchical models are not understood. Some pharmacological drugs, known as antiarrhythmics, modify the cardiac ionic currents supporting the fibrillation process within the atria and may modify the AF propagation dynamics terminating the fibrillation process. Other medications, theoretically non-antiarrhythmic, may slightly affect the fibrillation process in non-defined mechanisms. We evaluated whether the most commonly used anaesthetic agent, propofol, affects AF patterns. Partial least-squares (PLS) analysis was performed to reduce significant noise into the main latent variables to find the differences between groups. The final results showed an excellent discrimination between groups with slow atrial activity during the propofol infusion. (paper)
Wavelength detection in FBG sensor networks using least squares support vector regression

Science.gov (United States)

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.
Least-squares approximation of an improper by a proper correlation matrix using a semi-infinite convex program

NARCIS (Netherlands)

Knol, Dirk L.; ten Berge, Jos M.F.

1987-01-01

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977).
Regression model of support vector machines for least squares prediction of crystallinity of cracking catalysts by infrared spectroscopy

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
Temporal gravity field modeling based on least square collocation with short-arc approach

Science.gov (United States)

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.
A complex linear least-squares method to derive relative and absolute orientations of seismic sensors

OpenAIRE

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 Approach to the Alignment of the Generic High Precision Tracking System

Science.gov (United States)

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

Science.gov (United States)

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).
Respiratory mechanics by least squares fitting in mechanically ventilated patients: application on flow-limited COPD patients.

Science.gov (United States)

Volta, Carlo A; Marangoni, Elisabetta; Alvisi, Valentina; Capuzzo, Maurizia; Ragazzi, Riccardo; Pavanelli, Lina; Alvisi, Raffaele

2002-01-01

Although computerized methods of analyzing respiratory system mechanics such as the least squares fitting method have been used in various patient populations, no conclusive data are available in patients with chronic obstructive pulmonary disease (COPD), probably because they may develop expiratory flow limitation (EFL). This suggests that respiratory mechanics be determined only during inspiration. Eight-bed multidisciplinary ICU of a teaching hospital. Eight non-flow-limited postvascular surgery patients and eight flow-limited COPD patients. Patients were sedated, paralyzed for diagnostic purposes, and ventilated in volume control ventilation with constant inspiratory flow rate. Data on resistance, compliance, and dynamic intrinsic positive end-expiratory pressure (PEEPi,dyn) obtained by applying the least squares fitting method during inspiration, expiration, and the overall breathing cycle were compared with those obtained by the traditional method (constant flow, end-inspiratory occlusion method). Our results indicate that (a) the presence of EFL markedly decreases the precision of resistance and compliance values measured by the LSF method, (b) the determination of respiratory variables during inspiration allows the calculation of respiratory mechanics in flow limited COPD patients, and (c) the LSF method is able to detect the presence of PEEPi,dyn if only inspiratory data are used.
Classifying Physical Morphology of Cocoa Beans Digital Images using Multiclass Ensemble Least-Squares Support Vector Machine

Science.gov (United States)

Lawi, Armin; Adhitya, Yudhi

2018-03-01

The objective of this research is to determine the quality of cocoa beans through morphology of their digital images. Samples of cocoa beans were scattered on a bright white paper under a controlled lighting condition. A compact digital camera was used to capture the images. The images were then processed to extract their morphological parameters. Classification process begins with an analysis of cocoa beans image based on morphological feature extraction. Parameters for extraction of morphological or physical feature parameters, i.e., Area, Perimeter, Major Axis Length, Minor Axis Length, Aspect Ratio, Circularity, Roundness, Ferret Diameter. The cocoa beans are classified into 4 groups, i.e.: Normal Beans, Broken Beans, Fractured Beans, and Skin Damaged Beans. The model of classification used in this paper is the Multiclass Ensemble Least-Squares Support Vector Machine (MELS-SVM), a proposed improvement model of SVM using ensemble method in which the separate hyperplanes are obtained by least square approach and the multiclass procedure uses One-Against- All method. The result of our proposed model showed that the classification with morphological feature input parameters were accurately as 99.705% for the four classes, respectively.
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
Biased motion vector interpolation for reduced video artifacts.

NARCIS (Netherlands)

2011-01-01

In a video processing system where motion vectors are estimated for a subset of the blocks of data forming a video frame, and motion vectors are interpolated for the remainder of the blocks of the frame, a method includes determining, for at least at least one block of the current frame for which a
A library least-squares approach for scatter correction in gamma-ray tomography

Science.gov (United States)

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.
Optimal moving grids for time-dependent partial differential equations

Science.gov (United States)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

A least-squares minimization approach for model parameters estimate by using a new magnetic anomaly formula

Science.gov (United States)

Abo-Ezz, E. R.; Essa, K. S.

2016-04-01

A new linear least-squares approach is proposed to interpret magnetic anomalies of the buried structures by using a new magnetic anomaly formula. This approach depends on solving different sets of algebraic linear equations in order to invert the depth ( z), amplitude coefficient ( K), and magnetization angle ( θ) of buried structures using magnetic data. The utility and validity of the new proposed approach has been demonstrated through various reliable synthetic data sets with and without noise. In addition, the method has been applied to field data sets from USA and India. The best-fitted anomaly has been delineated by estimating the root-mean squared (rms). Judging satisfaction of this approach is done by comparing the obtained results with other available geological or geophysical information.
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.
An improved algorithm for the determination of the system paramters of a visual binary by least squares

Science.gov (United States)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also
Normalization Ridge Regression in Practice I: Comparisons Between Ordinary Least Squares, Ridge Regression and Normalization Ridge Regression.

Science.gov (United States)

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…
A task specific uncertainty analysis method for least-squares-based form characterization of ultra-precision freeform surfaces

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
Does model fit decrease the uncertainty of the data in comparison with a general non-model least squares fit?

International Nuclear Information System (INIS)

Pronyaev, V.G.

