[Research on fast implementation method of image Gaussian RBF interpolation based on CUDA].
Chen, Hao; Yu, Haizhong
2014-04-01
Image interpolation is often required during medical image processing and analysis. Although interpolation method based on Gaussian radial basis function (GRBF) has high precision, the long calculation time still limits its application in field of image interpolation. To overcome this problem, a method of two-dimensional and three-dimensional medical image GRBF interpolation based on computing unified device architecture (CUDA) is proposed in this paper. According to single instruction multiple threads (SIMT) executive model of CUDA, various optimizing measures such as coalesced access and shared memory are adopted in this study. To eliminate the edge distortion of image interpolation, natural suture algorithm is utilized in overlapping regions while adopting data space strategy of separating 2D images into blocks or dividing 3D images into sub-volumes. Keeping a high interpolation precision, the 2D and 3D medical image GRBF interpolation achieved great acceleration in each basic computing step. The experiments showed that the operative efficiency of image GRBF interpolation based on CUDA platform was obviously improved compared with CPU calculation. The present method is of a considerable reference value in the application field of image interpolation.
Efficient and exact mesh deformation using multiscale RBF interpolation
Kedward, L.; Allen, C. B.; Rendall, T. C. S.
2017-09-01
Radial basis function (RBF) interpolation is popular for mesh deformation due to robustness and generality, but the cost scales with the number of surface points sourcing the deformation as O (Ns3). Hence, there have been numerous works investigating efficient methods using reduced datasets. However, although reduced-data methods are efficient, they require a secondary method to treat an error vector field to ensure surface points not included in the primary deformation are moved to the correct location, and the volume mesh moved accordingly. A new method is presented which captures global and local motions at multiple scales using all the surface points, and so no correction stage is required; all surface points are used and a single interpolation built, but the cost and conditioning issues associated with RBF methods are eliminated. Moreover, the sparsity introduced is exploited using a wall distance function, to further reduce the cost. The method is compared to an efficient greedy method, and it is shown mesh quality is always comparable with or better than with the greedy method, and cost is comparable or cheaper at all stages. Surface mesh preprocessing is the dominant cost for reduced-data methods and this cost is reduced significantly here: greedy methods select points to minimise interpolation error, requiring repeated system solution and cost O (Nred4) to select Nred points; the multiscale method has no error, and the problem is transferred to a geometric search, with cost O (Ns log (Ns)), resulting in an eight orders of magnitude cost reduction for three-dimensional meshes. Furthermore, since the method is dependent on geometry, not deformation, it only needs to be applied once, prior to simulation, as the mesh deformation is decoupled from the point selection process.
Efficient algorithm for training interpolation RBF networks with equally spaced nodes.
Huan, Hoang Xuan; Hien, Dang Thi Thu; Tue, Huynh Huu
2011-06-01
This brief paper proposes a new algorithm to train interpolation Gaussian radial basis function (RBF) networks in order to solve the problem of interpolating multivariate functions with equally spaced nodes. Based on an efficient two-phase algorithm recently proposed by the authors, Euclidean norm associated to Gaussian RBF is now replaced by a conveniently chosen Mahalanobis norm, that allows for directly computing the width parameters of Gaussian radial basis functions. The weighting parameters are then determined by a simple iterative method. The original two-phase algorithm becomes a one-phase one. Simulation results show that the generality of networks trained by this new algorithm is sensibly improved and the running time significantly reduced, especially when the number of nodes is large.
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy
Flyer, Natasha; Fornberg, Bengt; Bayona, Victor; Barnett, Gregory A.
2016-09-01
Radial basis function-generated finite difference (RBF-FD) approximations generalize classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This greatly increases the geometric flexibility of the discretizations and makes it easier to carry out local refinement in critical areas. Many different types of radial functions have been considered in this RBF-FD context. In this study, we find that (i) polyharmonic splines (PHS) in conjunction with supplementary polynomials provide a very simple way to defeat stagnation (also known as saturation) error and (ii) give particularly good accuracy for the tasks of interpolation and derivative approximations without the hassle of determining a shape parameter. In follow-up studies, we will focus on how to best use these hybrid RBF polynomial bases for FD approximations in the contexts of solving elliptic and hyperbolic type PDEs.
Fast regularized image interpolation method
Hongchen Liu; Yong Feng; Linjing Li
2007-01-01
The regularized image interpolation method is widely used based on the vector interpolation model in which down-sampling matrix has very large dimension and needs large storage consumption and higher computation complexity. In this paper, a fast algorithm for image interpolation based on the tensor product of matrices is presented, which transforms the vector interpolation model to matrix form. The proposed algorithm can extremely reduce the storage requirement and time consumption. The simulation results verify their validity.
The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD
Shankar, Varun
2017-08-01
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter δ ∈ (0 , 1 ] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of stencils. We provide experimental evidence to support this generalization, and develop an automatic stabilization procedure based on local Lebesgue functions for the stable selection of stencil weights over a wide range of δ values. We provide an a priori estimate for the speedup of our method over RBF-FD that serves as a good predictor for the true speedup. We apply our method to parabolic partial differential equations with time-dependent inhomogeneous boundary conditions - Neumann in 2D, and Dirichlet in 3D. Our results show that our method can achieve as high as a 60× speedup in 3D over existing RBF-FD methods in the task of forming differentiation matrices.
Fuzzy Interpolation and Other Interpolation Methods Used in Robot Calibrations
Ying Bai
2012-01-01
Full Text Available A novel interpolation algorithm, fuzzy interpolation, is presented and compared with other popular interpolation methods widely implemented in industrial robots calibrations and manufacturing applications. Different interpolation algorithms have been developed, reported, and implemented in many industrial robot calibrations and manufacturing processes in recent years. Most of them are based on looking for the optimal interpolation trajectories based on some known values on given points around a workspace. However, it is rare to build an optimal interpolation results based on some random noises, and this is one of the most popular topics in industrial testing and measurement applications. The fuzzy interpolation algorithm (FIA reported in this paper provides a convenient and simple way to solve this problem and offers more accurate interpolation results based on given position or orientation errors that are randomly distributed in real time. This method can be implemented in many industrial applications, such as manipulators measurements and calibrations, industrial automations, and semiconductor manufacturing processes.
Classification data mining method based on dynamic RBF neural networks
Zhou, Lijuan; Xu, Min; Zhang, Zhang; Duan, Luping
2009-04-01
With the widely application of databases and sharp development of Internet, The capacity of utilizing information technology to manufacture and collect data has improved greatly. It is an urgent problem to mine useful information or knowledge from large databases or data warehouses. Therefore, data mining technology is developed rapidly to meet the need. But DM (data mining) often faces so much data which is noisy, disorder and nonlinear. Fortunately, ANN (Artificial Neural Network) is suitable to solve the before-mentioned problems of DM because ANN has such merits as good robustness, adaptability, parallel-disposal, distributing-memory and high tolerating-error. This paper gives a detailed discussion about the application of ANN method used in DM based on the analysis of all kinds of data mining technology, and especially lays stress on the classification Data Mining based on RBF neural networks. Pattern classification is an important part of the RBF neural network application. Under on-line environment, the training dataset is variable, so the batch learning algorithm (e.g. OLS) which will generate plenty of unnecessary retraining has a lower efficiency. This paper deduces an incremental learning algorithm (ILA) from the gradient descend algorithm to improve the bottleneck. ILA can adaptively adjust parameters of RBF networks driven by minimizing the error cost, without any redundant retraining. Using the method proposed in this paper, an on-line classification system was constructed to resolve the IRIS classification problem. Experiment results show the algorithm has fast convergence rate and excellent on-line classification performance.
A Parameterization Method from Conic Spline Interpolation
MA Long; GUO Feng-hua
2014-01-01
Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital step before constructing interpolation functions. The most widely used parameterization method is accumulative chord length parameterization. In this paper, we give out a better method based on the interpolation of conics. Based on this method, a sequence of fairer Hermite curves can be constructed.
COMPARISON OF DETEMINISTIC INTERPOLATION METHODS FOR THE ESTIMATION OF GROUNDWATER LEVEL
Agnieszka Kamińska
2014-10-01
Full Text Available This paper compares two spatial interpolation techniques – Radial Basis Functions (RBF and Inverse Distance Weighting (IDW – with the goal of determining which method creates the best representation of reality for measured groundwater levels in catchment area. The study used the results of research and field observations from the year 2011, in Sosnowica (West Polesie. The data set consists of groundwater levels measured at 15 points in three series of tests. Surface generation was obtained for each method. The water prediction maps showed spatial variation in the groundwater level in the study area and they are quite different. RBF method resulted in a smoother map. The analysis of the methods of interpolation of analyzed data with the help of cross validation statistics and plots showed that Radial Basis Functions creates better representation of reality for measured groundwater levels.
Optimal design of structures for earthquake loads by a hybrid RBF-BPSO method
Eysa Salajegheh; Saeed Gholizadeh; Mohsen Khatibina
2008-01-01
The optimal seismic design of structures requires that time history analyses (THA) be carried out repeatedly. This makes the optimal design process inefficient, in particular, if an evolutionary algorithm is used. To reduce the overall time required for structural optimization, two artificial intelligence strategies are employed. In the first strategy, radial basis function (RBF) neural networks are used to predict the time history responses of structures in the optimization flow. In the second strategy, a binary particle swarm optimization (BPSO) is used to find the optimum design. Combining the RBF and BPSO, a hybrid RBF-BPSO optimization method is proposed in this paper, which achieves fast optimization with high computational performance. Two examples are presented and compared to determine the optimal weight of structures under earthquake loadings using both exact and approximate analyses. The numerical results demonstrate the computational advantages and effectiveness of the proposed hybrid RBF-BPSO optimization method for the seismic design of structures.
Survey: interpolation methods in medical image processing.
Lehmann, T M; Gönner, C; Spitzer, K
1999-11-01
Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 x 1 up to 8 x 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6 x 6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N = 6 and N = 8 supporting points. For quantitative error evaluations, a set of 50 direct digital X rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sinc interpolators, all kernels with N = 6 or larger sizes perform significantly better than N = 2 or N = 3 point methods (p cubic 6 x 6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest
Revisiting Veerman’s interpolation method
Christiansen, Peter; Bay, Niels Oluf
2016-01-01
for comparison. Bulge testing and tensile testing of aluminium sheets containingelectro-chemically etched circle grids are performed to experimentally determine the forming limit of the sheet material.The forming limit is determined using (a) Veerman’s interpolation method, (b) exact Lagrangian interpolation...
Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.
2014-05-01
We present a computational method for solving the coupled problem of chemical transport in a fluid (blood) with binding/unbinding of the chemical to/from cellular (platelet) surfaces in contact with the fluid, and with transport of the chemical on the cellular surfaces. The overall framework is the Augmented Forcing Point Method (AFM) (\\emph{L. Yao and A.L. Fogelson, Simulations of chemical transport and reaction in a suspension of cells I: An augmented forcing point method for the stationary case, IJNMF (2012) 69, 1736-52.}) for solving fluid-phase transport in a region outside of a collection of cells suspended in the fluid. We introduce a novel Radial Basis Function-Finite Difference (RBF-FD) method to solve reaction-diffusion equations on the surface of each of a collection of 2D stationary platelets suspended in blood. Parametric RBFs are used to represent the geometry of the platelets and give accurate geometric information needed for the RBF-FD method. Symmetric Hermite-RBF interpolants are used for enforcing the boundary conditions on the fluid-phase chemical concentration, and their use removes a significant limitation of the original AFM. The efficacy of the new methods are shown through a series of numerical experiments; in particular, second order convergence for the coupled problem is demonstrated.
Yu, Yang; Wei, Wei; Chen, Li-ding; Yang, Lei; Zhang, Han-dan
2015-04-01
Based on 57 years (1957-2013) daily precipitation datasets of the 85 meteorological stations in the Loess Plateau region, different spatial interpolation methods, including ordinary kriging (OK), inverse distance weighting (IDW) and radial-based function (RBF), were conducted to analyze the spatial variation of annual average precipitation regionally. Meanwhile, the mean absolute error (MAE), the root mean square error (RMSE), the accuracy (AC) and the Pearson correlation coefficient (R) were compared among the interpolation results in order to quantify the effects of different interpolation methods on spatial variation of the annual average precipitation. The results showed that the Moran's I index was 0.67 for the 57 years annual average precipitation in the Loess Plateau region. Meteorological stations exhibited strong spatial correlation. The validation results of the 63 training stations and 22 test stations indicated that there were significant correlations between the training and test values among different interpolation methods. However, the RMSE (IDW = 51.49, RBF = 43.79) and MAE (IDW = 38.98, RBF = 34.61) of the IDW and the RBF showed higher values than the OK. In addition, the comparison of the four semi-variagram models (Circular, Spherical, Exponential and Gaussian) for the OK indicated that the circular model had the lowest MAE (32.34) and the highest accuracy (0.976), while the MAE of the exponential model was the highest (33.24). In conclusion, comparing the validation between the training data and test results of the different spatial interpolation methods, the circular model of the OK method was the best one for obtaining accurate spatial interpolation of annual average precipitation in the Loess Plateau region.
Research on interpolation methods in medical image processing.
Pan, Mei-Sen; Yang, Xiao-Li; Tang, Jing-Tian
2012-04-01
Image interpolation is widely used for the field of medical image processing. In this paper, interpolation methods are divided into three groups: filter interpolation, ordinary interpolation and general partial volume interpolation. Some commonly-used filter methods for image interpolation are pioneered, but the interpolation effects need to be further improved. When analyzing and discussing ordinary interpolation, many asymmetrical kernel interpolation methods are proposed. Compared with symmetrical kernel ones, the former are have some advantages. After analyzing the partial volume and generalized partial volume estimation interpolations, the new concept and constraint conditions of the general partial volume interpolation are defined, and several new partial volume interpolation functions are derived. By performing the experiments of image scaling, rotation and self-registration, the interpolation methods mentioned in this paper are compared in the entropy, peak signal-to-noise ratio, cross entropy, normalized cross-correlation coefficient and running time. Among the filter interpolation methods, the median and B-spline filter interpolations have a relatively better interpolating performance. Among the ordinary interpolation methods, on the whole, the symmetrical cubic kernel interpolations demonstrate a strong advantage, especially the symmetrical cubic B-spline interpolation. However, we have to mention that they are very time-consuming and have lower time efficiency. As for the general partial volume interpolation methods, from the total error of image self-registration, the symmetrical interpolations provide certain superiority; but considering the processing efficiency, the asymmetrical interpolations are better.
An interpolation method for stream habitat assessments
Sheehan, Kenneth R.; Welsh, Stuart A.
2015-01-01
Interpolation of stream habitat can be very useful for habitat assessment. Using a small number of habitat samples to predict the habitat of larger areas can reduce time and labor costs as long as it provides accurate estimates of habitat. The spatial correlation of stream habitat variables such as substrate and depth improves the accuracy of interpolated data. Several geographical information system interpolation methods (natural neighbor, inverse distance weighted, ordinary kriging, spline, and universal kriging) were used to predict substrate and depth within a 210.7-m2 section of a second-order stream based on 2.5% and 5.0% sampling of the total area. Depth and substrate were recorded for the entire study site and compared with the interpolated values to determine the accuracy of the predictions. In all instances, the 5% interpolations were more accurate for both depth and substrate than the 2.5% interpolations, which achieved accuracies up to 95% and 92%, respectively. Interpolations of depth based on 2.5% sampling attained accuracies of 49–92%, whereas those based on 5% percent sampling attained accuracies of 57–95%. Natural neighbor interpolation was more accurate than that using the inverse distance weighted, ordinary kriging, spline, and universal kriging approaches. Our findings demonstrate the effective use of minimal amounts of small-scale data for the interpolation of habitat over large areas of a stream channel. Use of this method will provide time and cost savings in the assessment of large sections of rivers as well as functional maps to aid the habitat-based management of aquatic species.
Seta, Ryo; Okubo, Kan; Tagawa, Norio
2009-01-01
Image interpolation can be performed by a convolution operation using the neighboring image values. To achieve accurate image interpolation, some of the conventional methods use basis function with large support, and therefore their implementation may have a large computational cost. Interpolation by the Hermite interpolating polynomials can be performed using image values and their derivatives. This makes it possible to realize the high-order interpolation with small support. In this study, ...
MINIMAL RATIONAL INTERPOLATION AND PRONYS METHOD
ANTOULAS, AC; WILLEMS, JC
1990-01-01
A new method is proposed for dealing with the rational interpolation problem. It is based on the reachability of an appropriately defined pair of matrices. This method permits a complete clarification of several issues raised, but not answered, by the so-called Prony method of fitting a linear model
Xiaolong Wang; Yi Wang; Zhizhu Cao; Weizhong Zou; Liping Wang; Guojun Yu; Bo Yu; Jinjun Zhang
2013-01-01
In general, proper orthogonal decomposition (POD) method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified...
The Diffraction Response Interpolation Method
Jespersen, Søren Kragh; Wilhjelm, Jens Erik; Pedersen, Peder C.
1998-01-01
medium, is presented. The DRIM is based on the velocity potential impulseresponse method, adapted to pulse-echo applications by the use of acoustical reciprocity. Specifically, the DRIM operates bydividing the reflector surface into planar elements, finding the diffraction response at the corners...... of the elements, calculating theresponse integrated over the surface element by time-domain convolutions with analytically determined filters, and summing theresponses from the individual surface elements. As the method is based on linearity, effects such as shadowing, higher-orderdiffraction, nonlinear...
Solving time-dependent problems by an RBF-PS method with an optimal shape parameter
Neves, A M A; Roque, C M C; Ferreira, A J M; Jorge, R M N [Departamento de Engenharia Mecanica e Gestao Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto (Portugal); Soares, C M M, E-mail: ana.m.neves@fe.up.p, E-mail: croque@fe.up.p, E-mail: ferreira@fe.up.p, E-mail: cristovao.mota.soares@dem.ist.utl.p, E-mail: rnatal@fe.up.p [IDMEC - Instituto de Engenharia Mecanica - Instituto Superior Tecnico, Av. Rovisco Pais, 1096 Lisboa Codex (Portugal)
2009-08-01
An hybrid technique is used for the solutions of static and time-dependent problems. The idea is to combine the radial basis function (RBF) collocation method and the pseudospectal (PS) method getting to the RBF-PS method. The approach presented in this paper includes a shape parameter optimization and produces highly accurate results. Different examples of the procedure are presented and different radial basis functions are used. One and two-dimensional problems are considered with various boundary and initial conditions. We consider generic problems, but also results on beams and plates. The displacement and the stress analysis are conducted for static and transient dynamic situations. Results obtained are in good agreement with exact solutions or references considered.
Research on Method of Character Recognition Based on Hough Transform and RBF Neural Network
Zhang Yin
2015-01-01
Full Text Available A method of character recognition based on Hough transform and RBF neural network is proposed through research on weight accumulation algorithm of Hough transform. According to the feature of characters’ structure by using the duality of point-line Hough transform was done. In this method, the number of the points on the same line in parameter space and the position coordinates of the elements in image mapping space were taken to RBF neural network recognition system as characteristic input vector. It reduced the dimension of character feature vector and reflected the overall distribution of character lattice and the essential feature of character shape. The simulation results indicated there were some merits in this improved method: capability of recognition is strong, the quantity of calculation is small, and the speed of calculation is quick.
Separation of Waves by Interpolation Method
孙鹤泉; 王永学
2003-01-01
The separation of waves by an interpolation method is presented in detail. The composite wave sequences measured with two wave gauges in the wave flume are separated very quickly into two series of incident and reflected waves in time domain via the simple interpolation and difference operations. Then, the reflection coefficient can be estimated easily and accurately without calculation of wave heights and phases. The intial phase of reflection can also be detected easily for improvement of the accuracy of calculation. The present method is applicable to both regular and irregular trains of waves based on the linear wave theory which are proved to be accurate through numerical sample tests. Physical experiments are conducted and compared with Goda′s method and analytical method with satisfactory results. Furthermore, the present method can be used for the absorbing wave-maker to extract reflected waves in real time.
Xiaolong Wang
2013-01-01
Full Text Available In general, proper orthogonal decomposition (POD method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified via two typical examples. Both results of the two methods are satisfying, and the results of cubic B-spline interpolation are more accurate than those of linear interpolation. The results are meaningful for guiding the application of the POD interpolation to complex multiparameter problems.
The periodic complex method in interpolation spaces
Avni, Eliran
2012-01-01
We discuss a question which relates to Calderon's complex interpolation method. More precisely, we will consider the so-called "periodic" complex interpolation method, studied by Peetre. (Which also corresponds to the spaces obtained by Calderon's construction using Banach space valued analytic functions, but defined on an annulus instead of the strip used by Calderon.) Cwikel showed that, using functions with a given period i\\lambda in the complex method mechanism, one obtains the same interpolation spaces as in the original version of the complex method, up to equivalence of norms. He also showed that one of the constants of this equivalence will, in some cases, "blow up" as \\lambda tends to zero. We will show that the equivalence constants tend to 1 as \\lambda tends to infinity. Intuitively, this means that when applying the complex method, it makes a very small difference if one restricts oneself to periodic functions, provided that the period is very large (or the corresponding annulus is very thin).
Estimating monthly temperature using point based interpolation techniques
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.
Vedadi, Farhang; Shirani, Shahram
2014-01-01
A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.
Numerical simulation of GEW equation using RBF collocation method
Hamid Panahipour
2012-08-01
Full Text Available The generalized equal width (GEW equation is solved numerically by a meshless method based on a global collocation with standard types of radial basis functions (RBFs. Test problems including propagation of single solitons, interaction of two and three solitons, development of the Maxwellian initial condition pulses, wave undulation and wave generation are used to indicate the efficiency and accuracy of the method. Comparisons are made between the results of the proposed method and some other published numerical methods.
[Brain potential mapping by a new method of polynomial interpolation].
Pérez-Cobo, J C; Asencor, F J; Sánchez-Suero, S; Pérez-Arroyo, M
1993-06-01
The mapping of evoked cerebral activity is largely determined by the choice of the interpolation system used. When the number of electrodes is very large, practically any interpolation system is valid, but the geometrical and anatomical limitations imposed by the animals normally chosen for these experiments impede the use of a large number of electrodes; hence the overriding importance of a workable interpolation system. The polynomic interpolation method on the monomial structure is presented as valid, and compared with the pseudolineal interpolation method, which is more commonly used.
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-03
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Dehghan, Mehdi; Mohammadi, Vahid
2017-08-01
In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.
Lihua Yang
2015-04-01
Full Text Available In order to improve the accuracy of grain production forecasting, this study proposed a new combination forecasting model, the model combined stepwise regression method with RBF neural network by assigning proper weights using inverse variance method. By comparing different criteria, the result indicates that the combination forecasting model is superior to other models. The performance of the models is measured using three types of error measurement, which are Mean Absolute Percentage Error (MAPE, Theil Inequality Coefficient (Theil IC and Root Mean Squared Error (RMSE. The model with smallest value of MAPE, Theil IC and RMSE stands out to be the best model in predicting the grain production. Based on the MAPE, Theil IC and RMSE evaluation criteria, the combination model can reduce the forecasting error and has high prediction accuracy in grain production forecasting, making the decision more scientific and rational.
Rainfall variation by geostatistical interpolation method
Glauber Epifanio Loureiro
2013-08-01
Full Text Available This article analyses the variation of rainfall in the Tocantins-Araguaia hydrographic region in the last two decades, based upon the rain gauge stations of the ANA (Brazilian National Water Agency HidroWeb database for the years 1983, 1993 and 2003. The information was systemized and treated with Hydrologic methods such as method of contour and interpolation for ordinary kriging. The treatment considered the consistency of the data, the density of the space distribution of the stations and the periods of study. The results demonstrated that the total volume of water precipitated annually did not change significantly in the 20 years analyzed. However, a significant variation occurred in its spatial distribution. By analyzing the isohyet it was shown that there is a displacement of the precipitation at Tocantins Baixo (TOB of approximately 10% of the total precipitated volume. This displacement can be caused by global change, by anthropogenic activities or by regional natural phenomena. However, this paper does not explore possible causes of the displacement.
Interpolation from Grid Lines: Linear, Transfinite and Weighted Method
Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen
2017-01-01
When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. 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 l...
Analysis of Spatial Interpolation in the Material-Point Method
Andersen, Søren; Andersen, Lars
2010-01-01
This paper analyses different types of spatial interpolation for the material-point method The interpolations include quadratic elements and cubic splines in addition to the standard linear shape functions usually applied. For the small-strain problem of a vibrating bar, the best results are obta......This paper analyses different types of spatial interpolation for the material-point method The interpolations include quadratic elements and cubic splines in addition to the standard linear shape functions usually applied. For the small-strain problem of a vibrating bar, the best results...... are obtained using quadratic elements. It is shown that for more complex problems, the use of partially negative shape functions is inconsistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations...
Comparison of interpolating methods for image resampling.
Parker, J; Kenyon, R V; Troxel, D E
1983-01-01
When resampling an image to a new set of coordinates (for example, when rotating an image), there is often a noticeable loss in image quality. To preserve image quality, the interpolating function used for the resampling should be an ideal low-pass filter. To determine which limited extent convolving functions would provide the best interpolation, five functions were compared: A) nearest neighbor, B) linear, C) cubic B-spline, D) high-resolution cubic spline with edge enhancement (a = -1), and E) high-resolution cubic spline (a = -0.5). The functions which extend over four picture elements (C, D, E) were shown to have a better frequency response than those which extend over one (A) or two (B) pixels. The nearest neighbor function shifted the image up to one-half a pixel. Linear and cubic B-spline interpolation tended to smooth the image. The best response was obtained with the high-resolution cubic spline functions. The location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned, and the response has the most smoothing when the resampled points are equidistant from the original coordinate points. Thus, at the expense of some increase in computing time, image quality can be improved by resampled using the high-resolution cubic spline function as compared to the nearest neighbor, linear, or cubic B-spline functions.
Polynomial interpolation methods for viscous flow calculations
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
Polynomial interpolation methods for viscous flow calculations
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
Numerical simulations of 1D inverse heat conduction problems using overdetermined RBF-MLPG method
Ahmad Shirzadi
2013-07-01
Full Text Available This paper proposes a numerical method to deal with the one-dimensional inverse heat conduction problem (IHCP. The initial temperature, a condition on an accessible part of the boundary and an additional temperature measurements in time at an arbitrary location in the domain are known, and it is required to determine the temperature and the heat flux on the remaining part of the boundary. Due to the missing boundary condition, the solution of this problem does not depend continuously on the data and therefore its numerical solution requires special care especially when noise is present in the measured data. In the proposed method, the time variable is eliminated by using finite differences approximation. The method uses a weak formulation of the problem to enjoy the stability condition. To avoid the numerical integration on the whole domain, the weak form equations are constructed on local subdomains. The approximate solution is assumed to be a linear combination of Multi Quadric (MQ radial basis function (RBF constructed on nodal points in the domain and on the boundary. Since the problem is known to be ill-posed, Thikhonov regularization strategy is employed to solve effectively the discrete ill-posed resultant linear system.
The Additional Interpolators Method for Variational Analysis in Lattice QCD
Schiel, Rainer W
2015-01-01
In this paper, I describe the Additional Interpolators Method, a new technique for variational analysis in lattice QCD. It is shown to be an excellent method which uses additional interpolators to remove backward in time running states that would otherwise contaminate the signal. The proof of principle, which also makes use of the Time-Shift Trick (Generalized Pencil-of-Functions method), will be delivered at an example on a $64^4$ lattice close to the physical pion mass.
[Comparison of spatial interpolation methods for daily meteorological elements].
Jiang, Xiao-Jian; Liu, Xiao-Jun; Huang, Fen; Jiang, Hai-Yan; Cao, Wei-Xing; Zhu, Yan
2010-03-01
A comparative study was made to evaluate the methods of inverse distance weighting (IDW), co-kriging (CK), and thin plate spline (TPS) in interpolating the average meteorological elements (including maximum air temperature, minimum air temperature, sunshine hours, and precipitation) of the 15th day per month from the 1951-2005 comprehensive observation data of 559 meteorological stations in China. The results showed that the RMSEs for the maximum and minimum air temperature in a year interpolated by TPS were the smallest (1.02 degrees C and 1.12 degrees C, respectively), and the R2 between the observed and predicted values were the highest (0.9916 and 0.9913, respectively), compared with those interpolated by IDW and CK. In four seasons, the smallest RMSEs for the maximum and minimum air temperature interpolated by TPS were observed in autumn (0.83 degrees C) and summer (0.86 degrees C), respectively, and the R2 between the observed and predicted values interpolated by TPS were higher in autumn than in other seasons. The RMSEs for the sunshine hours and precipitation in a year interpolated by TPS were the smallest (0.59 h and 1.01 mm, respectively), and the R2 between the observed and predicted values were the highest (0.9118 and 0.8135, respectively), compared with those interpolated by IDW and CK. In four seasons, the RMSE for the sunshine hours in winter interpolated by TPS was the smallest (0.49 h), and the R2 between the observed and predicted sunshine hours was the smallest (0.9293). The RMSE for the precipitation in winter interpolated by TPS was the smallest (0.33 mm), while the RMSE for the precipitation in summer interpolated by IDW was the smallest (2.01 mm). The R2 between the observed and predicted precipitation in winter interpolated by CK was the highest (0.8781). It was suggested that TPS could be the optimal spatial interpolation method in interpolating and rasterizing the daily meteorological elements in China.
Survey: interpolation methods for whole slide image processing.
Roszkowiak, L; Korzynska, A; Zak, J; Pijanowska, D; Swiderska-Chadaj, Z; Markiewicz, T
2017-02-01
Evaluating whole slide images of histological and cytological samples is used in pathology for diagnostics, grading and prognosis . It is often necessary to rescale whole slide images of a very large size. Image resizing is one of the most common applications of interpolation. We collect the advantages and drawbacks of nine interpolation methods, and as a result of our analysis, we try to select one interpolation method as the preferred solution. To compare the performance of interpolation methods, test images were scaled and then rescaled to the original size using the same algorithm. The modified image was compared to the original image in various aspects. The time needed for calculations and results of quantification performance on modified images were also compared. For evaluation purposes, we used four general test images and 12 specialized biological immunohistochemically stained tissue sample images. The purpose of this survey is to determine which method of interpolation is the best to resize whole slide images, so they can be further processed using quantification methods. As a result, the interpolation method has to be selected depending on the task involving whole slide images.
A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation
Mingzhu Li
2014-01-01
Full Text Available The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.
Compensating Interpolation Distortion by Using New Optimized Modular Method
Tofighi, Mohammad; Marvasti, Farokh
2012-01-01
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating the distortion of any interpolation based on modular method has been proposed. In this method the performance of the modular method is optimized by adding only some simply calculated coefficients. This approach causes drastic improvement in terms of signal-to-noise ratios with fewer modules compared to the classical modular method. Simulation results clearly confirm the improvement of the proposed method and also its superior robustness against additive noise.
Spatial interpolation methods for monthly rainfalls and temperatures in Basilicata
Ferrara A
2008-12-01
Full Text Available Spatial interpolated climatic data on grids are important as input in forest modeling because climate spatial variability has a direct effect on productivity and forest growth. Maps of climatic variables can be obtained by different interpolation methods depending on data quality (number of station, spatial distribution, missed data etc. and topographic and climatic features of study area. In this paper four methods are compared to interpolate monthly rainfall at regional scale: 1 inverse distance weighting (IDW; 2 regularized spline with tension (RST; 3 ordinary kriging (OK; 4 universal kriging (UK. Besides, an approach to generate monthly surfaces of temperatures over regions of complex terrain and with limited number of stations is presented. Daily data were gathered from 1976 to 2006 period and then gaps in the time series were filled in order to obtain monthly mean temperatures and cumulative precipitation. Basic statistics of monthly dataset and analysis of relationship of temperature and precipitation to elevation were performed. A linear relationship was found between temperature and altitude, while no relationship was found between rainfall and elevation. Precipitations were then interpolated without taking into account elevation. Based on root mean squared error for each month the best method was ranked. Results showed that universal kriging (UK is the best method in spatial interpolation of rainfall in study area. Then cross validation was used to compare prediction performance of tree different variogram model (circular, spherical, exponential using UK algorithm in order to produce final maps of monthly precipitations. Before interpolating temperatures were referred to see level using the calculated lapse rate and a digital elevation model (DEM. The result of interpolation with RST was then set to originally elevation with an inverse procedure. To evaluate the quality of interpolated surfaces a comparison between interpolated and
Entropy Generation Due to Natural Convection in a Partially Heated Cavity by Local RBF-DQ Method
Soleimani, S.; Qajarjazi, A.; Bararnia, H.
2011-01-01
The Local Radial Basis Function-Differential Quadrature (RBF-DQ) method is applied to twodimensional incompressible Navier-Stokes equations in primitive form. Numerical results of heatlines and entropy generation due to heat transfer and fluid friction have been obtained for laminar natural...... convection. The variations of the entropy generation for different Rayleigh numbers are also investigated. Comparison between the present results and previous works demonstrated excellent agreements which verify the accuracy and flexibility of the method in simulating the fluid mechanics and heat transfer...
A Radial Basis Function (RBF) Method for the Fully Nonlinear 1D Serre Green-Naghdi Equations
Fabien, Maurice S
2014-01-01
In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in time; the full discretization is obtained by the method of lines technique. For select test cases (see Bonnenton et al. [2] and Kim [11]) the approximation achieves spectral (exponential) accuracy. Complete \\textsc{matlab} code of the numerical implementation is included in this paper (the logic is easy to follow, and the code is under 100 lines).
The Algebra Theory for PolynomialInterpolation Method
2015-01-01
In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.
何文英; 毕孟飞; 李泽利; 王玉秋
2013-01-01
选取新安江流域48个雨量站点2000-2010年的降雨量数据以及地理地形资料,利用反距离权重(IDW)、径向基函数(RBF)、普通克里金(OK)和残差克里金(RK)方法进行插值,根据交叉验证结果筛选最佳的方法和参数.结果表明:年尺度上,考虑高程、纬度等地形因子影响的RK方法插值精度最高,然后是IDW,OK和RBF;邻近站点的搜索策略对IDW插值精度影响较大；考虑各向异性的OK法插值精度较高,模型之间的差别不大.月尺度上,IDW法对降雨量丰富的月份插值精度较高；RBF对降雨较少且分布均匀的月份插值效果好；数据越符合正态分布,OK法的插值精度越高；RK方法则适用于降雨与地理因素相关性好的月份.%The paper selected precipitation and geographic terrain data of 48 rainfall gage stations in the Xin'anjiang River basin from 2000 to 2010,and used inverse distance weight(IDW),radial basis function (RBF) ,ordinary Kriging (OK) and residual Kriging(RK) methods to interpolate and screened the best interpolation method and parameter according to the validated results. The results show that in annual scale the precision of RK method witch comprehensively considered the influences of elevation and latitude is the highest, then follows by IDW, OK and RBF; the search strategy of neighbor stations has greater impact on IDW interpolation accuracy; the precision of OK method witch considered anisotropic is higher, but the difference between the models is little. On monthly scale, the interpolation precision of IDW method to rich rainfall month is higher; the interpolation effect of RBF method to less and evenly distributed rainfall month is good; the data is more in accordance with normal distribution, the higher the interpolation accuracy of OK method; RK method is applicable to the month when the correlation between rainfall distribution and geographical factors is good.
A comparative analysis of different DEM interpolation methods
P.V. Arun
2013-12-01
Full Text Available Visualization of geospatial entities generally entails Digital Elevation Models (DEMs that are interpolated to establish three dimensional co-ordinates for the entire terrain. The accuracy of generated terrain model depends on the interpolation mechanism adopted and hence it is needed to investigate the comparative performance of different approaches in this context. General interpolation techniques namely Inverse Distance Weighted, kriging, ANUDEM, Nearest Neighbor, and Spline approaches have been compared. Differential ground field survey has been conducted to generate reference DEM as well as specific set of test points for comparative evaluation. We have also investigated the suitability of Shuttle Radar Topographic Mapper Digital Elevation Mapper for Indian terrain by comparing it with the Survey of India (SOI Digital Elevation Model (DEM. Contours were generated at different intervals for comparative analysis and found SRTM as more suitable. The terrain sensitivity of various methods has also been analyzed with reference to the study area.
Ahmadi Majid
2003-01-01
Full Text Available This paper introduces a novel method for the recognition of human faces in digital images using a new feature extraction method that combines the global and local information in frontal view of facial images. Radial basis function (RBF neural network with a hybrid learning algorithm (HLA has been used as a classifier. The proposed feature extraction method includes human face localization derived from the shape information. An efficient distance measure as facial candidate threshold (FCT is defined to distinguish between face and nonface images. Pseudo-Zernike moment invariant (PZMI with an efficient method for selecting moment order has been used. A newly defined parameter named axis correction ratio (ACR of images for disregarding irrelevant information of face images is introduced. In this paper, the effect of these parameters in disregarding irrelevant information in recognition rate improvement is studied. Also we evaluate the effect of orders of PZMI in recognition rate of the proposed technique as well as RBF neural network learning speed. Simulation results on the face database of Olivetti Research Laboratory (ORL indicate that the proposed method for human face recognition yielded a recognition rate of 99.3%.
RBF networks with mixed radial basis functions
Ciftcioglu, O.; Sariyildiz, I.S.
2000-01-01
After the introduction to neural network technology as multivariable function approximation, radial basis function (RBF) networks have been studied in many different aspects in recent years. From the theoretical viewpoint, approximation and uniqueness of the interpolation is studied and it has been
Chen, Xu; Xiang, Yang; Feng, Yu-Tao
2011-04-01
Spectral curvature destroys the co-registration of the spectra measured by dispersion imaging spectrometer. Using interpolation to re-sample the measured spectra at the non-offset mid-wavelengths can mitigate the spectral misregistration. It is very important to select an optimum interpolation method. The performances of six common interpolation methods are evaluated by comparing the residual errors in the corrected spectral radiance. The results indicate that, four-point cubic Lagrange interpolation and cubic spline interpolation are better than other four interpolation methods (linear Interpolation, three points quadratic polynomial interpolation, five points four-order Lagrange interpolation and cubic Hermite interpolation). For spectral offset of 10% deltalambda (deltalambda = 5 nm), the normalized errors in measured spectral radiance is PV = 0.06, that is reduced to PV interpolation with cubic Lagrange interpolation or cubic spline interpolation, but for other four methods they are PV > 0.035. Furthermore, for lower spectral resolution (deltalambda > 5 nm), cubic Lagrange interpolation is a little better than cubic spline interpolation; while for higher spectral resolution (deltalambda interpolation is a little better.
Barnett, Gregory A; Wicker, Louis J
2015-01-01
Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for the presented approach. Comparisons are done on Cartesian, hexagonal, and quasi-uniformly scattered node layouts. Since RBFs are independent of a coordinate system (and only depend on the distance between nodes), changing the node layout amounts to changing one line of code. In addition, consideration and guidelines are given on PHS order, polynomial degree and stencil size. The main advantages of the present method are: 1) capturing the basic physics of the problem surprisingly well, even at very coarse resol...
Immersed interface interpolation schemes for particle-mesh methods
Marichal, Yves; Chatelain, Philippe; Winckelmans, Grégoire
2016-12-01
The sharp and high-order treatment of arbitrary boundaries immersed in the computational domain remains a challenge to particle methods. While several techniques have been proposed to modify numerical stencils, e.g. Finite Difference ones, near the walls, the particle-mesh interpolation component of particle methods also has to be modified. This operation, mapping fields from the grid to the particles and vice-versa, has to be performed several times per computational step in the framework of particle-mesh methods. The present paper proposes an extension of classical particle-mesh interpolation approaches by computing high-order ghost fields based on the information about the solution behavior at the wall. This approach is further shown to be especially interesting when combined with a dimension-splitting Immersed Interface method to correct the spatial differential operators. Indeed, the associated corrections are computed at the intersection between the interface and the grid lines, making the necessary information for the ghost construction readily available. The mesh-to-particles and particles-to-mesh interpolation schemes are validated individually in convergence studies and, finally, both are applied to the advection-diffusion of a passive tracer past 2D objects.
WANG Hong-qi; WANG Xue-yuan; TANG Yu
2005-01-01
This paper designs an intelligent evaluation approach using a Radial Basis Function (RBF) Artificial Neural Network. We based our approach on establishing a comprehensive advantage evaluating index system that offers scientific substance for creating a development plan and the strategic management of high-tech industry and regional cluslers of high-tech enterprises. Furthermore, this paper selects some typical high-tech enterprises' data to make comprehensive training on the network system. Meanwhile, the paper chooses some enterprises as testing samples to test the method, the result of which proves that this method is truly effective. The research of this paper provides a comprehensive advantage evaluating and managing method for high-tech enterprise.
On the efficiency and accuracy of interpolation methods for spectral codes
Hinsberg, van M.A.T.; Thije Boonkkamp, ten J.H.M.; Toschi, F.; Clercx, H.J.H.
2012-01-01
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way m
A NEW DERIVATIVE FREE OPTIMIZATION METHOD BASED ON CONIC INTERPOLATION MODEL
倪勤; 胡书华
2004-01-01
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
Comparison of six methods for the interpolation of daily European climate data
Hofstra, N.; Haylock, M.; New, M.; Jones, P.; Frei, C.
2008-01-01
We compare versions of six interpolation methods for the interpolation of daily precipitation, mean, minimum and maximum temperature, and sea level pressure from station data over Europe from 1961 to 1990. The interpolation methods evaluated are global and local kriging, two versions of angular dist
Neural Network Methods for NURBS Curve and Surface Interpolation
秦开怀
1997-01-01
New algorithms based on artificial neural network models are presented for cubic NURBS curve and surface interpolation.When all th knot spans are identical,the NURBS curve interpolation procedure degenerates into that of uniform rational B-spline curves.If all the weights of data points are identical,then the NURBS curve interpolation procedure degenerates into the integral B-spline curve interpolation.
Construction of Large Period Symplectic Maps by Interpolative Methods
Warnock, Robert; Cai, Yunhai; /SLAC; Ellison, James A.; /New Mexico U.
2009-12-17
The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S, given in terms of interpolatory functions. Two ways to find the generator are considered: (1) Find its gradient from tracking data, then the generator itself as a line integral. (2) Compute the action integral on many orbits. A test of method (1) has been made in a difficult example: a full turn map for an electron ring with strong nonlinearity near the dynamic aperture. The method succeeds at fairly large amplitudes, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. For a generally applicable algorithm we propose method (2), realized with meshless interpolation methods.
3D Interpolation Method for CT Images of the Lung
Noriaki Asada
2003-06-01
Full Text Available A 3-D image can be reconstructed from numerous CT images of the lung. The procedure reconstructs a solid from multiple cross section images, which are collected during pulsation of the heart. Thus the motion of the heart is a special factor that must be taken into consideration during reconstruction. The lung exhibits a repeating transformation synchronized to the beating of the heart as an elastic body. There are discontinuities among neighboring CT images due to the beating of the heart, if no special techniques are used in taking CT images. The 3-D heart image is reconstructed from numerous CT images in which both the heart and the lung are taken. Although the outline shape of the reconstructed 3-D heart is quite unnatural, the envelope of the 3-D unnatural heart is fit to the shape of the standard heart. The envelopes of the lung in the CT images are calculated after the section images of the best fitting standard heart are located at the same positions of the CT images. Thus the CT images are geometrically transformed to the optimal CT images fitting best to the standard heart. Since correct transformation of images is required, an Area oriented interpolation method proposed by us is used for interpolation of transformed images. An attempt to reconstruct a 3-D lung image by a series of such operations without discontinuity is shown. Additionally, the same geometrical transformation method to the original projection images is proposed as a more advanced method.
Arslan, Hakan
2014-08-01
Groundwater level plays a significant role in coastal plains. Heavy pumping and excessive use of near-coast groundwater can increase the intrusion of seawater into the aquifers. In the present study, groundwater levels were measured at 59 groundwater wells at different times during pre- and post-irrigation seasons (April and September of the year 2012) in Çarşamba Plain, Turkey. To select the best method, two deterministic interpolation methods (inverse distance weighing (IDW) with the weights of 1, 2, and 3 and radial basis function (RBF) with spline with tension (SPT) and completely regularized spline (CRS)) and two stochastic methods (ordinary kriging (OK) with spherical, exponential, and Gaussian variograms) and cokriging (COK)) were compared and then the best interpolation method was used to evaluate the spatial distribution of groundwater levels in different seasons and seasonal changes. A total of nine different techniques were tested. Also, risky areas of seawater intrusion in coastal area were determined using the best methods for two periods. The performance of these interpolation methods is evaluated by using a validation test method. Statistical indices of correlation (R (2)), mean absolute error (MAE), and root-mean-square error (RMSE) were used to select and validate the best methods. Comparisons between predicted and observed values indicated RBF as the optimal method for groundwater level estimation in April and September. When the best method RBF and the worst method IDW were compared, significant differences were observed in the spatial distribution of groundwater. Results of the study also revealed that excessive groundwater withdrawals during the post-irrigation season dropped the groundwater levels up to 2.0 m in some sections. With regard to seawater intrusion, 9,103 ha of land area was determined to be highly risky and risky.
Interpolating point spread function anisotropy
Gentile, M; Meylan, G
2012-01-01
Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging...
PENG Lei; LIU Li; LONG Teng; GUO Xiaosong
2014-01-01
As a promising technique, surrogate-based design and optimization(SBDO) has been widely used in modern engineering design optimizations. Currently, static surrogate-based optimization methods have been successfully applied to expensive optimization problems. However, due to the low efficiency and poor flexibility, static surrogate-based optimization methods are difficult to efficiently solve practical engineering cases. At the aim of enhancing efficiency, a novel surrogate-based efficient optimization method is developed by using sequential radial basis function(SEO-SRBF). Moreover, augmented Lagrangian multiplier method is adopted to solve the problems involving expensive constraints. In order to study the performance of SEO-SRBF, several numerical benchmark functions and engineering problems are solved by SEO-SRBF and other well-known surrogate-based optimization methods including EGO, MPS, and IARSM. The optimal solutions, number of function evaluations, and algorithm execution time are recorded for comparison. The comparison results demonstrate that SEO-SRBF shows satisfactory performance in both optimization efficiency and global convergence capability. The CPU time required for running SEO-SRBF is dramatically less than that of other algorithms. In the torque arm optimization case using FEA simulation, SEO-SRBF further reduces 21% of thematerial volume compared with the solution from static-RBF subject to the stress constraint. This study provides the efficient strategy to solve expensive constrained optimization problems.