2003-01-01

The information entropy is taken as a measure of knowledge about the object and the reduced univariante variance as a common measure of uncertainty. Covariances in the model versus non-model least square fits are discussed
Antena Cerdas untuk Mitigasi Interferensi dengan Algoritma Least Mean Square

Directory of Open Access Journals (Sweden)

Rahmad Hidayat

2017-06-01

Full Text Available Antena cerdas pada dasarnya merupakan susunan antena dengan kemampuan pemrosesan sinyal untuk mengirim/menerima informasi secara adaptif. Kemampuan ini harus terus didalami untuk dicarikan algoritma adaptif terbaik bagi kemampuan beamforming yang diinginkan. Tulisan ini bertujuan untuk memberikan kajian dan analisis pengaruh algoritma Least Mean Square (LMS pada pengaturan nulling beam pola radiasi susunan antena cerdas dalam perannya terhadap mitigasi interferensi. Simulasi kinerja beamformer untuk sebanyak 250 iterasi dilakukan dengan tool Matlab pada kanal AWGN (Additional White Noise Gaussian dan parameter simulasi diubah untuk membandingkan dua buah harga step size m pada algoritma LMS untuk beberapa jumlah elemen antena. Pengaruh nilai step size m, terlihat pada jumlah iterasi yang dilangsungkan sebelum error noise minimum diperoleh, dimana dengan naiknya nilai step size ini maka semakin mengurangi jumlah iterasi, rata-rata menjadi 60. Dari pola respon amplitudo setelah proses beamforming , posisi sinyal utama (0 dB tepat di sudut 30° dan dihasilkan 15 posisi nulling untuk 16 elemen antena. Sumber interferensi dihilangkan / ditutup dengan menempatkan ’nulls’ dalam arah sumber interferensi tersebut di posisi 60° dan -40° dengan masing-masing level diperoleh berkisar sebesar -115 dB
Comparison of remove-compute-restore and least squares modification of Stokes' formula techniques to quasi-geoid determination over the Auvergne test area

DEFF Research Database (Denmark)

Yildiz, H.; Forsberg, René; Ågren, J.

2012-01-01

The remove-compute-restore (RCR) technique for regional geoid determination implies that both topography and low-degree global geopotential model signals are removed before computation and restored after Stokes' integration or Least Squares Collocation (LSC) solution. The Least Squares Modification...... area. All methods showed a reasonable agreement with GPS-levelling data, in the order of a 3-3.5 cm in the central region having relatively smooth topography, which is consistent with the accuracies of GPS and levelling. When a 1-parameter fit is used, the FFT method using kernel modification performs...
Modelo digital do terreno através de diferentes interpolações do programa Surfer 12 | Digital terrain model through different interpolations in the surfer 12 software

Directory of Open Access Journals (Sweden)

José Machado

2016-04-01

the MDT interpolation of measured points is required. The use of TDM, 3D surfaces and contours in moving fast computer programs and can create some problems, such as the type of interpolation used. This work aims to analyze the interpolation methods in points quoted from an irregular geometric figure generated by the Surfer program. They used 12 interpolations available (Data Metrics, Inverse Distance, Kriging, Local Polynomial, Minimum Curvature, Modified Shepard Method, Moving Average, Natural Neighbor, Nearest Neighbor, Polynomial Regression, Radial fuction and Triangulation with Linear Interpolation and analyzed the generated topographic maps. The relief was generated graphical representation via the MDT. They were awarded the excellent concepts, excellent, good, average and bad representation of relief and discussed according Relief representations to the listed geometric image. Data Metrics, Polynomial Regression, Moving Average e Local Polynomial (bad; Moving Average e Modified Shepard Method (regular; Nearest Neighbor (media; Inverse Distance (good; Kriging e Radial Function (great e Triangulation With Linear Interpolation e Natural Neighbor (excellent conditions to representation presented dates.
A wavelet and least square filter based spatial-spectral denoising approach of hyperspectral imagery

Science.gov (United States)

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.
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.
Estimation of direction of arrival of a moving target using subspace based approaches

Science.gov (United States)

Ghosh, Ripul; Das, Utpal; Akula, Aparna; Kumar, Satish; Sardana, H. K.

2016-05-01

In this work, array processing techniques based on subspace decomposition of signal have been evaluated for estimation of direction of arrival of moving targets using acoustic signatures. Three subspace based approaches - Incoherent Wideband Multiple Signal Classification (IWM), Least Square-Estimation of Signal Parameters via Rotation Invariance Techniques (LS-ESPRIT) and Total Least Square- ESPIRIT (TLS-ESPRIT) are considered. Their performance is compared with conventional time delay estimation (TDE) approaches such as Generalized Cross Correlation (GCC) and Average Square Difference Function (ASDF). Performance evaluation has been conducted on experimentally generated data consisting of acoustic signatures of four different types of civilian vehicles moving in defined geometrical trajectories. Mean absolute error and standard deviation of the DOA estimates w.r.t. ground truth are used as performance evaluation metrics. Lower statistical values of mean error confirm the superiority of subspace based approaches over TDE based techniques. Amongst the compared methods, LS-ESPRIT indicated better performance.
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)
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...
Comparison of least-squares vs. maximum likelihood estimation for standard spectrum technique of β−γ coincidence spectrum analysis

International Nuclear Information System (INIS)

Lowrey, Justin D.; Biegalski, Steven R.F.

2012-01-01

The spectrum deconvolution analysis tool (SDAT) software code was written and tested at The University of Texas at Austin utilizing the standard spectrum technique to determine activity levels of Xe-131m, Xe-133m, Xe-133, and Xe-135 in β–γ coincidence spectra. SDAT was originally written to utilize the method of least-squares to calculate the activity of each radionuclide component in the spectrum. Recently, maximum likelihood estimation was also incorporated into the SDAT tool. This is a robust statistical technique to determine the parameters that maximize the Poisson distribution likelihood function of the sample data. In this case it is used to parameterize the activity level of each of the radioxenon components in the spectra. A new test dataset was constructed utilizing Xe-131m placed on a Xe-133 background to compare the robustness of the least-squares and maximum likelihood estimation methods for low counting statistics data. The Xe-131m spectra were collected independently from the Xe-133 spectra and added to generate the spectra in the test dataset. The true independent counts of Xe-131m and Xe-133 are known, as they were calculated before the spectra were added together. Spectra with both high and low counting statistics are analyzed. Studies are also performed by analyzing only the 30 keV X-ray region of the β–γ coincidence spectra. Results show that maximum likelihood estimation slightly outperforms least-squares for low counting statistics data.
Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.

Science.gov (United States)

Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G

2016-06-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.
An estimation of the height system bias parameter N (0) using least squares collocation from observed gravity and GPS-levelling data

DEFF Research Database (Denmark)

Sadiq, Muhammad; Tscherning, Carl C.; Ahmad, Zulfiqar

2009-01-01

This paper deals with the analysis of gravity anomaly and precise levelling in conjunction with GPS-Levelling data for the computation of a gravimetric geoid and an estimate of the height system bias parameter N-o for the vertical datum in Pakistan by means of least squares collocation technique...... covariance parameters has facilitated to achieve gravimetric height anomalies in a global geocentric datum. Residual terrain modeling (RTM) technique has been used in combination with the EGM96 for the reduction and smoothing of the gravity data. A value for the bias parameter N-o has been estimated...... with reference to the local GPS-Levelling datum that appears to be 0.705 m with 0.07 m mean square error. The gravimetric height anomalies were compared with height anomalies obtained from GPS-Levelling stations using least square collocation with and without bias adjustment. The bias adjustment minimizes...
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...
Baseline configuration for GNSS attitude determination with an analytical least-squares solution

International Nuclear Information System (INIS)

Chang, Guobin; Wang, Qianxin; Xu, Tianhe

2016-01-01

The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance–covariance matrix. (paper)
Wave-equation Q tomography and least-squares migration

KAUST Repository

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

Validating the Galerkin least-squares finite element methods in predicting mixing flows in stirred tank reactors

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)
Kennard-Stone combined with least square support vector machine method for noncontact discriminating human blood species

Science.gov (United States)

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.
The Multivariate Regression Statistics Strategy to Investigate Content-Effect Correlation of Multiple Components in Traditional Chinese Medicine Based on a Partial Least Squares Method.

Science.gov (United States)

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.
Spatial interpolation schemes of daily precipitation for hydrologic modeling

Science.gov (United States)

Hwang, Y.; Clark, M.R.; Rajagopalan, B.; Leavesley, G.

2012-01-01

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs. ?? 2011 Springer-Verlag.
Least-squares wave-front reconstruction of Shack-Hartmann sensors and shearing interferometers using multigrid techniques

International Nuclear Information System (INIS)

Baker, K.L.

2005-01-01

This article details a multigrid algorithm that is suitable for least-squares wave-front reconstruction of Shack-Hartmann and shearing interferometer wave-front sensors. The algorithm detailed in this article is shown to scale with the number of subapertures in the same fashion as fast Fourier transform techniques, making it suitable for use in applications requiring a large number of subapertures and high Strehl ratio systems such as for high spatial frequency characterization of high-density plasmas, optics metrology, and multiconjugate and extreme adaptive optics systems
On the Performance of Maximum Likelihood versus Means and Variance Adjusted Weighted Least Squares Estimation in CFA

Science.gov (United States)

Beauducel, Andre; Herzberg, Philipp Yorck

2006-01-01

This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…
MO-DE-207A-10: One-Step CT Reconstruction for Metal Artifact Reduction by a Modification of Penalized Weighted Least-Squares (PWLS)

Energy Technology Data Exchange (ETDEWEB)

Kim, H; Chen, J [University of California San Francisco, San Francisco, CA (United States)

2016-06-15

Purpose: Metal objects create severe artifacts in kilo-voltage (kV) CT image reconstructions due to the high attenuation coefficients of high atomic number objects. Most of the techniques devised to reduce this artifact utilize a two-step approach, which do not reliably yield the qualified reconstructed images. Thus, for accuracy and simplicity, this work presents a one-step reconstruction method based on a modified penalized weighted least-squares (PWLS) technique. Methods: Existing techniques for metal artifact reduction mostly adopt a two-step approach, which conduct additional reconstruction with the modified projection data from the initial reconstruction. This procedure does not consistently perform well due to the uncertainties in manipulating the metal-contaminated projection data by thresholding and linear interpolation. This study proposes a one-step reconstruction process using a new PWLS operation with total-variation (TV) minimization, while not manipulating the projection. The PWLS for CT reconstruction has been investigated using a pre-defined weight, based on the variance of the projection datum at each detector bin. It works well when reconstructing CT images from metal-free projection data, which does not appropriately penalize metal-contaminated projection data. The proposed work defines the weight at each projection element under the assumption of a Poisson random variable. This small modification using element-wise penalization has a large impact in reducing metal artifacts. For evaluation, the proposed technique was assessed with two noisy, metal-contaminated digital phantoms, against the existing PWLS with TV minimization and the two-step approach. Result: The proposed PWLS with TV minimization greatly improved the metal artifact reduction, relative to the other techniques, by watching the results. Numerically, the new approach lowered the normalized root-mean-square error about 30 and 60% for the two cases, respectively, compared to the two
Determination of carbohydrates present in Saccharomyces cerevisiae using mid-infrared spectroscopy and partial least squares regression

OpenAIRE

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...
Estimation of active pharmaceutical ingredients content using locally weighted partial least squares and statistical wavelength selection.

OpenAIRE

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...
Due Date Assignment in a Dynamic Job Shop with the Orthogonal Kernel Least Squares Algorithm

Science.gov (United States)

Yang, D. H.; Hu, L.; Qian, Y.

2017-06-01

Meeting due dates is a key goal in the manufacturing industries. This paper proposes a method for due date assignment (DDA) by using the Orthogonal Kernel Least Squares Algorithm (OKLSA). A simulation model is built to imitate the production process of a highly dynamic job shop. Several factors describing job characteristics and system state are extracted as attributes to predict job flow-times. A number of experiments under conditions of varying dispatching rules and 90% shop utilization level have been carried out to evaluate the effectiveness of OKLSA applied for DDA. The prediction performance of OKLSA is compared with those of five conventional DDA models and back-propagation neural network (BPNN). The experimental results indicate that OKLSA is statistically superior to other DDA models in terms of mean absolute lateness and root mean squares lateness in most cases. The only exception occurs when the shortest processing time rule is used for dispatching jobs, the difference between OKLSA and BPNN is not statistically significant.
Least Squares Neural Network-Based Wireless E-Nose System Using an SnO₂ Sensor Array.

Science.gov (United States)

Shahid, Areej; Choi, Jong-Hyeok; Rana, Abu Ul Hassan Sarwar; Kim, Hyun-Seok

2018-05-06

Over the last few decades, the development of the electronic nose (E-nose) for detection and quantification of dangerous and odorless gases, such as methane (CH₄) and carbon monoxide (CO), using an array of SnO₂ gas sensors has attracted considerable attention. This paper addresses sensor cross sensitivity by developing a classifier and estimator using an artificial neural network (ANN) and least squares regression (LSR), respectively. Initially, the ANN was implemented using a feedforward pattern recognition algorithm to learn the collective behavior of an array as the signature of a particular gas. In the second phase, the classified gas was quantified by minimizing the mean square error using LSR. The combined approach produced 98.7% recognition probability, with 95.5 and 94.4% estimated gas concentration accuracies for CH₄ and CO, respectively. The classifier and estimator parameters were deployed in a remote microcontroller for the actualization of a wireless E-nose system.
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.
Least squares approach for initial data recovery in dynamic data-driven applications simulations

KAUST Repository

Douglas, C.