崔建新; 常宏; 刘泉均
2012-01-01
Based on the spatial interpolation technique served by GIS,this paper evaluated the prediction accuracies of three interpolation methods,i.e. Ordinary Krig(OK) ,Radical Basis Functions(RBF)and Inverse Distance Weighting (IDW) . Not only do these techniques have the capability of producing a prediction surface,but they can also provide some measure of the certainty or accuracy of the predictions. The results showed that there was a high similarity between Ok and RBF methods at the location of sand beam on which the measurement were conducted. However,there was a big discrepancy at the edge of the interpolation surface. The prediction temperature result of IDW method was lower than that of the OK and RBF methods. Companied with the results of cross-validation and site-validation,we could find that the fitting capacity of these methods follow the sequence of OK > RBF > IDW. Therefore,the OK method was used to produce the spatial patterns of soil temperature over the study area. In addition,the accuracy of the predictions was impacted by several factors,including sample distribution,season variability of soil temperature and so on.%对青海湖湖东克土沙地2010年6月份和8月份从6cm到71cm深度的8个层位土壤地温数据进行了插值方法上的对比研究,定量化评估了普通克里格(OK)、径向基函数法(RBF)以及反距离权重法(IDW)的预测精度.结果表明:OK方法与RBF插值结果在有数据监测点的沙梁位置具有高度一致性,但是在沙梁边缘区域表现出了较大的差异.而IDW插值结果比前两者预测结果要低.结合交叉验证以及站点验证结果,OK插值结果精度最高,RBF方法次之,IDW方法精度最低.因此,OK方法是该研究区内最佳的拟合模型.另外,模型预测精度受到样点分布以及土壤温度的季节变率等诸多因素影响.
Interpolating point spread function anisotropy
Gentile, M.; Courbin, F.; Meylan, G.
2013-01-01
Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). In all our methods we model the PSF using a single Moffat profile and we interpolate the fitted parameters at a set of required positions. This allowed us to win the Star-challenge of GREAT10, with the B-splines method. However, we also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics σ2sys better than the 1
Quantum realization of the bilinear interpolation method for NEQR.
Zhou, Ri-Gui; Hu, Wenwen; Fan, Ping; Ian, Hou
2017-05-31
In recent years, quantum image processing is one of the most active fields in quantum computation and quantum information. Image scaling as a kind of image geometric transformation has been widely studied and applied in the classical image processing, however, the quantum version of which does not exist. This paper is concerned with the feasibility of the classical bilinear interpolation based on novel enhanced quantum image representation (NEQR). Firstly, the feasibility of the bilinear interpolation for NEQR is proven. Then the concrete quantum circuits of the bilinear interpolation including scaling up and scaling down for NEQR are given by using the multiply Control-Not operation, special adding one operation, the reverse parallel adder, parallel subtractor, multiplier and division operations. Finally, the complexity analysis of the quantum network circuit based on the basic quantum gates is deduced. Simulation result shows that the scaled-up image using bilinear interpolation is clearer and less distorted than nearest interpolation.
Goudarzi, Nasser
2016-04-05
In this work, two new and powerful chemometrics methods are applied for the modeling and prediction of the (19)F chemical shift values of some fluorinated organic compounds. The radial basis function-partial least square (RBF-PLS) and random forest (RF) are employed to construct the models to predict the (19)F chemical shifts. In this study, we didn't used from any variable selection method and RF method can be used as variable selection and modeling technique. Effects of the important parameters affecting the ability of the RF prediction power such as the number of trees (nt) and the number of randomly selected variables to split each node (m) were investigated. The root-mean-square errors of prediction (RMSEP) for the training set and the prediction set for the RBF-PLS and RF models were 44.70, 23.86, 29.77, and 23.69, respectively. Also, the correlation coefficients of the prediction set for the RBF-PLS and RF models were 0.8684 and 0.9313, respectively. The results obtained reveal that the RF model can be used as a powerful chemometrics tool for the quantitative structure-property relationship (QSPR) studies.
Modified multistep method based on interpolation for solving ordinary differential problem
Ismail, Azman; Ahmad, Rokiah@Rozita; Din, Ummul Khair Salma; Hamid, Mohd Rosli A.
2014-06-01
This study is based on multistep method using interpolation formula. The coefficients of new formula are produced using modification on interpolation. This method is tested on ordinary differential equations. Comparisons are between the modified method and the classical Adams Bashforth and Adams-Moulton methods with equal step. Mathematica software is used to determine the new coefficients.
Ismail, Azman; Ahmad, Rokiah Rozita; Din, Ummul Khair Salma; Hamid, Mohd Rosli A.
2014-09-01
This study is based on third order multistep method using interpolation formula. The coefficients of new formula are produced using modification on interpolation. This method is tested on ordinary differential equations. Comparisons are between the modified method and the classical Adams Bashforth. Mathematica software is used to determine the new coefficients. The methods was found to be efficient when tested on ordinary differential equation.
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Randriambololona, Hugues
2011-01-01
We give a new generalization of the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in monogenous algebras over finite fields through interpolation on algebraic curves. Two key features of our method is that we allow asymmetric interpolation, as well as interpolation at arbitrary closed subschemes. This allows us to fix errors in, improve, and generalize, previous works of Shparlinski-Tsfasman-Vladut, Ballet, and Cenk-\\"Ozbudak. Besides, generalities on interpolation schemes, as well as an alternative method that solves certain constructiveness issues, are also discussed.
A new interpolation method for Antarctic surface temperature
Yetang Wang; Shugui Hou
2009-01-01
We propose a new methodology for the spatial interpolation of annual mean temperature into a regular grid with a geographic resolution of 0.01° for Antarctica by applying a recent compilation of the Antarctic temperature data.A multiple linear regression model of the dependence of temperature on some geographic parameters (i.e.,latitude,longitude,and elevation) is proposed empirically,and the kriging method is used to determine the spatial distribution of regional and local deviations from the temperature calculated from the multiple linear regression model.The modeled value and residual grids are combined to derive a high-resolution map of surface air temperature.The performance of our new methodology is superior to a variety of benchmark methods (e.g.,inverse distance weighting,kriging,and spline methods) via cross-validation techniques.Our simulation resembles well with those distinct spatial features of surface temperature,such as the decrease in annual mean surface temperature with increasing latitude and the distance away from the coast line;and it also reveals the complex topographic effects on the spatial distribution of surface temperature.
Smith, Bradford Scott, Jr.
The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation in elements downstream of a shock and having edges coincident with the shock showed a slight reduction in the solution error. However there was very little qualitative difference between solutions using polynomial and exponential interpolation. Regardless of the type of interpolation used, the shocks were smeared and oscillations were present both upstream and downstream of the shock waves. When a mesh adaptation scheme was implemented, exponential elements adjacent to the shock waves became much smaller and the numerical solution diverged. Changing the exponential elements to polynomial elements yielded a convergent solution. There appears to be no significant advantage to using exponential interpolation in comparison to Lagrange polynomial interpolation.
Solution of two-dimensional Fredholm integral equation via RBF-triangular method
Amir Fallahzadeh
2012-04-01
Full Text Available In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed method increases.
权值与结构双确定法的RBF神经网络分类器%RBF Neural Network Classifier with Weights and Structure Determination Method
张雨浓; 王茹; 廖柏林; 刘锦荣; 林键煜
2014-01-01
In order to solve the difficulties in determining the weights and structure of the radial basis function (RBF) neural network.Based on the weights-direct-determination (WDD)method and the relationship among centers,variances, the number of hidden-layer neurons and the performance of the neural network,a pruning-while-growing-type weights-and-structure-determination (PWGT-WASD)algorithm is proposed.On the basis of the PWGT-WASD algorithm,a kind of RBF neural network classifier is constructed,and its classifying and antinoise ability is further discussed in this paper.Com-puter numerical experiment results substantiate that the proposed PWGT-WASD algorithm can determine the centers,the va-riances and the optimal weights and structure of RBF neural network quickly and effectively.The constructed RBF pattern classifier has the superiority in terms of classification and antinoise ability.%为了解决径向基函数(RBF)神经网络权值与结构难以确定的问题，基于权值直接确定法，及隐层神经元中心、方差、数目与神经网络性能的关系，提出一种边增边删型的网络权值与结构双确定法。在此方法基础之上，构建一种 RBF神经网络分类器并探讨其分类性能和抗噪能力。计算机数值实验结果验证所提出的边增边删型的权值与结构双确定法能够快速、有效地确定网络的中心、方差和网络最优的权值与结构，所构造的模式分类器具有优越的分类性能和抗噪能力。
A hybrid method for image Denoising based on Wavelet Thresholding and RBF network
Sandeep Dubey
2012-06-01
Full Text Available Digital image denoising is crucial part of image pre-processing. The application of denoising process in satellite image data and also in television broadcasting. Image data sets collected by image sensors are generally contaminated by noise. Imperfect instruments, problems with the data acquisition process, and interfering natural phenomena can all degrade the data of interest. Furthermore, noise can be introduced by transmission errors and compression. Thus, denoising is often a necessary and the first step to be taken before the images data is analyzed. In this paper we proposed a novel methodology for image denoising. Image denoising method based on wavelet transform and radial basis neural network and also used concept of soft thresholding. Wavelet transform decomposed image in to different layers, the decomposed layer differentiate by horizontal, vertical and diagonal. For the test of our hybrid method, we used noise image dataset. This data provided by UCI machine learning website. Our proposed method compare with traditional method and our base paper method and getting better comparative result.
A RBF classification method of remote sensing image based on genetic algorithm
无
2006-01-01
The remote sensing image classification has stimulated considerable interest as an effective method for better retrieving information from the rapidly increasing large volume, complex and distributed satellite remote imaging data of large scale and cross-time, due to the increase of remote image quantities and image resolutions. In the paper, the genetic algorithms were employed to solve the weighting of the radial basis faction networks in order to improve the precision of remote sensing image classification. The remote sensing image classification was also introduced for the GIS spatial analysis and the spatial online analytical processing (OLAP) ,and the resulted effectiveness was demonstrated in the analysis of land utilization variation of Daqing city.
A NEW METHOD FOR THE CONSTRUCTION OF MULTIVARIATE MINIMAL INTERPOLATION POLYNOMIAL
Zhang Chuanlin
2001-01-01
The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is cansidered. Based on the algorithm to com pute the Grobner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satis fies the interpolation conditions is given.
Interpolation Methods for Dunn Logics and Their Extensions
S. Wintein (Stefan); Muskens, R. (Reinhard)
2017-01-01
textabstractThe semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these
STUDY OF BLOCKING EFFECT ELIMINATION METHODS BY MEANS OF INTRAFRAME VIDEO SEQUENCE INTERPOLATION
I. S. Rubina
2015-01-01
Full Text Available The paper deals with image interpolation methods and their applicability to eliminate some of the artifacts related to both the dynamic properties of objects in video sequences and algorithms used in the order of encoding steps. The main drawback of existing methods is the high computational complexity, unacceptable in video processing. Interpolation of signal samples for blocking - effect elimination at the output of the convertion encoding is proposed as a part of the study. It was necessary to develop methods for improvement of compression ratio and quality of the reconstructed video data by blocking effect elimination on the borders of the segments by intraframe interpolating of video sequence segments. The main point of developed methods is an adaptive recursive algorithm application with adaptive-sized interpolation kernel both with and without the brightness gradient consideration at the boundaries of objects and video sequence blocks. Within theoretical part of the research, methods of information theory (RD-theory and data redundancy elimination, methods of pattern recognition and digital signal processing, as well as methods of probability theory are used. Within experimental part of the research, software implementation of compression algorithms with subsequent comparison of the implemented algorithms with the existing ones was carried out. Proposed methods were compared with the simple averaging algorithm and the adaptive algorithm of central counting interpolation. The advantage of the algorithm based on the adaptive kernel size selection interpolation is in compression ratio increasing by 30%, and the advantage of the modified algorithm based on the adaptive interpolation kernel size selection is in the compression ratio increasing by 35% in comparison with existing algorithms, interpolation and quality of the reconstructed video sequence improving by 3% compared to the one compressed without interpolation. The findings will be
CHEN Yunlong; SHAN Xiujuan; JIN Xianshi; YANG Tao; DAI Fangqun; YANG Dingtian
2016-01-01
Spatial interpolation is a common tool used in the study of fishery ecology, especially for the construction of ecosystem models. To develop an appropriate interpolation method of determining fishery resources density in the Yellow Sea, we tested four frequently used methods, including inverse distance weighted interpolation (IDW), global polynomial interpolation (GPI), local polynomial interpolation (LPI) and ordinary kriging (OK). A cross-validation diagnostic was used to analyze the efficacy of interpolation, and a visual examination was conducted to evaluate the spatial performance of the different methods. The results showed that the original data were not normally distributed. A log transformation was then used to make the data fit a normal distribution. During four survey periods, an exponential model was shown to be the best semivariogram model in August and October 2014, while data from January and May 2015 exhibited the pure nugget effect. Using a paired-samplest test, no significant differences (P>0.05) between predicted and observed data were found in all four of the interpolation methods during the four survey periods. Results of the cross-validation diagnostic demonstrated that OK performed the best in August 2014, while IDW performed better during the other three survey periods. The GPI and LPI methods had relatively poor interpolation results compared to IDW and OK. With respect to the spatial distribution, OK was balanced and was not as disconnected as IDW nor as overly smooth as GPI and LPI, although OK still produced a few “bull’s-eye” patterns in some areas. However, the degree of autocorrelation sometimes limits the application of OK. Thus, OK is highly recommended if data are spatially autocorrelated. With respect to feasibility and accuracy, we recommend IDW to be used as a routine interpolation method. IDW is more accurate than GPI and LPI and has a combination of desirable properties, such as easy accessibility and rapid processing.
Spectral Gauss quadrature method with subspace interpolation for Kohn-Sham Density functional theory
Wang, Xin
Algorithms with linear-scaling ( (N)) computational complexity for Kohn-Sham density functional theory (K-S DFT) is crucial for studying molecular systems beyond thousands of atoms. Of the (N) methods that use a polynomial-based approximation of the density matrix, the linear-scaling spectral Gauss quadrature (LSSGQ) method (Suryanarayana et al., JMPS, 2013) has been shown to exhibit the fastest convergence. The LSSGQ method requires a Lanczos procedure at every node in a real-space mesh, leading to a large computational pre-factor. We propose a new interpolation scheme specific to the LSSGQ method that lift the need to perform a Lanczos procedure at every node in the real-mesh. This interpolation will be referred to as subspace interpolation. The key idea behind subspace interpolation is that there is a large overlap in the Krylov-subspaces produced by the Lanczos procedures of nodes that are close in real-space. The subspace interpolation scheme takes advantage of the block-Lanczos procedure to group the Krylov-subspaces from a few representative nodes to approximate the density matrix over a large collection of nodes. Subspace interpolation outperforms cubic-spline interpolation by several orders of magnitude.
Interpolation methods for thematic maps of soybean yield and soil chemical attributes
Nelson Miguel Betzek; Eduardo Godoy de Souza; Claudio Leones Bazzi; Ricardo Sobjak; Vanderlei Artur Bier; Erivelto Mercante
2017-01-01
...) in the construction of thematic maps of soybean yield and soil chemical attributes. A set of data referred to 55 sampling units for the construction maps of soybean yield and of eight soil chemical attributes, by different interpolation methods...
De-interlacing using nonlocal costs and Markov-chain-based estimation of interpolation methods.
Vedadi, Farhang; Shirani, Shahram
2013-04-01
A new method of de-interlacing is proposed. De-interlacing is revisited as the problem of assigning a sequence of interpolation methods (interpolators) to a sequence of missing pixels of an interlaced frame (field). With this assumption, our de-interlacing algorithm (de-interlacer), undergoes transitions from one interpolation method to another, as it moves from one missing pixel position to the horizontally adjacent missing pixel position in a missing row of a field. We assume a discrete countable-state Markov-chain model on the sequence of interpolators (Markov-chain states) which are selected from a user-defined set of candidate interpolators. An estimation of the optimum sequence of interpolators with the aforementioned Markov-chain model requires the definition of an efficient cost function as well as a global optimization technique. Our algorithm introduces for the first time using a nonlocal cost (NLC) scheme. The proposed algorithm uses the NLC to not only measure the fitness of an interpolator at a missing pixel position, but also to derive an approximation for transition matrix (TM) of the Markov-chain of interpolators. The TM in our algorithm is a frame-variate matrix, i.e., the algorithm updates the TM for each frame automatically. The algorithm finally uses a Viterbi algorithm to find the global optimum sequence of interpolators given the cost function defined and neighboring original pixels in hand. Next, we introduce a new MAP-based formulation for the estimation of the sequence of interpolators this time not by estimating the best sequence of interpolators but by successive estimations of the best interpolator at each missing pixel using Forward-Backward algorithm. Simulation results prove that, while competitive with each other on different test sequences, the proposed methods (one using Viterbi and the other Forward-Backward algorithm) are superior to state-of-the-art de-interlacing algorithms proposed recently. Finally, we propose motion
A New Method of Constructing Bivariate Vector Valued Rational Interpolation Function
Lin ZHENGI; Gong Qin ZHU
2011-01-01
At present,the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions.In order to get vector valued rational interpolation function with lower degree and better approximation effect,the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1(0≤di ≤ m) and d2 (0≤d2 ≤n),builds bivariate polynomial vector interpolation for each piece,then combines with them properly.As compared with previous methods,the new method given by this paper is easy to compute and the degree for the interpolants is lower.
Meshless RBF based pseudospectral solution of acoustic wave equation
Mishra, Pankaj K
2015-01-01
Chebyshev pseudospectral (PS) methods are reported to provide highly accurate solution using polynomial approximation. Use of polynomial basis functions in PS algorithms limits the formulation to univariate systems constraining it to tensor product grids for multi-dimensions. Recent studies have shown that replacing the polynomial by radial basis functions in pseudospectral method (RBF-PS) has the advantage of using irregular grids for multivariate systems. A RBF-PS algorithm has been presented here for the numerical solution of inhomogeneous Helmholtz's equation using Gaussian RBF for derivative approximation. Efficacy of RBF approximated derivatives has been checked through error analysis comparison with PS method. Comparative study of PS, RBF-PS and finite difference approach for the solution of a linear boundary value problem has been performed. Finally, a typical frequency domain acoustic wave propagation problem has been solved using Dirichlet boundary condition and a point source. The algorithm present...
A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets
Min Deng
2016-02-01
Full Text Available Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984–2009. Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods—e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.
Evaluation of intense rainfall parameters interpolation methods for the Espírito Santo State
José Eduardo Macedo Pezzopane
2009-12-01
Full Text Available Intense rainfalls are often responsible for the occurrence of undesirable processes in agricultural and forest areas, such as surface runoff, soil erosion and flooding. The knowledge of intense rainfall spatial distribution is important to agricultural watershed management, soil conservation and to the design of hydraulic structures. The present paper evaluated methods of spatial interpolation of the intense rainfall parameters (“K”, “a”, “b” and “c” for the Espírito Santo State, Brazil. Were compared real intense rainfall rates with those calculated by the interpolated intense rainfall parameters, considering different durations and return periods. Inverse distance to the 5th power IPD5 was the spatial interpolation method with better performance to spatial interpolated intense rainfall parameters.
Quantitative evaluation of convolution-based methods for medical image interpolation.
Meijering, E H; Niessen, W J; Viergever, M A
2001-06-01
Interpolation is required in a variety of medical image processing applications. Although many interpolation techniques are known from the literature, evaluations of these techniques for the specific task of applying geometrical transformations to medical images are still lacking. In this paper we present such an evaluation. We consider convolution-based interpolation methods and rigid transformations (rotations and translations). A large number of sinc-approximating kernels are evaluated, including piecewise polynomial kernels and a large number of windowed sinc kernels, with spatial supports ranging from two to ten grid intervals. In the evaluation we use images from a wide variety of medical image modalities. The results show that spline interpolation is to be preferred over all other methods, both for its accuracy and its relatively low computational cost.
A survey on RBF Neural Network for Intrusion Detection System
Henali Sheth
2014-12-01
Full Text Available Network security is a hot burning issue nowadays. With the help of technology advancement intruders or hackers are adopting new methods to create different attacks in order to harm network security. Intrusion detection system (IDS is a kind of security software which inspects all incoming and outgoing network traffic and it will generate alerts if any attack or unusual behavior is found in a network. Various approaches are used for IDS such as data mining, neural network, genetic and statistical approach. Among this Neural Network is more suitable approach for IDS. This paper describes RBF neural network approach for Intrusion detection system. RBF is a feed forward and supervise technique of neural network.RBF approach has good classification ability but its performance depends on its parameters. Based on survey we find that RBF approach has some short comings. In order to overcome this we need to do proper optimization of RBF parameters.
On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids
Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.
2017-03-01
The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.
On the Quality of Velocity Interpolation Schemes for Marker-in-Cell Method and Staggered Grids
Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.
2016-11-01
The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation scheme for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation schemes in combination with different advection schemes on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.
The Interpolation Method for Estimating the Above-Ground Biomass Using Terrestrial-Based Inventory
I Nengah Surati Jaya
2014-08-01
Full Text Available This paper examined several methods for interpolating biomass on logged-over dry land forest using terrestrial-based forest inventory in Labanan, East Kalimantan and Lamandau, Kota Wringing Barat, Central Kalimantan. The plot-distances examined was 1,000−1,050 m for Labanan and 1,000−899m for Lawanda. The main objective of this study was to obtain the best interpolation method having the most accurate prediction on spatial distribution of forest biomass for dry land forest. Two main interpolation methods were examined: (1 deterministic approach using the IDW method and (2 geo-statistics approach using Kriging with spherical, circular, linear, exponential, and Gaussian models. The study results at both sites consistently showed that the IDW method was better than the Kriging method for estimating the spatial distribution of biomass. The validation results using chi-square test showed that the IDW interpolation provided accurate biomass estimation. Using the percentage of mean deviation value (MD(%, it was also recognized that the IDWs with power parameter (p of 2 provided relatively low value , i.e., only 15% for Labanan, East Kalimantan Province and 17% for Lamandau, Kota Wringing Barat Central Kalimantan Province. In general, IDW interpolation method provided better results than the Kriging, where the Kriging method provided MD(% of about 27% and 21% for Lamandau and Labanan sites, respectively.
The Interpolating Element-Free Galerkin Method for 2D Transient Heat Conduction Problems
Na Zhao
2014-01-01
Full Text Available An interpolating element-free Galerkin (IEFG method is presented for transient heat conduction problems. The shape function in the moving least-squares (MLS approximation does not satisfy the property of Kronecker delta function, so an interpolating moving least-squares (IMLS method is discussed; then combining the shape function constructed by the IMLS method and Galerkin weak form of the 2D transient heat conduction problems, the interpolating element-free Galerkin (IEFG method for transient heat conduction problems is presented, and the corresponding formulae are obtained. The main advantage of this approach over the conventional meshless method is that essential boundary conditions can be applied directly. Numerical results show that the IEFG method has high computational accuracy.
Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.
2006-01-01
Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.
Xie, Yunfeng; Chen, Tong-bin; Lei, Mei; Yang, Jun; Guo, Qing-jun; Song, Bo; Zhou, Xiao-yong
2011-01-01
Mapping the spatial distribution of contaminants in soils is the basis of pollution evaluation and risk control. Interpolation methods are extensively applied in the mapping processes to estimate the heavy metal concentrations at unsampled sites. The performances of interpolation methods (inverse distance weighting, local polynomial, ordinary kriging and radial basis functions) were assessed and compared using the root mean square error for cross validation. The results indicated that all interpolation methods provided a high prediction accuracy of the mean concentration of soil heavy metals. However, the classic method based on percentages of polluted samples, gave a pollution area 23.54-41.92% larger than that estimated by interpolation methods. The difference in contaminated area estimation among the four methods reached 6.14%. According to the interpolation results, the spatial uncertainty of polluted areas was mainly located in three types of region: (a) the local maxima concentration region surrounded by low concentration (clean) sites, (b) the local minima concentration region surrounded with highly polluted samples; and (c) the boundaries of the contaminated areas.
Probabilistic Interpolation of the Curve via the Method of Hurwitz-Radon Matrices
Dariusz Jakóbczak
Full Text Available Mathematics and computer science are interested in methods of curve interpolation using the set of key points (knots. A proposed method of Hurwitz- Radon Matrices (MHR is such a method. This novel method is based on the family of Hurwitz-Radon (HR matr ...
Continuity constrained least-squares interpolation for SFO suppression in immersed boundary methods
Martins, Diogo M. C.; Albuquerque, Duarte M. S.; Pereira, José C. F.
2017-05-01
A new immersed boundary interpolation for discrete forcing methods is presented. The method decreases spurious oscillations in the pressure field and consequently in the body force calculations which are a common issue in several immersed boundary methods. The method applies a continuity constraint in the least-squares interpolation, and guarantees that adjacent interpolation polynomials are continuous between each other. This approach strictly enforces continuity in the flow reconstruction domain, reducing time discontinuities caused by the boundary conditions applied at the immersed boundary. Several moving body problems test cases are simulated, including a three dimensional one, to demonstrate the new method's capability of computing stable pressure fields, even for coarse grids and small CFL numbers, which are known to increase the pressure oscillations.
An Energy Conservative Ray-Tracing Method With a Time Interpolation of the Force Field
Yao, Jin [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-02-10
A new algorithm that constructs a continuous force field interpolated in time is proposed for resolving existing difficulties in numerical methods for ray-tracing. This new method has improved accuracy, but with the same degree of algebraic complexity compared to Kaisers method.
Hu, Ke-lin; Li, Bao-guo; Lu, Yi-zhong; Zhang, Feng-rong
2004-05-01
Accurate delineating of the spatial distribution of soil heavy metal content is essential for pollution assessment and remediation. The objective of this paper is to evaluate various spatial interpolation methods, including ordinary Kriging (OK), simple Kriging (SK), lognormal Kriging (LNK), universal Kriging (UK), disjunctive Kriging (DK) and inverse distance weighting interpolation (IDW) for estimating soil surface Hg content with lognormal distribution, the linear and second-order polynomial trend, and to determine the optimal interpolation method. The predicted errors, statistical feature values and prediction maps obtained by different interpolation methods were compared. The result indicated that first-order trend OK method performed better than both zero and second-order OK methods. Within the method of first-order trend OK, Gaussian semi-variogram model performed better than both the spherical and exponential models. The method using transformed data performed worse than the methods without data transformation because of the 'distortion' effect arising from log transformation. Those with trend effect were better than those without trend effect. First-order trend UK method is the best method among the six methods studied, while the IDW method is the least.
Optimal Alternative to the Akima's Method of Smooth Interpolation Applied in Diabetology
Emanuel Paul
2006-12-01
Full Text Available It is presented a new method of cubic piecewise smooth interpolation applied to experimental data obtained by glycemic profile for diabetics. This method is applied to create a soft useful in clinical diabetology. The method give an alternative to the Akima's procedure of the derivatives computation on the knots from [Akima, J. Assoc. Comput. Mach., 1970] and have an optimal property.
Interpolation Method Needed for Numerical Uncertainty Analysis of Computational Fluid Dynamics
Groves, Curtis; Ilie, Marcel; Schallhorn, Paul
2014-01-01
Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors in an unstructured grid, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors. Nomenclature
Šimonka, Vito; Nawratil, Georg; Hössinger, Andreas; Weinbub, Josef; Selberherr, Siegfried
2017-02-01
We investigate anisotropical and geometrical aspects of hexagonal structures of Silicon Carbide and propose a direction dependent interpolation method for oxidation growth rates. We compute three-dimensional oxidation rates and perform one-, two-, and three-dimensional simulations for 4H- and 6H-Silicon Carbide thermal oxidation. The rates of oxidation are computed according to the four known growth rate values for the Si- (0 0 0 1) , a- (1 1 2 bar 0) , m- (1 1 bar 0 0) , and C-face (0 0 0 1 bar) . The simulations are based on the proposed interpolation method together with available thermal oxidation models. We additionally analyze the temperature dependence of Silicon Carbide oxidation rates for different crystal faces using Arrhenius plots. The proposed interpolation method is an essential step towards highly accurate three-dimensional oxide growth simulations which help to better understand the anisotropic nature and oxidation mechanism of Silicon Carbide.
Evaluation of interpolating methods for daily precipitation at various station densities
Li, H.; Xu, C.-Y.; Chen, H.; Zhang, Z. X.; Xu, H. L.
2012-04-01
Spatial continuous data play a significant role in planning, risk assessment and decision making in climate research and geosciences. It is essential to get accurate grid precipitation data of high resolution in hydrological modeling and water resources management. In recent years, radar and satellite provide an alternative way for spatial precipitation data, but due to technique problems and deficient accuracy, interpolating the observed point data is still the common way to obtain gridding precipitation data for research and management purposes. Many interpolating methods have been proposed and great effort has been made to evaluate and compare them. But by far, no universal method is widely accepted because of the diversity in study regions, difference in climate situations, and differences in data quality and quantity, and selected methods in comparisons. It has been well known that the most paramount factor affecting the performance of interpolating methods is the density of sampling points. However, the performance of different interpolating methods at various sampling densities, which means the performance degradation caused by density changes, has not been deeply examined. This work focuses on the evaluation of interpolating methods in daily precipitation at various station densities and tries to provide guidance on choosing interpolating method under different circumstance. To fill this objective, we choose five commonly used or recommended interpolation methods, i.e. nearest neighbor (NN), inverse distance weighting (IDW), Gradient plus Inverse Distance Squared (GIDS), ordinary kriging (OK) and simple kriging (SK) at five designed sampling densities ranging from 22.6 to 9.8 stations per ten thousand square kilometers at Xiangjiang River basin during 2000 to 2005 when the precipitation data were in the highest density. Four criteria were used for method assessment, i.e., mean error (ME), root mean absolute error (RMSE), model efficient (EF) and index of
Zimmerman, Paul M
2013-05-14
The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method.
一种改进的RBF神经网络参数优化方法%Improved method for RBF neural network parameters optimization
张辉; 柴毅
2012-01-01
An improved method for RBF neural network parameters optimization is proposed. The number of nodes in the hidden layer is determined by using RAN (Resource Allocating Network), meanwhile strategy of pruning is introduced to remove those hidden units which make insignificant contribution to overall network output. Central position, width and weight of the neural network are optimized by the improved PSO (Particle Swarm Optimization) algorithm, so as to obtain the appropriate structure and control parameters. The new algorithm is used to predict the model of CSTR, and the result indicates that RBF neural network optimized by this algorithm has a smaller structure and high generalization ability.%提出了一种改进的RBF神经网络参数优化算法.通过资源分配网络算法确定隐含层节点个数,引入剪枝策略删除对网络贡献不大的节点,用改进的粒子群算法对RBF网络的中心、宽度、权值进行优化,使RBF网络不仅可以得到合适的结构,同时也可以得到合适的控制参数.将此算法用于连续搅拌釜反应器模型的预测,结果表明,此算法优化后的RBF网络结构小,并且具有较高的泛化能力.
A study of interpolation method in diagnosis of carpal tunnel syndrome
Alireza Ashraf
2013-01-01
Full Text Available Context: The low correlation between the patients′ signs and symptoms of carpal tunnel syndrome (CTS and results of electrodiagnostic tests makes the diagnosis challenging in mild cases. Interpolation is a mathematical method for finding median nerve conduction velocity (NCV exactly at carpal tunnel site. Therefore, it may be helpful in diagnosis of CTS in patients with equivocal test results. Aim: The aim of this study is to evaluate interpolation method as a CTS diagnostic test. Settings and Design: Patients with two or more clinical symptoms and signs of CTS in a median nerve territory with 3.5 ms ≤ distal median sensory latency <4.6 ms from those who came to our electrodiagnostic clinics and also, age matched healthy control subjects were recruited in the study. Materials and Methods: Median compound motor action potential and median sensory nerve action potential latencies were measured by a MEDLEC SYNERGY VIASIS electromyography and conduction velocities were calculated by both routine method and interpolation technique. Statistical Analysis Used: Chi-square and Student′s t-test were used for comparing group differences. Cut-off points were calculated using receiver operating characteristic curve. Results: A sensitivity of 88%, specificity of 67%, positive predictive value (PPV and negative predictive value (NPV of 70.8% and 84.7% were obtained for median motor NCV and a sensitivity of 98.3%, specificity of 91.7%, PPV and NPV of 91.9% and 98.2% were obtained for median sensory NCV with interpolation technique. Conclusions: Median motor interpolation method is a good technique, but it has less sensitivity and specificity than median sensory interpolation method.
The effect of interpolation methods in temperature and salinity trends in the Western Mediterranean
M. VARGAS-YANEZ
2012-04-01
Full Text Available Temperature and salinity data in the historical record are scarce and unevenly distributed in space and time and the estimation of linear trends is sensitive to different factors. In the case of the Western Mediterranean, previous works have studied the sensitivity of these trends to the use of bathythermograph data, the averaging methods or the way in which gaps in time series are dealt with. In this work, a new factor is analysed: the effect of data interpolation. Temperature and salinity time series are generated averaging existing data over certain geographical areas and also by means of interpolation. Linear trends from both types of time series are compared. There are some differences between both estimations for some layers and geographical areas, while in other cases the results are consistent. Those results which do not depend on the use of interpolated or non-interpolated data, neither are influenced by data analysis methods can be considered as robust ones. Those results influenced by the interpolation process or the factors analysed in previous sensitivity tests are not considered as robust results.
Interpolation method for live weight estimation based on age in Japanese quails
Senol Celik
Full Text Available ABSTRACT The objective of this study was to demonstrate live weight estimation based on age by using Newton Interpolation method for male and female quails for seven weeks of fattening. A total of 138-day-old quail chicks were used in the study. The study demonstrated a 6th-degree polynomial interpolation for the function values obtained at seven equal intervals from 7 to 49 days. Live weight increase prediction was calculated for male and female quails between the 7th and 49th days using Newton Interpolation. Daily live weight increase for male and female quails based on observed live weights was determined. Female quails displayed more live weight increase after the 19th day compared with males. Average live weight increase in male quails was 3.81 g, and 4.63 g for females until the 49th day. The highest live weight increase was observed during the fourth week for all quails. Sum of squared errors and coefficient of determination (R2 for fit of the model were calculated and the F test was performed. F, sum of squared errors, and R2 obtained by Newton Interpolation for male quails and female quail were very large: 0 (approximately zero and 0.999, respectively. The interpolation method is suitable for breeding studies.
The effect of interpolation methods in temperature and salinity trends in the Western Mediterranean
M. VARGAS-YANEZ
2012-12-01
Full Text Available Temperature and salinity data in the historical record are scarce and unevenly distributed in space and time and the estimation of linear trends is sensitive to different factors. In the case of the Western Mediterranean, previous works have studied the sensitivity of these trends to the use of bathythermograph data, the averaging methods or the way in which gaps in time series are dealt with. In this work, a new factor is analysed: the effect of data interpolation. Temperature and salinity time series are generated averaging existing data over certain geographical areas and also by means of interpolation. Linear trends from both types of time series are compared. There are some differences between both estimations for some layers and geographical areas, while in other cases the results are consistent. Those results which do not depend on the use of interpolated or non-interpolated data, neither are influenced by data analysis methods can be considered as robust ones. Those results influenced by the interpolation process or the factors analysed in previous sensitivity tests are not considered as robust results.
HU Zhijuan
2015-08-01
Full Text Available The lossy hologram compression method with three different interpolations is investigated to compress images holographically recorded with optical scanning holography.Without loss of major reconstruction details,results have shown that the lossy compression method is able to achieve high compression ratio of up to 100.
Yao, Xueling; Fu, Bojie; Lü, Yihe; Sun, Feixiang; Wang, Shuai; Liu, Min
2013-01-01
Many spatial interpolation methods perform well for gentle terrains when producing spatially continuous surfaces based on ground point data. However, few interpolation methods perform satisfactorily for complex terrains. Our objective in the present study was to analyze the suitability of several popular interpolation methods for complex terrains and propose an optimal method. A data set of 153 soil water profiles (1 m) from the semiarid hilly gully Loess Plateau of China was used, generated under a wide range of land use types, vegetation types and topographic positions. Four spatial interpolation methods, including ordinary kriging, inverse distance weighting, linear regression and regression kriging were used for modeling, randomly partitioning the data set into 2/3 for model fit and 1/3 for independent testing. The performance of each method was assessed quantitatively in terms of mean-absolute-percentage-error, root-mean-square-error, and goodness-of-prediction statistic. The results showed that the prediction accuracy differed significantly between each method in complex terrain. The ordinary kriging and inverse distance weighted methods performed poorly due to the poor spatial autocorrelation of soil moisture at small catchment scale with complex terrain, where the environmental impact factors were discontinuous in space. The linear regression model was much more suitable to the complex terrain than the former two distance-based methods, but the predicted soil moisture changed too sharply near the boundary of the land use types and junction of the sunny (southern) and shady (northern) slopes, which was inconsistent with reality because soil moisture should change gradually in short distance due to its mobility in soil. The most optimal interpolation method in this study for the complex terrain was the hybrid regression kriging, which produced a detailed, reasonable prediction map with better accuracy and prediction effectiveness.
Xueling Yao
Full Text Available Many spatial interpolation methods perform well for gentle terrains when producing spatially continuous surfaces based on ground point data. However, few interpolation methods perform satisfactorily for complex terrains. Our objective in the present study was to analyze the suitability of several popular interpolation methods for complex terrains and propose an optimal method. A data set of 153 soil water profiles (1 m from the semiarid hilly gully Loess Plateau of China was used, generated under a wide range of land use types, vegetation types and topographic positions. Four spatial interpolation methods, including ordinary kriging, inverse distance weighting, linear regression and regression kriging were used for modeling, randomly partitioning the data set into 2/3 for model fit and 1/3 for independent testing. The performance of each method was assessed quantitatively in terms of mean-absolute-percentage-error, root-mean-square-error, and goodness-of-prediction statistic. The results showed that the prediction accuracy differed significantly between each method in complex terrain. The ordinary kriging and inverse distance weighted methods performed poorly due to the poor spatial autocorrelation of soil moisture at small catchment scale with complex terrain, where the environmental impact factors were discontinuous in space. The linear regression model was much more suitable to the complex terrain than the former two distance-based methods, but the predicted soil moisture changed too sharply near the boundary of the land use types and junction of the sunny (southern and shady (northern slopes, which was inconsistent with reality because soil moisture should change gradually in short distance due to its mobility in soil. The most optimal interpolation method in this study for the complex terrain was the hybrid regression kriging, which produced a detailed, reasonable prediction map with better accuracy and prediction effectiveness.
Interpolation of meteorological data by kriging method for use in forestry
Ivetić Vladan
2010-01-01
Full Text Available Interpolation is a suitable method of computing the values of a spatial variable at the location which is impossible for measurement, based on the data obtained by the measurement of the same variable at the predetermined locations (e.g. weather stations. In this paper, temperature and rainfall values at 39 weather stations in Serbia and neighbouring countries were interpolated aiming at the research in forestry. The study results are presented in the form of an interactive map of Serbia, which allows a fast and simple determination of the analyzed variable at any point within its territory, which is presented by the example of 27 forest sites.
An Immersed Boundary method with divergence-free velocity interpolation and force spreading
Bao, Yuanxun; Donev, Aleksandar; Griffith, Boyce E.; McQueen, David M.; Peskin, Charles S.
2017-10-01
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.
Gou Fu-Yan; Liu Cai; Liu Yang; Feng Xuan; Cui Fang-Zi
2014-01-01
In seismic prospecting,fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent high-precision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model andfi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.
The Interpolation Method for Estimating the Above-Ground Biomass Using Terrestrial-Based Inventory
I Nengah Surati Jaya
2014-09-01
Full Text Available This paper examined several methods for interpolating biomass on logged-over dry land forest using terrestrial-based forest inventory in Labanan, East Kalimantan and Lamandau, Kota Wringing Barat, Central Kalimantan. The plot-distances examined was 1,000−1,050 m for Labanan and 1,000−899m for Lawanda. The main objective of this study was to obtain the best interpolation method having the most accurate prediction on spatial distribution of forest biomass for dry land forest. Two main interpolation methods were examined: (1 deterministic approach using the IDW method and (2 geo-statistics approach using Kriging with spherical, circular, linear, exponential, and Gaussian models. The study results at both sites consistently showed that the IDW method was better than the Kriging method for estimating the spatial distribution of biomass. The validation results using chi-square test showed that the IDW interpolation provided accurate biomass estimation. Using the percentage of mean deviation value (MD(%, it was also recognized that the IDWs with power parameter (p of 2 provided relatively low value , i.e., only 15% for Labanan, East Kalimantan Province and 17% for Lamandau, Kota Wringing Barat Central Kalimantan Province. In general, IDW interpolation method provided better results than the Kriging, where the Kriging method provided MD(% of about 27% and 21% for Lamandau and Labanan sites, respectively.Keywords: deterministic, geostatistics, IDW, Kriging, above-groung biomass
AN INTERPOLATION METHOD FOR DETERMINING THE FREQUENCIES OF PARAMETERIZED LARGE-SCALE STRUCTURES
Salvatore Nasisi
2015-12-01
Full Text Available Parametric Model Order Reduction (pMOR is an emerging category of models developed with the aim of describing reduced first and second-order dynamical systems. The use of a pROM turns out useful in a variety of applications spanning from the analysis of Micro-Electro-Mechanical Systems (MEMS to the optimization of complex mechanical systems because they allow predicting the dynamical behavior at any values of the quantities of interest within the design space, e.g. material properties, geometric features or loading conditions. The process underlying the construction of a pROM using an SVD-based method [18] accounts for three basic phases: a construction of several local ROMs (Reduced Order Models; b projection of the state-space vector onto a common subspace spanned by several transformation matrices derived in the first step; c use of an interpolation method capable of capturing for one or more parameters the values of the quantity of interest. One of the major difficulties encountered in this process has been identified at the level of the interpolation method and can be encapsulated in the following contradiction: if the number of detailed finite element analyses is high then an interpolation method can better describe the system for a given choice of a parameter but the time of computation is higher. In this paper is proposed a method for removing the above contradiction by introducing a new interpolation method (RSDM. This method allows to restore and make available to the interpolation tool certain natural components belonging to the matrices of the full FE model that are related on one side, to the process of reduction and on the other side, to the characteristics of a solid in the FE theory. This approach shows higher accuracy than methods used for the assessment of the system’s eigenbehavior. To confirm the usefulness of the RSDM a Hexapod will be analyzed.
An interpolating boundary element-free method (IBEFM) for elasticity problems
无
2010-01-01
The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.
王瑞; 史天运; 王彤
2011-01-01
对实测风速数据进行Kalman滤波,去除实测风速数据的偏差；通过归一化处理,消除数据中的冗余成分;针对RBF神经网络的预测误差会随着时间的推移而增大的问题,采用滚动式训练方法在线训练RBF神经网络;用训练好的RBF神经网络进行风速预测,再对预测结果进行反归一化处理,得到最终的预测风速.仿真结果表明,运用基于RBF神经网络的铁路短时风速预测方法对短时风速进行预测,最大相对误差仅为5.92％,可满足铁路防灾安全监控系统中风速预测子系统的要求.%The measured wind speed was processed with Kalman filter algorithm to eliminate deviations. The redundancies in the measured data were removed through normalization processing. Then, RBF neural network was online trained by using the rolling training method to deal with the problem that the prediction error of RBF neural network would increase as time went on. Finally, the wind speed was predicted by using the well-trained RBF neural network. The final forecasted wind speed was then obtained by anti-normalizing the output of RBF neural network. The simulation results show that the maximum relative error is only 5. 92% using the proposed railway short-time wind speed prediction algorithm based on RBF neural network, which can satisfy the requirements of the wind forecasting subsystem in railway disaster prevention and safety monitoring system.
Wu, G.; Skidmore, A.K.; Leeuw, de J.; Liu, X.; Prins, H.H.T.
2010-01-01
Measurements of photosynthetically active radiation (PAR), which are indispensable for simulating plant growth and productivity, are generally very scarce. This study aimed to compare two extrapolation and one interpolation methods for estimating daily PAR reaching the earth surface within the Poyan
Borges, Pablo de Amorim; Franke, Johannes; da Anunciação, Yumiko Marina Tanaka; Weiss, Holger; Bernhofer, Christian
2016-01-01
Available climatological information of Distrito Federal does not satisfy the requirements for detailed climate diagnosis, as they do not provide the necessary spatial resolution for water resources management purposes. Annual and seasonal climatology (1971-2000) of precipitation from 6 meteorological stations and 54 rain gauges from Central Brazil were used to test eight different spatial interpolation methods. Geographical factors (i.e., altitude, longitude and latitude) explain a large portion of precipitation in the region, and therefore, multivariate models were included. The performance of estimations was assessed through independent validation using mean square error, correlation coefficient and Nash-Sutcliffe efficiency criterion. Inverse distance weighting (IDW), ordinary kriging (OK) and the multivariate regression with interpolation of residuals by IDW (MRegIDW) and OK (MRegOK) have performed the lowest errors and the highest correlation and Nash-Sutcliffe efficiency criterion. In general, interpolation methods provide similar spatial distributions of rainfall wherever observation network is dense. However, the inclusion of geographical variables to the interpolation method should improve estimates in areas where the observation network density is low. Nevertheless, the assessment of uncertainties using a geostatistical method provides supplementary and qualitative information which should be considered when interpreting the spatial distribution of rainfall.
A comparison of different interpolation methods for wind data in Central Asia
Reinhardt, Katja; Samimi, Cyrus
2017-04-01
For the assessment of the global climate change and its consequences, the results of computer based climate models are of central importance. The quality of these results and the validity of the derived forecasts are strongly determined by the quality of the underlying climate data. However, in many parts of the world high resolution data are not available. This is particularly true for many regions in Central Asia, where the density of climatological stations has often to be described as thinned out. Due to this insufficient data base the use of statistical methods to improve the resolution of existing climate data is of crucial importance. Only this can provide a substantial data base for a well-founded analysis of past climate changes as well as for a reliable forecast of future climate developments for the particular region. The study presented here shows a comparison of different interpolation methods for the wind components u and v for a region in Central Asia with a pronounced topography. The aim of the study is to find out whether there is an optimal interpolation method which can equally be applied for all pressure levels or if different interpolation methods have to be applied for each pressure level. The European reanalysis data Era-Interim for the years 1989 - 2015 are used as input data for the pressure levels of 850 hPa, 500 hPa and 200 hPa. In order to improve the input data, two different interpolation procedures were applied: On the one hand pure interpolation methods were used, such as inverse distance weighting and ordinary kriging. On the other hand machine learning algorithms, generalized additive models and regression kriging were applied, considering additional influencing factors, e.g. geopotential and topography. As a result it can be concluded that regression kriging provides the best results for all pressure levels, followed by support vector machine, neural networks and ordinary kriging. Inverse distance weighting showed the worst
A novel interpolation method for MODIS land surface temperature data on the Tibetan Plateau
Yu, Wenjun; Wu, Tonghua; Nan, Zhuotong; Zhao, Lin; Wang, Zhiwei
2014-11-01
MODIS satellites provide continuous global observations on land surface temperature. It is more important in data-sparse area, such as on the Tibetan Plateau (TP) with very few meteorological stations. Images with severe data missing or poor quality pixels were often found in MODIS LST products, which mostly were caused by the influences of clouds. The traditional geo-statistic methods, including ordinary Kriging and inverse distance weighted (IDW) methods, cannot well interpolate missing-data pixels for a large area. Assuming that the changes of LST at one location would be similar with that at the locations with similar features, a novel method was proposed to interpolate the missing-data pixels by making use of other pixels with the most similar features. MODIS/Terra LST covering TP in 2005 were used as experimental data, and pixels with cloud coverage, average emissivity error greater than 0.04, and average LST error greater than 2K were identified as missing-data pixels. The images with less than 10% missing-data pixels were selected as reference images, in which the missing-data pixels were interpolated with IDW. Distances for different land surface features in images, such as DEM, slope, NDVI and LST, from the interpolating pixel to the other pixels with known LST were calculated. Similar pixels are identified as the distances less than a given threshold. Relationship of LST for those similar pixels was regressed, and was applied to estimate LSTs for the missing pixels. Compared with IDW and Kriging, the proposed method could interpolate the MODIS LST much better on the Tibetan Plateau.