2010-12-01

In this paper, we consider the initial data recovery and the solution update based on the local measured data that are acquired during simulations. Each time new data is obtained, the initial condition, which is a representation of the solution at a previous time step, is updated. The update is performed using the least squares approach. The objective function is set up based on both a measurement error as well as a penalization term that depends on the prior knowledge about the solution at previous time steps (or initial data). Various numerical examples are considered, where the penalization term is varied during the simulations. Numerical examples demonstrate that the predictions are more accurate if the initial data are updated during the simulations. © Springer-Verlag 2011.
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
Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

Science.gov (United States)

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.
Unlocking interpretation in near infrared multivariate calibrations by orthogonal partial least squares.

Science.gov (United States)

Stenlund, Hans; Johansson, Erik; Gottfries, Johan; Trygg, Johan

2009-01-01

Near infrared spectroscopy (NIR) was developed primarily for applications such as the quantitative determination of nutrients in the agricultural and food industries. Examples include the determination of water, protein, and fat within complex samples such as grain and milk. Because of its useful properties, NIR analysis has spread to other areas such as chemistry and pharmaceutical production. NIR spectra consist of infrared overtones and combinations thereof, making interpretation of the results complicated. It can be very difficult to assign peaks to known constituents in the sample. Thus, multivariate analysis (MVA) has been crucial in translating spectral data into information, mainly for predictive purposes. Orthogonal partial least squares (OPLS), a new MVA method, has prediction and modeling properties similar to those of other MVA techniques, e.g., partial least squares (PLS), a method with a long history of use for the analysis of NIR data. OPLS provides an intrinsic algorithmic improvement for the interpretation of NIR data. In this report, four sets of NIR data were analyzed to demonstrate the improved interpretation provided by OPLS. The first two sets included simulated data to demonstrate the overall principles; the third set comprised a statistically replicated design of experiments (DoE), to demonstrate how instrumental difference could be accurately visualized and correctly attributed to Wood's anomaly phenomena; the fourth set was chosen to challenge the MVA by using data relating to powder mixing, a crucial step in the pharmaceutical industry prior to tabletting. Improved interpretation by OPLS was demonstrated for all four examples, as compared to alternative MVA approaches. It is expected that OPLS will be used mostly in applications where improved interpretation is crucial; one such area is process analytical technology (PAT). PAT involves fewer independent samples, i.e., batches, than would be associated with agricultural applications; in
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
Generalized least squares and empirical Bayes estimation in regional partial duration series index-flood modeling

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...
Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

Science.gov (United States)

Rana, Md Masud

2017-01-01

This paper proposes an innovative internet of things (IoT) based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.
Q-Least Squares Reverse Time Migration with Viscoacoustic Deblurring Filters

KAUST Repository

Chen, Yuqing; Dutta, Gaurav; Dai, Wei; Schuster, Gerard T.

2017-01-01

Viscoacoustic least-squares reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. Compared to the conventional migration methods, it can compensate for the amplitude loss in the migrated images because of the strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM are often observed to have lower resolution when compared to the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we propose using viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM and Q-LSRTM when there is strong attenuation in the background medium. The proposed preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30 percent in some cases and significantly compensate for the lossy artifacts in RTM images.

Q-Least Squares Reverse Time Migration with Viscoacoustic Deblurring Filters

KAUST Repository

Chen, Yuqing

2017-08-02

Viscoacoustic least-squares reverse time migration (Q-LSRTM) linearly inverts for the subsurface reflectivity model from lossy data. Compared to the conventional migration methods, it can compensate for the amplitude loss in the migrated images because of the strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM are often observed to have lower resolution when compared to the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we propose using viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM and Q-LSRTM when there is strong attenuation in the background medium. The proposed preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30 percent in some cases and significantly compensate for the lossy artifacts in RTM images.
Lameness detection challenges in automated milking systems addressed with partial least squares discriminant analysis

DEFF Research Database (Denmark)

Garcia, Emanuel; Klaas, Ilka Christine; Amigo Rubio, Jose Manuel

2014-01-01

Lameness is prevalent in dairy herds. It causes decreased animal welfare and leads to higher production costs. This study explored data from an automatic milking system (AMS) to model on-farm gait scoring from a commercial farm. A total of 88 cows were gait scored once per week, for 2 5-wk periods......). The reference gait scoring error was estimated in the first week of the study and was, on average, 15%. Two partial least squares discriminant analysis models were fitted to parity 1 and parity 2 groups, respectively, to assign the lameness class according to the predicted probability of being lame (score 3...
The Use of Alternative Regression Methods in Social Sciences and the Comparison of Least Squares and M Estimation Methods in Terms of the Determination of Coefficient

Science.gov (United States)

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,…
A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

Science.gov (United States)

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
Using the partial least squares (PLS) method to establish critical success factor interdependence in ERP implementation projects

OpenAIRE

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...
[Discrimination of types of polyacrylamide based on near infrared spectroscopy coupled with least square support vector machine].

Science.gov (United States)

Zhang, Hong-Guang; Yang, Qin-Min; Lu, Jian-Gang

2014-04-01

In this paper, a novel discriminant methodology based on near infrared spectroscopic analysis technique and least square support vector machine was proposed for rapid and nondestructive discrimination of different types of Polyacrylamide. The diffuse reflectance spectra of samples of Non-ionic Polyacrylamide, Anionic Polyacrylamide and Cationic Polyacrylamide were measured. Then principal component analysis method was applied to reduce the dimension of the spectral data and extract of the principal compnents. The first three principal components were used for cluster analysis of the three different types of Polyacrylamide. Then those principal components were also used as inputs of least square support vector machine model. The optimization of the parameters and the number of principal components used as inputs of least square support vector machine model was performed through cross validation based on grid search. 60 samples of each type of Polyacrylamide were collected. Thus a total of 180 samples were obtained. 135 samples, 45 samples for each type of Polyacrylamide, were randomly split into a training set to build calibration model and the rest 45 samples were used as test set to evaluate the performance of the developed model. In addition, 5 Cationic Polyacrylamide samples and 5 Anionic Polyacrylamide samples adulterated with different proportion of Non-ionic Polyacrylamide were also prepared to show the feasibilty of the proposed method to discriminate the adulterated Polyacrylamide samples. The prediction error threshold for each type of Polyacrylamide was determined by F statistical significance test method based on the prediction error of the training set of corresponding type of Polyacrylamide in cross validation. The discrimination accuracy of the built model was 100% for prediction of the test set. The prediction of the model for the 10 mixing samples was also presented, and all mixing samples were accurately discriminated as adulterated samples. The
The Multivariate Regression Statistics Strategy to Investigate Content-Effect Correlation of Multiple Components in Traditional Chinese Medicine Based on a Partial Least Squares Method

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.
An integral conservative gridding--algorithm using Hermitian curve interpolation.

Science.gov (United States)

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-11-07

significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).
An integral conservative gridding-algorithm using Hermitian curve interpolation

International Nuclear Information System (INIS)

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-01-01

significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).
Selection of the optimal interpolation method for groundwater observations in lahore, pakistan

International Nuclear Information System (INIS)

Mahmood, K.; Ali, S.R.; Haider, A.; Tehseen, T.; Kanwal, S.

2014-01-01

This study was carried out to find an optimum method of interpolation for the depth values of groundwater in Lahore metropolitan, Pakistan. The methods of interpolation considered in the study were inverse distance weight (IDW), spline, simple Kriging, ordinary Kriging and universal Kriging. Initial analysis of the data suggests that the data was negatively skewed with value of skewness -1.028. The condition of normality was approximated by transforming the data using a box-cox transformation with lambda value of 3.892; the skewness value reduced to -0.00079. The results indicate that simple Kriging method is optimum for interpolation of groundwater observations for the used dataset with lowest bias of 0.00997, highest correlation coefficient with value 0.9434, mean absolute error 1.95 and root mean square error 3.19 m. Smooth and uniform contours with well described central depression zon in the city, as suggested by this studies, also supports the optimised interpolation method. (author)
Estimation and Forecasting in Vector Autoregressive Moving Average Models for Rich Datasets

DEFF Research Database (Denmark)

Dias, Gustavo Fruet; Kapetanios, George

We address the issue of modelling and forecasting macroeconomic variables using rich datasets, by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (...
An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

Science.gov (United States)

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.
Prediction of beef marblingusing Hyperspectral Imaging (HSI and Partial Least Squares Regression (PLSR

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.
ENTREPRENEURIAL ATTITUDE AND STUDENTS BUSINESS START-UP INTENTION: A PARTIAL LEAST SQUARE MODELING

Directory of Open Access Journals (Sweden)

Widayat Widayat

2017-03-01

Full Text Available This article is designed to examine the role of the entrepreneurial spirit, education and in building an attitude about working as an entrepreneur, and his influence on the intention to start a business, to the students. Data were collected using a questionnaire has been prepared and maintained the validity and reliability. Questionnaires given to the respondent students were selected as samples at several universities in Malang, East Java, Indonesia. The collected data were analyzed by using Partial Least Square. The analysis showed entrepreneurial spirit and education contribute to the formation of entrepreneurial attitudes. Attitudes are formed encourage entrepreneurship intentions to start a business significantly.
Modeling and control of PEMFC based on least squares support vector machines

International Nuclear Information System (INIS)

Li Xi; Cao Guangyi; Zhu Xinjian

2006-01-01

The proton exchange membrane fuel cell (PEMFC) is one of the most important power supplies. The operating temperature of the stack is an important controlled variable, which impacts the performance of the PEMFC. In order to improve the generating performance of the PEMFC, prolong its life and guarantee safety, credibility and low cost of the PEMFC system, it must be controlled efficiently. A nonlinear predictive control algorithm based on a least squares support vector machine (LS-SVM) model is presented for a family of complex systems with severe nonlinearity, such as the PEMFC, in this paper. The nonlinear off line model of the PEMFC is built by a LS-SVM model with radial basis function (RBF) kernel so as to implement nonlinear predictive control of the plant. During PEMFC operation, the off line model is linearized at each sampling instant, and the generalized predictive control (GPC) algorithm is applied to the predictive control of the plant. Experimental results demonstrate the effectiveness and advantages of this approach
Distributed weighted least-squares estimation with fast convergence for large-scale systems☆

Science.gov (United States)

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. PMID:25641976
Distributed weighted least-squares estimation with fast convergence for large-scale systems.

Science.gov (United States)

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.
A Comparison of Approaches for the Analysis of Interaction Effects between Latent Variables Using Partial Least Squares Path Modeling

Science.gov (United States)

Henseler, Jorg; Chin, Wynne W.

2010-01-01

In social and business sciences, the importance of the analysis of interaction effects between manifest as well as latent variables steadily increases. Researchers using partial least squares (PLS) to analyze interaction effects between latent variables need an overview of the available approaches as well as their suitability. This article…
Least mean square fourth based microgrid state estimation algorithm using the internet of things technology.

Directory of Open Access Journals (Sweden)

Md Masud Rana

Full Text Available This paper proposes an innovative internet of things (IoT based communication framework for monitoring microgrid under the condition of packet dropouts in measurements. First of all, the microgrid incorporating the renewable distributed energy resources is represented by a state-space model. The IoT embedded wireless sensor network is adopted to sense the system states. Afterwards, the information is transmitted to the energy management system using the communication network. Finally, the least mean square fourth algorithm is explored for estimating the system states. The effectiveness of the developed approach is verified through numerical simulations.
Pressurized water reactor monitoring. Study of detection, diagnostic and estimation (least squares and filtering) methods

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

[Main Components of Xinjiang Lavender Essential Oil Determined by Partial Least Squares and Near Infrared Spectroscopy].

Science.gov (United States)

Liao, Xiang; Wang, Qing; Fu, Ji-hong; Tang, Jun

2015-09-01

This work was undertaken to establish a quantitative analysis model which can rapid determinate the content of linalool, linalyl acetate of Xinjiang lavender essential oil. Totally 165 lavender essential oil samples were measured by using near infrared absorption spectrum (NIR), after analyzing the near infrared spectral absorption peaks of all samples, lavender essential oil have abundant chemical information and the interference of random noise may be relatively low on the spectral intervals of 7100~4500 cm(-1). Thus, the PLS models was constructed by using this interval for further analysis. 8 abnormal samples were eliminated. Through the clustering method, 157 lavender essential oil samples were divided into 105 calibration set samples and 52 validation set samples. Gas chromatography mass spectrometry (GC-MS) was used as a tool to determine the content of linalool and linalyl acetate in lavender essential oil. Then the matrix was established with the GC-MS raw data of two compounds in combination with the original NIR data. In order to optimize the model, different pretreatment methods were used to preprocess the raw NIR spectral to contrast the spectral filtering effect, after analysizing the quantitative model results of linalool and linalyl acetate, the root mean square error prediction (RMSEP) of orthogonal signal transformation (OSC) was 0.226, 0.558, spectrally, it was the optimum pretreatment method. In addition, forward interval partial least squares (FiPLS) method was used to exclude the wavelength points which has nothing to do with determination composition or present nonlinear correlation, finally 8 spectral intervals totally 160 wavelength points were obtained as the dataset. Combining the data sets which have optimized by OSC-FiPLS with partial least squares (PLS) to establish a rapid quantitative analysis model for determining the content of linalool and linalyl acetate in Xinjiang lavender essential oil, numbers of hidden variables of two
Performance Assessment of Spatial Interpolation of Precipitation for Hydrological Process Simulation in the Three Gorges Basin