A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation
Fiza Zafar
2015-01-01
Full Text Available We construct a new general class of derivative free n-point iterative methods of optimal order of convergence 2n-1 using rational interpolant. The special cases of this class are obtained. These methods do not need Newton’s iterate in the first step of their iterative schemes. Numerical computations are presented to show that the new methods are efficient and can be seen as better alternates.
Nikroo, Leila; Kompani-Zare, Mazda; Sepaskhah, Ali Reza; Shamsi, Seyed Rashid Fallah
2010-07-01
Prediction of groundwater depth and elevation is important in quantitative water management especially in arid areas. There are several basins in southwest of Iran, in Zagross Mountain, in which the water wells are distributed along a narrow elliptic ring band around the region. To find the most applicable interpolation method, both of the groundwater depth and elevation are predicted by different kriging methods. It is found that the groundwater elevation and depth can be predicted by different methods. Furthermore, it is found that the methods in which the trend is eliminated predicted the groundwater elevation and depth in central part of the region is with less standard error. Furthermore, the methods with no trend elimination, predicted the groundwater depths with less error near the water wells. Dividing the area to hydro-geologically homogeneous sub-areas improved the interpolation precision.
Fast Dynamic Meshing Method Based on Delaunay Graph and Inverse Distance Weighting Interpolation
Wang, Yibin; Qin, Ning; Zhao, Ning
2016-06-01
A novel mesh deformation technique is developed based on the Delaunay graph mapping method and the inverse distance weighting (IDW) interpolation. The algorithm maintains the advantages of the efficiency of Delaunay-graph-mapping mesh deformation while possess the ability for better controlling the near surface mesh quality. The Delaunay graph is used to divide the mesh domain into a number of sub-domains. On each of the sub-domains, the inverse distance weighting interpolation is applied to build a much smaller sized translation matrix between the original mesh and the deformed mesh, resulting a similar efficiency for the mesh deformation as compared to the fast Delaunay graph mapping method. The paper will show how the near-wall mesh quality is controlled and improved by the new method while the computational time is compared with the original Delaunay graph mapping method.
XU Liang; BI ChuanXing; CHEN XinZhao; CHEN Jian
2008-01-01
A new method based on interpolation using band-limited signal restoration method was proposed for enhancing the resolution of the nearfield acoustic holography. According to the band-limited property of the pressure on the hologram surface, a band-limited signal restoration method named Pa-poulis-Gerchberg algorithm was used to realize the interpolation of acoustic pressure. Therefore acoustic pressure data on the hologram surface were increased, the sampling interval was reduced, the information on evanescent waves which was lost because of the large sampling interval was partially recovered, and the resolution of nearfield acoustic holography image was improved. The experimental result shows that the method can enhance the resolution of the nearfield acoustic holography image efficiently.
A RBF Network Learning Scheme Using Immune Algorithm Based on Information Entropy
GONG Xin-bao; ZANG Xiao-gang; ZHOU Xi-lang
2005-01-01
A hybrid learning method combining immune algorithm and least square method is proposed to design the radial basis function(RBF) networks. The immune algorithm based on information entropy is used to determine the structure and parameters of RBF nonlinear hidden layer, and weights of RBF linear output layer are computed with least square method. By introducing the diversity control and immune memory mechanism, the algorithm improves the efficiency and overcomes the immature problem in genetic algorithm. Computer simulations demonstrate that the RBF networks designed in this method have fast convergence speed with good performances.
HybridN-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation
吴炎成; 朱首贤; 周林; 游小宝; 张文静
2016-01-01
The Eulerian−Lagrangian method (ELM) has been used by many ocean models as the solution of the advection equation, but the numerical error caused by interpolation imposes restriction on its accuracy. In the present study, hybrid N-order Lagrangian interpolation ELM (LiELM) is put forward in which theN-order Lagrangian interpolation is used at first, then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower. The calculation results of a step-shaped salinity advection model are analyzed, which show that higher order (N=3−8) LiELM can reduce the mean numerical error of salinity calculation, but the numerical oscillation error is still significant. Even number order LiELM makes larger numerical oscillation error than its adjacent odd number order LiELM. HybridN-order LiELM can remove numerical oscillation, and it significantly reduces the mean numerical error whenN is even and the current is in fixed direction, while it makes less effect on mean numerical error whenNis odd or the current direction changes periodically. Hybrid odd number order LiELM makes less mean numerical error than its adjacent even number order LiELM when the current is in the fixed direction, while the mean numerical error decreases asN increases when the current direction changes periodically, so odd number ofN may be better for application. Among various types of HybridN-order LiELM, the scheme reducingN-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
Sun, Yi-xiang; Wu, Chuan-zhou; Zhu, Ke-bao; Cui, Zhen-ling; Chen, Xin-ping; Zhang, Fu-suo
2009-03-01
Different from the large scale farm management in Europe and America, the scattered farmland management in China made the spatial variability of soil nutrients at county scale in this country more challenging. Taking soil Olsen-P in Wuhu County as an example, the influence of interpolation method and sampling number on the spatial prediction accuracy of soil nutrients was evaluated systematically. The results showed that local polynomial method, ordinary kriging, simple kriging, and disjunctive kriging had higher spatial prediction accuracy than the other interpolation methods. Considering of its simplicity, ordinary kriging was recommended to evaluate the spatial variability of soil Olsen-P within a county. The spatial prediction accuracy would increase with increasing soil sampling number. Taking the spatial prediction accuracy and soil sampling cost into consideration, the optimal sampling number should be from 500 to 1000 to evaluate the spatial variability of soil Olsen-P at county scale.
An Online Method for Interpolating Linear Parametric Reduced-Order Models
Amsallem, David
2011-01-01
A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.
Assareh, Ehsanolah; Poultangari, Iman [Dezful Branch, Islamic Azad University, Dezful (Iran, Islamic Republic of); Tandis, Emad [Mechanical Engineering Department, University of Jundi Shapor, Dezful (Iran, Islamic Republic of); Nedael, Mojtaba [Dept. of Energy Engineering, Graduate School of the Environment and Energy, Science and Research Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)
2016-10-15
Enhancing the energy production from wind power in low-wind areas has always been a fundamental subject of research in the field of wind energy industry. In the first phase of this research, an initial investigation was performed to evaluate the potential of wind in south west of Iran. The initial results indicate that the wind potential in the studied location is not sufficient enough and therefore the investigated region is identified as a low wind speed area. In the second part of this study, an advanced optimization model was presented to regulate the torque in the wind generators. For this primary purpose, the torque of wind turbine is adjusted using a Proportional and integral (PI) control system so that at lower speeds of the wind, the power generated by generator is enhanced significantly. The proposed model uses the RBF neural network to adjust the net obtained gains of the PI controller for the purpose of acquiring the utmost electricity which is produced through the generator. Furthermore, in order to edify and instruct the neural network, the optimal data set is obtained by a Hybrid genetic algorithm along with a gravitational search algorithm (HGA-GSA). The proposed method is evaluated by using a 5MW wind turbine manufactured by National Renewable Energy Laboratory (NREL). Final results of this study are indicative of the satisfactory and successful performance of the proposed investigated model.
Ly, S.
2013-01-01
Full Text Available Watershed management and hydrological modeling require data related to the very important matter of precipitation, often measured using raingages or weather stations. Hydrological models often require a preliminary spatial interpolation as part of the modeling process. The success of spatial interpolation varies according to the type of model chosen, its mode of geographical management and the resolution used. The quality of a result is determined by the quality of the continuous spatial rainfall, which ensues from the interpolation method used. The objective of this article is to review the existing methods for interpolation of rainfall data that are usually required in hydrological modeling. We review the basis for the application of certain common methods and geostatistical approaches used in interpolation of rainfall. Previous studies have highlighted the need for new research to investigate ways of improving the quality of rainfall data and ultimately, the quality of hydrological modeling.
Slemp, Wesley C. H.; Kapania, Rakesh K.; Tessler, Alexander
2010-01-01
Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory.
A method for interpolating asymmetric peak shapes in multiplet γ-ray spectra
WANG Si-Guang; MAO Ya-Jun; TANG Pei-Jia; ZHU Bo; LIANG Yu-Tie
2009-01-01
The peak shapes ofT-rays at various energies must be known before unfolding the multiplet spectra obtained by using semiconductor or scintillation detectors. Traditional methods describe isolated peaks with multi-parameter fitting functions, and assume that most of these parameters do not vary with energy because it is rare to find a spectrum with enough isolated peaks to constrain their dependence. We present an algorithm for interpolating the T-ray profile at any intermediate energy given a pair of isolated T-ray peaks from the spectrum under consideration. The algorithm is tested on experimental data and leads to a good agreement between the interpolated profile and the fitting function. This method is more accurate than the traditional approach, since all aspects of the peak shape are allowed to vary with energy. New definitions of Left-Half Width at Half Maximum, and Right-Half Width at Half Maximum for peak shape description are introduced in this paper.
Kriging-Based Finite Element Method: Element-By-Element Kriging Interpolation
W. Kanok-Nukulchai
2009-01-01
Full Text Available An enhancement of the finite element method with Kriging shape functions (K-FEM was recently proposed. In this method, the field variables of a boundary value problem are approximated using ‘element-by-element’ piecewise Kriging interpolation (el-KI. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.
A seismic interpolation and denoising method with curvelet transform matching filter
Yang, Hongyuan; Long, Yun; Lin, Jun; Zhang, Fengjiao; Chen, Zubin
2017-09-01
A new seismic interpolation and denoising method with a curvelet transform matching filter, employing the fast iterative shrinkage thresholding algorithm (FISTA), is proposed. The approach treats the matching filter, seismic interpolation, and denoising all as the same inverse problem using an inversion iteration algorithm. The curvelet transform has a high sparseness and is useful for separating signal from noise, meaning that it can accurately solve the matching problem using FISTA. When applying the new method to a synthetic noisy data sets and a data sets with missing traces, the optimum matching result is obtained, noise is greatly suppressed, missing seismic data are filled by interpolation, and the waveform is highly consistent. We then verified the method by applying it to real data, yielding satisfactory results. The results show that the method can reconstruct missing traces in the case of low SNR (signal-to-noise ratio). The above three problems can be simultaneously solved via FISTA algorithm, and it will not only increase the processing efficiency but also improve SNR of the seismic data.
Maiden, D E
1998-10-01
A method for constructing bicubic interpolation polynomials for the pressure P and internal energy E that are thermodynamically consistent at the mesh ponts and continuous across mesh boundaries is presented. The slope boundary conditions for the pressure and energy are derived from finite differences of the data and from Maxwell's consistency relation. Monotonicity of the sound speed and the specific heat is obtained by a bilinear interpolation of the slopes of the tabulated data. Monotonicity of the functions near steep gradients may be achieved by mesh refinement or by using a non-consistent bilinear to the data. Mesh refinement is very efficient for uniform-linear or uniform-logarithmic spaced data because a direct table lookup can be used. The direct method was compared to binary search and was 37 percent faster for logarithmic-spaced data and 106 percent faster for linear-spaced data. This improvement in speed is very important in the radiation-transport opacity-lookup part of the calculation. Interpolation in P-E space, with mesh refinement, can be made simple, robust, and conserve energy. In the final analysis the interpolation of the free energy and entropy (Maiden and Cook) remains a competitor.
Analysis of radial basis function interpolation approach
Zou You-Long; Hu Fa-Long; Zhou Can-Can; Li Chao-Liu; Dunn Keh-Jim
2013-01-01
The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman's RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.
On the applications of algebraic grid generation methods based on transfinite interpolation
Nguyen, Hung Lee
1989-01-01
Algebraic grid generation methods based on transfinite interpolation called the two-boundary and four-boundary methods are applied for generating grids with highly complex boundaries. These methods yield grid point distributions that allow for accurate application to regions of sharp gradients in the physical domain or time-dependent problems with small length scale phenomena. Algebraic grids are derived using the two-boundary and four-boundary methods for applications in both two- and three-dimensional domains. Grids are developed for distinctly different geometrical problems and the two-boundary and four-boundary methods are demonstrated to be applicable to a wide class of geometries.
Higher-order numerical methods derived from three-point polynomial interpolation
Rubin, S. G.; Khosla, P. K.
1976-01-01
Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.
Estimation of missing rainfall data using spatial interpolation and imputation methods
Radi, Noor Fadhilah Ahmad; Zakaria, Roslinazairimah; Azman, Muhammad Az-zuhri
2015-02-01
This study is aimed to estimate missing rainfall data by dividing the analysis into three different percentages namely 5%, 10% and 20% in order to represent various cases of missing data. In practice, spatial interpolation methods are chosen at the first place to estimate missing data. These methods include normal ratio (NR), arithmetic average (AA), coefficient of correlation (CC) and inverse distance (ID) weighting methods. The methods consider the distance between the target and the neighbouring stations as well as the correlations between them. Alternative method for solving missing data is an imputation method. Imputation is a process of replacing missing data with substituted values. A once-common method of imputation is single-imputation method, which allows parameter estimation. However, the single imputation method ignored the estimation of variability which leads to the underestimation of standard errors and confidence intervals. To overcome underestimation problem, multiple imputations method is used, where each missing value is estimated with a distribution of imputations that reflect the uncertainty about the missing data. In this study, comparison of spatial interpolation methods and multiple imputations method are presented to estimate missing rainfall data. The performance of the estimation methods used are assessed using the similarity index (S-index), mean absolute error (MAE) and coefficient of correlation (R).
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Zhang, Xiao-Zheng; Bi, Chuan-Xing; Zhang, Yong-Bin; Xu, Liang
2011-09-01
Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method (ESM) is proposed to reconstruct transient acoustic fields directly in the time domain. Since the equivalent source strengths solved by the traditional time-domain ESM formulation cannot be used to reconstruct the pressure on the source surface directly, an interpolation function is introduced to develop an interpolated time-domain ESM formulation which permits one to deduce an iterative reconstruction process. As the reconstruction process is ill-conditioned and especially there exists a cumulative effect of errors, the Tikhonov regularization is used to stabilize the process. Numerical examples of reconstructing transient acoustic fields from a baffled planar piston, an impulsively accelerating sphere and a cube box, respectively, demonstrate that the proposed method not only can effectively reconstruct transient acoustic fields in the time domain, but also can visualize acoustic fields in the space domain. And, in the first numerical example, the cumulative effect of errors and the validity of using the Tikhonov regularization to suppress the errors are described.
Effect of the precipitation interpolation method on the performance of a snowmelt runoff model
Jacquin, Alexandra
2014-05-01
Uncertainties on the spatial distribution of precipitation seriously affect the reliability of the discharge estimates produced by watershed models. Although there is abundant research evaluating the goodness of fit of precipitation estimates obtained with different gauge interpolation methods, few studies have focused on the influence of the interpolation strategy on the response of watershed models. The relevance of this choice may be even greater in the case of mountain catchments, because of the influence of orography on precipitation. This study evaluates the effect of the precipitation interpolation method on the performance of conceptual type snowmelt runoff models. The HBV Light model version 4.0.0.2, operating at daily time steps, is used as a case study. The model is applied in Aconcagua at Chacabuquito catchment, located in the Andes Mountains of Central Chile. The catchment's area is 2110[Km2] and elevation ranges from 950[m.a.s.l.] to 5930[m.a.s.l.] The local meteorological network is sparse, with all precipitation gauges located below 3000[m.a.s.l.] Precipitation amounts corresponding to different elevation zones are estimated through areal averaging of precipitation fields interpolated from gauge data. Interpolation methods applied include kriging with external drift (KED), optimal interpolation method (OIM), Thiessen polygons (TP), multiquadratic functions fitting (MFF) and inverse distance weighting (IDW). Both KED and OIM are able to account for the existence of a spatial trend in the expectation of precipitation. By contrast, TP, MFF and IDW, traditional methods widely used in engineering hydrology, cannot explicitly incorporate this information. Preliminary analysis confirmed that these methods notably underestimate precipitation in the study catchment, while KED and OIM are able to reduce the bias; this analysis also revealed that OIM provides more reliable estimations than KED in this region. Using input precipitation obtained by each method
MACKAY, W.W.; LUCCIO, A.U.
2006-06-23
It is important to have symplectic maps for the various electromagnetic elements in an accelerator ring. For some tracking problems we must consider elements which evolve during a ramp. Rather than performing a computationally intensive numerical integration for every turn, it should be possible to integrate the trajectory for a few sets of parameters, and then interpolate the transport map as a function of one or more parameters, such as energy. We present two methods for interpolation of symplectic matrices as a function of parameters: one method is based on the calculation of a representation in terms of a basis of group generators [2, 3] and the other is based on the related but simpler symplectification method of Healy [1]. Both algorithms guarantee a symplectic result.
Annalisa Di Piazza
2015-04-01
Full Text Available An exhaustive comparison among different spatial interpolation algorithms was carried out in order to derive annual and monthly air temperature maps for Sicily (Italy. Deterministic, data-driven and geostatistics algorithms were used, in some cases adding the elevation information and other physiographic variables to improve the performance of interpolation techniques and the reconstruction of the air temperature field. The dataset is given by air temperature data coming from 84 stations spread around the island of Sicily. The interpolation algorithms were optimized by using a subset of the available dataset, while the remaining subset was used to validate the results in terms of the accuracy and bias of the estimates. Validation results indicate that univariate methods, which neglect the information from physiographic variables, significantly entail the largest errors, while performances improve when such parameters are taken into account. The best results at the annual scale have been obtained using the the ordinary kriging of residuals from linear regression and from the artificial neural network algorithm, while, at the monthly scale, a Fourier-series algorithm has been used to downscale mean annual temperature to reproduce monthly values in the annual cycle.
Jianli Li
2013-01-01
Full Text Available In order to improve the precision of Strapdown Inertial Navigation System (SINS and reduce the complexity of the traditional calibration method, a novel calibration and compensation scheme is proposed. An optimization calibration method with four-direction rotations is designed to calculate all error coefficients of Ring Laser Gyroscope (RLG SINS in a series of constant temperatures. According to the actual working environment, the temperature errors of RLG SINS are compensated by a nonlinear interpolation compensation algorithm. The experimental results show that the inertial navigation errors of the proposed method are reduced.
Adaptive interpolation wavelet and homotopy perturbation method for partial differential equations
Ma, Q; Mei, S [College of Information and Electrical Engineering, China Agricultural University, 17 Qinghua Donglu Road, Beijing 100083 (China)], E-mail: meishuli@163.com
2008-02-15
The homotopy perturbation method proposed by Ji-Huan He has been developed to solve nonlinear matrix differential equations. This paper constructs an adaptive multilevel quasi-wavelet operator according to the interpolation wavelet theory, with which the nonlinear partial differential equations can be discretized adaptively in physical spaces as a matrix differential equation, its numerical solution can be obtained by using the homotopy perturbation method. Numerical results show that the homotopy perturbation method is not sensitive to the time step, so the arithmetic error mainly arises in the space step. Burgers equation is taken as examples to illustrate its effectiveness and convenience.
温伟斌; 蹇开林; 骆少明
2013-01-01
A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven-tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin-ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.
Mohammadi, Seyedeh Atefeh; Azadi, Majid; Rahmani, Morteza
2017-08-01
All numerical weather prediction (NWP) models inherently have substantial biases, especially in the forecast of near-surface weather variables. Statistical methods can be used to remove the systematic error based on historical bias data at observation stations. However, many end users of weather forecasts need bias corrected forecasts at locations that scarcely have any historical bias data. To circumvent this limitation, the bias of surface temperature forecasts on a regular grid covering Iran is removed, by using the information available at observation stations in the vicinity of any given grid point. To this end, the running mean error method is first used to correct the forecasts at observation stations, then four interpolation methods including inverse distance squared weighting with constant lapse rate (IDSW-CLR), Kriging with constant lapse rate (Kriging-CLR), gradient inverse distance squared with linear lapse rate (GIDS-LR), and gradient inverse distance squared with lapse rate determined by classification and regression tree (GIDS-CART), are employed to interpolate the bias corrected forecasts at neighboring observation stations to any given location. The results show that all four interpolation methods used do reduce the model error significantly, but Kriging-CLR has better performance than the other methods. For Kriging-CLR, root mean square error (RMSE) and mean absolute error (MAE) were decreased by 26% and 29%, respectively, as compared to the raw forecasts. It is found also, that after applying any of the proposed methods, unlike the raw forecasts, the bias corrected forecasts do not show spatial or temporal dependency.
A new family of multistep numerical integration methods based on Hermite interpolation
Sharifi, M. A.; Seif, M. R.
2014-01-01
In this paper, a new family of explicit and implicit multistep methods is presented both for the error-controlled and uncontrolled modes. The main concept is to replace the Newton interpolation with the Hermite interpolation, where the Hermite polynomial is fitted to the function values and its derivatives. This idea is very useful in the numerical solution of problems (e.g., orbit propagation problem) where higher-order derivatives can easily be computed. In addition to the theoretical concept, the stability regions of the proposed methods are determined. The new methods are more stable than the well-known multistep numerical integrators (i.e., Adams-Bashforth and Adams-Bashforth-Moulton) in the explicit, implicit, and predictor-corrector forms. Using the second-order derivatives gives smaller error constants in the proposed method. The new integrators are numerically tested for a few examples, and the solutions are compared with those of the well-known multistep methods. Moreover, the CPU time and absolute integration error are compared in the satellite orbit propagation problem using various integration methods. The CHAMP mission, i.e., a German small-satellite mission for geoscientific and atmospheric research and applications, is considered as a case study for comparing the achievable accuracy of the proposed method with the existing method for solving the two-body problem.
2003-01-01
The application of discreet interpolation or the finite differences methods for opal breccia deposit. The performance is carried out by computer application and graphical presentation for quartz and aluminium oxide.
A new interpolating method based on the variation of spectra energy using CMOS array
Tianjin Tang; Xiangqun Cao; Hongqiu Chen; Bin Lin
2005-01-01
@@ A new interpolating method to enhance the resolution of gratings using complementary metal-oxide semiconductor (CMOS) according to the variation of some specified spectral light intensities during the motion of scale grating in a periodic separation is proposed. CMOS image sensor (pixel array 648 × 488) was also introduced as receiving device and its stability was verified experimentally. Many factors in the experiment were analyzed theoretically and contrasted with experiment. The advantages of this novel method were featured by CMOS and the specified spectral variation of the energy distribution was discussed.
Mirzaei, Rouhollah; Sakizadeh, Mohamad
2016-02-01
Selection of appropriate interpolation methods for the conversion of discrete samples into continuous maps is a controversial issue in the environmental researches. The main objective of this study was to analyze the suitability of three interpolation methods for the discrimination of groundwater with respect to the water quality index (WQI). The groundwater quality data consisted of 17 variables associated with 65 wells located in Andimeshk-Shush Plain. Three spatial interpolation methods including ordinary kriging (OK), empirical Bayesian kriging (EBK), and inverse distance weighting (IDW) were utilized for modeling the groundwater contamination. In addition, different cross-validation indicators were applied to assess the performance of different interpolation methods. The results showed that the performance differed slightly among different methods, although the best performed interpolation method in this study was the empirical Bayesian kriging. Among the interpolation methods, IDW with weighting power of 4 estimated the most contaminated area, while OK estimated the lowest contaminated area. The weighting power of IDW had a significant influence on the estimation, meaning that the estimated contaminated area was increased when a greater weighting power was selected. The subtraction results indicated that there are slightly spatial differences among the contamination assessment results. Results of both standard deviation (SD) and coefficient of variation (CV) also showed that uncertainty was highest in the southern part of the study area, where the distribution of wells were more intensive than that of the northern part.
Elman, Howard C.; Forstall, Virginia
2017-04-01
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem at significantly lower cost, producing an accurate estimate of the solution. For nonlinear problems, however, standard methods do not achieve the desired cost savings. Empirical interpolation methods represent a modification of this methodology used for cases of nonlinear operators or nonaffine parameter dependence. These methods identify points in the discretization necessary for representing the nonlinear component of the reduced model accurately, and they incur online computational costs that are independent of the spatial dimension $N$. We will show that empirical interpolation methods can be used to significantly reduce the costs of solving parameterized versions of the Navier-Stokes equations, and that iterative solution methods can be used in place of direct methods to further reduce the costs of solving the algebraic systems arising from reduced-order models.
Bogaers, Alfred EJ
2016-10-01
Full Text Available In this paper we outline the use of radial basis function interpolation (RBF) to transfer information across non-matching and nonconforming interface meshes, with particular focus to partitioned fluid-structure interactions (FSI). In general...
Arslan, Hakan; Ayyildiz Turan, Nazlı
2015-08-01
Monitoring of heavy metal concentrations in groundwater potentially used for drinking and irrigation is very important. This study collected groundwater samples from 78 wells in July 2012 and analyzed them for 17 heavy metals (Pb, Zn, Cr, Mn, Fe, Cu, Cd, Co, Ni, Al, As, Mo, Se, B, Ti, V, Ba). Spatial distributions of these elements were identified using three different interpolation methods [inverse distance weighing (IDW), radial basis function (RBF), and ordinary kriging (OK)]. Root mean squared error (RMSE) and mean absolute error (MAE) for cross validation were used to select the best interpolation methods for each parameter. Multivariate statistical analysis [cluster analysis (CA) and factor analysis (FA)] were used to identify similarities among sampling sites and the contribution of variables to groundwater pollution. Fe and Mn levels exceeded World Health Organization (WHO) recommended limits for drinking water in almost all of the study area, and some locations had Fe and Mn levels that exceeded Food and Agriculture Organization (FAO) guidelines for drip irrigation systems. Al, As, and Cd levels also exceeded WHO guidelines for drinking water. Cluster analysis classified groundwater in the study area into three groups, and factor analysis identified five factors that explained 73.39% of the total variation in groundwater, which are as follows: factor 1: Se, Ti, Cr, Mo; factor 2: Ni, Mn, Co, Ba; factor 3: Pb, Cd; factor 4: B, V, Fe, Cu; and factor 5: AS, Zn. As a result of this study, it could be said that interpolation methods and multivariate statistical techniques gave very useful results for the determination of the source.
On Recovering Missing Ground Penetrating Radar Traces by Statistical Interpolation Methods
Gonzalo Safont
2014-08-01
Full Text Available Missing traces in ground penetrating radar (GPR B-scans (radargrams may appear because of limited scanning resolution, failures during the acquisition process or the lack of accessibility to some areas under test. Four statistical interpolation methods for recovering these missing traces are compared in this paper: Kriging, Wiener structures, Splines and the expectation assuming an independent component analyzers mixture model (E-ICAMM. Kriging is an adaptation to the spatial context of the linear least mean squared error estimator. Wiener structures improve the linear estimator by including a nonlinear scalar function. Splines are a commonly used method to interpolate GPR traces. This consists of piecewise-defined polynomial curves that are smooth at the connections (or knots between pieces. E-ICAMM is a new method proposed in this paper. E-ICAMM consists of computing the optimum nonlinear estimator (the conditional mean assuming a non-Gaussian mixture model for the joint probability density in the observation space. The proposed methods were tested on a set of simulated data and a set of real data, and four performance indicators were computed. Real data were obtained by GPR inspection of two replicas of historical walls. Results show the superiority of E-ICAMM in comparison with the other three methods in the application of reconstructing incomplete B-scans.
Shiqin Lyu
2013-01-01
estimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the the unknown boundary. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.
Liu, Ruimin; Chen, Yaxin; Sun, Chengchun; Zhang, Peipei; Wang, Jiawei; Yu, Wenwen; Shen, Zhenyao
2014-09-15
Interpolation processes and results are generally accompanied by uncertainty which affects the spatial and temporal properties of pollutants. Based on the 4 period sample data of total phosphorus (TP) collected from the Yangtze River Estuary (YRE) in 2010 and 2011, the uncertainty of spatial-temporal variation was analyzed with interpolation methods of inverse distance weighted (IDW), local polynomial interpolation (LPI), ordinary kriging (OK) and disjunctive kriging (DK). The root mean square errors (RMSE) and the mean relative errors (MRE) were used to analyze the accuracy of different interpolation methods. The results showed that the uncertainty of DK was the lowest and the uncertainty of LPI was the highest among the 4 methods. The subtraction results between different interpolation methods showed that there was some distinct area of value in the disparate interval (not in [-0.05, 0.05] (mg/L)) in the 4 seasonal results, which was mainly distributed in the boundary region and around some sample sites. Both standard deviation (SD) and coefficient of variance (CV) in August 2010 were the highest in the 4 seasons and annual mean. The uncertainty may be caused by choice of interpolation methods, spatial data discrepancy and the lack of sample data.
Development of the general interpolants method for the CYBER 200 series of supercomputers
Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.
1988-01-01
The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.
Ducru, Pablo; Josey, Colin; Dibert, Karia; Sobes, Vladimir; Forget, Benoit; Smith, Kord
2017-04-01
This article establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (Tj). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T0 to a higher temperature T - namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (Tj). The choice of the L2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (Tj) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [Tmin ,Tmax ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [ 300 K , 3000 K ] with only 9 reference temperatures.
Chen, Zhaoxue; Chen, Hao
2014-01-01
A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.
R. Khosravi
2014-09-01
Full Text Available Climatic change can impose physiological constraints on species and can therefore affect species distribution. Bioclimatic predictors, including annual trends, regimes, thresholds and bio-limiting factors are the most important independent variables in species distribution models. Water and temperature are the most limiting factors in arid ecosystem in central Iran. Therefore, mapping of climatic factors in species distribution models seems necessary. In this study, we describe the extraction of 20 important bioclimatic variables from climatic data and compare different interpolation methods including inverse distance weighting, ordinary kriging, kriging with external trend, cokriging, and five radial basis functions. Normal climatic data (1950-2010 in 26 synoptic stations in central Iran were used to extract bioclimatic data. Spatial correlation, heterogeneity and trend in data were evaluated using three models of semivariogram (spherical, exponential and Gaussian and the best model was selected using cross validation. The optimum model for bioclimatic variables was assessed based on the root mean square error and mean bias error. Exponential model was considered to be the best fit mathematical model to empirical semivariogram. IDW and cokriging were recognised as the best interpolating methods for average annual temperature and annual precipitation, respectively. Use of elevation as an auxiliary variable appeared to be necessary for optimizing interpolation methods of climatic and bioclimatic variables.
Roy, Subrata P.
2014-01-28
The method of moments with interpolative closure (MOMIC) for soot formation and growth provides a detailed modeling framework maintaining a good balance in generality, accuracy, robustness, and computational efficiency. This study presents several computational issues in the development and implementation of the MOMIC-based soot modeling for direct numerical simulations (DNS). The issues of concern include a wide dynamic range of numbers, choice of normalization, high effective Schmidt number of soot particles, and realizability of the soot particle size distribution function (PSDF). These problems are not unique to DNS, but they are often exacerbated by the high-order numerical schemes used in DNS. Four specific issues are discussed in this article: the treatment of soot diffusion, choice of interpolation scheme for MOMIC, an approach to deal with strongly oxidizing environments, and realizability of the PSDF. General, robust, and stable approaches are sought to address these issues, minimizing the use of ad hoc treatments such as clipping. The solutions proposed and demonstrated here are being applied to generate new physical insight into complex turbulence-chemistry-soot-radiation interactions in turbulent reacting flows using DNS. © 2014 Copyright Taylor and Francis Group, LLC.
Pressure Decimation and Interpolation (PDI) method for a baroclinic non-hydrostatic model
Shi, Jian; Shi, Fengyan; Kirby, James T.; Ma, Gangfeng; Wu, Guoxiang; Tong, Chaofeng; Zheng, Jinhai
2015-12-01
Non-hydrostatic models are computationally expensive in simulating density flows and mass transport problems due to the requirement of sufficient grid resolution to resolve density and flow structures. Numerical tests based on the Non-Hydrostatic Wave Model, NHWAVE (Ma et al., 2012), indicated that up to 70% of the total computational cost may be born by the pressure Poisson solver in cases with high grid resolution in both vertical and horizontal directions. However, recent studies using Poisson solver-based non-hydrostatic models have shown that an accurate prediction of wave dispersion does not require a large number of vertical layers if the dynamic pressure is properly discretized. In this study, we explore the possibility that the solution for the dynamic pressure field may, in general, be decimated to a resolution far coarser than that used in representing velocities and other transported quantities, without sacrificing accuracy of solutions. Following van Reeuwijk (2002), we determine the dynamic pressure field by solving the Poisson equation on a coarser grid and then interpolate the pressure field onto a finer grid used for solving for the remaining dynamic variables. With the Pressure Decimation and Interpolation (PDI) method, computational efficiency is greatly improved. We use three test cases to demonstrate the model's accuracy and efficiency in modeling density flows.
Using the Correlation Criterion to Position and Shape RBF Units for Incremental Modelling
Xun-Xian Wang; Sheng Chen; Chris J. Harris
2006-01-01
A novel technique is proposed for the incremental construction of sparse radial basis function (RBF) networks.The correlation between an RBF regressor and the training data is used as the criterion to position and shape the RBF node, and it is shown that this is equivalent to incrementally minimise the modelling mean square error. A guided random search optimisation method, called the repeated weighted boosting search, is adopted to append RBF nodes one by one in an incremental regression modelling procedure. The experimental results obtained using the proposed method demonstrate that it provides a viable alternative to the existing state-of-the-art modelling techniques for constructing parsimonious RBF models that generalise well.
[Application of inverse distance weighted interpolation method in contaminated site assessment].
Yang, Wen-Rui; Wang, Ru-Song; Huang, Jin-Lou; Chen, Zhan; Li, Feng
2007-09-01
There are many difficulties in ascertaining the area that needs to be remedied in contaminated site. This paper integrated the experts' judgments with grids as the sampling strategy in an abandoned pesticide plant in northern China, and applied a geostatistical method, inverse distance weighted interpolation (IDW), to simulate the pollutants- and risk spatial distribution. Based on soil environmental benchmark, two scenarios were designed for ascertaining the polluted area. The results showed that the area needed to be remedied and determined by IDW was somewhat larger, according to the national environmental 2nd standard for agricultural soils, but the area and cost needed for remedy were smaller and more economic and reasonable, based on the health risk threshold level and IDW method. A combination of IDW and health risk assessment in ascertaining polluted area would be a new way for site assessment and soil remediation in the future.
On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
Bayona, Victor; Flyer, Natasha; Fornberg, Bengt; Barnett, Gregory A.
2017-03-01
RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs. We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions. In particular, the drawbacks on accuracy and stability due to Runge's phenomenon are overcome once the RBF stencils exceed a certain size due to an underlying minimization property. Test problems include the classical 2-D driven cavity, and also a 3-D global electric circuit problem with the earth's irregular topography as its bottom boundary. The results we find are fully consistent with previous results for data interpolation.
Tubman, Norm; Hammes-Schiffer, Sharon; Ceperley, David
2016-01-01
Simulating nonadiabatic effects with many-body wave function approaches is an open field with many challenges. Recent interest has been driven by new algorithmic developments and improved theoretical understanding of properties unique to electron-ion wave functions. Fixed-node diffusion Monte Caro is one technique that has shown promising results for simulating electron-ion systems. In particular, we focus on the CH molecule for which previous results suggested a relatively significant contribution to the energy from nonadiabatic effects. We propose a new wave function ansatz for diatomic systems which involves interpolating the determinant coefficients calculated from configuration interaction methods. We find this to be an improvement beyond previous wave function forms that have been considered. The calculated nonadiabatic contribution to the energy in the CH molecule is reduced compared to our previous results, but still remains the largest among the molecules under consideration.
Xiao Jin-Biao; Zhang Ming-De; Sun Xiao-Han
2006-01-01
Based on the polynomial interpolation, a new finite difference (FD) method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present FD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.
Evaluation of linear interpolation method for missing value on solar radiation dataset in Perlis
Saaban, Azizan; Zainudin, Lutfi [School of Science Quantitative, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu [Faculty of Applied Science, Universiti Teknologi MARA, 02600 Arau, Perlis (Malaysia)
2015-05-15
This paper intends to reveal the ability of the linear interpolation method to predict missing values in solar radiation time series. Reliable dataset is equally tends to complete time series observed dataset. The absence or presence of radiation data alters long-term variation of solar radiation measurement values. Based on that change, the opportunities to provide bias output result for modelling and the validation process is higher. The completeness of the observed variable dataset has significantly important for data analysis. Occurrence the lack of continual and unreliable time series solar radiation data widely spread and become the main problematic issue. However, the limited number of research quantity that has carried out to emphasize and gives full attention to estimate missing values in the solar radiation dataset.
Kim, Sang-Wook
1988-01-01
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.
Deterministic System Identification Using RBF Networks
Joilson Batista de Almeida Rego
2014-01-01
Full Text Available This paper presents an artificial intelligence application using a nonconventional mathematical tool: the radial basis function (RBF networks, aiming to identify the current plant of an induction motor or other nonlinear systems. Here, the objective is to present the RBF response to different nonlinear systems and analyze the obtained results. A RBF network is trained and simulated in order to obtain the dynamical solution with basin of attraction and equilibrium point for known and unknown system and establish a relationship between these dynamical systems and the RBF response. On the basis of several examples, the results indicating the effectiveness of this approach are demonstrated.
Sun, Yuxin; Xiong, Zhenhua
2017-01-01
In turning processes, chatter is an unstable vibration which adversely affects surface finish and machine tool components. Stiffness variation (SV) is an effective strategy for chatter suppression by periodically modulating the stiffness around a nominal value. The dynamics of SV turning is governed by a time periodic delay differential equation (DDE) where the time-period/time-delay ratio (TPTDR) can be arbitrary. Recently, first-, second- and higher-order full-discretization methods (FDMs) have been reported as a popular class of methods for milling stability prediction. However, these FDMs can only deal with time periodic DDE where the TPTDR equals one. In this paper, two high-order FDMs using Lagrange interpolation (HLFDMs) are proposed for stability analysis of SV turning. On each discrete time interval, the time delay term is interpolated by the second-degree Lagrange polynomial, and the time periodic term is linearly interpolated. The state term is approximated using linear interpolation and second-degree Lagrange polynomial interpolation, achieving the first- and second-order HLFDM, respectively. Finally, the transition matrix over a single period is deduced for stability analysis via the Floquet theory. Benchmark examples of damped delay Mathieu equations are used to verify the proposed algorithm, which demonstrates that HLFDMs are highly efficient and accurate. In addition, the second-order HLFDM is used to investigate the effects of SV amplitude and frequency parameters. These results provide theoretical insights for the selection of SV parameters.
Hallisey, Elaine; Tai, Eric; Berens, Andrew; Wilt, Grete; Peipins, Lucy; Lewis, Brian; Graham, Shannon; Flanagan, Barry; Lunsford, Natasha Buchanan
2017-08-07
Transforming spatial data from one scale to another is a challenge in geographic analysis. As part of a larger, primary study to determine a possible association between travel barriers to pediatric cancer facilities and adolescent cancer mortality across the United States, we examined methods to estimate mortality within zones at varying distances from these facilities: (1) geographic centroid assignment, (2) population-weighted centroid assignment, (3) simple areal weighting, (4) combined population and areal weighting, and (5) geostatistical areal interpolation. For the primary study, we used county mortality counts from the National Center for Health Statistics (NCHS) and population data by census tract for the United States to estimate zone mortality. In this paper, to evaluate the five mortality estimation methods, we employed address-level mortality data from the state of Georgia in conjunction with census data. Our objective here is to identify the simplest method that returns accurate mortality estimates. The distribution of Georgia county adolescent cancer mortality counts mirrors the Poisson distribution of the NCHS counts for the U.S. Likewise, zone value patterns, along with the error measures of hierarchy and fit, are similar for the state and the nation. Therefore, Georgia data are suitable for methods testing. The mean absolute value arithmetic differences between the observed counts for Georgia and the five methods were 5.50, 5.00, 4.17, 2.74, and 3.43, respectively. Comparing the methods through paired t-tests of absolute value arithmetic differences showed no statistical difference among the methods. However, we found a strong positive correlation (r = 0.63) between estimated Georgia mortality rates and combined weighting rates at zone level. Most importantly, Bland-Altman plots indicated acceptable agreement between paired arithmetic differences of Georgia rates and combined population and areal weighting rates. This research contributes to
[Hybrid interpolation for CT metal artifact reducing].
Yu, Xiao-e; Li, Chan-juan; Chen, Wu-fan
2009-01-01
Numerous interpolation-based methods have been described for reducing metal artifacts in CT images, but due to the limit of the interpolation methods, interpolation alone often fails to meet the clinical demands. In this paper, we describe the use of quartic polynomial interpolation in reconstruction of the images of the metal implant followed by linear interpolation to eliminate the streaks. The two interpolation methods are combined according to their given weights to achieve good results.
Sharp Interpolation Inequalities on the Sphere:New Methods and Consequences
Jean DOLBEAULT; Maria J.ESTEBAN; Michal KOWALCZYK; Michael LOSS
2013-01-01
This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere,which in dimension greater than 1 interpolate between Poincaré,logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities.The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized.The authors address a series of related observations and give proofs based on symmetrization and the ultraspherical setting.
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 presented.Sampling s
Jenkins, Steven T.; Hilkert, J. M.
2008-04-01
Pointing and tracking applications usually require relative gimbal angles to be measured for reporting and controlling the line-of-sight angular position. Depending on the application, angular resolution and/or accuracy might jointly or independently determine the angle transducer requirements. In the past decade, encoders have been increasingly taking the place of inductive devices where the measurement of angles over a wide range is required. This is primarily due to the fact that encoders are now achieving very high resolution in smaller sizes than was previously possible. These advances in resolution are primarily due to improved encoder disk and detector technology along with developments in interpolation techniques. Measurement accuracy, on the other hand, is primarily determined by mounting and bearing eccentricity as it is with all angular measurement devices. For very demanding accuracy requirements, some type of calibration of the assembled system may be the only solution, in which case transducer repeatability is paramount. This paper describes a unique encoder-to-digital tracking converter concept for improving interpolation of optical encoders. The new method relies on Fraunhofer diffraction models to correct the non-ideal sin/cos outputs of the encoder detectors. Diffraction model concepts are used in the interpolation filters to predict the phase of non-ideal sin and cosine encoder outputs. The new method also minimizes many of the open loop pre-processing requirements and assumptions that limit interpolation accuracy and rate loop noise performance in ratiometric tracking converter designs.
Ou, Yu-Yen; Gromiha, M Michael; Chen, Shu-An; Suwa, Makiko
2008-06-01
Discriminating outer membrane proteins (OMPs) from other folding types of globular and membrane proteins is an important task both for identifying OMPs from genomic sequences and for the successful prediction of their secondary and tertiary structures. We have developed a method based on radial basis function networks and position specific scoring matrix (PSSM) profiles generated by PSI-BLAST and non-redundant protein database. Our approach with PSSM profiles has correctly predicted the OMPs with a cross-validated accuracy of 96.4% in a set of 1251 proteins, which contain 206 OMPs, 667 globular proteins and 378 alpha-helical inner membrane proteins. Furthermore, we applied our method on a dataset containing 114 OMPs, 187 TMH proteins and 195 globular proteins obtained with less than 20% sequence identity and obtained the cross-validated accuracy of 95%. This accuracy of discriminating OMPs is higher than other methods in the literature and our method could be used as an effective tool for dissecting OMPs from genomic sequences. We have developed a prediction server, TMBETADISC-RBF, which is available at http://rbf.bioinfo.tw/~sachen/OMP.html.
Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
Bayati, Mohsen; Tetali, Prasad
2009-01-01
We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erd{\\"o}s-R\\'{e}nyi graph $\\G(N,c/N)$ and random $r$-regular graph $\\G(N,r)$. For a variety of models, including independent sets, MAX-CUT, Coloring and K-SAT, we prove that the free energy both at a positive and zero temperature, appropriately rescaled, converges to a limit as the size of the underlying graph diverges to infinity. For example, as a special case we prove that the size of a largest independent set in these graphs, normalized by the number of nodes converges to a limit w.h.p., thus resolving an open problem, (see Conjecture 2.20 in \\cite{WormaldModelsRandomGraphs}, as well as \\cite{Aldous:FavoriteProblems}, \\cite{BollobasRiordanMetrics}, \\cite{JansonThomason}, and \\cite{AldousSteele:survey}). Our approach is based on extending and simplifying the interpolation method developed by Guerra and Toninelli \\cite{GuerraTon} and Franz and Leone \\cite{FranzLeone},...
Senjean, Bruno; Alam, Md Mehboob; Knecht, Stefan; Fromager, Emmanuel
2015-01-01
The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble density-functional approximations, with the extrapolation scheme of Savin [J. Chem. Phys. 140, 18A509 (2014)] is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter mu when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, can be adapted straightforwardly to LIM. This extrapolated LIM (ELIM) has been tested on a small test set consisting of He, Be, H2 and HeH+. Relatively accurate results have been obtained for the first singlet excitation energies with the typical mu=0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly-excited 2^1Sigma+g state in the stretched H2 molecule. Three-state ensemble ...
S. Safarpour
2017-09-01
Full Text Available Air pollution is a growing problem arising from domestic heating, high density of vehicle traffic, electricity production, and expanding commercial and industrial activities, all increasing in parallel with urban population. Monitoring and forecasting of air quality parameters are important due to health impact. One widely available metric of aerosol abundance is the aerosol optical depth (AOD. The AOD is the integrated light extinction coefficient over a vertical atmospheric column of unit cross section, which represents the extent to which the aerosols in that vertical profile prevent the transmission of light by absorption or scattering. Seasonal aerosol optical depth (AOD values at 550 nm derived from the Moderate Resolution Imaging Spectroradiometer (MODIS sensor onboard NASA’s Terra satellites, for the 10 years period of 2000 - 2010 were used to test 7 different spatial interpolation methods in the present study. The accuracy of estimations was assessed through visual analysis as well as independent validation based on basic statistics, such as root mean square error (RMSE and correlation coefficient. Based on the RMSE and R values of predictions made using measured values from 2000 to 2010, Radial Basis Functions (RBFs yielded the best results for spring, summer and winter and ordinary kriging yielded the best results for fall.
Elumalai, Vetrimurugan; Brindha, K; Sithole, Bongani; Lakshmanan, Elango
2017-04-01
Mapping groundwater contaminants and identifying the sources are the initial steps in pollution control and mitigation. Due to the availability of different mapping methods and the large number of emerging pollutants, these methods need to be used together in decision making. The present study aims to map the contaminated areas in Richards Bay, South Africa and compare the results of ordinary kriging (OK) and inverse distance weighted (IDW) interpolation techniques. Statistical methods were also used for identifying contamination sources. Na-Cl groundwater type was dominant followed by Ca-Mg-Cl. Data analysis indicate that silicate weathering, ion exchange and fresh water-seawater mixing are the major geochemical processes controlling the presence of major ions in groundwater. Factor analysis also helped to confirm the results. Overlay analysis by OK and IDW gave different results. Areas where groundwater was unsuitable as a drinking source were 419 and 116 km(2) for OK and IDW, respectively. Such diverse results make decision making difficult, if only one method was to be used. Three highly contaminated zones within the study area were more accurately identified by OK. If large areas are identified as being contaminated such as by IDW in this study, the mitigation measures will be expensive. If these areas were underestimated, then even though management measures are taken, it will not be effective for a longer time. Use of multiple techniques like this study will help to avoid taking harsh decisions. Overall, the groundwater quality in this area was poor, and it is essential to identify alternate drinking water source or treat the groundwater before ingestion.