Directory of Open Access Journals (Sweden)

Meiling Cheng

2017-11-01

Full Text Available Accurate assessment of spatial and temporal precipitation is crucial for simulating hydrological processes in basins, but is challenging due to insufficient rain gauges. Our study aims to analyze different precipitation interpolation schemes and their performances in runoff simulation during light and heavy rain periods. In particular, combinations of different interpolation estimates are explored and their performances in runoff simulation are discussed. The study was carried out in the Pengxi River basin of the Three Gorges Basin. Precipitation data from 16 rain gauges were interpolated using the Thiessen Polygon (TP, Inverse Distance Weighted (IDW, and Co-Kriging (CK methods. Results showed that streamflow predictions employing CK inputs demonstrated the best performance in the whole process, in terms of the Nash–Sutcliffe Coefficient (NSE, the coefficient of determination (R2, and the Root Mean Square Error (RMSE indices. The TP, IDW, and CK methods showed good performance in the heavy rain period but poor performance in the light rain period compared with the default method (least sophisticated nearest neighbor technique in Soil and Water Assessment Tool (SWAT. Furthermore, the correlation between the dynamic weight of one method and its performance during runoff simulation followed a parabolic function. The combination of CK and TP achieved a better performance in decreasing the largest and lowest absolute errors compared to any single method, but the IDW method outperformed all methods in terms of the median absolute error. However, it is clear from our findings that interpolation methods should be chosen depending on the amount of precipitation, adaptability of the method, and accuracy of the estimate in different rain periods.
Translation-aware semantic segmentation via conditional least-square generative adversarial networks

Science.gov (United States)

Zhang, Mi; Hu, Xiangyun; Zhao, Like; Pang, Shiyan; Gong, Jinqi; Luo, Min

2017-10-01

Semantic segmentation has recently made rapid progress in the field of remote sensing and computer vision. However, many leading approaches cannot simultaneously translate label maps to possible source images with a limited number of training images. The core issue is insufficient adversarial information to interpret the inverse process and proper objective loss function to overcome the vanishing gradient problem. We propose the use of conditional least squares generative adversarial networks (CLS-GAN) to delineate visual objects and solve these problems. We trained the CLS-GAN network for semantic segmentation to discriminate dense prediction information either from training images or generative networks. We show that the optimal objective function of CLS-GAN is a special class of f-divergence and yields a generator that lies on the decision boundary of discriminator that reduces possible vanished gradient. We also demonstrate the effectiveness of the proposed architecture at translating images from label maps in the learning process. Experiments on a limited number of high resolution images, including close-range and remote sensing datasets, indicate that the proposed method leads to the improved semantic segmentation accuracy and can simultaneously generate high quality images from label maps.
Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach

Science.gov (United States)

Katkovnik, Vladimir; Bioucas-Dias, José

2010-04-01

Multiple frequency interferometry is, basically, a phase acquisition strategy aimed at reducing or eliminating the ambiguity of the wrapped phase observations or, equivalently, reducing or eliminating the fringe ambiguity order. In multiple frequency interferometry, the phase measurements are acquired at different frequencies (or wavelengths) and recorded using the corresponding sensors (measurement channels). Assuming that the absolute phase to be reconstructed is piece-wise smooth, we use a nonparametric regression technique for the phase reconstruction. The nonparametric estimates are derived from a local least squares criterion, which, when applied to the multifrequency data, yields denoised (filtered) phase estimates with extended ambiguity (periodized), compared with the phase ambiguities inherent to each measurement frequency. The filtering algorithm is based on local polynomial (LPA) approximation for design of nonlinear filters (estimators) and adaptation of these filters to unknown smoothness of the spatially varying absolute phase [9]. For phase unwrapping, from filtered periodized data, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed algorithm yields state-of-the-art performance for continuous as well as for discontinues phase surfaces, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.
Square-root measurement for pure states

International Nuclear Information System (INIS)

Huang Siendong

2005-01-01

Square-root measurement is a very useful suboptimal measurement in many applications. It was shown that the square-root measurement minimizes the squared error for pure states. In this paper, the least squared error problem is reformulated and a new proof is provided. It is found that the least squared error depends only on the average density operator of the input states. The properties of the least squared error are then discussed, and it is shown that if the input pure states are uniformly distributed, the average probability of error has an upper bound depending on the least squared error, the rank of the average density operator, and the number of the input states. The aforementioned properties help explain why the square-root measurement can be effective in decoding processes
Numerical analysis of melting/solidification phenomena using a moving boundary problem analysis method X-FEM

International Nuclear Information System (INIS)

Uchibori, Akihiro; Ohshima, Hiroyuki

2008-01-01

A numerical analysis method for melting/solidification phenomena has been developed to evaluate a feasibility of several candidate techniques in the nuclear fuel cycle. Our method is based on the eXtended Finite Element Method (X-FEM) which has been used for moving boundary problems. Key technique of the X-FEM is to incorporate signed distance function into finite element interpolation to represent a discontinuous gradient of the temperature at a moving solid-liquid interface. Construction of the finite element equation, the technique of quadrature and the method to solve the equation are reported here. The numerical solutions of the one-dimensional Stefan problem, solidification in a two-dimensional square corner and melting of pure gallium are compared to the exact solutions or to the experimental data. Through these analyses, validity of the newly developed numerical analysis method has been demonstrated. (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
Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Science.gov (United States)

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.
Lossless medical image compression using geometry-adaptive partitioning and least square-based prediction.

Science.gov (United States)

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.
The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

Science.gov (United States)

Thamareerat, N; Luadsong, A; Aschariyaphotha, N

2016-01-01

In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.
A weighted least-squares lump correction algorithm for transmission-corrected gamma-ray nondestructive assay

International Nuclear Information System (INIS)

Prettyman, T.H.; Sprinkle, J.K. Jr.; Sheppard, G.A.

1993-01-01

With transmission-corrected gamma-ray nondestructive assay instruments such as the Segmented Gamma Scanner (SGS) and the Tomographic Gamma Scanner (TGS) that is currently under development at Los Alamos National Laboratory, the amount of gamma-ray emitting material can be underestimated for samples in which the emitting material consists of particles or lumps of highly attenuating material. This problem is encountered in the assay of uranium and plutonium-bearing samples. To correct for this source of bias, we have developed a least-squares algorithm that uses transmission-corrected assay results for several emitted energies and a weighting function to account for statistical uncertainties in the assay results. The variation of effective lump size in the fitted model is parameterized; this allows the correction to be performed for a wide range of lump-size distributions. It may be possible to use the reduced chi-squared value obtained in the fit to identify samples in which assay assumptions have been violated. We found that the algorithm significantly reduced bias in simulated assays and improved SGS assay results for plutonium-bearing samples. Further testing will be conducted with the TGS, which is expected to be less susceptible than the SGS to systematic source of bias
A Novel Method for Lithium-Ion Battery Online Parameter Identification Based on Variable Forgetting Factor Recursive Least Squares

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.
Review of the Palisades pressure vessel accumulated fluence estimate and of the least squares methodology employed

Energy Technology Data Exchange (ETDEWEB)

Griffin, P.J.

1998-05-01

This report provides a review of the Palisades submittal to the Nuclear Regulatory Commission requesting endorsement of their accumulated neutron fluence estimates based on a least squares adjustment methodology. This review highlights some minor issues in the applied methodology and provides some recommendations for future work. The overall conclusion is that the Palisades fluence estimation methodology provides a reasonable approach to a {open_quotes}best estimate{close_quotes} of the accumulated pressure vessel neutron fluence and is consistent with the state-of-the-art analysis as detailed in community consensus ASTM standards.
Review of the Palisades pressure vessel accumulated fluence estimate and of the least squares methodology employed

International Nuclear Information System (INIS)

Griffin, P.J.

1998-05-01

This report provides a review of the Palisades submittal to the Nuclear Regulatory Commission requesting endorsement of their accumulated neutron fluence estimates based on a least squares adjustment methodology. This review highlights some minor issues in the applied methodology and provides some recommendations for future work. The overall conclusion is that the Palisades fluence estimation methodology provides a reasonable approach to a open-quotes best estimateclose quotes of the accumulated pressure vessel neutron fluence and is consistent with the state-of-the-art analysis as detailed in community consensus ASTM standards
On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

Energy Technology Data Exchange (ETDEWEB)

Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

2015-12-15

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)
Comparison between the basic least squares and the Bayesian approach for elastic constants identification

Science.gov (United States)

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.
On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

Science.gov (United States)

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).
Concerning an application of the method of least squares with a variable weight matrix

Science.gov (United States)

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.
Two Enhancements of the Logarithmic Least-Squares Method for Analyzing Subjective Comparisons

Science.gov (United States)

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
Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

KAUST Repository

Migliorati, Giovanni

2015-08-28

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. The convergence estimates are given in mean-square sense with respect to the sampling measure. The noise may be correlated with the location of the evaluation and may have nonzero mean (offset). We consider both cases of bounded or square-integrable noise / offset. We prove conditions between the number of sampling points and the dimension of the underlying approximation space that ensure a stable and accurate approximation. Particular focus is on deriving estimates in probability within a given confidence level. We analyze how the best approximation error and the noise terms affect the convergence rate and the overall confidence level achieved by the convergence estimate. The proofs of our convergence estimates in probability use arguments from the theory of large deviations to bound the noise term. Finally we address the particular case of multivariate polynomial approximation spaces with any density in the beta family, including uniform and Chebyshev.

Optimum and robust 3D facies interpolation strategies in a heterogeneous coal zone (Tertiary As Pontes basin, NW Spain)

Energy Technology Data Exchange (ETDEWEB)

Falivene, Oriol; Cabrera, Lluis; Saez, Alberto [Geomodels Institute, Group of Geodynamics and Basin Analysis, Department of Stratigraphy, Paleontology and Marine Geosciences, Universitat de Barcelona, c/ Marti i Franques s/n, Facultat de Geologia, 08028 Barcelona (Spain)

2007-07-02

Coal exploration and mining in extensively drilled and sampled coal zones can benefit from 3D statistical facies interpolation. Starting from closely spaced core descriptions, and using interpolation methods, a 3D optimum and robust facies distribution model was obtained for a thick, heterogeneous coal zone deposited in the non-marine As Pontes basin (Oligocene-Early Miocene, NW Spain). Several grid layering styles, interpolation methods (truncated inverse squared distance weighting, truncated kriging, truncated kriging with an areal trend, indicator inverse squared distance weighting, indicator kriging, and indicator kriging with an areal trend) and searching conditions were compared. Facies interpolation strategies were evaluated using visual comparison and cross validation. Moreover, robustness of the resultant facies distribution with respect to variations in interpolation method input parameters was verified by taking into account several scenarios of uncertainty. The resultant 3D facies reconstruction improves the understanding of the distribution and geometry of the coal facies. Furthermore, since some coal quality properties (e.g. calorific value or sulphur percentage) display a good statistical correspondence with facies, predicting the distribution of these properties using the reconstructed facies distribution as a template proved to be a powerful approach, yielding more accurate and realistic reconstructions of these properties in the coal zone. (author)
Least-squares reverse time migration with local Radon-based preconditioning

KAUST Repository

Dutta, Gaurav

2017-03-08

Least-squares migration (LSM) can produce images with better balanced amplitudes and fewer artifacts than standard migration. The conventional objective function used for LSM minimizes the L2-norm of the data residual between the predicted and the observed data. However, for field-data applications in which the recorded data are noisy and undersampled, the conventional formulation of LSM fails to provide the desired uplift in the quality of the inverted image. We have developed a leastsquares reverse time migration (LSRTM) method using local Radon-based preconditioning to overcome the low signal-tonoise ratio (S/N) problem of noisy or severely undersampled data. A high-resolution local Radon transform of the reflectivity is used, and sparseness constraints are imposed on the inverted reflectivity in the local Radon domain. The sparseness constraint is that the inverted reflectivity is sparse in the Radon domain and each location of the subsurface is represented by a limited number of geologic dips. The forward and the inverse mapping of the reflectivity to the local Radon domain and vice versa is done through 3D Fourier-based discrete Radon transform operators. The weights for the preconditioning are chosen to be varying locally based on the relative amplitudes of the local dips or assigned using quantile measures. Numerical tests on synthetic and field data validate the effectiveness of our approach in producing images with good S/N and fewer aliasing artifacts when compared with standard RTM or standard LSRTM.
A library least-squares approach for scatter correction in gamma-ray tomography

International Nuclear Information System (INIS)

Meric, Ilker; Anton Johansen, Geir; Valgueiro Malta Moreira, Icaro

2015-01-01

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. - Highlights: • A LLS approach is proposed for scatter correction in gamma-ray tomography. • The validity of the LLS approach is tested through experiments. • Gain shift and pulse pile-up affect the accuracy of the LLS approach. • The LLS approach successfully estimates scatter profiles
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.
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
An Inequality Constrained Least-Squares Approach as an Alternative Estimation Procedure for Atmospheric Parameters from VLBI Observations

Science.gov (United States)