A vertical parallax reduction method for stereoscopic video based on adaptive interpolation
Li, Qingyu; Zhao, Yan
2016-10-01
The existence of vertical parallax is the main factor of affecting the viewing comfort of stereo video. Visual fatigue is gaining widespread attention with the booming development of 3D stereoscopic video technology. In order to reduce the vertical parallax without affecting the horizontal parallax, a self-adaptive image scaling algorithm is proposed, which can use the edge characteristics efficiently. In the meantime, the nonlinear Levenberg-Marquardt (L-M) algorithm is introduced in this paper to improve the accuracy of the transformation matrix. Firstly, the self-adaptive scaling algorithm is used for the original image interpolation. When the pixel point of original image is in the edge areas, the interpretation is implemented adaptively along the edge direction obtained by Sobel operator. Secondly the SIFT algorithm, which is invariant to scaling, rotation and affine transformation, is used to detect the feature matching points from the binocular images. Then according to the coordinate position of matching points, the transformation matrix, which can reduce the vertical parallax, is calculated using Levenberg-Marquardt algorithm. Finally, the transformation matrix is applied to target image to calculate the new coordinate position of each pixel from the view image. The experimental results show that: comparing with the method which reduces the vertical parallax using linear algorithm to calculate two-dimensional projective transformation, the proposed method improves the vertical parallax reduction obviously. At the same time, in terms of the impact on horizontal parallax, the proposed method has more similar horizontal parallax to that of the original image after vertical parallax reduction. Therefore, the proposed method can optimize the vertical parallax reduction.
庄述燕
2013-01-01
To install the reactive power compensation in grid connection point is an effective method to improve the voltage stability of wind power and ensure reliable operation. This paper designs a kind of STATCOM with superconducting magnetic energy storage. It achieves system decoupling of the feedback linearization using the inverse system method, and then controls the decoupled inverse system based on the RBF neural network sliding mode control. Simulation results show that the inverse system method and RBF neural network sliding mode control show a good effect in improving the system dynamic response speed and the system robustness. The results accord with the dynamic response characteristics of STATCOM with SMES.% 在并网点接入无功补偿器是提高电压稳定保证风电可靠运行的有效方法。设计一种带超导储能的静态无功补偿器，应用逆系统方法实现系统反馈线性化解耦，再采用RBF神经网络滑模控制对解耦逆系统进行控制。仿真结果表明：采用逆系统方法和RBF神经网络滑模控制对提高系统的动态响应速度和改善系统鲁棒性具有良好的效果，所得结果符合带超导储能的静态无功补偿器的动态响应特性。
A robust interpolation method for constructing digital elevation models from remote sensing data
Chen, Chuanfa; Liu, Fengying; Li, Yanyan; Yan, Changqing; Liu, Guolin
2016-09-01
A digital elevation model (DEM) derived from remote sensing data often suffers from outliers due to various reasons such as the physical limitation of sensors and low contrast of terrain textures. In order to reduce the effect of outliers on DEM construction, a robust algorithm of multiquadric (MQ) methodology based on M-estimators (MQ-M) was proposed. MQ-M adopts an adaptive weight function with three-parts. The weight function is null for large errors, one for small errors and quadric for others. A mathematical surface was employed to comparatively analyze the robustness of MQ-M, and its performance was compared with those of the classical MQ and a recently developed robust MQ method based on least absolute deviation (MQ-L). Numerical tests show that MQ-M is comparative to the classical MQ and superior to MQ-L when sample points follow normal and Laplace distributions, and under the presence of outliers the former is more accurate than the latter. A real-world example of DEM construction using stereo images indicates that compared with the classical interpolation methods, such as natural neighbor (NN), ordinary kriging (OK), ANUDEM, MQ-L and MQ, MQ-M has a better ability of preserving subtle terrain features. MQ-M replaces thin plate spline for reference DEM construction to assess the contribution to our recently developed multiresolution hierarchical classification method (MHC). Classifying the 15 groups of benchmark datasets provided by the ISPRS Commission demonstrates that MQ-M-based MHC is more accurate than MQ-L-based and TPS-based MHCs. MQ-M has high potential for DEM construction.
On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids
Kaus, B.; Pusok, A. E.; Popov, A.
2015-12-01
The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation
Mahacine Amrani
2008-06-01
Full Text Available Several methods are currently used to optimize edges and contours of geophysical data maps. A resistivity map was expectedto allow the electrical resistivity signal to be imaged in 2D in Moroccan resistivity survey in the phosphate mining domain. Anomalouszones of phosphate deposit “disturbances” correspond to resistivity anomalies. The resistivity measurements were taken at 5151discrete locations. Much of the geophysical spatial analysis requires a continuous data set and this study is designed to create that surface. This paper identifies the best spatial interpolation method to use for the creation of continuous data for Moroccan resistivity data of phosphate “disturbances” zones. The effectiveness of our approach for successfully reducing noise has been used much successin the analysis of stationary geophysical data as resistivity data. The interpolation filtering approach methods applied to modelingsurface phosphate “disturbances” was found to be consistently useful.
IMMUNE RBF NETWORK AND ITS APPLICATION IN THE MODULATION-STYLE RECOGNITION OF RADAR SIGNALS
Gong Xinbao; Zang Xiaogang; Zhou Xilang; Hu Guangrui
2003-01-01
Based on Immune Programming(IP), a novel Radial Basis Function (RBF) networkdesigning method is proposed. Through extracting the preliminary knowledge about the widthof the basis function as the vaccine to form the immune operator, the algorithm reduces thesearching space of canonical algorithm and improves the convergence speed. The application ofthe RBF network trained with the algorithm in the modulation-style recognition of radar signalsdemonstrates that the network has a fast convergence speed with good performances.
A Sliding Mode Control-based on a RBF Neural Network for Deburring Industry Robotic Systems
Yong Tao; Jiaqi Zheng; Yuanchang Lin
2016-01-01
A sliding mode control method based on radial basis function (RBF) neural network is proposed for the deburring of industry robotic systems. First, a dynamic model for deburring the robot system is established. Then, a conventional SMC scheme is introduced for the joint position tracking of robot manipulators. The RBF neural network based sliding mode control (RBFNN-SMC) has the ability to learn uncertain control actions. In the RBFNN-SMC scheme, the adaptive tuning algorithms for network par...
Senjean, Bruno; Jensen, Hans Jørgen Aa; Fromager, Emmanuel
2015-01-01
The computation of excitation energies in range-separated ensemble density-functional theory (DFT) is discussed. The latter approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range density functional, that complements the long-range wavefunction-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we simply propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) effectively introduces weight dependence effects. LIM has...
2014-11-19
treatment of nonaffine and nonlinear partial differential equations ., ESAIM, Math. Model. Numer. Anal. 41(3) (2007) 575–605. [8] Y. Maday, N. Nguyen, A...and Numerics of Partial Differential Equations , Vol. 4 of Springer INdAM Series, Springer Milan, 2013, pp. 221–235. [2] M. Barrault, Y. Maday, N...Nguyen, A. Patera, An empirical interpolation method: Application to efficient reduced-basis discretization of partial differential equations ., C. R
Interpolation functors and interpolation spaces
Brudnyi, Yu A
1991-01-01
The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...
Fabiano, E; Seidl, M; Della Sala, F
2016-01-01
We have tested the original interaction-strength-interpolation (ISI) exchange-correlation functional for main group chemistry. The ISI functional is based on an interpolation between the weak and strong coupling limits and includes exact-exchange as well as the G\\"orling-Levy second-order energy. We have analyzed in detail the basis-set dependence of the ISI functional, its dependence on the ground-state orbitals, and the influence of the size-consistency problem. We show and explain some of the expected limitations of the ISI functional (i.e. for atomization energies), but also unexpected results, such as the good performance for the interaction energy of dispersion-bonded complexes when the ISI correlation is used as a correction to Hartree-Fock.
Keenan, Kathryn E; Kourtis, Lampros C; Besier, Thor F; Lindsey, Derek P; Gold, Garry E; Delp, Scott L; Beaupre, Gary S
2009-08-01
Cartilage material properties are important for understanding joint function and diseases, but can be challenging to obtain. Three biphasic material properties (aggregate modulus, Poisson's ratio and permeability) can be determined using an analytical or finite element model combined with optimisation to find the material properties values that best reproduce an experimental creep curve. The purpose of this study was to develop an easy-to-use resource to determine biphasic cartilage material properties. A Cartilage Interpolant Response Surface was generated from interpolation of finite element simulations of creep indentation tests. Creep indentation tests were performed on five sites across a tibial plateau. A least-squares residual search of the Cartilage Interpolant Response Surface resulted in a best-fit curve for each experimental condition with corresponding material properties. These sites provided a representative range of aggregate moduli (0.48-1.58 MPa), Poisson's ratio (0.00-0.05) and permeability (1.7 x 10(- 15)-5.4 x 10(- 15) m(4)/N s) values found in human cartilage. The resource is freely available from https://simtk.org/home/va-squish.
Fuzzy linguistic model for interpolation
Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of); Adabitabar Firozja, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of)
2007-10-15
In this paper, a fuzzy method for interpolating of smooth curves was represented. We present a novel approach to interpolate real data by applying the universal approximation method. In proposed method, fuzzy linguistic model (FLM) applied as universal approximation for any nonlinear continuous function. Finally, we give some numerical examples and compare the proposed method with spline method.
Kaplan, A.; Smerdon, J. E.; Evans, M. N.
2010-12-01
Current-generation climate field reconstruction (CFR) methods, which are used to estimate, e.g., surface temperature values (t) at a predetermined grid from a synchronously available vector of proxy values (p), seek solutions assuming that a linear transform (B) connects deviations of these variables from their respective means tm and pm: t-tm=B(p-p_m). The transform operator B here would be a standard linear regression matrix B=Ctp}C{pp-1 (with Ctp= and Cpp= being cross-covariance and covariance matrices for t and p respectively) if only these matrices could be robustly calculated from available data. As things usually stand, however, instrumental data sets of t available for computing its cross-covariance with p can never provide more than 100-150 annual samples. On the other hand, due to a relatively low signal-to-noise ratio of individual proxy records, their assemblies used in global reconstructions normaly include on the order of 100 records or more. Hence various methods for regularizing the inversion of Cpp are used: ridge regression, truncated total least squares, canonical correlation analysis, local regression, etc. Suppose, however, that the target climate field is Gaussian with a known covariance C: t ˜{N}(tm,C), while a proxy vector is obtained from it by a known linear transform H (``proxy forward model''), subject to a Gaussian error: p=Ht+\\varepsilon, \\varepsilon ˜{N}(0,R). In this case, Cpp=HCHT+R and Ctp=CHT, so that under the regression solution given above becomes an optimal interpolation (OI) solution hat {t}=CHT(HCH^T+R)-1p with error covariance Q=C-CHT(HCH^T+R)-1HC. Moreover, the posterior distribution of t conditional on p is [t|p] ˜ {N}(hat {t},Q). If available climate records were very long, the distinction between the sample regression estimate and the better structured OI solution would be immaterial: the covariances estimated from the available sample would produce a result approaching the OI solution. However, under the reality
JinKui Wu; ShiWei Liu; LePing Ma; Jia Qin; JiaXin Zhou; Hong Wei
2016-01-01
The accuracy of spatial interpolation of precipitation data is determined by the actual spatial variability of the precipitation, the interpolation method, and the distribution of observatories whose selections are particularly important. In this paper, three spatial sampling programs, including spatial random sampling, spatial stratified sampling, and spatial sandwich sampling, are used to analyze the data from meteorological stations of northwestern China. We compared the accuracy of ordinary Kriging interpolation methods on the basis of the sampling results. The error values of the regional annual pre-cipitation interpolation based on spatial sandwich sampling, including ME (0.1513), RMSE (95.91), ASE (101.84), MSE (−0.0036), and RMSSE (1.0397), were optimal under the premise of abundant prior knowledge. The result of spatial stratified sampling was poor, and spatial random sampling was even worse. Spatial sandwich sampling was the best sampling method, which minimized the error of regional precipitation estimation. It had a higher degree of accuracy compared with the other two methods and a wider scope of application.
Đurđević, Boris; Jug, Irena; Jug, Danijel; Vukadinović, Vesna; Bogunović, Igor; Brozović, Bojana; Stipešević, Bojan
2017-04-01
Soil organic matter (SOM) plays crucial role in soil health and productivity and represents one of the key functions for determining soil degradation and soil suitability for crop production. Nowadays, continuing decline of organic matter in soils in agroecosystems, due to inappropriate agricultural practice (burning and removal of crop residue, overgrazing, inappropriate tillage, etc.) and environmental conditions (climate change, extreme weather conditions, erosion) leads to devastating soil degradation processes and decreases soil productivity. The main objectives of this research is to compare three different interpolation methods (Inverse Distance Weighting IDW, Ordinary kriging OK and Empirical Bayesian Kriging EBK) and provide best spatial predictor in order to ensure detailed analysis of the agricultural land in Osijek-Baranja County, Croatia. A number of 9,099 soil samples have been compiled from layer 0-30 cm and analyzed in laboratory. The average value of SOM in the study area was 2.66%, while 70.7 % of samples had SOM value below 3% in Osijek-Baranja County. Among the applied methods, the lowest root mean square error was recorded under Empirical Bayesian Kriging method which had most accurately assessed soil organic matter. The main advantage of EBK is that the process of creating a valid kriging model is automated so the manual parameter adjusting is eliminated, and this resulted with reduced uncertainty of EBK model. Conducted interpolation and visualization of data showed that 85.7% of agricultural land in Osijek-Baranja County has SOM content lower than 3%, which may indicate some sort of soil degradation process. By using interpolation methods combined with visualization of data, we can detect problematic areas much easier and with additional analysis, suggest measures to repair degraded soils. This kind of approach to problem solving in agriculture can be applied on various agroecological conditions and can significantly facilitate and
王冬生; 李世华; 周杏鹏
2011-01-01
针对自来水生产过程的原水水质评价问题,提出了一种基于PSO-RBF神经网络模型的原水水质评价方法.首先,根据水厂生产经验和历史数据分析,制定面向自来水生产过程的原水水质评价标准.然后,采用粒子群优化(PSO)算法训练的RBF神经网络模型,对苏州市相城水厂的进厂原水水质实施在线评价.最后,将进厂原水水质在线评价结果作为前馈量,增加相城水厂药剂(矾和臭氧)投加过程的前馈控制环节,使得药剂投加量能够根据原水水质的变化及时做出调整.实际应用效果表明,与改进前的反馈控制过程相比,过程出水水质更加平稳,提高了自来水生产过程应对原水水质变化的能力.%In consideration of the assessment problem of raw water quality oriented to drinking water treatment process, an assessment method of raw rater quality based on the PSO-RBF neural network model is proposed. First, on the basis of productive experiences and analysis of historical data in the waterworks, an assessment standard oriented to the process of drinking water treatment is established. Then, the radial basis function (RBF) neural network model trained by the particle swarm optimization ( PSO) algorithm is used for the on-line assessment of raw water quality in the Xiangcheng Waterworks of Suzhou city. Finally, feed-forward control elements are added to the pharmaceutical (alum and ozone) dosing control processes of Xiangcheng Waterworks, using the online assessment result as the feed-forward compensation. The results of the practical operation show that the produced water quality becomes more stable, and the adaptation ability of drinking water treatment to the variation of raw water quality is improved.
Santillan, J. R.; Serviano, J. L.; Makinano-Santillan, M.; Marqueso, J. T.
2016-09-01
In this paper, we investigated how survey configuration and the type of interpolation method can affect the accuracy of river flow simulations that utilize LIDAR DTM integrated with interpolated river bed as its main source of topographic information. Aside from determining the accuracy of the individually-generated river bed topographies, we also assessed the overall accuracy of the river flow simulations in terms of maximum flood depth and extent. Four survey configurations consisting of river bed elevation data points arranged as cross-section (XS), zig-zag (ZZ), river banks-centerline (RBCL), and river banks-centerline-zig-zag (RBCLZZ), and two interpolation methods (Inverse Distance-Weighted and Ordinary Kriging) were considered. Major results show that the choice of survey configuration, rather than the interpolation method, has significant effect on the accuracy of interpolated river bed surfaces, and subsequently on the accuracy of river flow simulations. The RMSEs of the interpolated surfaces and the model results vary from one configuration to another, and depends on how each configuration evenly collects river bed elevation data points. The large RMSEs for the RBCL configuration and the low RMSEs for the XS configuration confirm that as the data points become evenly spaced and cover more portions of the river, the resulting interpolated surface and the river flow simulation where it was used also become more accurate. The XS configuration with Ordinary Kriging (OK) as interpolation method provided the best river bed interpolation and river flow simulation results. The RBCL configuration, regardless of the interpolation algorithm used, resulted to least accurate river bed surfaces and simulation results. Based on the accuracy analysis, the use of XS configuration to collect river bed data points and applying the OK method to interpolate the river bed topography are the best methods to use to produce satisfactory river flow simulation outputs. The use of
J. R. Santillan
2016-09-01
Full Text Available In this paper, we investigated how survey configuration and the type of interpolation method can affect the accuracy of river flow simulations that utilize LIDAR DTM integrated with interpolated river bed as its main source of topographic information. Aside from determining the accuracy of the individually-generated river bed topographies, we also assessed the overall accuracy of the river flow simulations in terms of maximum flood depth and extent. Four survey configurations consisting of river bed elevation data points arranged as cross-section (XS, zig-zag (ZZ, river banks-centerline (RBCL, and river banks-centerline-zig-zag (RBCLZZ, and two interpolation methods (Inverse Distance-Weighted and Ordinary Kriging were considered. Major results show that the choice of survey configuration, rather than the interpolation method, has significant effect on the accuracy of interpolated river bed surfaces, and subsequently on the accuracy of river flow simulations. The RMSEs of the interpolated surfaces and the model results vary from one configuration to another, and depends on how each configuration evenly collects river bed elevation data points. The large RMSEs for the RBCL configuration and the low RMSEs for the XS configuration confirm that as the data points become evenly spaced and cover more portions of the river, the resulting interpolated surface and the river flow simulation where it was used also become more accurate. The XS configuration with Ordinary Kriging (OK as interpolation method provided the best river bed interpolation and river flow simulation results. The RBCL configuration, regardless of the interpolation algorithm used, resulted to least accurate river bed surfaces and simulation results. Based on the accuracy analysis, the use of XS configuration to collect river bed data points and applying the OK method to interpolate the river bed topography are the best methods to use to produce satisfactory river flow simulation outputs
Spatiotemporal Interpolation for Environmental Modelling
Ferry Susanto; Paulo de Souza; Jing He
2016-01-01
A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hy...
Improved Ternary Subdivision Interpolation Scheme
WANG Huawei; QIN Kaihuai
2005-01-01
An improved ternary subdivision interpolation scheme was developed for computer graphics applications that can manipulate open control polygons unlike the previous ternary scheme, with the resulting curve proved to be still C2-continuous. Parameterizations of the limit curve near the two endpoints are given with expressions for the boundary derivatives. The split joint problem is handled with the interpolating ternary subdivision scheme. The improved scheme can be used for modeling interpolation curves in computer aided geometric design systems, and provides a method for joining two limit curves of interpolating ternary subdivisions.
Despax, Aurélien; Perret, Christian; Garçon, Rémy; Hauet, Alexandre; Belleville, Arnaud; Le Coz, Jérôme; Favre, Anne-Catherine
2016-04-01
Quantifying the quality of discharge measurements by uncertainty analysis is a challenge in the hydrometric community. Discharge measurements are the first step to produce hydrometric data which are used in many hydrological studies like design of hydraulic structures or calibration of hydrological models for flood forecasting and warning. Thus associated uncertainty has to be estimated carefully. The velocity-area method is a common approach for estimating river discharge. It consists in integrating depths and point velocities through the cross-section. Due to the limited number of point measurements, the quality of the measurement depends mainly on the sampling strategy. Different methods of uncertainty estimation are available in the literature (ISO 748, Q+ and IVE). The main uncertainty component, noted um, is often related to the cross-sectional interpolation errors. However the computation of this term according to these approaches does not evaluate both the sampling strategy and the complexity of the cross-section. The FLAURE method (FLow Analog UnceRtainty Estimation) includes a new methodology to estimate this term. It is based on the study of high-resolution stream-gaugings (i.e. reference stream-gaugings made with a high number of verticals). The high-resolution measurements are first subsampled by reducing the number of verticals to generate a sample of realistic stream-gaugings. A statistical analysis is performed to estimate the um component and then a sampling quality index is defined. For each reference stream-gauging, it leads to a curve of um component as a function of the sampling quality index. This set of curves is finally used to compute the um component of any routine stream-gauging. Curves are then selected according to the similitude between the routine stream-gauging and reference stream-gaugings. The similitude between the routine stream-gauging and reference stream-gaugings is evaluated thanks to the Nash criteria computed on lateral
Performance Investigation of the RBF Localization Algorithm
Juraj Machaj
2013-01-01
Full Text Available In the present paper the impact of network properties on localization accuracy of Rank Based Fingerprinting algorithm will be investigated. Rank Based Fingerprinting (RBF will be described in detail together with Nearest Neighbour fingerprinting algorithms. RBF algorithm is a new algorithm and was designed as improvement of standard fingerprinting algorithms. Therefore exhaustive testing needs to be performed. This testing is mainly focused on optimal distribution of APs and its impact on positioning accuracy. Simulations were performed in Matlab environment in three different scenarios. In the first scenario different numbers of APs were implemented in the area to estimate the impact of APs number on the localization accuracy of the Rank Based Fingerprinting algorithm. The second scenario was introduced to evaluate the impact of APs placement in the localization area on the accuracy of the positioning using fingerprinting algorithms. The last scenario was proposed to investigate an impact of the number of heard APs and distribution of the RSS values on the accuracy of the RBF algorithm. Results achieved by the RBF algorithm in the first and second scenarios were compared to commonly used NN and WKNN algorithms.
铁路扣件图像检测中的RBF-SVM模型优化%Optimization of RBF-SVM model in railway fastener detection system
刘甲甲; 王凯; 袁建英; 江晓亮; 李柏林
2014-01-01
在开发的铁路扣件检测系统中，RBF-SVM被作为扣件图像分类识别的分类器。核参数的选择是RBF-SVM模型优化研究中的重要问题，将量子粒子群算法应用于参数的优化选择，在(c，γ)参数可调范围内产生初始种群，将种群中的个体作为RBF-SVM的参数进行学习；经过多次迭代获得最佳参数对(c，γ)，并将该参数对作为RBF-SVM的核参数训练支持向量机。实验表明，QPSO的性能优于传统的 PSO算法，该方法在解决支持向量机优化方面表现出了高效的收敛性和稳定性，并且在该方法的基础上形成的铁路扣件检测算法是切实可行的。%In the railway fastener detection system, RBF-SVM is used as image classifier for railway fasteners. The selection of kernel parameters is an important problem in RBF-SVM research. A parameter selection method based on quantum genet-ic algorithm(QPSO)is presented. Initial population is produced in the adjustable range of parameters c and γ, and individuals in it are used as the parameters of RBF-SVM to calculation; then by multi-iterations, the parameters (c,γ) are obtained which are corresponding to fitness of population, and used as kernel parameters of Radial Basis kernel Function of Support Vector Machine(RBF-SVM)to training model. The experimental results indicate that the QPSO algorithm outperforms PSO algorithm. It has a high convergence and stability, and the detection algorithm of rail fastener based on it is practicable.
Wu, Wei; Tang, Xiao-Ping; Ma, Xue-Qing; Liu, Hong-Bin
2016-08-01
Soil temperature variability data provide valuable information on understanding land-surface ecosystem processes and climate change. This study developed and analyzed a spatial dataset of monthly mean soil temperature at a depth of 10 cm over a complex topographical region in southwestern China. The records were measured at 83 stations during the period of 1961-2000. Nine approaches were compared for interpolating soil temperature. The accuracy indicators were root mean square error (RMSE), modelling efficiency (ME), and coefficient of residual mass (CRM). The results indicated that thin plate spline with latitude, longitude, and elevation gave the best performance with RMSE varying between 0.425 and 0.592 °C, ME between 0.895 and 0.947, and CRM between -0.007 and 0.001. A spatial database was developed based on the best model. The dataset showed that larger seasonal changes of soil temperature were from autumn to winter over the region. The northern and eastern areas with hilly and low-middle mountains experienced larger seasonal changes.
Spatial interpolation approach based on IDW with anisotropic spatial structures
Li, Jia; Duan, Ping; Sheng, Yehua; Lv, Haiyang
2015-12-01
In many interpolation methods, with its simple interpolation principle, Inverse distance weighted (IDW) interpolation is one of the most common interpolation method. There are anisotropic spatial structures with actual geographical spatial phenomenon. When the IDW interpolation is used, anisotropic spatial structures should be considered. Geostatistical theory has a characteristics of exploring anisotropic spatial structures. In this paper, spatial interpolation approach based on IDW with anisotropic spatial structures is proposed. The DEM data is tested in this paper to prove reliability of the IDW interpolation considering anisotropic spatial structures. Experimental results show that IDW interpolation considering anisotropic spatial structures can improve interpolation precision when sampling data has anisotropic spatial structures feature.
CLASSIFICATIONS OF EEG SIGNALS FOR MENTAL TASKS USING ADAPTIVE RBF NETWORK
薛建中; 郑崇勋; 闫相国
2004-01-01
Objective This paper presents classifications of mental tasks based on EEG signals using an adaptive Radial Basis Function (RBF) network with optimal centers and widths for the Brain-Computer Interface (BCI) schemes. Methods Initial centers and widths of the network are selected by a cluster estimation method based on the distribution of the training set. Using a conjugate gradient descent method, they are optimized during training phase according to a regularized error function considering the influence of their changes to output values. Results The optimizing process improves the performance of RBF network, and its best cognition rate of three task pairs over four subjects achieves 87.0%. Moreover, this network runs fast due to the fewer hidden layer neurons. Conclusion The adaptive RBF network with optimal centers and widths has high recognition rate and runs fast. It may be a promising classifier for on-line BCI scheme.
何耀耀; 许启发; 杨善林; 余本功
2013-01-01
According to the problem of short-term load forecasting in the power system, this paper proposed a probability density forecasting method using radical basis function (RBF) neural network quantile regression based on the existed researches on combination forecasting and probability interval prediction. The probability density function of load at any period in a day was evaluated. The proposed method can obtain more useful information than point prediction and interval prediction, and can implement the whole probability distribution forecasting for future load. The practical data of a city in China show that the proposed probability density forecasting method can gain more accurate result of point prediction and obtain the forecasting results of integrated probability density function of short-term load.%针对电力系统短期负荷预测问题,在现有的组合预测和概率性区间预测的基础上,提出了基于RBF神经网络分位数回归的概率密度预测方法,得出未来一天中任意时期负荷的概率密度函数,可以得到比点预测和区间预测更多的有用信息,实现了对未来负荷完整概率分布的预测.中国某市实际数据的预测结果表明,提出的概率密度预测方法不仅能得出较为精确的点预测结果,而且能够获得短期负荷完整的概率密度函数预测结果.
Normalized RBF networks: application to a system of integral equations
Golbabai, A; Seifollahi, S; Javidi, M [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: golbabai@iust.ac.ir, E-mail: seif@iust.ac.ir, E-mail: mojavidi@yahoo.com
2008-07-15
Linear integral and integro-differential equations of Fredholm and Volterra types have been successfully treated using radial basis function (RBF) networks in previous works. This paper deals with the case of a system of integral equations of Fredholm and Volterra types with a normalized radial basis function (NRBF) network. A novel learning algorithm is developed for the training of NRBF networks in which the BFGS backpropagation (BFGS-BP) least-squares optimization method as a recursive model is used. In the approach presented here, a trial solution is given by an NRBF network of incremental architecture with a set of unknown parameters. Detailed learning algorithms and concrete examples are also included.
Transfinite thin plate spline interpolation
Bejancu, Aurelian
2009-01-01
Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves or hypersurfaces, Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo Levi type to construct a semi-cardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon type functional.
Ruelland, D.; Ardoin-Bardin, S.; Billen, G.; Servat, E.
2008-10-01
SummaryThis paper examines the sensitivity of a hydrological model to several methods of spatial interpolation of rainfall data. The question is investigated in a context of scarcity of data over a large West African catchment (100,000 km 2) subject to a drastic trend of rain deficit since the 1970s. Thirteen widely scattered rainfall stations and their daily time series were used to interpolate gridded rainfall surfaces over the 1950-1992 period via various methods: Thiessen polygons, inverse distance weighted (IDW) method, thin smooth plate splines (spline), and ordinary kriging. The accuracy of these interpolated datasets was evaluated using two complementary approaches. First, a point-by-point assessment was conducted, involving comparison of the interpolated values by reference to observed point data. Second, a conceptual rainfall-runoff model (Hydrostrahler) was used in order to assess whether and to what extent the alternative sets of interpolated rainfall impacted on the hydrological simulations. A lumped modelling exercise over a long period (1952-1992) and a semi-distributed exercise over a short period (1971-1976) were performed, using calibrations aimed at optimizing a Nash-Sutcliffe criterion. The results were evaluated for each interpolated forcing dataset using statistical analysis and visual inspection of the simulated and observed hydrographs and the parameters obtained from calibration. Assessment of the interpolation methods by reference to point data indicates that interpolations using the IDW and kriging methods are more efficient than the simple Thiessen technique, and, to a lesser extent, than spline. The use of these data in a daily lumped modelling application shows a different ranking of the various interpolation methods with regard to various hydrological assessments. The model is particularly sensitive to the differences in the rainfall input volume produced by each interpolation method: the IDW dataset yields the highest hydrological
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
构造向量值有理插值函数的一种新方法%A NEW METHOD OF CONSTRUCTING VECTOR-VALUED RATIONAL INTERPOLATION FUNCTION
郑林; 朱功勤
2011-01-01
There is no general conclusion for the existence of vector-valued rational interpolation function based on the continued fraction expression, then the suitability of the construction method is restricted. This paper presents a new interpolation method and gives a simple algorithm to compute the vector-valued rational interpolation function. This method uses a special polynomial which is not based on the continued fraction form. The numerical example given illustrates the efficiency of the method.
Comparison of deterministic and stochastic methods to predict spatial variation of groundwater depth
Adhikary, Partha Pratim; Dash, Ch. Jyotiprava
2014-11-01
Accurate and reliable interpolation of groundwater depth over a region is a pre-requisite for efficient planning and management of water resources. The performance of two deterministic, such as inverse distance weighting (IDW) and radial basis function (RBF) and two stochastic, i.e., ordinary kriging (OK) and universal kriging (UK) interpolation methods was compared to predict spatio-temporal variation of groundwater depth. Pre- and post-monsoon groundwater level data for the year 2006 from 110 different locations over Delhi were used. Analyses revealed that OK and UK methods outperformed the IDW method, and UK performed better than OK. RBF also performed better than IDW and OK. IDW and RBF methods slightly underestimated and both the kriging methods slightly overestimated the prediction of water table depth. OK, RBF and UK yielded 27.52, 27.66 and 51.11 % lower RMSE, 27.49, 35.34 and 51.28 % lower MRE, and 14.21, 16.12 and 21.36 % higher R 2 over IDW. The isodepth-area curves indicated the possibility of exploitation of groundwater up to a depth of 20 m.
Birkholz, Adam B; Schlegel, H Bernhard
2016-05-14
Reaction path optimization is being used more frequently as an alternative to the standard practice of locating a transition state and following the path downhill. The Variational Reaction Coordinate (VRC) method was proposed as an alternative to chain-of-states methods like nudged elastic band and string method. The VRC method represents the path using a linear expansion of continuous basis functions, allowing the path to be optimized variationally by updating the expansion coefficients to minimize the line integral of the potential energy gradient norm, referred to as the Variational Reaction Energy (VRE) of the path. When constraints are used to control the spacing of basis functions and to couple the minimization of the VRE with the optimization of one or more individual points along the path (representing transition states and intermediates), an approximate path as well as the converged geometries of transition states and intermediates along the path are determined in only a few iterations. This algorithmic efficiency comes at a high per-iteration cost due to numerical integration of the VRE derivatives. In the present work, methods for incorporating redundant internal coordinates and potential energy surface interpolation into the VRC method are described. With these methods, the per-iteration cost, in terms of the number of potential energy surface evaluations, of the VRC method is reduced while the high algorithmic efficiency is maintained.
Classification based polynomial image interpolation
Lenke, Sebastian; Schröder, Hartmut
2008-02-01
Due to the fast migration of high resolution displays for home and office environments there is a strong demand for high quality picture scaling. This is caused on the one hand by large picture sizes and on the other hand due to an enhanced visibility of picture artifacts on these displays [1]. There are many proposals for an enhanced spatial interpolation adaptively matched to picture contents like e.g. edges. The drawback of these approaches is the normally integer and often limited interpolation factor. In order to achieve rational factors there exist combinations of adaptive and non adaptive linear filters, but due to the non adaptive step the overall quality is notably limited. We present in this paper a content adaptive polyphase interpolation method which uses "offline" trained filter coefficients and an "online" linear filtering depending on a simple classification of the input situation. Furthermore we present a new approach to a content adaptive interpolation polynomial, which allows arbitrary polyphase interpolation factors at runtime and further improves the overall interpolation quality. The main goal of our new approach is to optimize interpolation quality by adapting higher order polynomials directly to the image content. In addition we derive filter constraints for enhanced picture quality. Furthermore we extend the classification based filtering to the temporal dimension in order to use it for an intermediate image interpolation.
Valentín-Vargas, Alexis; Chorover, Jon; Maier, Raina M
2013-02-15
The Standard-Based Polynomial Interpolation (SBPIn) method is a new simple three-step protocol proposed to address common gel-to-gel variations for the comparison of sample profiles across multiple DGGE gels. The advantages of this method include no requirement for additional software or modification of the standard DGGE protocol.
Valentín-Vargas, Alexis; Chorover, Jon; Maier, Raina M.
2013-01-01
The Standard-Based Polynomial Interpolation (SBPIn) method is a new simple three-step protocol proposed to address common gel-to-gel variations for the comparison of sample profiles across multiple DGGE gels. The advantages of this method include no requirement for additional software or modification of the standard DGGE protocol. PMID:23234884
General Structures of Block Based Interpolational Function
ZOU LE; TANG SHUO; Ma Fu-ming
2012-01-01
We construct general structures of one and two variable interpolation function,without depending on the existence of divided difference or inverse differences,and we also discuss the block based osculatory interpolation in one variable case.Clearly,our method offers many flexible interpolation schemes for choices.Error terms for the interpolation are determined and numerical examples are given to show the effectiveness of the results.
Inverse Distance Weighted Interpolation Involving Position Shading
Li, Zhengquan; WU Yaoxiang
2015-01-01
Considering the shortcomings of inverse distance weighted (IDW) interpolation in practical applications, this study improved the IDW algorithm and put forward a new spatial interpolation method that named as adjusted inverse distance weighted (AIDW). In interpolating process, the AIDW is capable of taking into account the comprehensive influence of distance and position of sample point to interpolation point, by adding a coefficient (K) into the normal IDW formula. The coefficient (K) is used...
WU Guofeng; Jan de Leeuw; Andrew K. Skidmore; LIU Yaolin; Herbert H. T. Prins
2010-01-01
Measurements of photosynthetically active radiation (PAR), which are indispensable for simulating plant growth and productivity, are generally very scarce. This study aimed to compare two extrapolation and one interpolation methods for estimating daily PAR reaching the earth surface within the Poyang Lake national nature reserve, China. The daily global solar radiation records at Nanchang meteorological station and daily sunshine duration measurements at nine meteorological stations around Poyang Lake were obtained to achieve the objective. Two extrapolation methods of PARs using recorded and estimated global solar radiation at Nanchang station and three stations (Yongxiu, Xingzi and Duchang) near the nature reserve were carried out, respectively, and a spatial interpolation method combining triangulated irregular network (TIN) and inverse distance weighting (IDW) was implemented to estimate daily PAR. The performance evaluation of the three methods using the PARs measured at Dahuchi Conservation Station (day number of measurement = 105 days) revealed that: (1) the spatial interpolation method achieved the best PAR estimation (R2 = 0.89, s.e. = 0.99, F = 830.02, P ＜ 0.001＝; (2) the extrapolation method from Nanchang station obtained an unbiased result (R2 = 0.88, s.e. = 0.99, F = 745.29, P ＜ 0.001＝; however, (3) the extrapolation methods from Yongxiu, Xingzi and Duchang stations were not suitable for this specific site for their biased estimations. Considering the assumptions and principles supporting the extrapolation and interpolation methods, the authors conclude that the spatial interpolation method produces more reliable results than the extrapolation methods and holds the greatest potential in all tested methods, and more PAR measurements should be recorded to evaluate the seasonal, yearly and spatial stabilities of these models for their application to the whole nature reserve of Poyang Lake.
Myocardial Strain Imaging with High-Performance Adaptive Dynamic Grid Interpolation Method
Shuhui Bu,; Makoto Yamakawa,; Tsuyoshi Shiina,
2010-07-01
The accurate assessment of local myocardial strain is important for diagnosing ischemic heart diseases because decreased myocardial motion often appears in the early stage. Calculating the spatial derivation of displacement is a necessary step in the strain calculation, but the numerical calculation is extremely sensitive to noise. Commonly used smoothing methods are the moving-average and median filters; however, these methods have a trade-off between spatial resolution and accuracy. A novel smoothing/fitting method is proposed for overcoming this problem. In this method, the detected displacement vectors are discretized at mesh nodes, and virtual springs are connected between adjacent nodes. By controlling the elasticity of the virtual springs, misdetected displacements are fitted without the above problem. Further improvements can be achieved by applying a Kalman filter for position tracking, and then calculating the strain from the accumulated displacement vectors. From the simulation results, we conclude that the proposed method improves the accuracy and spatial resolution of the strain images.
A Model to Predict Rolling Force of Finishing Stands with RBF Neural Networks
无
2005-01-01
In view of intrinsic imperfection of traditional models of rolling force, in order to improve the prediction accuracy of rolling force, a new method combining radial basis function (RBF) neural networks with traditional models to predict rolling force was proposed. The off-line simulation indicates that the predicted results are much more accurate than that with traditional models.
RBF-Type Artificial Neural Network Model Applied in Alloy Design of Steels
YOU Wei; LIU Ya-xiu; BAI Bing-zhe; FANG Hong-sheng
2008-01-01
RBF model, a new type of artificial neural network model was developed to design the content of carbon in low-alloy engineering steels. The errors of the ANN model are. MSE 0. 052 1, MSRE 17. 85%, and VOF 1. 932 9. The results obtained are satisfactory. The method is a powerful aid for designing new steels.
Li, Lixin; Zhou, Xiaolu; Kalo, Marc; Piltner, Reinhard
2016-07-25
Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF)-based and inverse distance weighting (IDW)-based spatiotemporal interpolation methods on a data set of PM2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM), is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM2.5 refers to particles with a mean aerodynamic diameter less than or equal to 2.5 micrometers. Based on the error statistics results of k-fold cross validation, the SF-based method performed better overall than the IDW-based method. The interpolation results generated by the SF-based method are combined with population data to estimate the population exposure to PM2.5 in the contiguous U.S. We investigated the seasonal variations, identified areas where annual and daily PM2.5 were above the standards, and calculated the population size in these areas. Finally, a web application is developed to interpolate and visualize in real time the spatiotemporal variation of ambient air pollution across the contiguous U.S. using air pollution data from the U.S. Environmental Protection Agency (EPA)'s AirNow program.
Lixin Li
2016-07-01
Full Text Available Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF-based and inverse distance weighting (IDW-based spatiotemporal interpolation methods on a data set of PM2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM, is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM2.5 refers to particles with a mean aerodynamic diameter less than or equal to 2.5 micrometers. Based on the error statistics results of k-fold cross validation, the SF-based method performed better overall than the IDW-based method. The interpolation results generated by the SF-based method are combined with population data to estimate the population exposure to PM2.5 in the contiguous U.S. We investigated the seasonal variations, identified areas where annual and daily PM2.5 were above the standards, and calculated the population size in these areas. Finally, a web application is developed to interpolate and visualize in real time the spatiotemporal variation of ambient air pollution across the contiguous U.S. using air pollution data from the U.S. Environmental Protection Agency (EPA’s AirNow program.
Spatiotemporal Interpolation for Environmental Modelling
Ferry Susanto
2016-08-01
Full Text Available A variation of the reduction-based approach to spatiotemporal interpolation (STI, in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications.
Spatiotemporal Interpolation for Environmental Modelling.
Susanto, Ferry; de Souza, Paulo; He, Jing
2016-08-06
A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania's South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW) method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications.
Dmitrijus Styra
2011-04-01
Full Text Available Equivalent dose rate measurements were carried out in the Baltic Sea coast near Juodkrantė. The measurements were performed at the ground level and 1 meter above it at 63 points within the territory of 2,0´0,2 km on 2 July 2008 and 10 July 2008 under conditions of northern and southern wind directions respectively. The extreme rates of the equivalent dose rate were 51 and 90 nSv/h respectively which means that the structure of the equivalent dose field was unhomogeneous. The method of optimal interpollation was used to calculate and evaluate the structure of the equivalent dose rate field. This method was used in 3 cases when 63, 33 and 18 numbers of measurement were carried out. The identical structures of the equivalent dose field were accepted. Using 18 measurement points, coincidence between the measured and calculated values of the equivalent dose rate was satisfactory. Difference between the measured and calculated values does not exceed 15% in 80% of the measurement points.Article in Lithuanian
Krypiak-Gregorczyk, Anna; Wielgosz, Paweł; Jarmołowski, Wojciech
2017-04-01
The ionosphere plays a crucial role in space weather that affects satellite navigation as the ionospheric delay is one of the major errors in GNSS. On the other hand, GNSS observations are widely used to determine the amount of ionospheric total electron content (TEC). An important aspect in the electron content estimation at regional and global scale is adopting the appropriate interpolation strategy. In this paper we propose and validate a new method for regional TEC modeling based on least squares collocation (LSC) with noise variance estimation. This method allows for providing accurate TEC maps with high spatial and temporal resolution. Such maps may be used to support precise GNSS positioning and navigation, e.g. in RTK mode and also in the ionosphere studies. To test applicability of new TEC maps to positioning, double-difference ionospheric corrections were derived from the maps and their accuracy was analyzed. In addition, the corrections were applied to GNSS positioning and validated in ambiguity resolution domain. The tests were carried out during a strong ionospheric storm when the ionosphere is particularly difficult to model. The performance of the new approach was compared to IGS and UPC global, and CODE regional TEC maps. The results showed an advantage of our solution with resulting accuracy of the relative ionospheric corrections usually better than 10 cm, even during the ionospheric disturbances. This proves suitability of our regional TEC maps for, e.g. supporting fast ambiguity resolution in kinematic GNSS positioning.
Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Institut Matematik Kejuruteraan (IMK), Universiti Malaysia Perlis, 02600 Arau, Perlis (Malaysia); Saaban, Azizan, E-mail: azizan.s@uum.edu.my [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu, E-mail: mohdnazari@perlis.uitm.edu.my [Faculty of Applied Science, Universiti Teknologi Mara, 02600 Arau, Perlis (Malaysia)
2015-12-11
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu
2015-12-01
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
A Regularized SNPOM for Stable Parameter Estimation of RBF-AR(X) Model.
Zeng, Xiaoyong; Peng, Hui; Zhou, Feng
2017-01-20
Recently, the radial basis function (RBF) network-style coefficients AutoRegressive (with exogenous inputs) [RBF-AR(X)] model identified by the structured nonlinear parameter optimization method (SNPOM) has attracted considerable interest because of its significant performance in nonlinear system modeling. However, this promising technique may occasionally confront the problem that the parameters are divergent in the optimization process, which may be a potential issue ignored by most researchers. In this paper, a regularized SNPOM, together with the regularization parameter detection technique, is presented to estimate the parameters of RBF-AR(X) models. This approach first separates the parameters of an RBF-AR(X) model into a linear parameters set and a nonlinear parameters set, and then combines a gradient-based nonlinear optimization algorithm for estimating the nonlinear parameters and the regularized least squares method for estimating the linear parameters. Several examples demonstrate that the proposed approach is effective to cope with the potential unstable problem in the parameters search process, and may also yield better or similar multistep forecasting accuracy and better robustness than the previous method.
Gap interpolation by inpainting methods : Application to Ground and Space-based Asteroseismic data
Pires, Sandrine; Garcia, Rafael A; Ballot, Jérôme; Stello, Dennis; Sato, Kumiko
2014-01-01
In asteroseismology, the observed time series often suffers from incomplete time coverage due to gaps. The presence of periodic gaps may generate spurious peaks in the power spectrum that limit the analysis of the data. Various methods have been developed to deal with gaps in time series data. However, it is still important to improve these methods to be able to extract all the possible information contained in the data. In this paper, we propose a new approach to handle the problem, the so-called inpainting method. This technique, based on a sparsity prior, enables to judiciously fill-in the gaps in the data, preserving the asteroseismic signal, as far as possible. The impact of the observational window function is reduced and the interpretation of the power spectrum is simplified. This method is applied both on ground and space-based data. It appears that the inpainting technique improves the oscillation modes detection and estimation. Additionally, it can be used to study very long time series of many star...
Interpolation theory of anisotropic finite elements and applications
CHEN ShaoChun; XIAO LiuChao
2008-01-01
Interpolation theory is the foundation of finite element methods. In this paper, after reviewing some existed interpolation theorems of anisotropic finite element methods, we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
Interpolation theory of anisotropic finite elements and applications
2008-01-01
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton’s formula of polynomial interpolation as well as its applications.
Calculation of electromagnetic parameter based on interpolation algorithm
Zhang, Wenqiang, E-mail: zwqcau@gmail.com [College of Engineering, China Agricultural University, Beijing 100083 (China); Bionic and Micro/Nano/Bio Manufacturing Technology Research Center, Beihang University, Beijing 100191 (China); Yuan, Liming; Zhang, Deyuan [Bionic and Micro/Nano/Bio Manufacturing Technology Research Center, Beihang University, Beijing 100191 (China)
2015-11-01
Wave-absorbing material is an important functional material of electromagnetic protection. The wave-absorbing characteristics depend on the electromagnetic parameter of mixed media. In order to accurately predict the electromagnetic parameter of mixed media and facilitate the design of wave-absorbing material, based on the electromagnetic parameters of spherical and flaky carbonyl iron mixture of paraffin base, this paper studied two different interpolation methods: Lagrange interpolation and Hermite interpolation of electromagnetic parameters. The results showed that Hermite interpolation is more accurate than the Lagrange interpolation, and the reflectance calculated with the electromagnetic parameter obtained by interpolation is consistent with that obtained through experiment on the whole. - Highlights: • We use interpolation algorithm on calculation of EM-parameter with limited samples. • Interpolation method can predict EM-parameter well with different particles added. • Hermite interpolation is more accurate than Lagrange interpolation. • Calculating RL based on interpolation is consistent with calculating RL from experiment.