Halsig, Sebastian; Artz, Thomas; Iddink, Andreas; Nothnagel, Axel

2016-12-01

On its way through the atmosphere, radio signals are delayed and affected by bending and attenuation effects relative to a theoretical path in vacuum. In particular, the neutral part of the atmosphere contributes considerably to the error budget of space-geodetic observations. At the same time, space-geodetic techniques become more and more important in the understanding of the Earth's atmosphere, because atmospheric parameters can be linked to the water vapor content in the atmosphere. The tropospheric delay is usually taken into account by applying an adequate model for the hydrostatic component and by additionally estimating zenith wet delays for the highly variable wet component. Sometimes, the Ordinary Least Squares (OLS) approach leads to negative estimates, which would be equivalent to negative water vapor in the atmosphere and does, of course, not reflect meteorological and physical conditions in a plausible way. To cope with this phenomenon, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization and use inequality constraints to force the tropospheric parameters to be non-negative allowing for a more realistic tropospheric parameter estimation in a meteorological sense. Because deficiencies in the a priori hydrostatic modeling are almost fully compensated by the tropospheric estimates, the ICLS approach urgently requires suitable a priori hydrostatic delays. In this paper, we briefly describe the ICLS method and validate its impact with regard to station positions.
Securing a cyber physical system in nuclear power plants using least square approximation and computational geometric approach

International Nuclear Information System (INIS)

Gawand, Hemangi Laxman; Bhattacharjee, A. K.; Roy, Kallol

2017-01-01

In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications
Securing a cyber physical system in nuclear power plants using least square approximation and computational geometric approach

Energy Technology Data Exchange (ETDEWEB)

Gawand, Hemangi Laxman [Homi Bhabha National Institute, Computer Section, BARC, Mumbai (India); Bhattacharjee, A. K. [Reactor Control Division, BARC, Mumbai (India); Roy, Kallol [BHAVINI, Kalpakkam (India)

2017-04-15

In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.
Securing a Cyber Physical System in Nuclear Power Plants Using Least Square Approximation and Computational Geometric Approach

Directory of Open Access Journals (Sweden)

Hemangi Laxman Gawand

2017-04-01

Full Text Available In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA software. A targeted attack (also termed a control aware attack on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.
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.
Linear Methods for Image Interpolation

OpenAIRE

Pascal Getreuer

2011-01-01

We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
Spatial interpolation

NARCIS (Netherlands)

Stein, A.

1991-01-01

The theory and practical application of techniques of statistical interpolation are studied in this thesis, and new developments in multivariate spatial interpolation and the design of sampling plans are discussed. Several applications to studies in soil science are

Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm 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 and the energetic variational approach for two-phase flow Science.gov (United States) Adler, J. H.; Brannick, J.; Liu, C.; Manteuffel, T.; Zikatanov, L. 2011-07-01 This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques. 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... Linear Methods for Image Interpolation Directory of Open Access Journals (Sweden) Pascal Getreuer 2011-09-01 Full Text Available We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation. Interpolation of daily rainfall using spatiotemporal models and clustering KAUST Repository Militino, A. F. 2014-06-11 Accumulated daily rainfall in non-observed locations on a particular day is frequently required as input to decision-making tools in precision agriculture or for hydrological or meteorological studies. Various solutions and estimation procedures have been proposed in the literature depending on the auxiliary information and the availability of data, but most such solutions are oriented to interpolating spatial data without incorporating temporal dependence. When data are available in space and time, spatiotemporal models usually provide better solutions. Here, we analyse the performance of three spatiotemporal models fitted to the whole sampled set and to clusters within the sampled set. The data consists of daily observations collected from 87 manual rainfall gauges from 1990 to 2010 in Navarre, Spain. The accuracy and precision of the interpolated data are compared with real data from 33 automated rainfall gauges in the same region, but placed in different locations than the manual rainfall gauges. Root mean squared error by months and by year are also provided. To illustrate these models, we also map interpolated daily precipitations and standard errors on a 1km2 grid in the whole region. © 2014 Royal Meteorological Society. Interpolation of daily rainfall using spatiotemporal models and clustering KAUST Repository Militino, A. F.; Ugarte, M. D.; Goicoa, T.; Genton, Marc G. 2014-01-01 Accumulated daily rainfall in non-observed locations on a particular day is frequently required as input to decision-making tools in precision agriculture or for hydrological or meteorological studies. Various solutions and estimation procedures have been proposed in the literature depending on the auxiliary information and the availability of data, but most such solutions are oriented to interpolating spatial data without incorporating temporal dependence. When data are available in space and time, spatiotemporal models usually provide better solutions. Here, we analyse the performance of three spatiotemporal models fitted to the whole sampled set and to clusters within the sampled set. The data consists of daily observations collected from 87 manual rainfall gauges from 1990 to 2010 in Navarre, Spain. The accuracy and precision of the interpolated data are compared with real data from 33 automated rainfall gauges in the same region, but placed in different locations than the manual rainfall gauges. Root mean squared error by months and by year are also provided. To illustrate these models, we also map interpolated daily precipitations and standard errors on a 1km2 grid in the whole region. © 2014 Royal Meteorological Society. Estimating the Acquisition Price of Enshi Yulu Young Tea Shoots Using Near-Infrared Spectroscopy by the Back Propagation Artificial Neural Network Model in Conjunction with Backward Interval Partial Least Squares Algorithm Science.gov (United States) Wang, Sh.-P.; Gong, Z.-M.; Su, X.-Zh.; Liao, J.-Zh. 2017-09-01 Near infrared spectroscopy and the back propagation artificial neural network model in conjunction with backward interval partial least squares algorithm were used to estimate the purchasing price of Enshi yulu young tea shoots. The near-infrared spectra regions most relevant to the tea shoots price model (5700.5-5935.8, 7613.6-7848.9, 8091.8-8327.1, 8331-8566.2, 9287.5-9522.5, and 9526.6-9761.9 cm-1) were selected using backward interval partial least squares algorithm. The first five principal components that explained 99.96% of the variability in those selected spectral data were then used to calibrate the back propagation artificial neural tea shoots purchasing price model. The performance of this model (coefficient of determination for prediction 0.9724; root-mean-square error of prediction 4.727) was superior to those of the back propagation artificial neural model (coefficient of determination for prediction 0.8653, root-mean-square error of prediction 5.125) and the backward interval partial least squares model (coefficient of determination for prediction 0.5932, root-mean-square error of prediction 25.125). The acquisition price model with the combined backward interval partial least squares-back propagation artificial neural network algorithms can evaluate the price of Enshi yulu tea shoots accurately, quickly and objectively. A novel approach to the experimental study on methane/steam reforming kinetics using the Orthogonal Least Squares method Science.gov (United States) 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.

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