A new interpolation method to model thickness, isopachs, extent, and volume of tephra fall deposits
Yang, Qingyuan; Bursik, Marcus
2016-10-01
Tephra thickness distribution is the primary piece of information used to reconstruct the histories of past explosive volcanic eruptions. We present a method for modeling tephra thickness with less subjectivity than is the case with hand-drawn isopachs, the current, most frequently used method. The algorithm separates the thickness of a tephra fall deposit into a trend and local variations and models them separately using segmented linear regression and ordinary kriging. The distance to the source vent and downwind distance are used to characterize the trend model. The algorithm is applied to thickness datasets for the Fogo Member A and North Mono Bed 1 tephras. Simulations on subsets of data and cross-validation are implemented to test the effectiveness of the algorithm in the construction of the trend model and the model of local variations. The results indicate that model isopach maps and volume estimations are consistent with previous studies and point to some inconsistencies in hand-drawn maps and their interpretation. The most striking feature noticed in hand-drawn mapping is a lack of adherence to the data in drawing isopachs locally. Since the model assumes a stable wind field, divergences from the predicted decrease in thickness with distance are readily noticed. Hence, wind direction, although weak in the case of Fogo A, was not unidirectional during deposition. A combination of the isopach algorithm with a new, data transformation can be used to estimate the extent of fall deposits. A limitation of the algorithm is that one must estimate "by hand" the wind direction based on the thickness data.
BLOCK BASED NEWTON-LIKE BLENDING INTERPOLATION
Qian-jin Zhao; Jie-qing Tan
2006-01-01
Newton's polynomial interpolation may be the favourite linear interpolation in the sense that it is built up by means of the divided differences which can be calculated recursively and produce useful intermediate results. However Newton interpolation is in fact point based interpolation since a new interpolating polynomial with one more degree is obtained by adding a new support point into the current set of support points once at a time. In this paper we extend the point based interpolation to the block based interpolation. Inspired by the idea of the modern architectural design, we first divide the original set of support points into some subsets (blocks), then construct each block by using whatever interpolation means, linear or rational and finally assemble these blocks by Newton's method to shape the whole interpolation scheme. Clearly our method offers many flexible interpolation schemes for choices which include the classical Newton's polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of our method.
Veselý, P; Ventruba, J
2009-10-01
The main goal of our study was to prove the statistical significant difference between the threshold interpolation logMAR method on ETDRS chart and the whole-line method on Snellen chart with Sloan letters. We had 108 measurements with the threshold interpolation method and the whole-line method on ETDRS chart and the whole-line method on Snellen chart. The average value measured with the threshold method in ETDRS was 1,132 (min. 0,660, max. 1,580), with the whole-line method on ETDRS it was 1,134 (min. 0,630, max. 1,580) and with the whole-line method on Snellen chart it was 1,183 (min. 0,630, max. 1,600). We have proved statistical significant difference between the threshold interpolation method made on ETDRS chart and the whole-line method made on Snellen chart (p Snellen chart were overvalued. The exact and reliable measuring of visual acuity is an important component of further examinations (e.g. contrast sensitivity, perimetry, tonometry), which enable us to make a correct diagnosis of pathological changes on human eye structures.
航测数据处理中的空间插值方法比较%Spatial Interpolation Methods in Aerial Survey Data Processing
王颖; 祝民强; 乔康宁
2011-01-01
航测数据的航线间距与采样点间距差异很大,生成等值线时需要进行空间插值.以云南省江川地区的航测数据为实验数据源,分别采用反距离权重插值(IDW)、规则样条函数插值(Regularized Spline)、张力样条函数(Tension Spline)插值和Kriging插值等4种插值方法,对航测数据进行分析与比较,从中选出一种最优的插值方法及其参数,以提高航空放射性测量数据的预浏精度和质量.验证结果表明,4种插值方法,相对均方差(RMSE)的排列顺序为:Tension Spline < Regularized Spline < IDW < Kriging,且插值分析中Tension所绘制的铀含量等值线也为最佳分布.因此,Tension插值方法在该航测数据处理中插值效果最好,预测的精度也最高.%The route distance of aerial survey data is quite different from the sample points distance. When sample points generate contours, they need spatial interpolation. This paper took the aerial survey data of Jiangchuan of Yunnan Province as the experimental data source, and applied the Inverse Distance Weighted( IDW ), Regularized Spline, Tension Spline, Kriging four interpolation methods respectively for analyzing and comparing aerial survey data to chose one of the optimal interpolation methods and its parameters,so forth to improve the accuracy and quality of aerial radiological survey data. The validation results showed that the order of Relative Mean Square Error(RMSE) of the four kinds of interpolation methods is Tension Spline ＜ Regularized Spline ＜ IDW ＜ Kriging, and Tension interpolation methods’contour map is the most optimal distribution in the interpolation analyze. Therefore, Tension of Spline interpolation methods’effort is the most natural and the highest prediction accuracy in the aerial survey data processing.
Logarithmic Spiral-based Construction of RBF Classifiers
Mohamed Wajih Guerfala
2017-02-01
Full Text Available Clustering process is defined as grouping similar objects together into homogeneous groups or clusters. Objects that belong to one cluster should be very similar to each other, but objects in different clusters will be dissimilar. It aims to simplify the representation of the initial data. The automatic classification recovers all the methods allowing the automatic construction of such groups. This paper describes the design of radial basis function (RBF neural classifiers using a new algorithm for characterizing the hidden layer structure. This algorithm, called k-means Mahalanobis distance, groups the training data class by class in order to calculate the optimal number of clusters of the hidden layer, using two validity indexes. To initialize the initial clusters of k-means algorithm, the method of logarithmic spiral golden angle has been used. Two real data sets (Iris and Wine are considered to improve the efficiency of the proposed approach and the obtained results are compared with basic literature classifier
Study on Comparative Teaching of Interpolation Method by Using Matlab%用Matlab进行插值法比较教学研究
陈锟; 田晓梅
2012-01-01
Interpolation method is the important teaching content in Numerical Analysis courses, and is foundation for numerical integration and numerical differentiation and initial value problems in ordinary differential equations. This paper discusses the basic idea of interpolation problem and several common interpolation methods, and mainly compares the polynomial interpolation algorithms. Utilizing the superiority of Matlab in numerical calculation, com- parative teaching of interpolation algorithms is presented by using Matlab in teaching practice. The results show that the students can quickly comprehend the knowledge and conduct the applicable verification in the comparative reac- hing. The pretty teaching result is got.%插值方法是＂数值分析＂课程中非常重要的教学内容,也是数值微分、数值积分和常微分方程初值问题数值解的基础。本文探讨了插值问题的基本思想和常用的几种插值方法,重点比较了代数多项式插值方法。利用Matlab在科学计算中的优势,在实践教学中用Matlab进行了插值方法的对比教学研究。结果表明：通过比较教学使学生较快掌握了插值算法知识点,并能应用于实际科学研究项目之中,取得了较好的教学效果。
熊亮; 赵俊锴
2015-01-01
Assessment of compressive strength of substation concrete column is an important foundation of damage degree and bearing capacity of construction.An RBF neural network model (RBF-NN )is applied to assessing compressive strength of concrete by ultrasonic and rebound combined method.An experimental method is given for compressive strength of concrete test by ultrasonic and rebound combined method.It is proved that RBF-NN model has higher evaluation precision than that of regression calculation by experimental test and emulation analysis.%变电站混凝土立柱抗压强度的评定是判断变电站混凝土结构损伤程度、剩余承载力的重要依据。设计了一个 RBF 神经网络模型，将其应用于超声回弹综合法评定变电站混凝土立柱抗压强度，给出了用超声回弹法进行混凝土强度测试的方法。经试验测试和仿真分析表明，所提出的 RBF 神经网络比传统的回归计算方法具有更高的评估精度。
Inverse Distance Weighted Interpolation Involving Position Shading
LI Zhengquan
2015-01-01
Full Text Available Considering the shortcomings of inverse distance weighted (IDW interpolation in practical applications, this study improved the IDW algorithm and put forward a new spatial interpolation method that named as adjusted inverse distance weighted (AIDW. In interpolating process, the AIDW is capable of taking into account the comprehensive influence of distance and position of sample point to interpolation point, by adding a coefficient (K into the normal IDW formula. The coefficient (K is used to adjust interpolation weight of the sample point according to its position in sample points. Theoretical analysis and practical application indicates that the AIDW algorithm could diminish or eliminate the IDW interpolation defect of non-uniform distribution of sample points. Consequently the AIDW interpolating is more reasonable, compared with the IDW interpolating. On the other hand, the contour plotting of the AIDW interpolation could effectively avoid the implausible isolated and concentric circles that originated from the defect of the IDW interpolation, with the result that the contour derived from the AIDW interpolated surface is more similar to the professional manual identification.
Zhang, J.; Liu, Q.; Li, X.; Niu, H.; Cai, E.
2015-12-01
In recent years, wireless sensor network (WSN) emerges to collect Earth observation data at relatively low cost and light labor load, while its observations are still point-data. To learn the spatial distribution of a land surface parameter, interpolating the point data is necessary. Taking soil moisture (SM) for example, its spatial distribution is critical information for agriculture management, hydrological and ecological researches. This study developed a method to interpolate the WSN-measured SM to acquire the spatial distribution in a 5km*5km study area, located in the middle reaches of HEIHE River, western China. As SM is related to many factors such as topology, soil type, vegetation and etc., even the WSN observation grid is not dense enough to reflect the SM distribution pattern. Our idea is to revise the traditional Kriging algorithm, introducing spectral variables, i.e., vegetation index (VI) and abledo, from satellite imagery as supplementary information to aid the interpolation. Thus, the new Extended-Kriging algorithm operates on the spatial & spectral combined space. To run the algorithm, first we need to estimate the SM variance function, which is also extended to the combined space. As the number of WSN samples in the study area is not enough to gather robust statistics, we have to assume that the SM variance function is invariant over time. So, the variance function is estimated from a SM map, derived from the airborne CASI/TASI images acquired in July 10, 2012, and then applied to interpolate WSN data in that season. Data analysis indicates that the new algorithm can provide more details to the variation of land SM. Then, the Leave-one-out cross-validation is adopted to estimate the interpolation accuracy. Although a reasonable accuracy can be achieved, the result is not yet satisfactory. Besides improving the algorithm, the uncertainties in WSN measurements may also need to be controlled in our further work.
Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ
Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A;
2012-01-01
This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...... in solution of partial differential equations (PDEs)....
Mark Rivard
2010-04-01
Full Text Available Purpose: The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function gL(r and 2D anisotropy function F(r,θ table entries for radial distancer and polar angle θ. The objectives of this study are as follows: 1 to evaluate interpolation methods in order to accurately derive gL(r and F(r,θ from the reported data; 2 to determine the minimum number of entries in gL(r and F(r,θ that allow reproduction of dose distributions with sufficient accuracy.Material and methods: Four high-energy photon-emitting brachytherapy sources were studied: 60Co model Co0.A86, 137Cs model CSM-3, 192Ir model Ir2.A85-2, and 169Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2–8 (integer steps and 10 cm. Four different angular steps were evaluated for F(r,θ: 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for gL(r. Linear-linear interpolation was used to obtain F(r,θ with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC calculations for thefour sources with the same grid.Results: Linear interpolation of gL(r provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F(r,θ using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60Co, 192Ir, and 169Yb, while 137Cs agreement was ≤ 1.5% for θ < 15°.Conclusions: The radial mesh studied was adequate for interpolating gL(r for high-energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F(r,θ close to the source longitudinalaxis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.
AMMI模型的DEM内插方法不确定性研究%Uncertainty Analysis of Different DEM Interpolation Methods Based on AMMI Model
赵明伟; 汤国安; 田剑
2012-01-01
Analysis of evaluation of interpolation models is a hot topic in the DEM interpolation studies. Most studies focused on the interpolation model in the last decades, while ignored the influencing factors between the interpolation models and environments. That is to say, on the one side, different interpolation models influence the accuracy of the analysis result; on the other side, difference environments also influence the accuracy of a certain interpolation model. In order to analysis the applicability of different interpolation methods in different environments, this paper selected test areas under different geomorphic types, and used the AMMI model to analyse the accuracy of the different interpolation models and the applicability of the studied models to different geomorphic types. The experiment results showed that the AMMI model could test the influencing factors between the interpolation models and the environments. Taking the test of this paper as an example, in the Northern Shaanxi region, the ordinary Kriging model is the best choice in the DEM construction. Finally, by analyzing the correlation coefficient between the environment coefficient and several landform parameters, it can be found that the slope gradient could represent the first environment coefficient.%内插模型的精度评价问题一直是DEM内插研究中的热点问题.以往较多的研究关注插值模型本身的精度评价,却忽略了插值模型与应用环境之间的交互作用,例如,普通克里金方法作DEM内插一般精度较差,但是当插值区域平坦时,该方法的插值精度却很高,这表明该方法对平坦地形的插值问题具有较好的适应性.为了分析不同插值模型在不同地形环境下的适用性,本文选取陕北黄土高原地区不同地貌类型的实验样区,应用AMMI模型对不同内插模型的精度,以及对不同地貌类型的适用性进行评价,该模型最大的特点是很好地结合了方差分析与回归分析
Kananenka, Alexei A; Lan, Tran Nguyen; Gull, Emanuel; Zgid, Dominika
2016-01-01
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about two orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be double...
基于System Generator的内插位同步法%An interpolation bit synchronized method based on System Generator
赵秋明; 何克森; 陈小飞
2014-01-01
针对数字接收机中如何全数字地实现位同步,设计了一种内插位同步法。利用内插与 Gardner算法相结合的原理设计位同步,通过 System Generator进行建模仿真,并直接生成代码下载到 FPGA实现位同步。利用 QPSK信号进行仿真分析,FPGA硬件协同仿真进行验证。实验结果表明,内插位同步法具有很好的位同步效果。%In order to realize the synchronization of the digital receivers,a kind of interpolation bit synchronization method is designed.The bit synchronization is designed by combining interpolation theory with the Gardner algorithm.Through the simulation of System Generator,the generated code is downloaded to the FPGA to achieve the synchronization.The simula-tion analysis uses QPSK signal to verify the FPGA hardware component simulation.The experimental results show that the interpolation bit synchronization method has a good synchronization performance.
2D Sketch based recognition of 3D freeform shapes by using the RBF Neural Network
Qin, S F; Sun, Guangmin; Wright, D K; Lim, S.; Khan, U.; Mao, C.
2005-01-01
This paper presents a novel free-form surface recognition method from 2D freehand sketching. The approach is based on the Radial basis function (RBF), an artificial intelligence technique. A simple three-layered network has been designed and constructed. After training and testing with two types of surfaces (four sided boundary surfaces and four close section surfaces), it has been shown that the method is useful in freeform surface recognition. The testing results are very satisfactory.
2D sketch based recognition of 3D freeform shape by using the RBF neural network
Qin, SF; Sun, GM; Wright, DK; Lim, S.; Khan, U.; Mao, C.
2005-01-01
This paper presents a novel free-form surface recognition method from 2D freehand sketching. The approach is based on the Radial basis function (RBF), an artificial intelligence technique. A simple three-layered network has been designed and constructed. After training and testing with two types of surfaces (four sided boundary surfaces and four close section surfaces), it has been shown that the method is useful in freeform surface recognition. The testing results are very satisfactory.
Tranchant, B.J.S.; Vincent, A.P. [Montreal Univ., PQ (Canada). Dept. of Physics; Centre for Research on Computation and its Applications (CERCA), Montreal, PQ (Canada)
2000-06-01
This study demonstrates that ordinary kriging in spherical coordinates using experimental semivariograms provides highly usable results, especially near the pole in winter and/or where there could be data missing over large areas. In addition, kriging allows display of the spatial variability of daily ozone measurements at different pressure levels. Three satellite data sets were used: total ozone mapping spectrometer (TOMS) data, solar backscattered ultra violet (SBUV), and the stratospheric aerosol and gas experiment (SAGE II) ozone profiles. Since SBUV is a nadir-viewing instrument, measurements are only taken along the sun-synchronous polar orbits of the satellite. SAGE II is a limb-viewing solar occulation instrument, and measurements have high vertical resolution but poor daily coverage. TOMS has wider coverage with equidistant distribution of data (resolution 1 x 1.25 ) but provides no vertical information. Comparisons of the resulting SBUV-interpolated (column-integrated) ozone field with TOMS data are strongly in agreement, with a global correlation of close to 98%. Comparisons of SBUV-interpolated ozone profiles with daily SAGE II profiles are relatively good, and comparable to those found in the literature. The interpolated ozone layers at different pressure levels are shown. (orig.)
Liu, Jinkun
2013-01-01
Radial Basis Function (RBF) Neural Network Control for Mechanical Systems is motivated by the need for systematic design approaches to stable adaptive control system design using neural network approximation-based techniques. The main objectives of the book are to introduce the concrete design methods and MATLAB simulation of stable adaptive RBF neural control strategies. In this book, a broad range of implementable neural network control design methods for mechanical systems are presented, such as robot manipulators, inverted pendulums, single link flexible joint robots, motors, etc. Advanced neural network controller design methods and their stability analysis are explored. The book provides readers with the fundamentals of neural network control system design. This book is intended for the researchers in the fields of neural adaptive control, mechanical systems, Matlab simulation, engineering design, robotics and automation. Jinkun Liu is a professor at Beijing University of Aeronautics and Astronauti...
A Hybrid RBF-SVM Ensemble Approach for Data Mining Applications
M.Govindarajan
2014-02-01
Full Text Available One of the major developments in machine learning in the past decade is the ensemble method, which finds highly accurate classifier by combining many moderately accurate component classifiers. This paper addresses using an ensemble of classification methods for data mining applications like intrusion detection, direct marketing, and signature verification. In this research work, new hybrid classification method is proposed for heterogeneous ensemble classifiers using arcing and their performances are analyzed in terms of accuracy. A Classifier ensemble is designed using a Radial Basis Function (RBF and Support Vector Machine (SVM as base classifiers. Here, modified training sets are formed by resampling from original training set; classifiers constructed using these training sets and then combined by voting. The proposed RBF-SVM hybrid system is superior to individual approach for intrusion detection, direct marketing, and signature verification in terms of classification accuracy.
熊敏诠
2012-01-01
Delaunay三角剖分方法在空间分析中具有重要地位,文中简要介绍了Delaunay三角网特性和常用的3类算法,并对随机增长法实现过程进行了详细阐述.根据三角分片线性插值原理,求得插值系数,实现对任意点的三角分片线性插值.利用2008年中国2200个观测站的08时24 h降水量资料,对全中国范围及划分的8个区域内相应的0.28125°×0.28125°降水量格点场,使用交叉检验方法,对比分析了三角分片线性插值和反距离权重法的估值准确率.结果表明:在各区域,三角分片线性插值法的均方根误差偏小；在站点较密集的区域,均方根误差、平均绝对误差比较中,三角分片线性插值都有一定的优势；在平均误差对比中,三角分片线性插值优势明显,在全中国范围交叉检验中,三角分片线性插值法对应的年平均误差是0.005 mm,而反距离权重法为-0.107 mm,对其可能的原因进行了分析,证明了Delaunay三角剖分法的合理性.同时,从图形上展示了降水量的Delaunay三角网的三维结构图和三角分片线性插值后的格点场,在直观上,Delaunay三角剖分后得到降水分布和实况保持一致,并有较好的视觉效果；通过三角分片线性插值得到的格点场降水量分布图,克服了反距离权重法的固有缺陷,使获得的降水量格点场趋于合理,提高了插值精度.最后,探讨了Delaunay三角网在气象领域的应用前景.%Delaunay triangulated method plays an important role in the spatial analysis. The characteristic of Delaunay triangu-lation and three kinds of generation algorithm are introduced in this article. The stochastic growth algorithm is also discussed in detail. Based on the principle of the triangulated slice linear interpolation the coefficient is attained and thus the value at an arbitrary point can be calculated through the triangulated slice linear interpolation algorithm. By using the daily precipitation
Compensation for unmatched uncertainty with adaptive RBF network
user
radial basis function (RBF) neural networks have showed strong universal approximation ability for unknown ..... w is the ideal constant weight, the ... w with the weight estimation error )(~ twi ..... Gaussian networks for direct adaptive control.
INTERPOLATION METHODS AND ACCURACY ANALYSIS BASED ON GRID QUASI-GEOID MODEL%基于似大地水准面格网的插值方法及精度分析
张兴福; 魏德宏
2011-01-01
There are two factors: affecting the accuracy of GPS height transformation based on quasi-geoid model, the geodetic height accuracy and interpolated height anomaly accuracy. On the basis of the simulation and practical quasi-geoid models, the effect and accuracy of GPS height anomaly interpolation are analyzed with four methods, including inverse distance interpolation, linear interpolation, Shepard interpolation and Chebyshev interpolation, the results show that the Chebyshev interpolation method is accurate and stable for the high resolution quasi-geoid model.%影响由似大地水准面模型进行GPS高程转换的因素有两个:GPS点大地高的测量精度和该点内插高程异常的精度.利用模拟以及某一区域似大地水准面模型比较了反距离加权插值、线性插值、谢别德插值以及切比雪夫插值方法用于GPS点高程异常内插的精度,结果表明:对于分辨率较高的似大地水准面,切比雪夫插值具有很好的内插效果.
Image Interpolation Through Surface Reconstruction
ZHANG Ling; LI Xue-mei
2013-01-01
Reconstructing an HR (high-resolution) image which preserves the image intrinsic structures from its LR ( low-resolution) counterpart is highly challenging. This paper proposes a new surface reconstruction algorithm applied to image interpolation. The interpolation surface for the whole image is generated by putting all the quadratic polynomial patches together. In order to eliminate the jaggies of the edge, a new weight function containing edge information is incorporated into the patch reconstruction procedure as a constraint. Extensive experimental results demonstrate that our method produces better results across a wide range of scenes in terms of both quantitative evaluation and subjective visual quality.
Liu, Lin; Shen, Songhua; Liu, Qiang
2006-11-01
A novel method to detect power quality disturbance of distribution power system combing complex wavelet transform (WT) with radial basis function (RBF) neural network is presented. The paper tries to explain to design complex supported orthogonal wavelets by Morlet compactly supported orthogonal real wavelets, and then explore the extraction of disturbance signal to obtain the feature information, and finally propose several novel wavelet combined information (CI) to analyze the disturbance signal, superior to real wavelet analysis result. The feature obtained from WT coefficients are inputted into RBF network for power quality disturbance pattern recognition. The power quality disturbance recognition model is established and the synthesized method of recursive orthogonal least squares algorithm (ROLSA) with improved Givens transform is used to fulfill the network structure and parameter identification. By means of choosing enough samples to train the recognition model, the type of disturbance can be obtained when signal representing fault is inputted to the trained network. The results of simulation analysis show that the complex WT combined with RBF network are more sensitive to signal singularity, and found to be significant improvement over current methods in real-time detection and better noise proof ability.
A RBF Based Local Gridfree Scheme for Unsteady Convection-Diffusion Problems
Sanyasiraju VSS Yedida
2009-12-01
Full Text Available In this work a Radial Basis Function (RBF based local gridfree scheme has been presented for unsteady convection diffusion equations. Numerical studies have been made using multiquadric (MQ radial function. Euler and a three stage Runge-Kutta schemes have been used for temporal discretization. The developed scheme is compared with the corresponding finite difference (FD counterpart and found that the solutions obtained using the former are more superior. As expected, for a fixed time step and for large nodal densities, thought the Runge-Kutta scheme is able to maintain higher order of accuracy over the Euler method, the temporal discretization is independent of the improvement in the solution which in the developed scheme has been achived by optimizing the shape parameter of the RBF.
Nonlinear Adaptive PID Control for Greenhouse Environment Based on RBF Network
Guanghui Li
2012-04-01
Full Text Available This paper presents a hybrid control strategy, combining Radial Basis Function (RBF network with conventional proportional, integral, and derivative (PID controllers, for the greenhouse climate control. A model of nonlinear conservation laws of enthalpy and matter between numerous system variables affecting the greenhouse climate is formulated. RBF network is used to tune and identify all PID gain parameters online and adaptively. The presented Neuro-PID control scheme is validated through simulations of set-point tracking and disturbance rejection. We compare the proposed adaptive online tuning method with the offline tuning scheme that employs Genetic Algorithm (GA to search the optimal gain parameters. The results show that the proposed strategy has good adaptability, strong robustness and real-time performance while achieving satisfactory control performance for the complex and nonlinear greenhouse climate control system, and it may provide a valuable reference to formulate environmental control strategies for actual application in greenhouse production.
Nonlinear adaptive PID control for greenhouse environment based on RBF network.
Zeng, Songwei; Hu, Haigen; Xu, Lihong; Li, Guanghui
2012-01-01
This paper presents a hybrid control strategy, combining Radial Basis Function (RBF) network with conventional proportional, integral, and derivative (PID) controllers, for the greenhouse climate control. A model of nonlinear conservation laws of enthalpy and matter between numerous system variables affecting the greenhouse climate is formulated. RBF network is used to tune and identify all PID gain parameters online and adaptively. The presented Neuro-PID control scheme is validated through simulations of set-point tracking and disturbance rejection. We compare the proposed adaptive online tuning method with the offline tuning scheme that employs Genetic Algorithm (GA) to search the optimal gain parameters. The results show that the proposed strategy has good adaptability, strong robustness and real-time performance while achieving satisfactory control performance for the complex and nonlinear greenhouse climate control system, and it may provide a valuable reference to formulate environmental control strategies for actual application in greenhouse production.
A Hybrid Framework using RBF and SVM for Direct Marketing
M. Govidarajan
2013-05-01
Full Text Available one of the major developments in machine learning in the past decade is the ensemble method, which finds highly accurate classifier by combining many moderately accurate component classifiers. This paper addresses using an ensemble of classification methods for direct marketing. Direct marketing has become an important application field for data mining. In direct marketing, companies or organizations try to establish and maintain a direct relationship with their customers in order to target them individually for specific product offers or for fund raising. A variety of techniques have been employed for analysis ranging from traditional statistical methods to data mining approaches. In this research work, new hybrid classification method is proposed by combining classifiers in a heterogeneous environment using arcing classifier and their performances are analyzed in terms of accuracy. A Classifier ensemble is designed using Radial Basis Function (RBF and Support Vector Machine (SVM as base classifiers. Here, modified training sets are formed by resampling from original training set; classifiers constructed using these training sets and then combined by voting. Empirical results illustrate that the proposed hybrid systems provide more accurate direct marketing system.
姚应水; 叶明全
2011-01-01
目的 RBF神经网络是一种重要的数据挖掘分类模型,探讨RBF神经网络在解决判别分析问题中的应用.方法 通过实例比较RBF神经网络和logistic回归模型的性能优劣.结果 RBF神经网络的回代拟合效果和泛化能力明显优于logistic回归模型.结论RBF神经网络在医学统计学领域中具有较好的应用前景.%Objective RBF neural network is an important data mining classification model in data mining. To explore the application of RBF neural network on medical discriminant analysis through comparing with logistic regression. Methods Comparing the prediction results by some statistical indexes of the RBF neural network and the logistic regression by using an example. Results The comparison results of the prediction performance between RBF neural network and logistic regression show that RBF neural network is much better than logistic regression for the data. Conclusion RBF neural network will make a better facture of its appfi-cadon in medical researches.
针对Kriging插值结果的空间查询方法%Spatial query method for Kriging interpolation result
杜久升; 陈宜金; 侯争
2013-01-01
Kriging插值方法及其各种改进模型已被广泛应用,但由于其插值结果是栅格形式,因此不利于与矢量数据叠加分析.为了更加便捷地使用插值结果,在衡量Voronoi图和最小外接矩形特点的基础上,提出了适用于Kriging插值结果的数据结构及空间查询方法.查询某一点位的特征值时,先通过区域的最小外接矩形初步判断出该位置可能存在的区域,进而逐一判断点与所选区域的空间关系,根据点所在区域的属性值得到该点位的特征值.该方法实现了对Kriging插值结果的空间查询,其正确性通过某露天矿的实际运行数据得到了验证.实验结果表明,该方法的查询效率控制在毫秒级,能够满足矿区车载终端程序及类似应用的需求.%The Kriging interpolation method and its improved models have been widely used, but the interpolation result is raster format and goes against the overlay analysis with vector data. Considering the characteristics of Minimum Enclosing Rectangle ( MER) and Voronoi diagram, data structure and spatial query method fit for Kriging interpolation result were proposed. When querying the eigenvalue of a point, by traversing the MERs of various regions, polygons that the point may be in were selected at first. Then the exact polygon was determined by judging the spatial relationship between the point and each polygon. Finally, the eigenvalue of this point was obtained, because it was an attribute of the exact polygon. This query method realized the spatial query of Kriging interpolation. Its validity has been verified by the result of practical operation in an open-pit. The experimental results indicate the query time of this method is controlled in milliseconds, so it is able to meet the requirements of vehicle terminal program in open-pit and other similar applications.
郭小燕; 张明
2013-01-01
针对RBF神经网络确定核函数中心时没有考虑输入样本分类指标权重的问题,提出了一种动态加权聚类算法.在算法中利用样本之间的加权距离代替了欧氏距离作为选定核函数中心的量度.在此基础上,建立了信用评价模型,利用已知类别的样本对模型进行训练,再利用训练好的模型对未知类别的样本进行预测,实验结果验证了模型的有效性.%A dynamic weighting cluster algorithm is proposed in this article in view of the problem of input sample's classification weight being not considered by formerly RBF neural network. In this algorithm, the weighting distance replaces the Euclidean distance to act the role of measurement to the cluster. Based on this, the credit evaluation model is established, which is trained by known category sample. Then the trained model is used to forecast the unknown category sample, the experimental result confirms the model' s validity.
Kammerlander, David; Botti, Silvana; Marques, Miguel A. L.; Marini, Andrea; Attaccalite, Claudio
2012-09-01
The Bethe-Salpeter equation is a widely used approach to describe optical excitations in bulk semiconductors. It leads to spectra that are in very good agreement with experiment, but the price to pay for such accuracy is a very high computational burden. One of the main bottlenecks is the large number of k points required to obtain converged spectra. In order to circumvent this problem we propose a strategy to solve the Bethe-Salpeter equation based on a double-grid technique coupled to a Wannier interpolation of the Kohn-Sham band structure. This strategy is then benchmarked for a particularly difficult case, the calculation of the absorption spectrum of GaAs, and for the well-studied case of Si. The considerable gains observed in these cases fully validate our approach, and open the way for the application of the Bethe-Salpeter equation to large and complex systems.
Transition elements based on transfinite interpolation
Odabas, Onur R.; Sarigul-Klijn, Nesrin
1993-01-01
In this study the transfinite interpolation methodology, a 'blending-function' method in particular, is utilized for the formulation of transition elements. The method offers a formal way of meeting continuity requirements in a transition element. Element shape functions are derived by blending the continuity requirements of individual boundary segments. The blending directions are naturally orthogonal in rectangular domains therefore interpolation of the boundaries over rectangular 2D and 3D elements can be performed with minimal effort. In triangular domains, however, the choice of blending directions and interpolants is not straightforward. For that reason, two interpolation techniques are proposed for blending of the boundaries of triangular domains. A series of transition elements of various classes compatible with elements of different orders and dimensions is developed and the full potential of the transfinite interpolation, as it applies to element formulation, is explored.
张锦明; 郭丽萍; 张小丹
2012-01-01
Interpolation method is one of the most important factors which influence on the accuracy of DEM. However, there are few researches on how interpolation parameters influence interpolation method as well as the interpolation accuracy at last. The interpolation parameters of distance weighted interpolation method was considered as the research object, and respectively selected 6 kinds discrete data as the original data. Then metrics of RMSE was used to measure RMSE of the generated DEM in order to study that how interpolation parameters, including weighted index, search points, search directions, search radius in distance weighted interpolation method affected the accuracy of DEM interpolation. It was drawn: firstly, in the aspect of search directions, it was not obvious to use the four-direction and eight-direction to improve the accuracy of DEM interpolation; secondly, the best search points were 8~12 points; thirdly, when the weighted index was higher than 3, the impact of the change in weighted index on DEM accuracy tended to be not obvious, the best weighted index should be 2 or 3; finally, the degree of influence on the accuracy of DEM interpolation was "the power index>the search points>the search direction".%插值算法是影响DEM精度的主要因素之一,对于插值参数如何影响插值算法并最终影响插值精度却研究较少.这里以反距离加权插值算法中的插值参数为实验对象,选取了6种不同地貌类型的离散点数据,基于中误差度量指标,运用交叉验证方法研究权指数、搜索点数、搜索方向对DEM插值精度的影响.实验结果表明:1)在搜索方向方面,四方向搜索和八方向搜索对提高DEM插值精度并不明显；2)搜索点数为8～12点是较好的选择；3)当权指数≥3时,对DEM插值精度的影响不明显,2或3是较好的选择；4)3因素对DEM插值精度的显著性影响顺序为“权指数＞搜索点数＞搜索方向”.
Clarkson, Brian W.
Light Detection and Ranging (LiDAR) derived Digital Elevation Models (DEMs) provide accurate, high resolution digital surfaces for precise topographic analysis. The following study investigates the accuracy of LiDAR derived DEMs by calculating the Root Mean Square Error (RMSE) of multiple interpolation methods with grid cells ranging from 0.5 to 10-meters. A raster cell with smaller dimensions will drastically increase the amount of detail represented in the DEM by increasing the number of elevation values across the study area. Increased horizontal resolutions have raised the accuracy of the interpolated surfaces and the contours generated from the digitized landscapes. As the raster grid cells decrease in size, the level of detail of hydrological processes will significantly improve compared to coarser resolutions including the publicly available National Elevation Datasets (NEDs). Utilizing a LiDAR derived DEM with the lowest RMSE as the 'ground truth', watershed boundaries were delineated for a sub-basin of the Clear Creek Watershed within the territory of the Seneca Nation of Indians located in Southern Erie County, NY. An investigation of the watershed area and boundary location revealed considerable differences comparing the results of applying different interpretation methods on DEM datasets of different horizontal resolutions. Stream networks coupled with watersheds were used to calculate peak flow values for the 10-meter NEDs and LiDAR derived DEMs.
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
徐平; 杜向锋
2014-01-01
This article details several typical mathematical models of the interpolation methods of quasi-geoid,and compiles the corresponding model interpolation software on the basis of these models.Meanwhile,by using the interpolation methods provided by the inter-polation software and a certain quasi-geoid model,some GPS/leveling data are calculated by using elevation interpolation.Through the analysis of the interpolation results,some useful conclusions are drawn.%详细介绍了几种常用的似大地水准面插值方法的数学模型，并根据这些模型编写了相应的模型内插软件，利用该内插软件提供的内插方法及某似大地水准面模型，对一些GPS/水准数据进行了高程内插计算，通过对内插结果的分析获得了一些有益的结论。
张芹; 郭力; 张秉超
2012-01-01
针对混凝土中氯离子扩散过程中扩散系数的非均质性导致的非线性问题,采用区域分解法并融入无网格法中的径向基函数求解思想,建立了时空一致径向基函数配点法.该方法将时间和空间区域同时分解,在相应子域上对未知函数进行径向基函数展开.针对含有Neumann边界条件的非均质扩散问题建立了Hermite型近似函数配点求解方法.该方法避免了对时间域采用差分法求解引起的迭代求解困难,对求解非均质扩散系数的问题求解具有一定优势.用Matlab语言编制了相应的求解程序,通过2个非均质扩散问题算例,验证了所提方法的正确性和有效性.所提方法为研究复杂环境下混凝土结构的耐久性问题提供了一种新的数值方法.%According to the nonlinear problem caused by heterogeneous diffusivity in the diffusion process of chloride ion in concrete, a time-space consistent collocation method is developed with the domain decomposition method and the methodology of the radial basis function (RBF) in the mesh-less method. Unknown arguments are expanded via RBFs in the corresponding sub-domain with simultaneous decomposing of the time and space domain. Additionally, a Hermite collocation method of the RBF is constructed to solve the heterogeneous diffusion problem with Neumann boundary conditions. Compared with the finite difference process on solving time domain issues, the proposed method reduces the difficulty of iterative procedure and results in a more easy application to heterogeneous diffusion problems. The Matlab program of the developed method is subsequently implemented. Two numerical examples are performed to evaluate the accuracy and efficiency of the developed model. The examples clearly demonstrate that the developed method has more distinguished advantages than the finite element method in analyzing heterogeneous diffusion problems. The proposed method provides new guidelines for the
Xing-hua; WANG
2007-01-01
Explicit representations for the Hermite interpolation and their derivatives of any order are provided.Furthermore,suppose that the interpolated function f has continuous derivatives of sufficiently high order on some sufficiently small neighborhood of a given point x and any group of nodes are also given on the neighborhood.If the derivatives of any order of the Hermite interpolation polynomial of f at the point x are applied to approximating the corresponding derivatives of the function f(x),the asymptotic representations for the remainder are presented.
Loop Subdivision Surface Based Progressive Interpolation
Fu-Hua (Frank) Cheng; Feng-Tao Fan; Shu-Hua Lai; Cong-Lin Huang; Jia-Xi Wang; Jun-Hai Yong
2009-01-01
A new method for constructing interpolating Loop subdivision surfaces is presented. The new method is an extension of the progressive interpolation technique for B-splines. Given a triangular mesh M, the idea is to iteratively upgrade the vertices of M to generate a new control mesh M such that limit surface of M would interpolate M. It can be shown that the iterative process is convergent for Loop subdivision surfaces. Hence, the method is well-defined. The new method has the advantages of both a local method and a global method, i.e., it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes. The meshes considered here can be open or closed.
Creasy, Arch; Barker, Gregory; Carta, Giorgio
2017-03-01
A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high-throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high-throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column.
Image Interpolation Using Kriging Technique for Spatial Data
Jassim, Firas Ajil; Altaany, Fawzi Hasan
2013-01-01
Image interpolation has been used spaciously by customary interpolation techniques. Recently, Kriging technique has been widely implemented in simulation area and geostatistics for prediction. In this article, Kriging technique was used instead of the classical interpolation methods to predict the unknown points in the digital image array. The efficiency of the proposed technique was proven using the PSNR and compared with the traditional interpolation techniques. The results showed that Krig...
Distance in spatial interpolation of daily rain gauge data
Ahrens, B.
2006-01-01
Spatial interpolation of rain gauge data is important in forcing of hydrological simulations or evaluation of weather predictions, for example. This paper investigates the application of statistical distance, like one minus common variance of observation time series, between data sites instead of geographical distance in interpolation. Here, as a typical representative of interpolation methods the inverse distance weighting interpolation is applied and the test data is daily precipitation obs...
Study on the Average Temperature of Forage Growth Period Interpolation Method%天然牧草生育期平均气温插值方法研究
于士凯; 姚艳敏; 王德营; 唐鹏钦; 陈仲新; 王道龙
2012-01-01
天然牧草生育期平均气温是牧草生长、生态环境保护等模型的重要参数.为了找出适宜天然牧草生育期平均气温的差值方法,以内蒙古自治区为研究区域,根据气温的垂直变化规律,将不同经纬度和海拔高度上的气象站点牧草生育期平均气温数据根据海拔高程投影到虚拟0海平面上,利用反距离插值(IDW)、样条函数(Spline)插值、克里金(Kriging)插值3种插值方法进行研究区域牧草生育期平均气温的空间分布推算,再运用DEM数据进行校正,比较分析最适宜的牧草生育期平均气温空间插值方法.3种插值方法平均误差为:IDW插值(-1.34％)＞Spline插值(1.11％)＞Kriging插值(0.36％)；RMSE值:Kriging插值＜IDW插值＜Spline插值,其值分别为0.36＜0.69＜0.74.MAE值:Kriging插值＜Spline插值＜IDW插值,其值分别为0.14＜0.33＜0.35.研究结果表明,克里金(Kriging)插值为牧草生育期平均气温最优插值方法.%The average temperature of forage growth period was an important parameter for the model of grass crop growth and eco-environmental protection. In order to find out the optimum method for the average temperature interpolation of grass growth period, this paper took the Inner Mongolia Autonomous Region as the study areas. Firstly, according to the temperature vertical changing regularities, the average temperature data in pasture growth period of all climate sites were projected in different longitude and latitude to the virtual 0 sea level based on the latitude. Spline, IDW, Kriging interpolation methods were used to carry on the data interpolation. And then DEM data was used to conduct the temperature correction. The average errors of three interpolation methods were: IDW interpolation (-1.34%) > Spline Interpolation (1.11%) > the Kriging Interpolation (0.36%). The RMSE value: Kriging interpolation < IDW interpolation < Spline interpolation and the values were 0.36 < 0.69 < 0.74. The MAE value
V. Bayona
2015-04-01
Full Text Available A numerical model based on Radial Basis Function-generated Finite Differences (RBF-FD is developed for simulating the Global Electric Circuit (GEC within the Earth's atmosphere, represented by a 3-D variable coefficient linear elliptic PDE in a spherically-shaped volume with the lower boundary being the Earth's topography and the upper boundary a sphere at 60 km. To our knowledge, this is (1 the first numerical model of the GEC to combine the Earth's topography with directly approximating the differential operators in 3-D space, and related to this (2 the first RBF-FD method to use irregular 3-D stencils for discretization to handle the topography. It benefits from the mesh-free nature of RBF-FD, which is especially suitable for modeling high-dimensional problems with irregular boundaries. The RBF-FD elliptic solver proposed here makes no limiting assumptions on the spatial variability of the coefficients in the PDE (i.e. the conductivity profile, the right hand side forcing term of the PDE (i.e. distribution of current sources or the geometry of the lower boundary.
New method to interpolate images using Doo Sabin subdivision%基于Doo Sabin细分的图像插值
梁云; 王栋
2011-01-01
图像插值是放大低分辨率图像以适应目标显示屏幕的一种重要方法.保持图像的几何特征是保证放大图像质量的一个有效途径.基于Doo Sabin细分,提出了一种新的图像插值方法.该方法首先通过一次映射关系获取高分辨图像的部分数据;然后根据高分辨率图像中未知像素点的几何特征将它们分类;再根据Doo Sabin细分方法由已知像素点插值出所有未知像素点.未知像素点的值是与最相关的邻近像素点的加权均值,加权策略根据像素点间的相对位置由Doo Sabin细分推演获得.实验证明,与现有插值方法相比,基于Doo Sabin细分的图像插值能够更好地保持上采样图像的边缘的尖锐特性,减少锯齿现象,获取高质量的高分辨率图像.%Image interpolation is an important method to magnify images with low resolution to adapt to the target screens.To preserve the geometry feature of the original image is an effective way to improve the quality of magnified images. This paper proposed a new method to interpolate images based on Doo Sabin subdivision. The method adopted the essential idea of subdividing the quadrilateral mesh to enhance the sampling images of low resolution. Firstly, part of the data of high resolution images was obtained by mapping low resolution images. Secondly we classified the unknown pixels of high resolution images according to their geometric features. Then we interpolated all the unknown pixels by the assigned pixels. Values of the unknown pixels were the weighted average of their neighboring pixels. The weighted strategy was deduced by Doo Sabin subdivision. Experiments show that our method can preserve the sharp feature of image edges, decrease zigzags and achieve better results than the previous methods.
Influence of Different Interpolation Methods on Spatial Uncertainty of Rainfall%不同插值方法对降水量空间不确定性的影响
胡刚; 赵刚; 宋慧
2012-01-01
鉴于点状数据的降水插值方法在时间和空间两个方面具有不确定性,从空间角度出发,以山东省多年平均降水量为例,采用交叉验证方法,对反比距离权重法、克里金方法、径向基函数法、全局多项式法和局部多项式法5种常用插值方法的整体插值精度和分区后各分区的插值精度分别进行分析验证.研究认为:山东省整体插值的最优方法为反比距离权重法；分区插值的最优方法中,平原地区为克里金方法、丘陵地区为全局多项式法、鲁中山地为反比距离权重法.并在此基础上,对整体插值精度和分区插值精度作了比较.研究结果可为区域降水插值模型的选取提供指导,同时分区插值的思路可为后续相关研究提供借鉴.%The uncertainty of precipitation using different forms of interpolation comes from two aspects:time and space. We,taking Shandong's annual average precipitation as an example, make a comparation of the five common methods, that is, inverse distance weighting,kriging,radical basis function,global polynomial and local polynomial,in integral interpolator and zonal interpolator. By using cross-validation, the methods' precision was given. Hie conclusion is that the best integral interpolator is the inverse distance weighting method,and the zonal methods are kriging in plain,global polynomial in hilly ground,inverse distance weighting in mountain area. Then the exactness of integral interpolator and zonal interpolator was analyzed and the precipitation distribution of Shandong was given. The research on integral interpolation and zonal interpolation can be a guide for the choice of spatial interpolation,meanwhile,the mentality of zonal interpolator can be used as a reference for following researches.
Diversification improves interpolation
Giesbrecht, Mark
2011-01-01
We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers. Building on the recent work of Garg and Schost, we improve on the best-known algorithm for interpolation over large finite fields by presenting a Las Vegas randomized algorithm that uses fewer black box evaluations. Using related techniques, we also address numerical interpolation of sparse complex polynomials, and provide the first provably stable algorithm (in the sense of relative error) for this problem, at the cost of modestly more interpolation points. A key new technique is a randomization which makes all coefficients of the unknown polynomial distinguishable, producing what we call a diverse polynomial. Another departure of our algorithms from most previous approaches is that they do not rely on root finding as a subroutine. We show how these improvements affect the practical performance with trial implementations.
Extension Of Lagrange Interpolation
Mousa Makey Krady
2015-01-01
Full Text Available Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Extension Of Lagrange Interpolation
Mousa Makey Krady
2015-01-01
Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Significance of initial interpolation in band-limited signal interpolation
Yegnanarayana, B.; Fathima, S. Tanveer; Nehru, B. T. K. R.; Venkataramanan, B.
1989-01-01
An improved version of the Papoulis algorithm for bandlimited signal interpolation is presented. This algorithm uses the concept of initial interpolation. The justification for initial interpolation is developed only through experimental studies. It is shown that the performance of the interpolation scheme depends on the number and distribution of the known data samples.
BIVARIATE LAGRANGE-TYPE VECTOR VALUED RATIONAL INTERPOLANTS
Chuan-qing Gu; Gong-qing Zhu
2002-01-01
An axiomatic definition to bivariate vector valued rational interpolation on distinct plane interpolation points is at first presented in this paper. A two-variable vector valued rational interpolation formula is explicitly constructed in the following form: the determinantal formulas for denominator scalar polynomials and for numerator vector polynomials,which possess Lagrange-type basic function expressions. A practical criterion of existence and uniqueness for interpolation is obtained. In contrast to the underlying method, the method of bivariate Thiele-type vector valued rational interpolation is reviewed.
EOS Interpolation and Thermodynamic Consistency
Gammel, J. Tinka [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-16
As discussed in LA-UR-08-05451, the current interpolator used by Grizzly, OpenSesame, EOSPAC, and similar routines is the rational function interpolator from Kerley. While the rational function interpolator is well-suited for interpolation on sparse grids with logarithmic spacing and it preserves monotonicity in 1-d, it has some known problems.
EOS Interpolation and Thermodynamic Consistency
Gammel, J. Tinka [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-16
As discussed in LA-UR-08-05451, the current interpolator used by Grizzly, OpenSesame, EOSPAC, and similar routines is the rational function interpolator from Kerley. While the rational function interpolator is well-suited for interpolation on sparse grids with logarithmic spacing and it preserves monotonicity in 1-d, it has some known problems.
Evolving RBF neural networks for adaptive soft-sensor design.
Alexandridis, Alex
2013-12-01
This work presents an adaptive framework for building soft-sensors based on radial basis function (RBF) neural network models. The adaptive fuzzy means algorithm is utilized in order to evolve an RBF network, which approximates the unknown system based on input-output data from it. The methodology gradually builds the RBF network model, based on two separate levels of adaptation: On the first level, the structure of the hidden layer is modified by adding or deleting RBF centers, while on the second level, the synaptic weights are adjusted with the recursive least squares with exponential forgetting algorithm. The proposed approach is tested on two different systems, namely a simulated nonlinear DC Motor and a real industrial reactor. The results show that the produced soft-sensors can be successfully applied to model the two nonlinear systems. A comparison with two different adaptive modeling techniques, namely a dynamic evolving neural-fuzzy inference system (DENFIS) and neural networks trained with online backpropagation, highlights the advantages of the proposed methodology.
Polynomial Interpolation in the Elliptic Curve Cryptosystem
Liew K. Jie
2011-01-01
Full Text Available Problem statement: In this research, we incorporate the polynomial interpolation method in the discrete logarithm problem based cryptosystem which is the elliptic curve cryptosystem. Approach: In this study, the polynomial interpolation method to be focused is the Lagrange polynomial interpolation which is the simplest polynomial interpolation method. This method will be incorporated in the encryption algorithm of the elliptic curve ElGamal cryptosystem. Results: The scheme modifies the elliptic curve ElGamal cryptosystem by adding few steps in the encryption algorithm. Two polynomials are constructed based on the encrypted points using Lagrange polynomial interpolation and encrypted for the second time using the proposed encryption method. We believe it is safe from the theoretical side as it still relies on the discrete logarithm problem of the elliptic curve. Conclusion/Recommendations: The modified scheme is expected to be more secure than the existing scheme as it offers double encryption techniques. On top of the existing encryption algorithm, we managed to encrypt one more time using the polynomial interpolation method. We also have provided detail examples based on the described algorithm.
Interferometric interpolation of sparse marine data
Hanafy, Sherif M.
2013-10-11
We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green\\'s function and a model-based Green\\'s function for a water-layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up- and downgoing separation of both recorded and model-based Green\\'s functions can help in minimizing artefacts in a virtual shot gather. If the up- and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non-stationary 1D multi-channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f-k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method. © 2013 European Association of Geoscientists & Engineers.
Segment adaptive gradient angle interpolation.
Zwart, Christine M; Frakes, David H
2013-08-01
We introduce a new edge-directed interpolator based on locally defined, straight line approximations of image isophotes. Spatial derivatives of image intensity are used to describe the principal behavior of pixel-intersecting isophotes in terms of their slopes. The slopes are determined by inverting a tridiagonal matrix and are forced to vary linearly from pixel-to-pixel within segments. Image resizing is performed by interpolating along the approximated isophotes. The proposed method can accommodate arbitrary scaling factors, provides state-of-the-art results in terms of PSNR as well as other quantitative visual quality metrics, and has the advantage of reduced computational complexity that is directly proportional to the number of pixels.
THE USE OF SEMI INHERITED LU FACTORIZATION OF MATRICES IN INTERPOLATION OF DATA
MOHAMMAD ALI FARIBORZI ARAGHI
2009-04-01
Full Text Available The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.
Multivariate Birkhoff interpolation
Lorentz, Rudolph A
1992-01-01
The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well a...
Duality, Tangential Interpolation, and Toeplitz Corona Problems
Raghupathi, Mrinal
2009-01-01
In this paper we extend a method of Arveson and McCullough to prove a tangential interpolation theorem for subalgebras of $H^\\infty$. This tangential interpolation result implies a Toelitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent-Wick and Douglas-Sarkar.
Application of Nonlinear Predictive Control Based on RBF Network Predictive Model in MCFC Plant
CHEN Yue-hua; CAO Guang-yi; ZHU Xin-jian
2007-01-01
This paper described a nonlinear model predictive controller for regulating a molten carbonate fuel cell (MCFC). A detailed mechanism model of output voltage of a MCFC was presented at first. However, this model was too complicated to be used in a control system. Consequently, an off line radial basis function (RBF) network was introduced to build a nonlinear predictive model. And then, the optimal control sequences were obtained by applying golden mean method. The models and controller have been realized in the MATLAB environment. Simulation results indicate the proposed algorithm exhibits satisfying control effect even when the current densities vary largely.
Identification of TSS in the Human Genome Based on a RBF Neural Network
Zhi-Hong Peng; Jie Chen; Li-Jun Cao; Ting-Ting Gao
2006-01-01
The identification of functional motifs in a DNA sequence is fundamentally a statistical pattern recognition problem. This paper introduces a new algorithm for the recognition of functional transcription start sites (TSSs) in human genome sequences, in which a RBF neural network is adopted, and an improved heuristic method for a 5-tuple feature viable construction, is proposed and implemented in two RBFPromoter and ImpRBFPromoter packages developed in Visual C++6.0. The algorithm is evaluated on several different test sequence sets. Compared with several other promoter recognition programs, this algorithm is proved to be more flexible, with stronger learning ability and higher accuracy.
A FAST MORPHING-BASED INTERPOLATION FOR MEDICAL IMAGES: APPLICATION TO CONFORMAL RADIOTHERAPY
Hussein Atoui
2011-05-01
Full Text Available A method is presented for fast interpolation between medical images. The method is intended for both slice and projective interpolation. It allows offline interpolation between neighboring slices in tomographic data. Spatial correspondence between adjacent images is established using a block matching algorithm. Interpolation of image intensities is then carried out by morphing between the images. The morphing-based method is compared to standard linear interpolation, block-matching-based interpolation and registrationbased interpolation in 3D tomographic data sets. Results show that the proposed method scored similar performance in comparison to registration-based interpolation, and significantly outperforms both linear and block-matching-based interpolation. This method is applied in the context of conformal radiotherapy for online projective interpolation between Digitally Reconstructed Radiographs (DRRs.
DESIGN AND IMPLEMENTATION OF OPTIMUM INTERPOLATION FILTER USING FARROW STRUCTURE
NAVJOT SINGH,
2011-05-01
Full Text Available The Farrow Structure provides an efficient way to implement the interpolation filter using polynomialapproximation method for arbitrary sample rate change. The lagrange polynomial approximation method providesalmost exact reconstruction of the new interpolated signal as of the input sampled signal. In this paper, cubiclagrange polynomial and 4th order lagrange polynomial approximation methods have been used to implement thedesign of the interpolation filter based on Farrow Structure. The optimum filter coefficients have been calculatedusing both polynomial approximation methods. The performance of the two methods has been compared to get theoptimum solution to the design of the interpolation filter using Farrow structure.
Wen-Yeau Chang
2013-01-01
Full Text Available This paper proposes an equivalent circuit parameters measurement and estimation method for proton exchange membrane fuel cell (PEMFC. The parameters measurement method is based on current loading technique; in current loading test a no load PEMFC is suddenly turned on to obtain the waveform of the transient terminal voltage. After the equivalent circuit parameters were measured, a hybrid method that combines a radial basis function (RBF neural network and enhanced particle swarm optimization (EPSO algorithm is further employed for the equivalent circuit parameters estimation. The RBF neural network is adopted such that the estimation problem can be effectively processed when the considered data have different features and ranges. In the hybrid method, EPSO algorithm is used to tune the connection weights, the centers, and the widths of RBF neural network. Together with the current loading technique, the proposed hybrid estimation method can effectively estimate the equivalent circuit parameters of PEMFC. To verify the proposed approach, experiments were conducted to demonstrate the equivalent circuit parameters estimation of PEMFC. A practical PEMFC stack was purposely created to produce the common current loading activities of PEMFC for the experiments. The practical results of the proposed method were studied in accordance with the conditions for different loading conditions.
Interpolating Operators for Multiapproximation
Eman S. Bhaya
2010-01-01
Full Text Available Problem statement: There are no simple definitions of operators for best multiapproximation and best one sided multiapproximation which work for any measurable function in Lp for, p>0. This study investigated operators that are good for best multiapproximation and best one sided multiapproximation. Approach: We first introduced some direct results related to the approximation problem of continuous functions by Hermit-Fejer interpolation based on the zeros of Chebyshev polynomials of the first or second kind in terms of the usual modulus of continuity. They were then improved to spaces Lp for pn(f of measurable functions, that operator based on the zeros of Chepyshev polynomials of the first kind and prove that for any measurable function defined on Lp[-1,1 ]d the sequence Hn(f converges uniformly to f. Results: The resulting operators were defined for functions f such that f(k, k = 0,1, is of bounded variation. Then, the order of best onesided trigonometric approximation to bounded measurable functions in terms of the average modulus of smoothness was characterized. Estimates characterizing the order of best onesided approximation in terms of the k-th averaged modulus of smoothness for any function in spaces Lp, pp[-1,1]d by defining a new operator for onesided approximation and prove a direct theorem for best one sided multiapproximation in terms of the first order averaged moduli of smoothness. Conclusion: The proposed method successfully construct operators for best multi approximation and best one sided multiapproximation for any measurable function in Lp for, p>0.
Tricubic polynomial interpolation.
Birkhoff, G
1971-06-01
A new triangular "finite element" is described; it involves the 12-parameter family of all quartic polynomial functions that are "tricubic" in that their variation is cubic along any parallel to any side of the triangle. An interpolation scheme is described that approximates quite accurately any smooth function on any triangulated domain by a continuously differentiable function, tricubic on each triangular element.
M. H. Nazarifar
2014-01-01
Full Text Available Water is the main constraint for production of agricultural crops. The temporal and spatial variations in water requirement for agriculture products are limiting factors in the study of optimum use of water resources in regional planning and management. However, due to unfavorable distribution and density of meteorological stations, it is not possible to monitor the regional variations precisely. Therefore, there is a need to estimate the evapotranspiration of crops at places where meteorological data are not available and then extend the findings from points of measurements to regional scale. Geostatistical methods are among those methods that can be used for estimation of evapotranspiration at regional scale. The present study attempts to investigate different geostatistical methods for temporal and spatial estimation of water requirements for wheat crop in different periods. The study employs the data provided by 16 synoptic and climatology meteorological stations in Hamadan province in Iran. Evapotranspiration for each month and for the growth period were determined using Penman-Mantis and Torrent-White methods for different water periods based on Standardized Precipitation Index (SPI. Among the available geostatistical methods, three methods: Kriging Method, Cokriging Method, and inverse weighted distance were selected, and analyzed, using GS+ software. Analysis and selection of the suitable geostatistical method were performed based on two measures, namely Mean Absolute Error (MAE and Mean Bias Error (MBE. The findings suggest that, in general, during the drought period, Kriging method is the proper one for estimating water requirements for the six months: January, February, April, May, August, and December. However, weighted moving average is a better estimation method for the months March, June, September, and October. In addition, Kriging is the best method for July. In normal conditions, Kriging is suitable for April, August, December
Reyes Lopez, Y.; Yervilla Herrera, H.; Viamontes Esquivel, A.; Recarey Morfa, C. A.
2009-07-01
In the following paper we developed a new method to interpolate large volumes of scattered data, focused mainly on the results of the Mesh free Methods, Points Methods and the Particles Methods application. Through this one, we use local radial basis function as interpolating functions. We also use over-tree as the data structure that allows to accelerate the localization of the data that influences to interpolate the values at a new point, speeding up the application of scientific visualization techniques to generate images from large data volumes from the application of Mesh-free Methods, Points and Particle Methods, in the resolution of diverse models of physics-mathematics. As an example, the results obtained after applying this method using the local interpolation functions of Shepard are shown. (Author) 22 refs.
Dawes, Richard; Thompson, Donald L; Wagner, Albert F; Minkoff, Michael
2008-02-28
An accurate and efficient method for automated molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating moving least-squares (IMLS) method is developed with the flexibility to fit various ab initio data: (1) energies, (2) energies and gradients, or (3) energies, gradients, and Hessian data. The method is automated and flexible so that a PES can be optimally generated for trajectories, spectroscopy, or other applications. High efficiency is achieved by employing local IMLS in which fitting coefficients are stored at a limited number of expansion points, thus eliminating the need to perform weighted least-squares fits each time the potential is evaluated. An automatic point selection scheme based on the difference in two successive orders of IMLS fits is used to determine where new ab initio data need to be calculated for the most efficient fitting of the PES. A simple scan of the coordinate is shown to work well to identify these maxima in one dimension, but this search strategy scales poorly with dimension. We demonstrate the efficacy of using conjugate gradient minimizations on the difference surface to locate optimal data point placement in high dimensions. Results that are indicative of the accuracy, efficiency, and scalability are presented for a one-dimensional model potential (Morse) as well as for three-dimensional (HCN), six-dimensional (HOOH), and nine-dimensional (CH4) molecular PESs.
Differentiation of digital tb images using texture analysis and rbf classifier.
Priya, E; Srinivasan, S; Ramakrishnan, S
2012-01-01
In this work, differentiation of positive and negative images of Tuberculosis (TB) sputum smear has been attempted using statistical method based on Gray Level Co-occurrence Matrix (GLCM). The sputum smear images (N=100) recorded under standard image acquisition protocol are considered for this work. Second order statistical texture analysis is performed on the acquired images using GLCM method and a set of nineteen features are derived. Principal Component Analysis (PCA) is then employed to reduce feature sets, to enhance the efficiency of differentiation and to reduce the redundancy. These feature sets are further classified using Radial Basis Function (RBF) classifier. Results show that GLCM is able to differentiate positive and negative TB images. Correlation is found to be high for many of the parameters. Application of PCA reduced the number of features to four which had maximum magnitude in the first principal component. Higher classification accuracy is achieved using RBF classifier. It appears that this method of texture analysis could be useful to develop automated system for characterization and classification of digital TB sputum smear images.
雷海峰; 何政伟; 陈敏
2012-01-01
DEM （Digital Elevation Model） is a mathematical or digital model of the terrain surface,the different treatment to the expression of the terrain surface may be called surface modeling. In the surface modeling, the surface interpolation is the key of the surface rebuild. In the article, on the one hand two kinds of frequently-used interpolation functions was introduced, on the other hand the author use routine method to judge the precision of the two kinds interpolation methods.%DEM（Digital Elevation Model）是地形表面的一个数学或数字模型,对地形表面进行表达的各种处理可称为表面建模,在表面建模中,表面内插是表面重建的关键,文章对两种常用的表面内插进行了介绍并对两种内插方法的精度用常规的取点判定模型进行了判断定。
基于体素相似度的医学图像层间插值方法%Interslice interpolation method for medical image based on voxel similarity
马伟; 陈家新; 潘维薇
2012-01-01
断层图像层间插值是医学图像三维重建的一个重要环节,但现有插值算法易引起图像边界模糊或效率低下的不足.为此提出一种基于体素相似度的医学图像层间插值算法.该算法根据断层图像的体素相关性和组织本身特征信息计算其体素的相似度,并利用其相似度对插值点进行分类插值.实验结果表明,和已有的算法比较,新算法较好地提高了插值图像的质量,并且计算量大为减少.%Cross-sectional interpolation is one of the key steps in 3D reconstruction of medical images. Considering the shortcomings of current interpolation methods, such as blurring the object boundary and low computational efficiency, an interstice interpolation method for medical images based on voxel similarity was proposed in this paper. According to the principle of voxel relativity in cross-section images and structures feature, this method calculated the relativity of voxels to classify pixels and interpolated it. The experimental results illustrate that the new method has less computational complexity and better improves the quality of image than the previous interpolation methods.
汪媛媛; 杨忠芳; 余涛; 文宇博; 夏学齐; 白荣杰
2011-01-01
Soil carbon storage is the focus in the studies on greenhouse effect and global change. Total organic carbon storage and average organic carbon storage in surface soil are calculated by means of Unit Soil Carbon Storage in this study. Different interpolation models such as Inverse Distance Weighted, Global Polynomial Interpolation, Local Polynomial Interpolation, Radial Basis Function and Kringing are analyzed and compared. The interpolation results show that mean error, average absolute error and root mean standard error are the minimum when using the GPI, the RBF and the Kringing models respectively. The quadratic equationmodel of original Kringing achieves the highest accuracy.%土壤碳储量问题是大气温室效应和全球变化研究的热点问题.本文采用“单位土壤碳量”方法,计算了吉林省大安市表层土壤有机碳总储量和平均土壤有机碳储量,以为全球碳循环研究提供精确的基础数据.分析和比较了反距离加权、全局多项式、局部多项式、径向基函数和普通克里格等不同插值模型对表层单位土壤有机碳储量空间插值结果的影响,结果表明全局多项式插值的均差最小,径向基函数中张力样条法的平均绝对误差最小,普通克里格法的标准差最小.综合分析来看,普通克里格的有理二次方程式模型插值精度最高.
Application of BP NN and RBF NN in Modeling Activated Sludge System
王维斌; 郑丕谔; 李金勇
2003-01-01
Based on the operation data from a certain wastewater treatment plant(WWTP) in northeast China, the models of back propagation neural network(BP NN) and radial basis function neural network(RBF NN) have been designed respectively and the ability of convergence and generalization has been analyzed separately. As for BP NN, the effects of numbers of layers and nodes have been studied; as for RBF NN, the influences of the number of nodes and the RBF′s width have been studied. It is concluded that BP NN has converged much slowly in comparison with RBF NN. The conclusion that the RBF NN is suitable for modeling activated sludge system has been drawn. An automatically optimum design program for RBF NN has been developed, through which the RBF NN model of traditional activated sludge system has been established.
Poultangari, Iman; Shahnazi, Reza; Sheikhan, Mansour
2012-09-01
In order to control the pitch angle of blades in wind turbines, commonly the proportional and integral (PI) controller due to its simplicity and industrial usability is employed. The neural networks and evolutionary algorithms are tools that provide a suitable ground to determine the optimal PI gains. In this paper, a radial basis function (RBF) neural network based PI controller is proposed for collective pitch control (CPC) of a 5-MW wind turbine. In order to provide an optimal dataset to train the RBF neural network, particle swarm optimization (PSO) evolutionary algorithm is used. The proposed method does not need the complexities, nonlinearities and uncertainties of the system under control. The simulation results show that the proposed controller has satisfactory performance.
Wang, Zhongqi; Yang, Bo; Kang, Yonggang; Yang, Yuan
2016-01-01
Fixture plays an important part in constraining excessive sheet metal part deformation at machining, assembly, and measuring stages during the whole manufacturing process. However, it is still a difficult and nontrivial task to design and optimize sheet metal fixture locating layout at present because there is always no direct and explicit expression describing sheet metal fixture locating layout and responding deformation. To that end, an RBF neural network prediction model is proposed in this paper to assist design and optimization of sheet metal fixture locating layout. The RBF neural network model is constructed by training data set selected by uniform sampling and finite element simulation analysis. Finally, a case study is conducted to verify the proposed method.
Yeşilkanat, Cafer Mert; Kobya, Yaşar; Taşkın, Halim; Çevik, Uğur
2017-09-01
The aim of this study was to determine spatial risk dispersion of ambient gamma dose rate (AGDR) by using both artificial neural network (ANN) and fuzzy logic (FL) methods, compare the performances of methods, make dose estimations for intermediate stations with no previous measurements and create dose rate risk maps of the study area. In order to determine the dose distribution by using artificial neural networks, two main networks and five different network structures were used; feed forward ANN; Multi-layer perceptron (MLP), Radial basis functional neural network (RBFNN), Quantile regression neural network (QRNN) and recurrent ANN; Jordan networks (JN), Elman networks (EN). In the evaluation of estimation performance obtained for the test data, all models appear to give similar results. According to the cross-validation results obtained for explaining AGDR distribution, Pearson's r coefficients were calculated as 0.94, 0.91, 0.89, 0.91, 0.91 and 0.92 and RMSE values were calculated as 34.78, 43.28, 63.92, 44.86, 46.77 and 37.92 for MLP, RBFNN, QRNN, JN, EN and FL, respectively. In addition, spatial risk maps showing distributions of AGDR of the study area were created by all models and results were compared with geological, topological and soil structure. Copyright © 2017 Elsevier Ltd. All rights reserved.
C2 quartic spline surface interpolation
张彩明; 汪嘉业
2002-01-01
This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.
Marta Béjar-Pizarro
2016-11-01
Full Text Available Land subsidence resulting from groundwater extractions is a global phenomenon adversely affecting many regions worldwide. Understanding the governing processes and mitigating associated hazards require knowing the spatial distribution of the implicated factors (piezometric levels, lithology, ground deformation, usually only known at discrete locations. Here, we propose a methodology based on the Kriging with External Drift (KED approach to interpolate sparse point measurements of variables influencing land subsidence using high density InSAR measurements. In our study, located in the Alto Guadalentín basin, SE Spain, these variables are GPS vertical velocities and the thickness of compressible soils. First, we estimate InSAR and GPS rates of subsidence covering the periods 2003–2010 and 2004–2013, respectively. Then, we apply the KED method to the discrete variables. The resulting continuous GPS velocity map shows maximum subsidence rates of 13 cm/year in the center of the basin, in agreement with previous studies. The compressible deposits thickness map is significantly improved. We also test the coherence of Sentinel-1 data in the study region and evaluate the applicability of this methodology with the new satellite, which will improve the monitoring of aquifer-related subsidence and the mapping of variables governing this phenomenon.
Interpolation of Vector Measures
Ricardo del CAMPO; Antonio FERN(A)NDEZ; Fernando MAYORAL; Francisco NARANJO; Enrique A. S(A)NCHEZ-P(E)REZ
2011-01-01
Let (Ω, ∑) be a measurable space and m0: ∑→ X0 and m1: ∑ -→ X1 be positive vector measures with values in the Banach K(o)the function spaces X0 and X1. If 0 < α < 1, we define a X10-αXα1 and we analyze the space of integrable functions with respect to measure [m0, m1]α in order to prove suitable extensions of the classical Stein-Weiss formulas that hold for the complex interpolation of Lp-spaces.Since each p-convex order continuous K(o)the function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.
Multiscale empirical interpolation for solving nonlinear PDEs
Calo, Victor M.
2014-12-01
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton\\'s methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.
NO mediates downregulation of RBF after a prolonged reduction of renal perfusion pressure in SHR
Sørensen, Charlotte Mehlin; Leyssac, Paul Peter; Skott, Ole
2003-01-01
The aim of the study was to investigate mechanisms underlying the downregulation of renal blood flow (RBF) after a prolonged reduction in renal perfusion pressure (RPP) in adult spontaneously hypertensive rats (SHR). We tested the effect on the RBF response of clamping plasma ANG II in sevoflurane...... of plasma ANG II concentrations, general COX inhibition, and specific inhibition of COX-2. In contrast, clamping the NO system diminished the ability of SHR to downregulate RBF to a lower level. The downregulation of RBF was not associated with a resetting of the lower limit of autoregulation in the control...... of vasoconstrictory prostaglandins....
Tatar Afshin
2016-03-01
Full Text Available Raw natural gases usually contain water. It is very important to remove the water from these gases through dehydration processes due to economic reasons and safety considerations. One of the most important methods for water removal from these gases is using dehydration units which use Triethylene glycol (TEG. The TEG concentration at which all water is removed and dew point characteristics of mixture are two important parameters, which should be taken into account in TEG dehydration system. Hence, developing a reliable and accurate model to predict the performance of such a system seems to be very important in gas engineering operations. This study highlights the use of intelligent modeling techniques such as Multilayer perceptron (MLP and Radial Basis Function Neural Network (RBF-ANN to predict the equilibrium water dew point in a stream of natural gas based on the TEG concentration of stream and contractor temperature. Literature data set used in this study covers temperatures from 10 °C to 80 °C and TEG concentrations from 90.000% to 99.999%. Results showed that both models are accurate in prediction of experimental data and the MLP model gives more accurate predictions compared to RBF model.
方亮; 何方; 吕莎莎; 叶寅; 宫志峰
2011-01-01
With Dongzhi County in Anhui Province for example, the paer systematically studies several interpolation mathods, including the inverse distance weighting method, radial basis functions interpolation, global polynomial interpolation method, local polynomial method, ordinary kriging interpolation method, simple kriging interpolation method, universal kriging ineterpolation method and disjunctive kriging interpolation method, as well as their impact on the accuracy of the evaluation on the spatial variation of regional soil organic matter. Resuls indicate that, ordinary kriging interpolation mathod is better than others, therefore, it should be applied to the interpolation analysis o the soil organie matter in Dongzhi County.%以安徽省东至县为例,系统研究了反距离加权插值法、径向基插值法、全局多项式插值法、局部多项式插值法、普通克里格插值法、简单克里格插值法、泛克里格插值法和析取克里格插值法对区域土壤有机质空间变异评价准确性的影响.结果表明,普通克里格插值法优于其他插值方法,所以东至县土壤有机质的插值分析应使用普通克里格插值法.
径向基函数插值方法在动网格技术中的应用%Radial Basis Function Interpolation in Moving Mesh Technique
林言中; 陈兵; 徐旭
2012-01-01
A spring stream method used for unstructured grid and a transfinite interpolation method used for structured grid are discussed. A method using radial basis function is proposed, which resolves moving mesh problem without any grid-connectivity information. Corresponding mesh numerical program is developed. Rotation of a two-dimensional rhombic aerofoil and deformation of a three-dimensional F104 aerofoil are taken as examples to show effects of function and radius on mesh quality and numerical efficiency. Results are compared with mesh-deformation using lineal spring method. It validats availability of the RBF method. We concluded that the RBF method is remarked with simple data structure, high numerical efficiency and strong adapting ability for large mesh deformation. It could be applied to CFD dynamic mesh problems.%分析用于非结构网格的弹簧比拟和用于结构网格的无限插值动态网格方法在实际应用中的优缺点,提出无需网格连接关系的基于径向基函数(radial basis functions,RBF)插值的动网格技术并编制相应的网格运动计算程序.以二维菱形翼的旋转运动及三维菱形翼的柔性变形为例,分析不同基函数和紧支半径的选取对网格质量及计算效率的影响,并通过与弹簧比拟方法的对比验证了RBF方法的有效性.结果表明:RBF方法数据结构简单,计算效率高,适应大变形能力强,可以有效地实现计算流体力学中的网格运动问题.
Interpolation of Ideal Measures by Abstract K and J Spaces
Luz M. FERN(A)NDEZ-CABRERA; Ant(o)n MART(I)NEZ
2007-01-01
We work with the abstract K and J interpolation method generated by a sequence latticeΓ.We investigate the deviation of an interpolated operator from a given operator ideal by establishingformulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictionsof the operator.Formulae are given in terms of the norms of the shift operators on Γ.
段祝庚; 肖化顺; 袁伟湘
2016-01-01
【目的】基于森林区域离散点云特点，利用不同插值方法构建冠层高度模型，并对不同插值方法进行比较、分析和评价，为森林冠层高度模型插值方法选择提供参考。【方法】以30 m ×30 m 样方离散点云数据为试验数据，采用开源软件 SAGS-GIS利用 B样条插值( B-Spline)、普通克里金插值法( OK)、线性插值三角网法( TLI)、反距离加权插值法(IDW)4种插值方法分别构建森林冠层高度模型，对森林冠层高度模型的平面视图、三维视图、剖面图及其像元统计量进行比较和分析；同时对反距离加权插值法的插值参数搜索半径进行讨论、比较和分析。【结果】对于森林区域空间分布均匀且存在高度突变的点云数据，B-Spline插值对空值区域都进行了填充，林冠空隙也被过分填充，且 CHM 像元最大值明显偏离原始插值数据； TLI插值的 CHM 显得比较破碎； OK 插值法对影像过度平滑，生成的 CHM 影像模糊；而 IDW插值法对冠层顶部进行了适当填充和平滑，但冠层边缘不被过度平滑，保留高度突变，同时林冠空隙仍然保留也不被过分填充。IDW 插值应选择合适的搜索半径，搜索半径为原始点云间隔的1.5～2.5倍较为合适。【结论】IDW插值法优于 B-Spline，OK，TLI插值法，生成的 CHM 能较准确反映森林冠层的真实自然形态，有利于森林参数的提取。%Objective]According to the characteristics of the discrete point cloud in forest area,canopy height model ( CHM ) was built through different interpolation methods. The results of the different interpolation methods were compared,analyzed and evaluated in order to provide the reference for choice of interpolation methods. [Method]In this study,the discrete point cloud data in plots(30 m × 30 m) were used as the experimental data. CHMs were generated by B-Spline,triangulation with linear interpolation ( TLI
Interpolation of rational matrix functions
Ball, Joseph A; Rodman, Leiba
1990-01-01
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...
Chen, Hai-Wen; McGurr, Michael; Brickhouse, Mark
2015-05-01
We present new results from our ongoing research activity for chemical threat detection using hyper-spectral imager (HSI) detection techniques by detecting nontraditional threat spectral signatures of agent usage, such as protective equipment, coatings, paints, spills, and stains that are worn by human or on trucks or other objects. We have applied several current state-of-the-art HSI target detection methods such as Matched Filter (MF), Adaptive Coherence Estimator (ACE), Constrained Energy Minimization (CEM), and Spectral Angle Mapper (SAM). We are interested in detecting several chemical related materials: (a) Tyvek clothing is chemical resistance and Tyvek coveralls are one-piece garments for protecting human body from harmful chemicals, and (b) ammonium salts from background could be representative of spills from scrubbers or related to other chemical activities. The HSI dataset that we used for detection covers a chemical test field with more than 50 different kinds of chemicals, protective materials, coatings, and paints. Among them, there are four different kinds of Tyvek material, three types of ammonium salts, and one yellow jugs. The imagery cube data were collected by a HSI sensor with a spectral range of 400-2,500nm. Preliminary testing results are promising, and very high probability of detection (Pd) and low probability of false detection are achieved with the usage of full spectral range (400- 2,500nm). In the second part of this paper, we present our newly developed HSI sharpening technique. A new Band Interpolation and Local Scaling (BILS) method has been developed to improve HSI spatial resolution by 4-16 times with a low-cost high-resolution pen-chromatic camera and a RGB camera. Preliminary results indicate that this new technique is promising.
Interpolation of bilinear operators and compactness
da Silva, Eduardo Brandani
2012-01-01
The behavior of bilinear operators acting on interpolation of Banach spaces for the $\\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\\rho$ method.
崔维; 丁玲
2016-01-01
为了提高采摘机器人自主导航和路径规划能力，提出了基于计算机视觉路径规划和 RBF 神经网络自适应逼近算法的导航方法。使用图像分割、平滑处理和边缘检测技术，根据图像像素灰度值确定了导航线的位置，利用逐行扫描的方法得到了导航离散点。路径规划和跟踪使用RBF神经网络逼近算法，通过逼近误差和权值控制路径跟踪的精度，系统响应的执行端使用液压伺服系统，提高了机器人自主导航的精度。以黄瓜采摘作为研究对象，在日光温室对机器人采摘作业进行了测试，通过测试得到了 RBF 神经网络的路径跟踪误差曲线。测试结果表明：机器人可以很好地逼近跟踪规划路径，其计算精度较高，跟踪效果较好。%In order to improve the ability of autonomous navigation and path planning of picking robot , a navigation meth-od is proposed based on computer vision path planning and RBF neural network adaptive approximation algorithm .The use of image segmentation , smoothing and edge detection technology ,the navigation line positions are determined accord-ing to the image pixel gray value using progressive scan method of navigation discrete points .The path planning and tracking using RBF neural network approximation algorithm , the accuracy of the system response is controlled by the ac-curacy of the error and weight control .Taking cucumber as the research object , it tested the robot picking operation in greenhouse , and obtained the path tracking error curve of RBF neural network .The test results show that the robot can get a good approximation of the path .
Interpolation of diffusion weighted imaging datasets.
Dyrby, Tim B; Lundell, Henrik; Burke, Mark W; Reislev, Nina L; Paulson, Olaf B; Ptito, Maurice; Siebner, Hartwig R
2014-12-01
Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal to the voxel size showed that conventional higher-order interpolation methods improved the geometrical representation of white-matter tracts with reduced partial-volume-effect (PVE), except at tract boundaries. Simulations and interpolation of ex-vivo monkey brain DWI datasets revealed that conventional interpolation methods fail to disentangle fine anatomical details if PVE is too pronounced in the original data. As for validation we used ex-vivo DWI datasets acquired at various image resolutions as well as Nissl-stained sections. Increasing the image resolution by a factor of eight yielded finer geometrical resolution and more anatomical details in complex regions such as tract boundaries and cortical layers, which are normally only visualized at higher image resolutions. Similar results were found with typical clinical human DWI dataset. However, a possible bias in quantitative values imposed by the interpolation method used should be considered. The results indicate that conventional interpolation methods can be successfully applied to DWI datasets for mining anatomical details that are normally seen only at higher resolutions, which will aid in tractography and microstructural mapping of tissue compartments.
Singularity-preserving image interpolation using wavelet transform extrema extrapolation
Zhai, Guangtao; Zhang, Yang; Zheng, Xiaoshi
2003-09-01
One common task of image interpolation is to enhance the resolution of the image, which means to magnify the image without loss in its clarity. Traditional methods often assume that the original images are smooth enough so as to possess continues derivatives, which tend to blur the edges of the interpolated image. A novel fast image interpolation algorithm based on wavelet transform and multi-resolution analysis is proposed in this paper. It uses interpolation and extrapolation polynomial to estimate the higher resolution informatoin of the image and generate a new sub-band of wavelet transform coefficients to get processed image with shaper edges and preserved singularities.
Comparing interpolation techniques for annual temperature mapping across Xinjiang region
Ren-ping, Zhang; Jing, Guo; Tian-gang, Liang; Qi-sheng, Feng; Aimaiti, Yusupujiang
2016-11-01
Interpolating climatic variables such as temperature is challenging due to the highly variable nature of meteorological processes and the difficulty in establishing a representative network of stations. In this paper, based on the monthly temperature data which obtained from the 154 official meteorological stations in the Xinjiang region and surrounding areas, we compared five spatial interpolation techniques: Inverse distance weighting (IDW), Ordinary kriging, Cokriging, thin-plate smoothing splines (ANUSPLIN) and Empirical Bayesian kriging(EBK). Error metrics were used to validate interpolations against independent data. Results indicated that, the ANUSPLIN performed best than the other four interpolation methods.
A Huber-derived Robust Multi-quadric Interpolation Method for DEM Construction%DEM建模的多面函数Huber抗差算法
陈传法; 刘凤英; 闫长青; 戴洪磊; 郭金运; 刘国林
2016-01-01
In this paper,we propose a robust multi-quadric method (MQ-H) based on Huber loss function to conduct interpolations of contaminated spatial points,especially those derived from remote-sensing techniques.The objective function of the MQ-H has two main parts;an improved Huber loss function and a regularized penalty term used to improve robustness and avoid overfitting,respectively.A mathematical surface,subject to model error with different distributions,was employed to comparatively analyze the robustness of the MQ-H,the classical MQ,and a least absolute deviation based MQ (MQ-L).The results indicated that when sample errors follow a normal distribution or a Laplacian distribution,the performance of MQ-H is comparatively better than those of MQ,and more accurate than MQ-L.For sample errors with a contaminated normal distribution and Cauchy distribution,MQ-H is more robust than MQ-L and MQ.Moreover,MQ with the improved Huber loss function is superior to MQ with the classical Huber loss function.A real-world example of DEM construction with stereo-image-derived elevation points indicates that compared to the classical interpolation methods including IDW (inverse distance weighting),OK (ordinary Kriging) and ANUDEM (Australian National University DEM),MQ-H has a better ability to reduce the impact of outliers while maintaining subtle terrain features suitable for qualitative analysis.%为了抑制采样点中粗差对数字高程模型(digital elevation model,DEM)建模的影响,以较高精度的多面函数(multi-quadric,MQ)为基函数,由改进Huber损失函数和权重惩罚项组成目标函数,发展了MQ抗差插值算法(MQ-H).通过优化MQ-H目标函数,采样点权重计算最终转换为方程组求解.以数学曲面为研究对象,将MQ-H计算结果与传统MQ及最小绝对偏差MQ(MQ-I)进行比较,结果表明:当采样误差服从正态分布时,MQ-H计算精度与传统MQ相当,而远高于MQ L;当采样误差服从拉普拉斯分布时,MQ-H计
Implementation of pattern recognition algorithm based on RBF neural network
Bouchoux, Sophie; Brost, Vincent; Yang, Fan; Grapin, Jean Claude; Paindavoine, Michel
2002-12-01
In this paper, we present implementations of a pattern recognition algorithm which uses a RBF (Radial Basis Function) neural network. Our aim is to elaborate a quite efficient system which realizes real time faces tracking and identity verification in natural video sequences. Hardware implementations have been realized on an embedded system developed by our laboratory. This system is based on a DSP (Digital Signal Processor) TMS320C6x. The optimization of implementations allow us to obtain a processing speed of 4.8 images (240x320 pixels) per second with a correct rate of 95% of faces tracking and identity verification.
Assessing manual lifting tasks based on segment angle interpolations.
Chang, Chien-Chi; Xu, Xu; Faber, Gert S; Kingma, Idsart; Dennerlein, Jack
2012-01-01
This study investigates the effects of the number of interpolation points on the prediction accuracy of segment angle trajectory during lifting. Ten participants performed various lifting tasks while a motion tracking system recorded their movements. Two-point through ten-point equal time-spaced segment angles extracted from major segment trajectory data captured by the motion tracking system were used to re-generate the whole body lifting motion by using polynomial and cubic spline interpolation methods. The root mean square error (RMSE) between the reference (motion tracking system) and the estimated (interpolation method) segment angle trajectories were calculated to quantify the prediction accuracy. The results showed that the cubic spline interpolation will yield a smaller RMSE value than one based on the polynomial interpolation. While increasing the number of interpolation points can reduce the RMSE of the estimated segment angle trajectories, there was a diminishing advantage in continuing to add interpolation points. A sensitivity analysis suggests that if the estimation of the segment angles at each interpolation point deviates considerably from the real value, and cannot be controlled at a low level (interpolation points will not improve the estimation accuracy.
Distance in spatial interpolation of daily rain gauge data
B. Ahrens
2006-01-01
Full Text Available Spatial interpolation of rain gauge data is important in forcing of hydrological simulations or evaluation of weather predictions, for example. This paper investigates the application of statistical distance, like one minus common variance of observation time series, between data sites instead of geographical distance in interpolation. Here, as a typical representative of interpolation methods the inverse distance weighting interpolation is applied and the test data is daily precipitation observed in Austria. Choosing statistical distance instead of geographical distance in interpolation of available coarse network observations to sites of a denser network, which is not reporting for the interpolation date, yields more robust interpolation results. The most distinct performance enhancement is in or close to mountainous terrain. Therefore, application of statistical distance in the inverse distance weighting interpolation or in similar methods can parsimoniously densify the currently available observation network. Additionally, the success further motivates search for conceptual rain-orography interaction models as components of spatial rain interpolation algorithms in mountainous terrain.
Ferranti, Francesco; Rolain, Yves
2017-01-01
This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results.
Interpolation of diffusion weighted imaging datasets
Dyrby, Tim B; Lundell, Henrik; Burke, Mark W
2014-01-01
Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer...... anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal...... to the voxel size showed that conventional higher-order interpolation methods improved the geometrical representation of white-matter tracts with reduced partial-volume-effect (PVE), except at tract boundaries. Simulations and interpolation of ex-vivo monkey brain DWI datasets revealed that conventional...
Interpolation and partial differential equations
MALIGRANDA, Lech; Persson, Lars-Erik; Wyller, John
1994-01-01
One of the main motivations for developing the theory of interpolation was to apply it to the theory of partial differential equations (PDEs). Nowadays interpolation theory has been developed in an almost unbelievable way {see the bibliography of Maligranda [Interpolation of Operators and Applications (1926-1990), 2nd ed. (Luleå University, Luleå, 1993), p. 154]}. In this article some model examples are presented which display how powerful this theory is when dealing with PDEs. One main aim i...
Complementary Lidstone Interpolation and Boundary Value Problems
Pinelas Sandra
2009-01-01
Full Text Available We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial of degree , which involves interpolating data at the odd-order derivatives. For we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a th order differential equation and the complementary Lidstone boundary conditions.
Positivity Preserving Interpolation Using Rational Bicubic Spline
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.
Local and Nonlocal Regularization to Image Interpolation
Yi Zhan
2014-01-01
Full Text Available This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.
The accuracy assessment in areal interpolation:An empirical investigation
2008-01-01
Areal interpolation is the process of transferring data from source zones to target zones. While method development remains a top research priority in areal interpo-lation,the accuracy assessment aspect also begs for attention. This paper reports an empirical experience on probing an areal interpolation method to highlight the power and potential pitfalls in accuracy assessment. A kriging-based interpolation algorithm is evaluated by several approaches. It is found that accuracy assessment is a powerful tool to understand an interpolation method,e.g. the utility of ancillary data and semi-variogram modeling in kriging in our case study. However,different assessment methods and spatial units on which assessment is conducted can lead to rather different results. The typical practice to assess accuracy at the source zone level may overestimate interpolation accuracy. Assessment at the target zone level is suggested as a supplement.
Research on the Arc Interpolation for the Nonstandard Section Curve of the Piston
秦月霞; 胡德金
2004-01-01
The transverse section of piston skirt is not a standard circle and is with high precision. So the section curve should be interpolated through the high accuracy method of circular are interpolation before NC machining. In order to smooth the connection of adjacent arcs and shorten the NC machining program, an interpolation method based on Chebyshev theory of function approximation is proposed here. According to the analysis of the interpolation error, the algorithm is simple and with high precision. By this way the fewest interpolating circular arc segments can be got, and the manufacture requirement is satisfied with the circular arc interpolating curves.
基于RBF神经网络的语音情感识别%Speech Emotion Recognition Based on RBF Neural Network
张海燕; 唐建芳
2011-01-01
The principle of radial base function neural network and its train algorithm are introduced in this paper.Meanwhile,the model of speech emotion recognition based on RBF neural network is established.In the recognition experiments,BP neural network and RBF neural network are compared in the same testing environment.The recognition rate of RBF neural network is 3% more than BP neural network.The results show that the method based on RBF neural network speech emotion recognition is effective.%介绍了径向基函数神经网络的原理、训练算法,并建立了RBF神经网络的语音情感识别的模型。在实验中比较了BP神经网络与RBF神经网络分别用于语音情感识别识别率,RBF神经网络的平均识别率高于BP神经网络3%。结果表明,基于RBF神经网络的语音情感识别方法的有效性。
Special interpolation to minimize grain in printer color separation
Zeng, Huanzhao
2005-01-01
A 3-D lookup table (LUT) approach has been developed for color separation for color inkjet printers to better control the color separation and ink limit. This method starts from the color separation for critical points, followed by 1-D interpolation to determine the color separation for grid points in critical lines, followed by 2-D interpolations to determine the color separation for grid points in critical planes, followed by 3-D interpolation to determine the color separation for the remaining grid points in the 3-D LUT. To control the spreading of K and high-density ink to some regions, such as the highlight region and the flesh tone region, we start from controlling the ink propagation in line interpolation, which is a fairly easy step, then control the ink propagation in planes, and finally control the ink propagation in 3-D interpolation. With this process, a 3-D LUT for the conversion from a printer RGB space or a virtual CMY space to an n-colorant space is built to maximize the printer gamut and to minimize grain. This paper describes the details of special interpolations to fill the grids in a 3-D color separation LUT, which includes controlling ink propagation in grids on selected lines, followed by special interpolations to minimize grain in plane-interpolation, followed by special interpolations to fill the remaining grids in the 3-D LUT.
Study of RBF Nerve Network Tuning PD Control Algoritm of Bilateral Servo System
Guang Wen
2013-01-01
Full Text Available In construction tele-robot system. When p-f architecture force feedback was used, the impact of large feedback force result in the strike-like feeling on the operators hand. If the amplitude is high, it will cause the control unstable. So a improved force feedback control method with the feature of a T-S fuzzy feedback coefficient, which could be modified online nonlinearly and continuously, is developed. A RBF-PID force controller is also designed, and formed a bilateral hydraulic servo control system. The experimental results indicate that the new improved control method reduced the impact of the feedback force, enhanced the compliance and transparency of the tele-operation of construction tele-robot system.
RBF Nerve Network Tuning PD Control Scheme for Tele-operation Robot Servo System
Guang Wen
2013-11-01
Full Text Available In the bilateral hydraulic servo control system of a construction tele-robot with in-situ force sensing, the p-f type force feedback architecture is liable to result in an impact on the operator hand, and its high amplitude will cause the control unstable. In order to solve this problem an improved force feedback control method with the feature of a T-S fuzzy feedback coefficient, which could be modified online nonlinearly and continuously, is proposed. And a RBF-PID force controller is also designed, and formed a bilateral hydraulic servo control system. The experimental results indicate that the new improved control method reduced the impact of the feedback force, the compliance and transparency of the tele-operation of construction tele-robot system are enhanced.
GONG Huanchun
2014-01-01
In order to diagnose the unit economic performance online,the radial basis function (RBF) process neural network with two hidden layers was introduced to online prediction of steam turbine exhaust enthalpy.Thus,the model reflecting complicated relationship between the steam turbine exhaust enthalpy and the relative operation parameters was established.Moreover,the enthalpy of final stage extraction steam and exhaust from a 300 MW unit turbine was taken as the example to perform the online calculation. The results show that,the average relative error of this method is less than 1%,so the accuracy of this al-gorithm is higher than that of the BP neutral network.Furthermore,this method has advantages of high convergence rate,simple structure and high accuracy.
Application of RBF Neural Network in OptimizingMachining Parameters
朱喜林; 吴博达; 武星星
2004-01-01
In machining processes, errors of rough in dimension, shape and location lead to changes in processing quantity, and the material of a workpiece may not be uniform. For these reasons, cutting force changes in machining, making the machining system deformable. Consequently errors in workpieces may occur. This is called the error reflection phenomenon. Generally, such errors can be reduced through repeated processing while using appropriate processing quantity in each processing based on operator's experience.According to the theory of error reflection, the error reflection coefficient indicates the extent to which errors of rough influence errors of workpieces. It is related to several factors such as machining condition, hardness of the workpiece, etc. This non-linear relation cannot be worked out using any formula. RBF neural network can approximate a non-linear function within any precision and be trained fast. In this paper, non-linear mapping ability of a fuzzy-neural network is utilized to approximate the non-linear relation. After training of the network with swatch collection obtained in experiments, an appropriate output can be obtained when an input is given. In this way, one can get the required number of processing and the processing quantity each time from the machining condition. Angular rigidity of a machining system,hardness of workpiece, etc., can be input in a form of fuzzy values. Feasibility in solving error reflection and optimizing machining parameters with a RBF neural network is verified by a simulation test with MATLAB.
Reconstruction of ploughed soil surface with 3D fractal interpolation
Liu, Y.; Lu, Z.; Hoogmoed, W.B.; Li, X.
2014-01-01
By using a laser profiler, the roughness of ploughed soil surface was obtained. 3D fractal interpolation method was used to interpolate several kinds of reduced measured surface data which were reduced from the original measured ploughed soil surface elevation data in different reduction rates. Also
Visualizing and Understanding the Components of Lagrange and Newton Interpolation
Yang, Yajun; Gordon, Sheldon P.
2016-01-01
This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…
A FRACTAL-BASED STOCHASTIC INTERPOLATION SCHEME IN SUBSURFACE HYDROLOGY
The need for a realistic and rational method for interpolating sparse data sets is widespread. Real porosity and hydraulic conductivity data do not vary smoothly over space, so an interpolation scheme that preserves irregularity is desirable. Such a scheme based on the properties...
Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface
Xinru Liu
2014-01-01
Full Text Available A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.
Adaptive Global Sliding Mode Control for MEMS Gyroscope Using RBF Neural Network
Yundi Chu
2015-01-01
Full Text Available An adaptive global sliding mode control (AGSMC using RBF neural network (RBFNN is proposed for the system identification and tracking control of micro-electro-mechanical system (MEMS gyroscope. Firstly, a new kind of adaptive identification method based on the global sliding mode controller is designed to update and estimate angular velocity and other system parameters of MEMS gyroscope online. Moreover, the output of adaptive neural network control is used to adjust the switch gain of sliding mode control dynamically to approach the upper bound of unknown disturbances. In this way, the switch item of sliding mode control can be converted to the output of continuous neural network which can weaken the chattering in the sliding mode control in contrast to the conventional fixed gain sliding mode control. Simulation results show that the designed control system can get satisfactory tracking performance and effective estimation of unknown parameters of MEMS gyroscope.
An Adaptive-PSO-Based Self-Organizing RBF Neural Network.
Han, Hong-Gui; Lu, Wei; Hou, Ying; Qiao, Jun-Fei
2016-10-24
In this paper, a self-organizing radial basis function (SORBF) neural network is designed to improve both accuracy and parsimony with the aid of adaptive particle swarm optimization (APSO). In the proposed APSO algorithm, to avoid being trapped into local optimal values, a nonlinear regressive function is developed to adjust the inertia weight. Furthermore, the APSO algorithm can optimize both the network size and the parameters of an RBF neural network simultaneously. As a result, the proposed APSO-SORBF neural network can effectively generate a network model with a compact structure and high accuracy. Moreover, the analysis of convergence is given to guarantee the successful application of the APSO-SORBF neural network. Finally, multiple numerical examples are presented to illustrate the effectiveness of the proposed APSO-SORBF neural network. The results demonstrate that the proposed method is more competitive in solving nonlinear problems than some other existing SORBF neural networks.
A disposition of interpolation techniques
Knotters, M.; Heuvelink, G.B.M.
2010-01-01
A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated v
A disposition of interpolation techniques
Knotters, M.; Heuvelink, G.B.M.
2010-01-01
A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated v
Interpolating function and Stokes Phenomena
Honda, Masazumi
2015-01-01
When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional $\\varphi^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.
基于GIS的海洋底栖生物栖息密度空间插值方法%Study on spatial interpolation method of benthos density based on GIS
刘春洋; 李轶平; 董婧
2012-01-01
在地理信息系统即GIS的支持下,分别采用反距离加权(inverse distance weighted,IDW)、普通克里格(ordinary kriging,OK)、规则样条(regularize spline,RS)和张力样条(tension spline,Ts)4种插值方法对2006年7月获得的大连湾底栖生物栖息密度的数据进行空间插值处理,并对插值结果的精确度进行交叉验证,分析和比较不同插值方法获得的分布图.结果表明,插值精确度普通克里格＞反距离加权＞张力样条＞规则样条;4种方法均能较客观的模拟出底栖生物栖息密度的分布趋势,但是在整体趋势和局部趋势两方面的综合考虑下,普通克里格的表现效果更好.文章进一步指出,在确定站位数量及分布前提下,插值结果的精确度可以通过选择空间插值方法得以改善,但其根本还是取决于站位布置的数量和其分布合理性.%Under the aegis of Geostatistics and Geographic Information Systems, four interpolation methods including Inveise distance weighting (IDW), Ordinary Kriging (OK), Regularize Spline (RS) and Tension Spline (TS) are devoted to the spatial interpolation of density belong to the bentho, which obtained at Dalian Bay in 2006 Jul. At the Cross-validation linked to the accuracy of the interpolation results and analysis of the distribution maps were made. It was obtained bom different methods. The conclusion shows the accuracy tendency, Ordinary Kriging > Inverse distance weighting > Tension Spline > Regularize Spline. From the observation of the distribution maps, four methods mentioned above can simulate the accuracy tendency of die benthos'density objectively. However, the overall and local trend into account, the representation of Ordinary Kriging is the best. The investigation also showed that the accuracy of the interpolation results can be improved by option of the spatial interpolation methods, when the number and distribution of berths are unalterable.
Delibasis, Konstantinos K; Kechriniotis, Aristides
2014-07-01
In this paper, we present a novel formula of the bivariate Hermite interpolating (BHI) polynomial in the case of support points arranged on a grid with variable step. This expression is applicable when interpolation of a bivariate function is required, given its value and the values of its partial derivatives of arbitrarily high order, at the support points. The proposed formula is a generalization of an existing formula for the bivariate Hermite polynomial. It is also algebraically much simpler, thus can be computed more efficiently. In order to apply Hermite interpolation to image interpolation, we simplify the proposed (BHI) to handle support points on a regular unit-step grid. The values of image partial derivatives are arithmetically approximated using compact finite differences. The proposed method is being assessed in a number of image interpolation experiments that include a synthetic image, for which the values of the partial derivatives are computed analytically, as well as a collection of images from different medical modalities. The proposed BHI with up to second-order image partial derivatives, outperforms the convolution-based interpolation methods, as well as generalized interpolation methods with the same number of support points that was compared with, in the majority of image interpolation experiments. The computational load of the proposed BHI is calculated and its behaviour with respect to its controlling parameters is investigated.
Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions
Qianjin Zhao; Jieqing Tan
2007-01-01
This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction.Finally assemble these blocks by Newton's method to shape the whole interpolation scheme.Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton's polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally,numerical examples are given to show the effectiveness of the proposed method.
Feed-rate-controlled method of iterative algorithm for curve interpolation%迭代算法的曲线插补进给速度控制方法
邓昌奇; 廖辉
2013-01-01
在数控加工中,为了满足较高的加工精度和保持恒定的进给速度要求,提高数控加工复杂零件的能力,数控系统插补器需要采用较复杂的插补算法,其计算量大,耗时多,影响加工速度.针对这一问题,根据参数曲线数控插补原理,指出了Taylor展开算法和迭代算法,给定曲线,利用当前弦长和当前插补点,精确算出下一插补点.在迭代次数和迭代误差都小于设定值时结束迭代,即可算出下一插补点,且保持当前点和速度,否则继续迭代直到满足要求为止,给出了基于迭代算法的曲线实时插补进给速度的控制方法.仿真实例结果表明,提出的算法能够满足各种不同参数曲线的加工.与常规插补算法相比,该算法通用性强,计算量小,进给误差小,计算精度高,提高了加工效率.%In order to maintain a high machining accuracy and a constant speed feed-rate in CNC machining and improve the machining capability of CNC in handing complex part,the complicated interpolation algorithm needs to be used in CNC interpolation,which is time-consuming for large amount of computation,thus the machining speed is influenced.To solve this problem,based on the principle of parametric curve paths CNC interpolating,it is pointed out that Taylor series and iterative algorithm,given curve,using the chord length and the interpolation point,accurately calculate the next interpolation points.In the number of iterations and iterative error are less than the set value when the end of the iteration,next interpolation points can be calculated,and keep the current point and speed,otherwise continue iterative algorithm until they meet the requirements,feed-rate-controlled method based on iterative algorithm for curve real-time interpolation has also been given.The simulation results demonstrate that the proposed algorithm can satisfy the machining of a variety of different parametric curves.Compared with the conventional interpolation
Pattern-oriented memory interpolation of sparse historical rainfall records
Matos, J. P.; Cohen Liechti, T.; Portela, M. M.; Schleiss, A. J.
2014-03-01
The pattern-oriented memory (POM) is a novel historical rainfall interpolation method that explicitly takes into account the time dimension in order to interpolate areal rainfall maps. The method is based on the idea that rainfall patterns exist and can be identified over a certain area by means of non-linear regressions. Having been previously benchmarked with a vast array of interpolation methods using proxy satellite data under different time and space availabilities, in the scope of the present contribution POM is applied to rain gauge data in order to produce areal rainfall maps. Tested over the Zambezi River Basin for the period from 1979 to 1997 (accurate satellite rainfall estimates based on spaceborne instruments are not available for dates prior to 1998), the novel pattern-oriented memory historical interpolation method has revealed itself as a better alternative than Kriging or Inverse Distance Weighing in the light of a Monte Carlo cross-validation procedure. Superior in most metrics to the other tested interpolation methods, in terms of the Pearson correlation coefficient and bias the accuracy of POM's historical interpolation results are even comparable with that of recent satellite rainfall products. The new method holds the possibility of calculating detailed and performing daily areal rainfall estimates, even in the case of sparse rain gauging grids. Besides their performance, the similarity to satellite rainfall estimates inherent to POM interpolations can contribute to substantially extend the length of the rainfall series used in hydrological models and water availability studies in remote areas.
李东升; 施昆; 毕廷涛; 任敏栓
2011-01-01
以云南省会泽县者海镇土壤中重金属的含量与分布状况进行数据采集,采用ArcGIS中的地统计分析模块对土壤中重金属分布进行空间插值研究.运用反距离加权插值、多项式插值、径向基函数插值法和克里金插值对土壤中重金属的进行插值比较,发现当土壤中的重金属基本符合正态分布是Kriging插值效果较好,而当数据为非正态分布其它的方法能够更好对该地区重金属发布进行模拟.%Through acquisition data of heavy metal content and the distribution in the soil of Yunnan Province Huize County Zhehai Town， statistical analysis module in ArcGIS is used to conduct the spatial interpolation research of heavy metal distribution in the soil. Comparing the interpolation of heavy metal in the soil with the reverse distance weighting method , polynomial interpolation method,radial basis function method and Kriging method ,it discovered that if heavy metal contain fit the normal distribution Kriging method can obtain a better simulate effect than other method, if it does not other methods will be better.
Curve interpolation based on Catmull-Clark subdivision scheme
无
2003-01-01
An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing "symmetric zonal meshes", which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm, such as interpolating single open curve or closed curve, a mesh of nonintersecting or intersecting curve. The interpolating surface is C2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh, i.e. the surface is only C0 along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.
Comparative study and error analysis of digital elevation model interpolations
CHEN Ji-long; WU Wei; LIU Hong-bin
2008-01-01
Researchers in P.R.China commonly create triangulate irregular networks (TINs) from contours and then convert TINs into digital elevation models (DEMs). However, the DEM produced by this method can not precisely describe and simulate key hydrological features such as rivers and drainage borders. Taking a hilly region in southwestern China as a research area and using ArcGISTM software, we analyzed the errors of different interpolations to obtain distributions of the errors and precisions of different algorithms and to provide references for DEM productions. The results show that different interpolation errors satisfy normal distributions, and large error exists near the structure line of the terrain. Furthermore, the results also show that the precision of a DEM interpolated with the Australian National University digital elevation model (ANUDEM) is higher than that interpolated with TIN. The DEM interpolated with TIN is acceptable for generating DEMs in the hilly region of southwestern China.
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Matt, Michael Andreas
2012-01-01
Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C1 splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C2 splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the Alfeld split, where each tetrahedron
MDI Synoptic Charts of Magnetic Field: Interpolation of Polar Fields
Liu, Yang; Hoeksema, J. T.; Zhao, X.; Larson, R. M.
2007-05-01
In this poster, we compare various methods for interpolation of polar field for the MDI synoptic charts of magnetic field. By examining the coronal and heliospheric magnetic field computed from the synoptic charts based on a Potential Field Source Surface model (PFSS), and by comparing the heliospheric current sheets and footpoints of open fields with the observations, we conclude that the coronal and heliospheric fields calculated from the synoptic charts are sensitive to the polar field interpolation, and a time-dependent interpolation method using the observed polar fields is the best among the seven methods investigated.
Occlusion-Aware View Interpolation
Janusz Konrad
2009-01-01
Full Text Available View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
Occlusion-Aware View Interpolation
Ince Serdar
2008-01-01
Full Text Available Abstract View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
Tsitouras, Ch.; Papageorgiou, G.; Kalvouridis, T.
1992-12-01
Runge-Kutta-Nystrom (RKN) codes for the solution of the initial value problem for the general second-order differential system were developed recently, although the methodology on which they are based was known many years ago. The efficiency of several general Runge-Kutta-Nystrom (GRKN) methods is examined by posing some criteria of cost and accuracy. These methods supplied with the corresponding interpolants are applied to some problems of celestial dynamics. The results obtained show that these codes have good responses in the approximation of the solution of these problems.
朱晖; 马孝义; 李忠娟; 李贤波
2012-01-01
Precipitation is an important climate elements. With the increasing need tor spatial precipitation lntormatlon, spatial inter- polation method of precipitation is widely used. Taking 25 Baojixia Irrigation sites 1961-1990, 30-year average precipitation data for spatial interpolation to use software ArcGIS. Using Overall Polynomial method, IDW method, Kriging interpolation method to do re search on spatial interpolation is carried in Baojixia Irrigation. Results show that there is a great difference in precipitation distribu- tion in Baojixia Irrigation. The precipitation in the southwest of Baojixia Irrigation is more than that in Northeast. @The interpola- tion methods have advantages as well as disadvantages. The Simple Kriging Method works best in the whole analysis. Simple Kriging method is used to receive the precipitation forecast data. @Simple Kriging Method can better reflect the spatial distribution of precipi- tation in Baoiixia Irri~ation, but accuracy is not high enough, so interpolation accuracy is to be further enhanced.%降水量是重要的气候要素，随着降水量空间信息需求的日益增加，降水量的空间插值应用及其广泛。运用软件ArcGIS将宝鸡峡灌区25个基本站点1961—1990年30年平均降水量数据进行空间插值，采用整体多项式法、反离权重法、克里金插值方法研究宝鸡峡地区降水的空间分布，通过对比分析得出：①宝鸡峡地区降水量在空间上变化较大，总体上东南部多于西北部。②几种插值方法各有优缺点，整体看克里金方法误差均值和误差均方差较小，预测效果最佳，可以更好的得到降水量的预测值。③采用简单克里金法虽然可以较好地反映宝鸡峡灌区降水量的空间分布但精度还是不够高的，插值精度还有待进一步提高。
Mehl, S.; Hill, M.C.
2004-01-01
This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.
Spatial interpolation of monthly mean air temperature data for Latvia
Aniskevich, Svetlana
2016-04-01
Temperature data with high spatial resolution are essential for appropriate and qualitative local characteristics analysis. Nowadays the surface observation station network in Latvia consists of 22 stations recording daily air temperature, thus in order to analyze very specific and local features in the spatial distribution of temperature values in the whole Latvia, a high quality spatial interpolation method is required. Until now inverse distance weighted interpolation was used for the interpolation of air temperature data at the meteorological and climatological service of the Latvian Environment, Geology and Meteorology Centre, and no additional topographical information was taken into account. This method made it almost impossible to reasonably assess the actual temperature gradient and distribution between the observation points. During this project a new interpolation method was applied and tested, considering auxiliary explanatory parameters. In order to spatially interpolate monthly mean temperature values, kriging with external drift was used over a grid of 1 km resolution, which contains parameters such as 5 km mean elevation, continentality, distance from the Gulf of Riga and the Baltic Sea, biggest lakes and rivers, population density. As the most appropriate of these parameters, based on a complex situation analysis, mean elevation and continentality was chosen. In order to validate interpolation results, several statistical indicators of the differences between predicted values and the values actually observed were used. Overall, the introduced model visually and statistically outperforms the previous interpolation method and provides a meteorologically reasonable result, taking into account factors that influence the spatial distribution of the monthly mean temperature.
A parameterization of observer-based controllers: Bumpless transfer by covariance interpolation
Stoustrup, Jakob; Komareji, Mohammad
2009-01-01
This paper presents an algorithm to interpolate between two observer-based controllers for a linear multivariable system such that the closed loop system remains stable throughout the interpolation. The method interpolates between the inverse Lyapunov functions for the two original state feedbacks...... and between the Lyapunov functions for the two original observer gains to determine an intermediate observer based controller....
徐传燕; 丁康; 林慧斌; 杨志坚
2011-01-01
谐波信号离散频谱分析的比值校正法(内插法)在无噪声时是一种准确的校正方法,只存在计算时的舍入误差,但在包含噪声尤其信噪比较低时,校正精度会有所下降,甚至误差很大.研究了比值校正法的幅值与相位加不同的窗函数及加性高斯白噪声时的统计方差公式,并通过不同信噪比下的仿真验证了其准确性.建议避免在归一化频率误差较低的情况下使用加矩形窗的比值校正法来校正相位.%Without noise, Interpolation method for discrete spectrum is an accurate correction method except rounding errors. However, the estimation accuracy can be greatly reduced when a signal corrupted with noise, and even turns out to be meaningless. The paper investigates the influences of windowing and additive White Gaussian Noise on the accuracy of amplitude and phase based on interpolation method. Analytical expressions of the estimator variance for amplitude and phase correction are derived. Simulation results confirm the validity of the presented analysis. We suggest to avoid using interpolation method under the condition that the rectangular window is adopted to correct the phase when the normalization frequency error is small.
李俊杰; 严家斌
2015-01-01
径向基点插值法(RPIM)作为一种插值型无网格方法，为改善无网格点插值法(PIM)在形函数构造过程中可能出现的矩阵奇异性问题而提出的一种方法，该算法支持域无量纲尺寸的选择区间大，能更好地处理各类工程与科学计算问题。介绍了RPIM的近似原理，给出了径向基函数形状参数的推荐值；从大地电磁二维变分问题出发利用Galerkin法结合高斯积分公式推导出相应的系统矩阵离散表达式；为提高RPIM的计算效率，将RPIM与有限元法(FEM)耦合，提出了有限元－径向基点插值法(FE-RPIM)，多个模型的数值计算验证了RPIM精度高、处理复杂模型便利及耦合法计算复杂模型高效的特点。%Polynomial basis interpolation method (RPIM), as a kind of typical interpolation meshfree method, was proposed to overcome the defects of point interpolation method (PIM) that the construction process of the shape function involves the matrix inverse operation. This method overcomes the matrix inverse problem, and supports the wider domain dimensionless size interval to better deal with all kinds of engineering and scientific computing problems. The approximate principle of RPIM was introduced in detail, and the discrete system matrix expression corresponding to the magnetotelluric two-dimensional variational problem by combining the Galerkin method and the gauss integral formula was deduced. In order to overcome the defects of low computational efficiency of RPIM, the finite element−radial point interpolation method (FE−RPIM) based on coupling the FEM and RPIM was proposed. The conclusions were verified by the numerical calculation of several models. The results show that RPIM has the advantage of high precision and convenience to calculate complex models, and FE-RPIM has the characteristics of high calculation efficiency for complex models.
Interpolation by two-dimensional cubic convolution
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
Ahn, Kang-Hyun; Halpern, Howard J
2007-03-01
Spectral-spatial images reconstructed from a small number of projections suffer from streak artifacts that are seen as noise, particularly in the spectral dimension. Interpolation in projection space can reduce artifacts in the reconstructed images. The reduction of background artifacts improves lineshape fitting. In this work, we compared the performances of angular interpolation implemented using linear, cubic B-spline, and sinc methods. Line width maps were extracted from 4-D EPR images of phantoms using spectral fitting to evaluate each interpolation method and its robustness to noise. Results from experiment and simulation showed that the cubic B-spline, angular interpolation was preferable to either sinc or linear interpolation methods.
Steady State Stokes Flow Interpolation for Fluid Control
Bhatacharya, Haimasree; Nielsen, Michael Bang; Bridson, Robert
2012-01-01
Fluid control methods often require surface velocities interpolated throughout the interior of a shape to use the velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics — velocity extrapolation in the normal direction and potential flow...... — suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures...... the rotational components and is suitable for controlling liquid animations where tangential motion is pronounced, such as in a breaking wave...
Image super-resolution using windowed ordinary Kriging interpolation
Zhang, Qianying; Wu, Jitao
2015-02-01
This paper presents a novel interpolation approach for single image super-resolution based on ordinary Kriging interpolation, which has been widely used in geostatistics. The proposed method simultaneously considers the intensity distances and geometry of the pixel data. We employ a new intensity distance definition and local windows surrounding each unknown high-resolution pixel to implement the algorithm. The proposed approach is able to produce adaptive weights and edge preservation is achieved. Our experimental results show the efficiency of the proposed approach compared to conventional interpolation methods in terms of the peak signal-to-noise (PNSR) and visual perception.
Truth-value transmittal fuzzy reasoning interpolator
YAN Jianping; LEUNG Yee
2005-01-01
In this paper, we firstly associate fuzzy reasoning algorithm with the interpolation algorithm and discuss the limitation of defuzzification methods used commonly in the fuzzy reasoning algorithm. Secondly, we give a new fuzzy reasoning algorithm in case of single input, called the truth-value transmittal method, and discuss its properties. Finally, we analyze the rationality to adopy the truth-value transmittal method as the defuzzification method of full implication triple I method, and show that although CRI and triple I fuzzy reasoning method are different from fuzzy output set, they are uniform finally under the truth-value transmittal defuzzification method.
Interpolation in Spaces of Functions
K. Mosaleheh
2006-03-01
Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces
COMPARISONS BETWEEN DIFFERENT INTERPOLATION TECHNIQUES
G. Garnero
2014-01-01
In the present study different algorithms will be analysed in order to spot an optimal interpolation methodology. The availability of the recent digital model produced by the Regione Piemonte with airborne LIDAR and the presence of sections of testing realized with higher resolutions and the presence of independent digital models on the same territory allow to set a series of analysis with consequent determination of the best methodologies of interpolation. The analysis of the residuals on the test sites allows to calculate the descriptive statistics of the computed values: all the algorithms have furnished interesting results; all the more interesting, notably for dense models, the IDW (Inverse Distance Weighing algorithm results to give best results in this study case. Moreover, a comparative analysis was carried out by interpolating data at different input point density, with the purpose of highlighting thresholds in input density that may influence the quality reduction of the final output in the interpolation phase.
Geological Visualization System with GPU-Based Interpolation
Huang, L.; Chen, K.; Lai, Y.; Chang, P.; Song, S.
2011-12-01
There has been a large number of research using parallel-processing GPU to accelerate the computation. In Near Surface Geology efficient interpolations are critical for proper interpretation of measured data. Additionally, an appropriate interpolation method for generating proper results depends on the factors such as the dense of the measured locations and the estimation model. Therefore, fast interpolation process is needed to efficiently find a proper interpolation algorithm for a set of collected data. However, a general CPU framework has to process each computation in a sequential manner and is not efficient enough to handle a large number of interpolation generally needed in Near Surface Geology. When carefully observing the interpolation processing, the computation for each grid point is independent from all other computation. Therefore, the GPU parallel framework should be an efficient technology to accelerate the interpolation process which is critical in Near Surface Geology. Thus in this paper we design a geological visualization system whose core includes a set of interpolation algorithms including Nearest Neighbor, Inverse Distance and Kriging. All these interpolation algorithms are implemented using both the CPU framework and GPU framework. The comparison between CPU and GPU implementation in the aspect of precision and processing speed shows that parallel computation can accelerate the interpolation process and also demonstrates the possibility of using GPU-equipped personal computer to replace the expensive workstation. Immediate update at the measurement site is the dream of geologists. In the future the parallel and remote computation ability of cloud will be explored to make the mobile computation on the measurement site possible.
Abghari, H.; van de Giesen, N.; Mahdavi, M.; Salajegheh, A.
2009-04-01
Artificial intelligence modeling of nonstationary rainfall-runoff has some restrictions in simulation accuracy due to the complexity and nonlinearity of training patterns. Preprocessing of trainings dataset could determine homogeneity of rainfall-runoff patterns before modeling. In this presentation, a new hybrid model of Artificial Intelligence in conjunction with clustering is introduced and applied to flow prediction. Simulation of Nazloochaei river flow in North-West Iran was the case used for development of a PNN-RBF model. PNN classify a training dataset in two groups based on Parezen theory using unsupervised classification. Subsequently each data group is used to train and test two RBF networks and the results are compared to the application of all data in a RBF network without classification. Results show that classification of rainfall-runoff patterns using PNN and prediction of runoff with RBF increase prediction precise of networks. Keywords: Probabilistic Neural Network, Radial Base Function Neural Network, Parezen theory, River Flow Prediction
RBF network designing based on artificial immune%基于人工免疫系统的RBF网络设计
朱亚男
2015-01-01
由于传统的RBF网络学习方法存在诸多的不足，本文提出基于免疫机制的三级RBF网络学习方法：在第一级得到网络隐层节点数作为疫苗，不仅可自行构建网络，还降低了第二级搜索空间的复杂度；第二级利用人工免疫算法对解空间进行多点搜索，得到全局最优的隐层非线性参数；第三级采用最小二乘法确定网络输出层线性参数，极大地降低了第二级结构的维数，提高了算法效率。经典型Hermit多项式逼近实验验证了该方法训练得到的RBF网络性能优越。%In order to improve the traditional RBF learning strategy, a three-level RBF network learning algorithm based on immune system is proposed, which can calculates the number of the hidden-layer neurons in the first level as immune vaccine, the network can be established and adjusted by itself, and the complexity of search space in the second level can be reduced. The global optimum hidden-layer nonlinear parameters are searched for in the second level by parallel searching with artificial immune algorithm. The output-layer linear parameters are estimated in the third level with least square method, which makes the design dimension of the second level decreased and the algorithm efficiency improved. The experiment of Hermit polynomial approximation shows that the performance of the RBF network trained by the algorithm is superior.
Application of RBF neural network to fault diagnosis in heliostats filed%RBF神经网络在定日镜场故障诊断中的应用
王成昱; 万定生; 郭铁铮
2011-01-01
针对定日镜场故障与征兆之间的关系特点,介绍了RBF神经网络运用于定日镜场故障诊断的基本方法.利用MATLAB神经网络工具箱建立和训练RBF神经网络,并对网络进行了测试.结果说明RBF神经网络在定目镜场故障诊断中具有较高的准确性和可靠性.%For the characteristic of the relationship between faults and symptoms, the basic principle and method of application of RBF neural network technique for the fault diagnosis in heliostats filed were introduced. The RBF neural network was built by using the neural network toolbox of MATLAB. The test result showed the use of the RBF network neural model was accurate and reliable.
Kriging interpolating cosmic velocity field
Yu, Yu; Zhang, Jun; Jing, Yipeng; Zhang, Pengjie
2015-10-01
Volume-weighted statistics of large-scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of the uncertainties of galaxy density bias entangled in observed number density-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. Therefore, the exploration of velocity assignment methods with well-controlled sampling artifacts is of great importance. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number nk of the nearby particles to interpolate, and the density nP of the observed sample are investigated. First, we find that Kriging induces 1% and 3% systematics at k ˜0.1 h Mpc-1 when nP˜6 ×1 0-2(h-1 Mpc )-3 and nP˜6 ×1 0-3(h-1 Mpc )-3 , respectively. The deviation increases for decreasing nP and increasing k . When nP≲6 ×1 0-4(h-1 Mpc )-3 , a smoothing effect dominates small scales, causing significant underestimation of the velocity power spectrum. Second, increasing nk helps to recover small-scale power. However, for nP≲6 ×1 0-4(h-1 Mpc )-3 cases, the recovery is limited. Finally, Kriging is more sensitive to the variogram prior for a lower sample density. The most straightforward application of Kriging on the cosmic velocity field does not show obvious advantages over the nearest-particle method [Y. Zheng, P. Zhang, Y. Jing, W. Lin, and J. Pan, Phys. Rev. D 88, 103510 (2013)] and could not be directly applied to cosmology so far. However, whether potential improvements may be achieved by more delicate versions of Kriging is worth further investigation.
Backprojection by upsampled Fourier series expansion and interpolated FFT.
Tabei, M; Ueda, M
1992-01-01
A fast backprojection method through the use of interpolated fast Fourier transform (FFT) is presented. The computerized tomography (CT) reconstruction by the convolution backprojection (CBP) method has produced precise images. However, the backprojection part of the conventional CBP method is not very efficient. The authors propose an alternative approach to interpolating and backprojecting the convolved projections onto the image frame. First, the upsampled Fourier series expansion of the convolved projection is calculated. Then, using a Gaussian function, it is projected by the aliasing-free interpolation of FFT bins onto a rectangular grid in the frequency domain. The total amount of computation in this procedure for a 512x512 image is 1/5 of the conventional backprojection method with linear interpolation. This technique also allows the arbitrary control of the frequency characteristics.
Four-band compactly supported orthogonal symmetric interpolating scaling function
水鹏朗; 保铮
2001-01-01
An efficient method is proposed to design 4-band scaling functions w ith the following five advantages: compact support, orthogonality, symmetry, regularity, and interpolation; and a family of such scaling functions with the shortest support is given.
李增兵; 赵庚星; 赵倩倩; 李百红; 武婕
2012-01-01
耕地是农业生产的重要资源,耕地地力评价是耕地质量建设的重要手段,与之相关的土壤养分插值技术关系到耕地地力评价精度与可用性.以历城区为研究对象,将历城区划分为历城平原区和丘陵区,分析其采样点养分分布情况、评价指标中涉及的土壤有机质、有效磷、速效钾、有效锌、有效硼的空间变异情况.分别用反距离权重插值法(IDW)和普通克里格插值法(OK)对历城全区、平原区和丘陵区的土壤养分进行插值,通过交叉验证、叠加对比分析等方法比较不同情况下不同插值方法的精度,并对比分析基于不同插值方法的耕地地力评价结果.结果显示,IDW和OK2种方法都具有较高精度,其中IDW插值方法较适宜于丘陵区,而OK插值方法则适宜于平原区；对于有多种参评元素参与的县域耕地地力评价,采用2种方法的评价结果相差不大.基于实用性与精确性结合原则,IDW方法是县域耕地地力评价养分空间内插的最佳选择.%Farmland was an important resource of agricultural production, and cultivated land fertility evaluation is an important guarantee for quality construction of arable land, soil nutrients interpolation techniques affect the evaluation of farmland accuracy and availability immediately. This paper took data of Licheng County as an example, the city was classified into plain and hilly region based on the landform condition. We analyzed distribution and spatial variation via the sample point data, including organic matter, available phosphorus, rapid available potassium, available zinc and available boron. This paper carried on interpolation of soil nutrients by the model of Inverse Distance Weighted and Ordinary Kriging in Licheng plain and hilly regions. Moreover, we compared the two kinds of interpolation method by the way of cross-validation and comparative analysis. At the same time, compared and analyzed the different
贾伟宽; 赵德安; 刘晓洋; 唐书萍; 阮承治; 姬伟
2015-01-01
In order to improve the recognition precision and speed for apple, and further improve the harvesting efficiency of apple harvesting robot, an apple recognition method based on combiningK-means clustering segmentation with genetic radial basis function (RBF) neural network is proposed. Firstly, the captured apple image is transformed into L*a*b* color space, and then under this color space, theK-means clustering algorithm is used to segment the apple image. The color feature components and shape components of segmented image are extracted respectively. The color features include R, G, B, H, S and I, a total of 6 feature components; and the shape features include circular variance, density, ratio of perimeter square to area, and 7 Hu invariant moments, a total of 10 shape components. These extracted 16 features are used as the inputs of neural network to train RBF neural network, and get the apple recognition model. Due to some inherent defects the RBF neural network has, such as low learning rate, easily causing over fitting phenomenon, genetic algorithm (GA) is introduced to optimize the connection weights and the number of hidden layer neurons. In this study, a new optimization way is adopted, that is, the hybrid encoding of the number of hidden layer neurons and connection weights is carried out simultaneously. This moment, the learning of weights is not completed, and the least mean square (LMS) is used to further learn the connection weights. Finally, an optimized neural network model (GA-RBF-LMS) is established, which is to improve the operating efficiency and recognition precision. In the experiments, there are 150 images captured, and they have 229 apples; among them 50 images are selected as training samples, and the rest as testing samples. Every image for training sample has only one apple, so the testing samples have 179 apples. In order to get the precise model, fruits of apple are together with branches and leaves for training during the training
LIP: The Livermore Interpolation Package, Version 1.4
Fritsch, F N
2011-07-06
This report describes LIP, the Livermore Interpolation Package. Because LIP is a stand-alone version of the interpolation package in the Livermore Equation of State (LEOS) access library, the initials LIP alternatively stand for the 'LEOS Interpolation Package'. LIP was totally rewritten from the package described in [1]. In particular, the independent variables are now referred to as x and y, since the package need not be restricted to equation of state data, which uses variables {rho} (density) and T (temperature). LIP is primarily concerned with the interpolation of two-dimensional data on a rectangular mesh. The interpolation methods provided include piecewise bilinear, reduced (12-term) bicubic, and bicubic Hermite (biherm). There is a monotonicity-preserving variant of the latter, known as bimond. For historical reasons, there is also a biquadratic interpolator, but this option is not recommended for general use. A birational method was added at version 1.3. In addition to direct interpolation of two-dimensional data, LIP includes a facility for inverse interpolation (at present, only in the second independent variable). For completeness, however, the package also supports a compatible one-dimensional interpolation capability. Parametric interpolation of points on a two-dimensional curve can be accomplished by treating the components as a pair of one-dimensional functions with a common independent variable. LIP has an object-oriented design, but it is implemented in ANSI Standard C for efficiency and compatibility with existing applications. First, a 'LIP interpolation object' is created and initialized with the data to be interpolated. Then the interpolation coefficients for the selected method are computed and added to the object. Since version 1.1, LIP has options to instead estimate derivative values or merely store data in the object. (These are referred to as 'partial setup' options.) It is then possible to pass the object
Louvet, S.; Paturel, J. E.; Mahé, G.; Rouché, N.; Koité, M.
2016-01-01
The climatic evolution of the Bani river watershed, the main tributary to the upper Niger River, is approached through the spatiotemporal variability of rainfall grids over the 1950-2006 period. The analyses are conducted, and their results compared, using four different methods of spatial interpolation of rainfall fields: the spline, kriging, weighted inverse distance, and nearest neighbor methods. The largest changes are observed for all of these grids, but differences—and in some cases divergent results—appear in the details. The analysis shows a substantial decline in rainfall, particularly marked in the center of the basin, during the 1970-2000 period with respect to the 1950-1969 period, and a slight upturn in the northern part, mainly since the beginning of the 1990s. The rainfall deficit can be attributed to a combination of factors: an earlier and drier end of the rainy season, less precipitation in the middle of the rainy season, more dry days and lower amounts of precipitation on rainy days. Two drought indices—the Effective Drought Index and Standardized Precipitation Index—revealed that the maximum duration of drought events increased most in the central part of the basin. Lastly, to supplement this comparison of methods of spatial interpolation of rainfall fields, the sensitivity of a hydrological model (GR2M) to rainfall data was tested. Given the distribution and density of rain gauge stations available in the Bani watershed, the kriging method is found to yield the best hydrological modeling performance.
张兴飞
2012-01-01
The normal height of the station can be obtained Lhrough GPS technology combined with lugh precision and high-resolution quasi-geoid refinement model. It can replace the conventional level measurements to reduce labor-intensive and improve efficiency.There are two factors that affect the accuracy: the accuracy of the geodetic height of the GPS station and its interpolation method. On Lhe basis of the geoid of Shenzhen with one-kilometer resolution, the effect and accuracy of CPS height anomaly interpolation are analyzed and the results show that the Kriging interpolation method is accurate and qtable for the high resolution quasi-geoid model.%地面点的正常高可以通过GPS技术结合高精度、高分辨率的似大地水准面模型获得,以代替劳动强度大效率低的传统水准(或高程)测量.影响精度的因素有两个:GPS点大地高的测量精度和该点内插高程异常的精度.本文主要针对深圳市1km格网似大地水准面数据,利用克里金法内插拟合高程异常值,用实例说明克里金法在深圳市似大地水准面的应用中可以满足大比例尺数字化测图的需要.
Hachani, Maha; Fourment, Lionel
2010-06-01
This paper describes the effect of tool discretization accuracy on the simulation of forming processes, especially for processes where the contact area is quite small with respect to the component size. For smoothing contact surface discretized by linear triangles, an algorithm is followed to develop a higher order quadratic interpolation of the curved surface from the positions and normal vectors of the nodes, as proposed by Nagata. Normal vectors are calculated at each node from the existing discretized surface by considering a patch of surrounding elements. This is accomplished by the mean of normal voting strategy. The efficiency and reliability of the resulting contact model are checked through several examples like indenting and ironing a bulk parallelepiped. It is also applied to complex ring rolling, form rolling and extrusion problems.
Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition
Lin, C.-H. [Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 821, Taiwan (China); Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)], E-mail: eechl53@cc.kyu.edu.tw; Du, Y.-C.; Chen Tainsong [Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)
2009-11-30
This paper proposes a method for cardiac arrhythmias recognition using the nonlinear interpolation fractal classifier. A typical electrocardiogram (ECG) consists of P-wave, QRS-complexes, and T-wave. Iterated function system (IFS) uses the nonlinear interpolation in the map and uses similarity maps to construct various data sequences including the fractal patterns of supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. Grey relational analysis (GRA) is proposed to recognize normal heartbeat and cardiac arrhythmias. The nonlinear interpolation terms produce family functions with fractal dimension (FD), the so-called nonlinear interpolation function (NIF), and make fractal patterns more distinguishing between normal and ill subjects. The proposed QRS classifier is tested using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Compared with other methods, the proposed hybrid methods demonstrate greater efficiency and higher accuracy in recognizing ECG signals.
Circular Interpolation Algorithms of 5-Axis Simultaneous CNC System
ZHENG Kuijing; SHANG Bo
2006-01-01
Spatial circular arc can be machined conveniently by a 5-axis NC machine tool. Based on the data sampling method, circular interpolation in two-dimensional plane is discussed briefly. The key is to solve the problem of circular center expressed in the workpiece coordinate system by means of the transformation matrix. Circular interpolation in three-dimensional space is analyzed in detail. The method of undetermined coefficient is used to solve the center of the spatial circle and the method of coordinate transformation is used to transform the spatial circle into the XY_plane. Circular arc in three-dimensional space can be machined by the positional 5-axis machining and the conical surface can be machined by the continuous 5-axis machining. The velocity control is presented to avoid the feedrate fluctuation. The interpolation algorithms are tested by a simulation example and the interpolation algorithms are proved feasible. The algorithms are applied to the 5-axis CNC system software.
3D Medical Image Interpolation Based on Parametric Cubic Convolution
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.
席港港; 赵庆志; 王军; 田晓文
2012-01-01
逐点比较法直线插补方法在开环数控系统中被广泛采用,但其存在插补误差大、直线光滑性差等缺点.针对以上问题,提出了改进的逐点比较法直线插补算法,避免了无穷大导数计算、多分支判断编程复杂等缺陷,提高了逐点比较法的直线插补精度.%Point-to-point comparison method of straight lines is widely used in open loop control system,but it exists some weaknesses such as high interpolation error and poor smoothness of straight line.For above problems,an improved point-to-point comparison method of straight lines is given which can avoid shortages of counting the infinity of derivative and complex programming of many branches,and also improve the interpolation precision of point-to-point comparison method of straight lines.
Femoropopliteal artery centerline interpolation using contralateral shape.
Tran, David N; Fleischmann, Dominik; Rakshe, Tejas; Roos, Justus E; Rosenberg, Jarrett; Straka, Matus; Napel, Sandy
2007-09-01
Curved planar reformation allows comprehensive visualization of arterial flow channels, providing information about calcified and noncalcified plaques and degrees of stenoses. Existing semiautomated centerline-extraction algorithms for curved planar reformation generation fail in severely diseased and occluded arteries. We explored whether contralateral shape information could be used to reconstruct centerlines through femoropopliteal occlusions. We obtained CT angiography data sets of 29 subjects (16m/13f, 19-86yo) without peripheral arterial occlusive disease and five consecutive subjects (1m/4f, 54-85yo) with unilateral femoropopliteal arterial occlusions. A gradient-based method was used to extract the femoropopliteal centerlines in nondiseased segments. Centerlines of the five occluded segments were manually determined by four experts, two times each. We interpolated missing centerlines in 2475 simulated occlusions of various occlusion lengths in nondiseased subjects. We used different curve registration methods (reflection, similarity, affine, and global polynomial) to align the nonoccluded segments, matched the end points of the occluded segments to the corresponding patent end points, and recorded maximum Euclidean distances to the known centerlines. We also compared our algorithm to an existing knowledge-based PCA interpolation algorithm using the nondiseased subjects. In the five subjects with real femoropopliteal occlusions, we measured the maximum Euclidean distance and the percentage of the interpolation that remained within a typical 3 mm radius vessel. In the nondiseased subjects, we found that the rigid registration methods were not significantly (pinterpolation of centerlines through arterial occlusions.
General-form 3-3-3 interpolation kernel and its simplified frequency-response derivation
Deng, Tian-Bo
2016-11-01
An interpolation kernel is required in a wide variety of signal processing applications such as image interpolation and timing adjustment in digital communications. This article presents a general-form interpolation kernel called 3-3-3 interpolation kernel and derives its frequency response in a closed-form by using a simple derivation method. This closed-form formula is preliminary to designing various 3-3-3 interpolation kernels subject to a set of design constraints. The 3-3-3 interpolation kernel is formed through utilising the third-degree piecewise polynomials, and it is an even-symmetric function. Thus, it will suffice to consider only its right-hand side when deriving its frequency response. Since the right-hand side of the interpolation kernel contains three piecewise polynomials of the third degree, i.e. the degrees of the three piecewise polynomials are (3,3,3), we call it the 3-3-3 interpolation kernel. Once the general-form frequency-response formula is derived, we can systematically formulate the design of various 3-3-3 interpolation kernels subject to a set of design constraints, which are targeted for different interpolation applications. Therefore, the closed-form frequency-response expression is preliminary to the optimal design of various 3-3-3 interpolation kernels. We will use an example to show the optimal design of a 3-3-3 interpolation kernel based on the closed-form frequency-response expression.
Tao Hu
2013-01-01
Full Text Available Horizontal attenuation total reflection Fourier transformation infrared spectroscopy (HATR-FT-IR studies on cuscutae semen and its confusable varieties Japanese dodder and sinapis semen combined with discrete wavelet transformation (DWT and radial basis function (RBF neural networks have been conducted in order to classify them. DWT is used to decompose the FT-IRs of cuscutae semen, Japanese dodder, and sinapis semen. Two main scales are selected as the feature extracting space in the DWT domain. According to the distribution of cuscutae semen, Japanese dodder, and sinapis semen’s FT-IRs, three feature regions are determined at detail 3, and two feature regions are determined at detail 4 by selecting two scales in the DWT domain. Thus five feature parameters form the feature vector. The feature vector is input to the RBF neural networks to train so as to accurately classify the cuscutae semen, Japanese dodder, and sinapis semen. 120 sets of FT-IR data are used to train and test the proposed method, where 60 sets of data are used to train samples, and another 60 sets of FT-IR data are used to test samples. Experimental results show that the accurate recognition rate of cuscutae semen, Japanese dodder, and sinapis semen is average of 100.00%, 98.33%, and 100.00%, respectively, following the proposed method.
Complementary Lidstone Interpolation and Boundary Value Problems
Ravi P. Agarwal
2009-01-01
Full Text Available We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial P2m(t of degree 2m, which involves interpolating data at the odd-order derivatives. For P2m(t we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a (2m+1th order differential equation and the complementary Lidstone boundary conditions.
Nonlinear Interpolation and Total Variation Diminishing Schemes
Dubois, François
2010-01-01
The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We prove that under general hypotheses the method of lines in well posed in $\\ ell^{\\infty} \\cap {\\rm BV} $ and we give precise sufficient conditions to establish that the total variation is diminishing. We observe that the second order accuracy can be maintained even at non sonic extrema. We establish also that both the TVD property and second order accuracy can be maintained after discretization in time with the second order accurate Heun scheme. Numerical illustration for the advection equation is presented.
李学斌
2014-01-01
在模具和航空等制造业，常会遇到复杂曲线曲面的数控加工。为满足提高加工NURBS曲线曲面精度和高速加工的要求，提出了将NURBS曲面采用等参数线法离散成一族NURBS曲线的直接插补算法。其优点是可将一阶、二阶导矢和控制弓高误差而自动调整进给速度的计算放在插补前的预处理中集中进行。%In the mould and aviation manufacturing industries, it is often faced with the numerical control machining of the complex curves and surfaces. In order to satisfy the requirements of improving the precision of machining NURBS curves and surfaces and the requirements of high-speed machining, the direct interpolation algorithm that can discrete the NURBS surfaces into the gens of NURBS curves by using the isoparametric curve method is presented. The advantage of this method is that the guide vectors of the first order and the second order and the calculation of automatically adjusting the feeding speed for control of the bow height error can be pretreated before interpolation.
Rough RBF Neural Network Based on Extreme Learning%基于极速学习的粗糙RBF神经网络
马刚; 丁世飞; 史忠植
2012-01-01
提出了一种用于训练粗糙RBF神经网络（rough RBF neural networks,R-RBF）的极速学习机（extreme learning machine,ELM）方法,通过引入矩阵的Moore-Penrose逆,将传统的迭代学习方法转换为一种求线性方程的极小范数最小二乘解的方法.实验证明,在训练精度、训练时间上都能够达到非常优越的性能,其泛化精度能够提升50%以上.%The paper proposes a method of training rough RBF neural networks（R-RBF） using the extreme learning machine（ELM）, which eonverts the traditional iterative training method to solve norm least-squares solution of general linear system by introducing Moore-Penrose inverse. Experiments show that it can reach a very superior performance in both time and aeeuraey when ELM trains the Rough RBF Neural Networks, which can improve the generalization accuracy more than 50% compared with the traditional thinking of adjusting parameters iterative[y.
A NEW ALGORITHM OF THE NONLINEAR ADAPTIVE INTERPOLATION
Shi Lingfeng; Guo Baolong
2006-01-01
The paper presents a new algorithm of NonLinearly Adaptive Interpolation (NLAI). NLAI is based on both the gradients and the curvature of the signals with the predicted subsection. It is characterized by adaptive nonlinear interpolation method with extracting the characteristics of signals. Experimental research testifies the validity of the algorithm using the echoes of the Ground Penetrating Radar (GPR). A comparison of this algorithm with other traditional algorithms demonstrates that it is feasible.
Considerations Related to Interpolation of Experimental Data Using Piecewise Functions
Stelian Alaci
2016-12-01
Full Text Available The paper presents a method for experimental data interpolation by means of a piecewise function, the points where the form of the function changes being found simultaneously with the other parameters utilized in an optimization criterion. The optimization process is based on defining the interpolation function using a single expression founded on the Heaviside function and regarding the optimization function as a generalised infinitely derivable function. The exemplification of the methodology is made via a tangible example.
孙伟; 刘正江; 李新民; 黄建萍; 陈焕
2013-01-01
提出了局部均值分解(Local mean decomposition,简称LMD)方法和径向基函数神经网络(Radial Basis Function Neural Network,简称RBF)相结合的滚动轴承故障诊断方法.LMD方法是一种新的自适应时频分析方法,能够有效地提取故障特征.该方法首先采用LMD对滚动轴承振动信号进行分解,计算分解得到的PF分量能量比,作为特征向量输入到RBF神经网络中,进行故障分类和识别.通过真实滚动轴承数据的故障诊断实验,验证了该方法的有效性.
Interpolation of climate variables and temperature modeling
Samanta, Sailesh; Pal, Dilip Kumar; Lohar, Debasish; Pal, Babita
2012-01-01
Geographic Information Systems (GIS) and modeling are becoming powerful tools in agricultural research and natural resource management. This study proposes an empirical methodology for modeling and mapping of the monthly and annual air temperature using remote sensing and GIS techniques. The study area is Gangetic West Bengal and its neighborhood in the eastern India, where a number of weather systems occur throughout the year. Gangetic West Bengal is a region of strong heterogeneous surface with several weather disturbances. This paper also examines statistical approaches for interpolating climatic data over large regions, providing different interpolation techniques for climate variables' use in agricultural research. Three interpolation approaches, like inverse distance weighted averaging, thin-plate smoothing splines, and co-kriging are evaluated for 4° × 4° area, covering the eastern part of India. The land use/land cover, soil texture, and digital elevation model are used as the independent variables for temperature modeling. Multiple regression analysis with standard method is used to add dependent variables into regression equation. Prediction of mean temperature for monsoon season is better than winter season. Finally standard deviation errors are evaluated after comparing the predicted temperature and observed temperature of the area. For better improvement, distance from the coastline and seasonal wind pattern are stressed to be included as independent variables.
An Algorithm for Interpolating Ship Motion Vectors
Qinyou Hu
2014-03-01
Full Text Available Interpolation of ship motion vectors is able to be used for estimating the lost ship AIS dynamic information, which is important for replaying marine accidents and for analysing marine traffic data. The previous methods can only interpolate ship's position, while not including ship's course and speed. In this paper, vector function is used to express the relationship between the ship's time and space coordinates, and the tangent of the vector function and its change rate are able to express physical characteristics of ship's course, speed and acceleration. The given AIS dynamic information can be applied to calculate the parameters of ship's vector function and then the interpolation model for ship motion vectors is developed to estimate the lost ship dynamic information at any given moment. Experiment results show that the ship motion vector function is able to depict the characteristics of ship motions accurately and the model can estimate not only the ship's position but also ship's course and speed at any given moment with limited differences.
Solving the Schroedinger equation using Smolyak interpolants.
Avila, Gustavo; Carrington, Tucker
2013-10-07
In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased.
陈宁; 于德介; 吕辉; 夏百战
2014-01-01
In order to improve the accuracy of simulation analysis of plate structural-acoustic coupled systems,the finite element-least square point interpolation method (FE-LSPIM)was extended to solve plate structural -acoustic coupled problems and a coupled FE-LSPIM for plate structural-acoustic coupled systems was proposed.With the proposed method,the shape functions of the finite element method and the least square point interpolation were used for local approximation,the element-compatibility of the finite element method and the quadratic polynomial completeness of LSPIM were inherited.Thus,the accuracy of simulation analysis could be improved.Numerical example of a box structural-acoustic coupled model was presented.Its results showed that using FE-LSPIMachieves a higher accuracy,compared with using FEMand smoothed FEMfor simulation of plate structural -acoustic coupled problems.%为提高板结构-声场耦合分析的计算精度，将有限元-最小二乘点插值法（Finite Element-Least Square Point Interpolation Method，FE-LSPIM）推广到板结构-声场耦合问题的分析中，提出了板结构-声场耦合问题分析的 FE-LSPIM/FE-LSPIM方法，推导了 FE-LSPIM/FE-LSPIM分析板结构-声场耦合问题的计算公式。FE-LSPIM/FE-LSPIM方法应用有限元单元形函数和最小二乘点插值法进行局部逼近，继承了有限元法的单元兼容性和最小二乘插值法的二次多项式完备性，提高了计算精度。以一六面体声场-结构耦合模型为研究对象进行分析，结果表明，与板结构-声场耦合问题分析的 FEM/FEM和光滑有限元/有限元（Smoothed Finite Element Method /Finite Element Method，SFEM/FEM）相比，FE-LSPIM/FE-LSPIM在分析板结构-声场耦合问题时具有更高的精度。
Frame Interpolation Based on Visual Correspondence and Coherency Sensitive Hashing
Lingling Zi
2013-01-01
Full Text Available The technology of frame interpolation can be applied in intelligent monitoring systems to improve the quality of surveillance video. In this paper, a region-guided frame interpolation algorithm is proposed by introducing two innovative improvements. On the one hand, a detection approach is presented based on visual correspondence for detecting the motion regions that correspond to attracted objects in video sequences, which can narrow the prediction range of interpolated frames. On the other hand, spatial and temporal mapping rules are proposed using coherency sensitive hashing, which can obtain more accurate predicted values of interpolated pixels. Experiments show that the proposed method can achieve encouraging performance in terms of visual quality and quantitative measures.
VLSI ARCHITECTURE OF AN AREA EFFICIENT IMAGE INTERPOLATION
John Moses C
2014-05-01
Full Text Available Image interpolation is widely used in many image processing applications, such as digital camera, mobile phone, tablet and display devices. Image interpolation is a method of estimating the new data points within the range of discrete set of known data points. Image interpolation can also be referred as image scaling, image resizing, image re-sampling and image zooming. This paper presents VLSI (Very Large Scale Integration architecture of an area efficient image interpolation algorithm for any two dimensional (2-D image scalar. This architecture is implemented in FPGA (Field Programmable Gate Array and the performance of this system is simulated using Xilinx system generator and synthesized using Xilinx ISE smulation tool. Various VLSI parameters such as combinational path delay, CPU time, memory usage, number of LUTs (Look Up Tables are measured from the synthesis report.
An Adaptive Weighting Algorithm for Interpolating the Soil Potassium Content
Liu, Wei; Du, Peijun; Zhao, Zhuowen; Zhang, Lianpeng
2016-04-01
The concept of spatial interpolation is important in the soil sciences. However, the use of a single global interpolation model is often limited by certain conditions (e.g., terrain complexity), which leads to distorted interpolation results. Here we present a method of adaptive weighting combined environmental variables for soil properties interpolation (AW-SP) to improve accuracy. Using various environmental variables, AW-SP was used to interpolate soil potassium content in Qinghai Lake Basin. To evaluate AW-SP performance, we compared it with that of inverse distance weighting (IDW), ordinary kriging, and OK combined with different environmental variables. The experimental results showed that the methods combined with environmental variables did not always improve prediction accuracy even if there was a strong correlation between the soil properties and environmental variables. However, compared with IDW, OK, and OK combined with different environmental variables, AW-SP is more stable and has lower mean absolute and root mean square errors. Furthermore, the AW-SP maps provided improved details of soil potassium content and provided clearer boundaries to its spatial distribution. In conclusion, AW-SP can not only reduce prediction errors, it also accounts for the distribution and contributions of environmental variables, making the spatial interpolation of soil potassium content more reasonable.
Clavier, Amandine; Ruby, Vincent; Rincheval-Arnold, Aurore; Mignotte, Bernard; Guénal, Isabelle
2015-09-01
In accordance with its tumor suppressor role, the retinoblastoma protein pRb can ensure pro-apoptotic functions. Rbf1, the Drosophila homolog of Rb, also displays a pro-apoptotic activity in proliferative cells. We have previously shown that the Rbf1 pro-apoptotic activity depends on its ability to decrease the level of anti-apoptotic proteins such as the Bcl-2 family protein Buffy. Buffy often acts in an opposite manner to Debcl, the other Drosophila Bcl-2-family protein. Both proteins can localize at the mitochondrion, but the way they control apoptosis still remains unclear. Here, we demonstrate that Debcl and the pro-fission gene Drp1 are necessary downstream of Buffy to trigger a mitochondrial fragmentation during Rbf1-induced apoptosis. Interestingly, Rbf1-induced apoptosis leads to a Debcl- and Drp1-dependent reactive oxygen species production, which in turn activates the Jun Kinase pathway to trigger cell death. Moreover, we show that Debcl and Drp1 can interact and that Buffy inhibits this interaction. Notably, Debcl modulates Drp1 mitochondrial localization during apoptosis. These results provide a mechanism by which Drosophila Bcl-2 family proteins can control apoptosis, and shed light on a link between Rbf1 and mitochondrial dynamics in vivo. © 2015. Published by The Company of Biologists Ltd.
RBF-Based Monocular Vision Navigation for Small Vehicles in Narrow Space below Maize Canopy
Lu Liu
2016-06-01
Full Text Available Maize is one of the major food crops in China. Traditionally, field operations are done by manual labor, where the farmers are threatened by the harsh environment and pesticides. On the other hand, it is difficult for large machinery to maneuver in the field due to limited space, particularly in the middle and late growth stage of maize. Unmanned, compact agricultural machines, therefore, are ideal for such field work. This paper describes a method of monocular visual recognition to navigate small vehicles between narrow crop rows. Edge detection and noise elimination were used for image segmentation to extract the stalks in the image. The stalk coordinates define passable boundaries, and a simplified radial basis function (RBF-based algorithm was adapted for path planning to improve the fault tolerance of stalk coordinate extraction. The average image processing time, including network latency, is 220 ms. The average time consumption for path planning is 30 ms. The fast processing ensures a top speed of 2 m/s for our prototype vehicle. When operating at the normal speed (0.7 m/s, the rate of collision with stalks is under 6.4%. Additional simulations and field tests further proved the feasibility and fault tolerance of our method.
Camera, Corrado; Bruggeman, Adriana; Hadjinicolaou, Panos; Michaelides, Silas; Lange, Manfred A.
2015-04-01
Space-time variability of precipitation plays a key role as a driver of many processes in different environmental fields like hydrology, ecology, biology, agriculture, and natural hazards. The objective of this study was to compare two approaches for statistical downscaling of precipitation from climate models. The study was applied to the island of Cyprus, an orographically complex terrain. The first approach makes use of a spatial temporal Neyman-Scott Rectangular Pulses (NSRP) model and a previously tested interpolation scheme (Camera et al., 2014). The second approach is based on the use of the single site NSRP model and a simplified gridded scheme based on scaling coefficients obtained from past observations. The rainfall generators were evaluated on the period 1980-2010. Both approaches were subsequently used to downscale three RCMs from the EU ENSEMBLE project to calculate climate projections (2020-2050). The main advantage of the spatial-temporal approach is that it allows creating spatially consistent daily maps of precipitation. On the other hand, due to the assumptions made using a stochastic generator based on homogeneous Poisson processes, it shows a smoothing out of all the rainfall statistics (except mean and variance) all over the study area. This leads to high errors when analyzing indices related to extremes. Examples are the number of days with rainfall over 50 mm (R50 - mean error 65%), the 95th percentile value of rainy days (RT95 - mean error 19%), and the mean annual rainfall recorded on days with rainfall above the 95th percentile (RA95 - mean error 22%). The single site approach excludes the possibility of using the created gridded data sets for case studies involving spatial connection between grid cells (e.g. hydrologic modelling), but it leads to a better reproduction of rainfall statistics and properties. The errors for the extreme indices are in fact much lower: 17% for R50, 4% for RT95, and 2% for RA95. Future projections show a
Interpolating of climate data using R
Reinhardt, Katja
2017-04-01
Interpolation methods are used in many different geoscientific areas, such as soil physics, climatology and meteorology. Thereby, unknown values are calculated by using statistical calculation approaches applied on known values. So far, the majority of climatologists have been using computer languages, such as FORTRAN or C++, but there is also an increasing number of climate scientists using R for data processing and visualization. Most of them, however, are still working with arrays and vector based data which is often associated with complex R code structures. For the presented study, I have decided to convert the climate data into geodata and to perform the whole data processing using the raster package, gstat and similar packages, providing a much more comfortable way for data handling. A central goal of my approach is to create an easy to use, powerful and fast R script, implementing the entire geodata processing and visualization into a single and fully automated R based procedure, which allows avoiding the necessity of using other software packages, such as ArcGIS or QGIS. Thus, large amount of data with recurrent process sequences can be processed. The aim of the presented study, which is located in western Central Asia, is to interpolate wind data based on the European reanalysis data Era-Interim, which are available as raster data with a resolution of 0.75˚ x 0.75˚ , to a finer grid. Therefore, various interpolation methods are used: inverse distance weighting, the geostatistical methods ordinary kriging and regression kriging, generalized additve model and the machine learning algorithms support vector machine and neural networks. Besides the first two mentioned methods, the methods are used with influencing factors, e.g. geopotential and topography.
姜剑; 王兆清; 庄美玲
2015-01-01
The nonlinear vibration of multi-degree-of-freedom systems can be modeled by initial value problem of nonlinear differential equation,this paper mainly studied the application of barycentric rational interpolation iterative collocation method to solve nonlinear vibration of multi-degree-of-freedom systems. A linear iterative scheme is constructed for approximating nonlinear differential equations. The linear differential equations are discretized into algebraic equations by applying Barycentric rational interpolation differential matrixes. Then, the numerical results of nonlinear vibration problem can be obtained by solving the algebraic equations with iteration method. The examples of nonlinear vibration of coupled systems demonstrated the proposed method is simple, effective and excellent stability and can accurately simulate various physical quantities of the nonlinear vibration.%多自由度非线性振动的数学模型为非线性微分方程组的初值问题。文章运用重心有理插值迭代配点法研究了求解多自由度非线性振动的问题；通过构造一个逼近非线性微分方程组的线性化迭代格式，采用重心有理插值微分矩阵离散线性化微分方程组，由线性化迭代计算最终得到非线性方程组的数值解。结果表明：依据算例的解析解和数值解比较，重心有理插值迭代配点法能够高精度计算模拟多自由度非线性振动的各项物理量，并且简单有效，具有优异的计算稳定性。
Precipitation interpolation and corresponding uncertainty assessment using copulas
Bardossy, A.; Pegram, G. G.
2012-12-01
Spatial interpolation of rainfall over different time and spatial scales is necessary in many applications of hydrometeorology. The specific problems encountered in rainfall interpolation include: the large number of calculations which need to be performed automatically the quantification of the influence of topography, usually the most influential of exogenous variables how to use observed zero (dry) values in interpolation, because their proportion increases the shorter the time interval the need to estimate a reasonable uncertainty of the modelled point/pixel distributions the need to separate (i) temporally highly correlated bias from (ii) random interpolation errors at different spatial and temporal scales the difficulty of estimating uncertainty of accumulations over a range of spatial scales. The approaches used and described in the presentation employ the variables rainfall and altitude. The methods of interpolation include (i) Ordinary Kriging of the rainfall without altitude, (ii) External Drift Kriging with altitude as an exogenous variable, and less conventionally, (iii) truncated Gaussian copulas and truncated v-copulas, both omitting and including the altitude of the control stations as well as that of the target (iv) truncated Gaussian copulas and truncated v-copulas for a two-step interpolation of precipitation combining temporal and spatial quantiles for bias quantification. It was found that truncated Gaussian copulas, with the target's and all control the stations' altitudes included as exogenous variables, produce the lowest Mean Square error in cross-validation and, as a bonus, model with the least bias. In contrast, the uncertainty of interpolation is better described by the v-copulas, but the Gaussian copulas have the advantage of computational effort (by three orders of magnitude) which justifies their use in practice. It turns out that the uncertainty estimates of the OK and EDK interpolants are not competitive at any time scale, from daily
Constructing triangular patch by basic approximation operator plus additional interpolation operator
ZHANG Caiming; Jl Xiuhua; YANG Xingqiang
2005-01-01
A new method for constructing triangular patches is presented. The triangular patch that interpolates the given boundary curves and cross-boundary slopes is constructed by a basic approximation operator plus an additional interpolation operator. The basic approximation operator is constructed by a polynomial surface of degree five which approximates the given interpolation conditions. The additional interpolation operator is formed by the side-vertex method. The basic and the additional operators have different roles in constructing the triangular patch: the first one makes the triangular patch approximate the given interpolation conditions with a polynomial approximation precision of degree five, while the second one makes it satisfy the given interpolation conditions. The triangular patch reproduces polynomial surfaces of degree five. Comparison results of the new method with the other two methods are included.
Erkan Beşdok
2009-08-01
Full Text Available This paper introduces a comparison of training algorithms of radial basis function (RBF neural networks for classification purposes. RBF networks provide effective solutions in many science and engineering fields. They are especially popular in the pattern classification and signal processing areas. Several algorithms have been proposed for training RBF networks. The Artificial Bee Colony (ABC algorithm is a new, very simple and robust population based optimization algorithm that is inspired by the intelligent behavior of honey bee swarms. The training performance of the ABC algorithm is compared with the Genetic algorithm, Kalman filtering algorithm and gradient descent algorithm. In the experiments, not only well known classification problems from the UCI repository such as the Iris, Wine and Glass datasets have been used, but also an experimental setup is designed and inertial sensor based terrain classification for autonomous ground vehicles was also achieved. Experimental results show that the use of the ABC algorithm results in better learning than those of others.
Multinode rational operators for univariate interpolation
Dell'Accio, Francesco; Di Tommaso, Filomena; Hormann, Kai
2016-10-01
Birkhoff (or lacunary) interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about function and its derivatives. A Birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space. In this talk we split up the initial problem in subproblems having a unique polynomial solution and use multinode rational basis functions in order to obtain a global interpolant.
An artificial Radial Basis Function (RBF) neural network model was developed for the prediction of mass transfer of the phospholipids from canola meal in supercritical CO2 fluid. The RBF kind of artificial neural networks (ANN) with orthogonal least squares (OLS) learning algorithm were used for mod...
Removal of Baseline Wander Noise from Electrocardiogram (ECG) using Fifth-order Spline Interpolation
John A. OJO; Temilade B. ADETOYI; Solomon A. Adeniran
2016-01-01
Baseline wandering can mask some important features of the Electrocardiogram (ECG) signal hence it is desirable to remove this noise for proper analysis and display of the ECG signal. This paper presents the implementation and evaluation of spline interpolation and linear phase FIR filtering methods to remove this noise. Spline interpolation method requires the QRS waves to be first detected and fifth-order (quintic) interpolation technique applied to determine the smo...
顾传青; 张莺
2007-01-01
A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.
BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS
Xiao-yuan Qian
2002-01-01
Non-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced.The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.
RBF multiuser detector with channel estimation capability in a synchronous MC-CDMA system.
Ko, K; Choi, S; Kang, C; Hong, D
2001-01-01
The authors propose a multiuser detector with channel estimation capability using a radial basis function (RBF) network in a synchronous multicarrier-code division multiple access (MC-CDMA) system. The authors propose to connect an RBF network to the frequency domain to effectively utilize the frequency diversity. Simulations were performed over frequency-selective and multi-path fading channels. These simulations confirmed that the proposed receiver can be used both for the channel estimation and as a multi-user receiver, thus permitting an increase in the number of active users.
On-line identification of hybrid systems using an adaptive growing and pruning RBF neural network
Alizadeh, Tohid
2008-01-01
This paper introduces an adaptive growing and pruning radial basis function (GAP-RBF) neural network for on-line identification of hybrid systems. The main idea is to identify a global nonlinear model that can predict the continuous outputs of hybrid systems. In the proposed approach, GAP......-RBF neural network uses a modified unscented kalman filter (UKF) with forgetting factor scheme as the required on-line learning algorithm. The effectiveness of the resulting identification approach is tested and evaluated on a simulated benchmark hybrid system....
Spatial Sampling Strategies for the Effect of Interpolation Accuracy
Hairong Zhang
2015-12-01
Full Text Available Spatial interpolation methods are widely used in various fields and have been studied by several scholars with one or a few specific sampling datasets that do not reflect the complexity of the spatial characteristics and lead to conclusions that cannot be widely applied. In this paper, three factors that affect the accuracy of interpolation have been considered, i.e., sampling density, sampling mode, and sampling location. We studied the inverse distance weighted (IDW, regular spline (RS, and ordinary kriging (OK interpolation methods using 162 DEM datasets considering six sampling densities, nine terrain complexities, and three sampling modes. The experimental results show that, in selective sampling and combined sampling, the maximum absolute errors of interpolation methods rapidly increase and the estimated values are overestimated. In regular-grid sampling, the RS method has the highest interpolation accuracy, and IDW has the lowest interpolation accuracy. However, in both selective and combined sampling, the accuracy of the IDW method is significantly improved and the RS method performs worse. The OK method does not significantly change between the three sampling modes. The following conclusion can be obtained from the above analysis: the combined sampling mode is recommended for sampling, and more sampling points should be added in the ridges, valleys, and other complex terrain. The IDW method should not be used in the regular-grid sampling mode, but it has good performance in the selective sampling mode and combined sampling mode. However, the RS method shows the opposite phenomenon. The sampling dataset should be analyzed before using the OK method, which can select suitable models based on the analysis results of the sampling dataset.
汤博; 佟玲※; 康绍忠
2013-01-01
to calculate ET0 using the Penman-Monteith equation recommended by FAO in 1998. We calculated ET0 using Penman-Monteith equation which was recommended by FAO according to weather data of 3 years (2003-2005) for 162 agricultural weather stations in the Haihe river basin. The temporal and spatial vatiations of ET0 were calculated by four interpolation models of Spline, Ordinary Kriging (OK), Inverse Distance Weighted (IDW) and Regression in ArcGIS. The results showed that when the spatial stations density is less-than 1.3 station every 10 000 km2, the Regression interpolation model was better than the other 3 interpolations;the OK and IDW model were recommended when the spatial stations density is greater-than 1.3 and less-than 4.3 station every 10 000 km2;when the spatial stations density is greater than 4.3 station every 10 000 km2, the results showed no big difference for three interpolations (OK, IDW, Regression). Spline method showed the worst results. In a word, Regression interpolation model presented higher accuracy if the spatial stations density is less-than 1.3 station every 10 000 km2;the OK and IDW interpolation model presented higher accuracy if the spatial stations density is greater than 1.3 and less than 4.3 station every 10 000 km2.% 流域参考作物蒸发蒸腾量（ET0）插值方法的研究对流域尺度作物耗水时空变化规律有重要意义。该文通过海河流域162个国家农业气象站3a（2003－2005年）旬值气象资料，利用Penman-Monteith公式计算了这些站点ET0，采用ArcGIS软件中常用的Spline、IDW和Ordinary Kriging（OK）法，以及近些年研究较多的线性回归Regression 插值法，对不同站点密度条件下的 ET0进行空间插值。分析了各空间插值方法在不同站点密度条件下的优劣性，并且给出了本流域内各种站点密度范围条件下计算 ET0最适宜的插值方法。结果表明以站点密度1.3个/万km2为界，当站点密度低于此密度
Speaker Adaptation with Transformation Matrix Linear Interpolation
XU Xiang-hua; ZHU Jie
2004-01-01
A transformation matrix linear interpolation (TMLI) approach for speaker adaptation is proposed. TMLI uses the transformation matrixes produced by MLLR from selected training speakers and the testing speaker. With only 3 adaptation sentences, the performance shows a 12.12% word error rate reduction. As the number of adaptation sentences increases, the performance saturates quickly. To improve the behavior of TMLI for large amounts of adaptation data, the TMLI+MAP method which combines TMLI with MAP technique is proposed. Experimental results show TMLI+MAP achieved better recognition accuracy than MAP and MLLR+MAP for both small and large amounts of adaptation data.
李晓晖; 袁峰; 贾蔡; 张明明; 周涛发
2012-01-01
This paper took Cu element of Tongling Ore Cluster area as an example, studied on the effect of inverse distance weighted interpolation method and Kriging interpolation method on the multifractal filtering method. The research showed that, compared with raw inverse distance weighted interpolation method and Kriging interpolation method, whether based on inverse distance weighted interpolation method and Kriging interpolation method, the Cu element anomaly field which is decomposed by multifractal filtering (S-A) method could indicate the Cu ore field more accurately. The anomaly field based on the Kriging interpolation result a-chieved better results than that base on the inverse distance weighted interpolation result, the former was more significantly correlated with the distribution of Cu deposits, which is decomposed by multifractal filtering (S-A) method would have the application value for metallogenic prediction at deposit scale.%本文以铜陵矿集区土壤Cu元素含量数据为例,对比研究反距离加权插值法和克里格插值法对S-A多重分形滤波的影响.与单纯的反距离加权插值和克里格插值结果相比,无论是基于反距离加权插值还是克里格插值,多重分形滤波(S-A)方法分解得到的铜陵矿集区Cu元素异常场对已知Cu矿田的指示均更加准确.基于克里格插值结果的异常场相比于基于反距离加权插值结果的异常场,具有更好的异常识别效果,与铜陵矿集区已知Cu矿床分布的空间相关性更加显著,具有矿田尺度的成矿预测价值.
Temporal interpolation in Meteosat images
Larsen, Rasmus; Hansen, Johan Dore; Ersbøll, Bjarne Kjær;
a threshold between clouds and land/water. The temperature maps are estimated using observations from the image sequence itself at cloud free pixels and ground temperature measurements from a series of meteor ological observation stations in Europe. The temporal interpolation of the images is bas ed on a path...... in such animated films are perceived as being jerky due to t he low temporal sampling rate in general and missing images in particular. In order to perform a satisfactory temporal interpolation we estimate and use the optical flow corresponding to every image in the sequenc e. The estimation of the optical flow...... is based on images sequences where the clouds are segmented from the land/water that might a lso be visible in the images. Because the pixel values measured correspond directly to temperature and because clouds (normally) are colder than land/water we use an estimated lan d temperature map to perform...
Yield statistics of interpolated superoscillations
Katzav, Eytan; Perlsman, Ehud; Schwartz, Moshe
2017-01-01
Yield optimized interpolated superoscillations have been recently introduced as a means for possibly making the use of the phenomenon of superoscillation practical. In this paper we study how good is a superoscillation that is not optimal. Namely, by how much is the yield decreased when the signal departs from the optimal one. We consider two situations. One is the case where the signal strictly obeys the interpolation requirement and the other is when that requirement is relaxed. In the latter case the yield can be increased at the expense of deterioration of signal quality. An important conclusion is that optimizing superoscillations may be challenging in terms of the precision needed, however, storing and using them is not at all that sensitive. This is of great importance in any physical system where noise and error are inevitable.
INTERPOLATION WITH RESTRICTED ARC LENGTH
Petar Petrov
2003-01-01
For given data (ti,yi), I= 0,1,…,n,0 = t0 ＜t1 ＜…＜tn = 1we study constrained interpolation problem of Favard type inf{‖f"‖∞|f∈W2∞[0,1],f(ti)=yi,i=0,…,n,l(f;[0,1])≤l0}, wherel(f";[0,1])=∫1 0 / 1+f'2(x)dx is the arc length off in [0,1]. We prove the existence of a solution f* of the above problem, that is a quadratic spline with a second derivative f"* , which coincides with one of the constants - ‖f"*‖∞,0,‖f"*‖∞ between every two consecutive knots. Thus, we extend a result ofKarlin concerning Favard problem, to the case of restricted length interpolation.
Inverse spatial principal component analysis for geophysical survey data interpolation
Li, Qingmou; Dehler, Sonya A.
2015-04-01
The starting point for data processing, visualization, and overlay with other data sources in geological applications often involves building a regular grid by interpolation of geophysical measurements. Typically, the sampling interval along survey lines is much higher than the spacing between survey lines because the geophysical recording system is able to operate with a high sampling rate, while the costs and slower speeds associated with operational platforms limit line spacing. However, currently available interpolating methods often smooth data observed with higher sampling rate along a survey line to accommodate the lower spacing across lines, and much of the higher resolution information is not captured in the interpolation process. In this approach, a method termed as the inverse spatial principal component analysis (isPCA) is developed to address this problem. In the isPCA method, a whole profile observation as well as its line position is handled as an entity and a survey collection of line entities is analyzed for interpolation. To test its performance, the developed isPCA method is used to process a simulated airborne magnetic survey from an existing magnetic grid offshore the Atlantic coast of Canada. The interpolation results using the isPCA method and other methods are compared with the original survey grid. It is demonstrated that the isPCA method outperforms the Inverse Distance Weighting (IDW), Kriging (Geostatistical), and MINimum Curvature (MINC) interpolation methods in retaining detailed anomaly structures and restoring original values. In a second test, a high resolution magnetic survey offshore Cape Breton, Nova Scotia, Canada, was processed and the results are compared with other geological information. This example demonstrates the effective performance of the isPCA method in basin structure identification.
Noise-induced bias for convolution-based interpolation in digital image correlation.
Su, Yong; Zhang, Qingchuan; Gao, Zeren; Xu, Xiaohai
2016-01-25
In digital image correlation (DIC), the noise-induced bias is significant if the noise level is high or the contrast of the image is low. However, existing methods for the estimation of the noise-induced bias are merely applicable to traditional interpolation methods such as linear and cubic interpolation, but are not applicable to generalized interpolation methods such as BSpline and OMOMS. Both traditional interpolation and generalized interpolation belong to convolution-based interpolation. Considering the widely use of generalized interpolation, this paper presents a theoretical analysis of noise-induced bias for convolution-based interpolation. A sinusoidal approximate formula for noise-induced bias is derived; this formula motivates an estimating strategy which is with speed, ease, and accuracy; furthermore, based on this formula, the mechanism of sophisticated interpolation methods generally reducing noise-induced bias is revealed. The validity of the theoretical analysis is established by both numerical simulations and actual subpixel translation experiment. Compared to existing methods, formulae provided by this paper are simpler, briefer, and more general. In addition, a more intuitionistic explanation of the cause of noise-induced bias is provided by quantitatively characterized the position-dependence of noise variability in the spatial domain.
Gribov ambiguities at the Landau -- maximal Abelian interpolating gauge
Pereira, A D
2014-01-01
In a previous work, we presented a new method to account for the Gribov ambiguities in non-Abelian gauge theories. The method consists on the introduction of an extra constraint which directly eliminates the infinitesimal Gribov copies without the usual geometric approach. Such strategy allows to treat gauges with non-hermitian Faddeev-Popov operator. In this work, we apply this method to a gauge which interpolates among the Landau and maximal Abelian gauges. The result is a local and power counting renormalizable action, free of infinitesimal Gribov copies. Moreover, the interpolating tree-level gluon propagator is derived.
Wavelet-based multicomponent matching pursuit trace interpolation
Choi, Jihun; Byun, Joongmoo; Seol, Soon Jee; Kim, Young
2016-09-01
Typically, seismic data are sparsely and irregularly sampled due to limitations in the survey environment and these cause problems for key seismic processing steps such as surface-related multiple elimination or wave-equation-based migration. Various interpolation techniques have been developed to alleviate the problems caused by sparse and irregular sampling. Among many interpolation techniques, matching pursuit interpolation is a robust tool to interpolate the regularly sampled data with large receiver separation such as crossline data in marine seismic acquisition when both pressure and particle velocity data are used. Multicomponent matching pursuit methods generally used the sinusoidal basis function, which have shown to be effective for interpolating multicomponent marine seismic data in the crossline direction. In this paper, we report the use of wavelet basis functions which further enhances the performance of matching pursuit methods for de-aliasing than sinusoidal basis functions. We also found that the range of the peak wavenumber of the wavelet is critical to the stability of the interpolation results and the de-aliasing performance and that the range should be determined based on Nyquist criteria. In addition, we reduced the computational cost by adopting the inner product of the wavelet and the input data to find the parameters of the wavelet basis function instead of using L-2 norm minimization. Using synthetic data, we illustrate that for aliased data, wavelet-based matching pursuit interpolation yields more stable results than sinusoidal function-based one when we use not only pressure data only but also both pressure and particle velocity together.
Zhiwei Pan
2016-05-01
Full Text Available Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton (IC-GN algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
Constrained reverse diffusion for thick slice interpolation of 3D volumetric MRI images.
Neubert, Aleš; Salvado, Olivier; Acosta, Oscar; Bourgeat, Pierrick; Fripp, Jurgen
2012-03-01
Due to physical limitations inherent in magnetic resonance imaging scanners, three dimensional volumetric scans are often acquired with anisotropic voxel resolution. We investigate several interpolation approaches to reduce the anisotropy and present a novel approach - constrained reverse diffusion for thick slice interpolation. This technique was compared to common methods: linear and cubic B-Spline interpolation and a technique based on non-rigid registration of neighboring slices. The methods were evaluated on artificial MR phantoms and real MR scans of human brain. The constrained reverse diffusion approach delivered promising results and provides an alternative for thick slice interpolation, especially for higher anisotropy factors.
An integral conservative gridding--algorithm using Hermitian curve interpolation.
Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K
2008-11-07
The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to
The Gaussian Radial Basis Function Method for Plasma Kinetic Theory
Hirvijoki, Eero; Belli, Emily; Embréus, Ola
2015-01-01
A fundamental macroscopic description of a magnetized plasma is the Vlasov equation supplemented by the nonlinear inverse-square force Fokker-Planck collision operator [Rosenbluth et al., Phys. Rev., 107, 1957]. The Vlasov part describes advection in a six-dimensional phase space whereas the collision operator involves friction and diffusion coefficients that are weighted velocity-space integrals of the particle distribution function. The Fokker-Planck collision operator is an integro-differential, bilinear operator, and numerical discretization of the operator is far from trivial. In this letter, we describe a new approach to discretize the entire kinetic system based on an expansion in Gaussian Radial Basis functions (RBFs). This approach is particularly well-suited to treat the collision operator because the friction and diffusion coefficients can be analytically calculated. Although the RBF method is known to be a powerful scheme for the interpolation of scattered multidimensional data, Gaussian RBFs also...
Fatma Zohra Chelali
2015-01-01
Full Text Available Face recognition has received a great attention from a lot of researchers in computer vision, pattern recognition, and human machine computer interfaces in recent years. Designing a face recognition system is a complex task due to the wide variety of illumination, pose, and facial expression. A lot of approaches have been developed to find the optimal space in which face feature descriptors are well distinguished and separated. Face representation using Gabor features and discrete wavelet has attracted considerable attention in computer vision and image processing. We describe in this paper a face recognition system using artificial neural networks like multilayer perceptron (MLP and radial basis function (RBF where Gabor and discrete wavelet based feature extraction methods are proposed for the extraction of features from facial images using two facial databases: the ORL and computer vision. Good recognition rate was obtained using Gabor and DWT parameterization with MLP classifier applied for computer vision dataset.
Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing
2016-12-08
Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.
BLOCK BASED NEWTON-LIKE BLENDING OSCULATORY RATIONAL INTERPOLATION
Shuo Tang; Le Zou; Chensheng Li
2010-01-01
With Newton's interpolating formula,we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton's polynomial interpolation as its special case.A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.
Performance prediction for Grid workflow activities based on features-ranked RBF network
Wang Jie; Duan Rubing; Farrukh Nadeem
2009-01-01
Accurate performance prediction of Grid workflow activities can help Grid schedulers map activities to appropriate Grid sites. This paper describes an approach based on features-ranked RBF neural network to predict the performance of Grid workflow activities. Experimental results for two kinds of real world Grid workflow activities are presented to show effectiveness of our approach.
Spatial Interpolation of Ewert's Index of Continentality in Poland
Szymanowski, Mariusz; Bednarczyk, Piotr; Kryza, Maciej; Nowosad, Marek
2016-10-01
The article presents methodological considerations on the spatial interpolation of Ewert's index of continentality for Poland. The primary objective was to perform spatial interpolation and generate maps of the index combined with selection of an optimal interpolation method and validation of the use of the decision tree proposed by Szymanowski et al. (Meteorol Z 22:577-585, 2013). The analysis involved four selected years and a multi-year average of the period 1981-2010 and was based on data from 111 meteorological stations. Three regression models: multiple linear regression (MLR), geographically weighted regression (GWR), and mixed geographically weighted regression were used in the analysis as well as extensions of two of them to the residual kriging form. The regression models were compared demonstrating a better fit of the local model and, hence, the non-stationarity of the spatial process. However, the decisive role in the selection of the interpolator was assigned to the possibility of extension of the regression model to residual kriging. A key element here is the autocorrelation of the regression residuals, which proved to be significant for MLR and irrelevant for GWR. This resulted in exclusion of geographically weighted regression kriging from further analysis. The multiple linear regression kriging was found as the optimal interpolator. This was confirmed by cross validation combined with an analysis of improvement of the model in accordance with the criterion of the mean absolute error (MAE). The results obtained facilitate modification of the scheme of selection of an optimal interpolator and development of guidelines for automation of interpolation of Ewert's index of continentality for Poland.
Spatial Interpolation of Ewert's Index of Continentality in Poland
Szymanowski, Mariusz; Bednarczyk, Piotr; Kryza, Maciej; Nowosad, Marek
2017-02-01
The article presents methodological considerations on the spatial interpolation of Ewert's index of continentality for Poland. The primary objective was to perform spatial interpolation and generate maps of the index combined with selection of an optimal interpolation method and validation of the use of the decision tree proposed by Szymanowski et al. (Meteorol Z 22:577-585, 2013). The analysis involved four selected years and a multi-year average of the period 1981-2010 and was based on data from 111 meteorological stations. Three regression models: multiple linear regression (MLR), geographically weighted regression (GWR), and mixed geographically weighted regression were used in the analysis as well as extensions of two of them to the residual kriging form. The regression models were compared demonstrating a better fit of the local model and, hence, the non-stationarity of the spatial process. However, the decisive role in the selection of the interpolator was assigned to the possibility of extension of the regression model to residual kriging. A key element here is the autocorrelation of the regression residuals, which proved to be significant for MLR and irrelevant for GWR. This resulted in exclusion of geographically weighted regression kriging from further analysis. The multiple linear regression kriging was found as the optimal interpolator. This was confirmed by cross validation combined with an analysis of improvement of the model in accordance with the criterion of the mean absolute error (MAE). The results obtained facilitate modification of the scheme of selection of an optimal interpolator and development of guidelines for automation of interpolation of Ewert's index of continentality for Poland.
Field mapping of EEG by unbiased polynomial interpolation.
Ashida, H; Tatsuno, J; Okamoto, J; Maru, E
1984-06-01
The technique for field mapping of EEG using interpolation by an unbiased estimator of two-dimensional isotropic higher-order polynomial is developed. Assuming that the observed EEG contains noise, this method permits free positioning of the electrodes and does not reveal artificial oscillations as large as those of the Gibbs' phenomenon as in the case of the widely used Fourier interpolation. In the example of RMS (root mean square) amplitude at anesthesia, the onset of the fast activities began to appear clearly in the frontal and occipital area. By this method, not only RMS amplitude, but also instantaneous amplitude, such as visual evoked potential and somatosensory evoked potential, can be mapped.
Realization of a 5-axis NURBS Interpolation with Controlled Angular Velocity
LIU Yuan; LI Hui; WANG Yongzhang
2012-01-01
5-axis machine tool plays an important role in high-speed and high-precision computer numerical control (CNC) machining of workpieces with complex shapes.A non-uniform rational B-spline (NURBS) interpolation format for 5-axis machining is proposed to adapt to the high speed machining (HSM).With this interpolation format,angles between orientation vectors are chosen as parameters of orientation B-spline constructed by an open controller to achieve reasonable orientation vectors in real-time interpolation process.Coordinated motion between linear axes and rotary axes is achieved by building a polynomial spline which relates interpolation arc lengths of position spline to angles of orientation spline.Algorithm routine of this interpolation format and its realization methods in the supported controller are discussed in detail.Finally,performance of the proposed NURBS interpolation format is demonstrated by a practical example.
A combination of parabolic and grid slope interpolation for 2D tissue displacement estimations.
Albinsson, John; Ahlgren, Åsa Rydén; Jansson, Tomas; Cinthio, Magnus
2017-08-01
Parabolic sub-sample interpolation for 2D block-matching motion estimation is computationally efficient. However, it is well known that the parabolic interpolation gives a biased motion estimate for displacements greater than |y.2| samples (y = 0, 1, …). Grid slope sub-sample interpolation is less biased, but it shows large variability for displacements close to y.0. We therefore propose to combine these sub-sample methods into one method (GS15PI) using a threshold to determine when to use which method. The proposed method was evaluated on simulated, phantom, and in vivo ultrasound cine loops and was compared to three sub-sample interpolation methods. On average, GS15PI reduced the absolute sub-sample estimation errors in the simulated and phantom cine loops by 14, 8, and 24% compared to sub-sample interpolation of the image, parabolic sub-sample interpolation, and grid slope sub-sample interpolation, respectively. The limited in vivo evaluation of estimations of the longitudinal movement of the common carotid artery using parabolic and grid slope sub-sample interpolation and GS15PI resulted in coefficient of variation (CV) values of 6.9, 7.5, and 6.8%, respectively. The proposed method is computationally efficient and has low bias and variance. The method is another step toward a fast and reliable method for clinical investigations of longitudinal movement of the arterial wall.
黄开勇; 唐咸艳; 王晓敏; 刘勇; 张海英; 陈世艺; 尹晔; 杨莉
2012-01-01
Objective To explore the geographical distribution and prevalence trend of death caused by road traffic injuries in Guilin city of Guangxi Zhuang Autonomous Region from 2000 to 2009,and to provide scientific evidence for control and prevention of road traffic injury. Methods A distribution map of death caused by road traffic injuries in Guilin city was compiled with inverse distance weighted interpolation method using ArcGIS 9.2,taking the electronic map of Guilin city as a background. Results The map reflected accurately the geographical distribution and prevalence trend of death caused by road traffic injuries in Guilin city. Conclusion The map drawn with inverse distance weighted interpolation method is reliable,convenient,and feasible.%目的 探讨广西桂林市2000-2009年道路交通伤害(RTI)死亡的地理分布和集中趋势,为预防和减少RTI的发生提供科学依据.方法 以桂林市电子地图为背景,利用ArcGIS 9.2地统计分析模块中的反距离加权(IDW)插值法绘制桂林市RTI死亡的分布地图.结果 2000-2009年桂林市秀峰区、叠彩区、象山区、七星区和雁山区发生RTI合计3 603次,死亡506例,受伤2911例,直接经济损失为1011.2万元；2000-2008年每年发生RTI次数均以象山区最多,2009年以七星区最多；2000-2004年桂林市RTI造成的死亡人数以雁山区和象山区最多；2005-2006年以叠彩区、象山区和雁山区较多；2007 -2009年以七星区、象山区和雁山区较多；2000-2009年桂林市RTI死亡人数分布的IDW插值结果表明,RTI导致的死亡人数以雁山区最多,其次为象山区.结论 2000-2009年桂林市RTI导致的死亡人数以雁山区最多；IDW插值法制图结果较为可信.
Mingjian Sun
2015-01-01
Full Text Available Photoacoustic imaging is an innovative imaging technique to image biomedical tissues. The time reversal reconstruction algorithm in which a numerical model of the acoustic forward problem is run backwards in time is widely used. In the paper, a time reversal reconstruction algorithm based on particle swarm optimization (PSO optimized support vector machine (SVM interpolation method is proposed for photoacoustics imaging. Numerical results show that the reconstructed images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation based time reversal algorithm, which can provide higher imaging quality by using significantly fewer measurement positions or scanning times.
段晋芳; 王青杵; 王改玲; 郭青霞
2010-01-01
以山西省永定河流域20个国家基本气象站点43年平均降水数据为基础,运用ArcGIS软件地统计学模块进行空间降水插值试验,分别采用了反距离加权法(IDW)、径向基函数法(RBF)和克里格法(KRIGING)3种常见的空间内插方法,探讨了山西永定河降水的空间分布.分析发现,3种插值方法在分析区域降水空间分布方面各有优缺点,其均方根预测误差(RMS)的排列顺序为KRIGING<RBF
3D Morphing Using Strain Field Interpolation
Han-Bing Yan; Shi-Min Hu; Ralph R Martin
2007-01-01
In this paper, we present a new technique based on strain fields to carry out 3D shape morphing for applicationsin computer graphics and related areas.Strain is an important geometric quantity used in mechanics to describe the deformation of objects.We apply it in a novel way to analyze and control deformation in morphing.Using position vector fields, the strain field relating source and target shapes can be obtained.By interpolating this strain field between zero and a final desired value we can obtain the position field for intermediate shapes.This method ensures that the 3D morphing process is smooth.Locally, volumes suffer minimal distortion, and no shape jittering or wobbling happens: other methods do not necessarily have these desirable properties.We also show how to control the method so that changes of shape (in particular, size changes) vary linearly with time.
Size-Dictionary Interpolation for Robot's Adjustment
Morteza eDaneshmand
2015-05-01
Full Text Available This paper describes the classification and size-dictionary interpolation of the three-dimensional data obtained by a laser scanner to be used in a realistic virtual fitting room, where automatic activation of the chosen mannequin robot, while several mannequin robots of different genders and sizes are simultaneously connected to the same computer, is also considered to make it mimic the body shapes and sizes instantly. The classification process consists of two layers, dealing, respectively, with gender and size. The interpolation procedure tries to find out which set of the positions of the biologically-inspired actuators for activation of the mannequin robots could lead to the closest possible resemblance of the shape of the body of the person having been scanned, through linearly mapping the distances between the subsequent size-templates and the corresponding position set of the bioengineered actuators, and subsequently, calculating the control measures that could maintain the same distance proportions, where minimizing the Euclidean distance between the size-dictionary template vectors and that of the desired body sizes determines the mathematical description. In this research work, the experimental results of the implementation of the proposed method on Fits.me's mannequin robots are visually illustrated, and explanation of the remaining steps towards completion of the whole realistic online fitting package is provided.
National Oceanic and Atmospheric Administration, Department of Commerce — The document presents the methods, formulas and citations used by the BNDO to process physical, chemical, and biological data for deep hydrology including...
Sparse representation based image interpolation with nonlocal autoregressive modeling.
Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming
2013-04-01
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.
DESIGN OF A NEW INTERPOLATED CONTROLLER FOR STABILIZATION OF A SET OF INTERPOLATED PLANTS
无
2000-01-01
Stabilization of a plant with variable operating conditions was considered. The plant is assumed to lie in a set of interpolated models composed of all interpolations generated between certain sets of proper stable coprime factorizations of transfer functions of two representative models that are defined at two representative operating points. An interpolated controller that is linear interpolation of coprime factorizations of two stabilizing controllers for the two representative models is designed to stabilize this set of interpolated models. Design of such an interpolated controller was converted to a feasibility problem constrained by several LMIs and a BMI, and a two-step iteration algorithm was employed to solve it.
Bagheri, H.; Sadjadi, S. Y.; Sadeghian, S.
2013-09-01
One of the most significant tools to study many engineering projects is three-dimensional modelling of the Earth that has many applications in the Geospatial Information System (GIS), e.g. creating Digital Train Modelling (DTM). DTM has numerous applications in the fields of sciences, engineering, design and various project administrations. One of the most significant events in DTM technique is the interpolation of elevation to create a continuous surface. There are several methods for interpolation, which have shown many results due to the environmental conditions and input data. The usual methods of interpolation used in this study along with Genetic Algorithms (GA) have been optimised and consisting of polynomials and the Inverse Distance Weighting (IDW) method. In this paper, the Artificial Intelligent (AI) techniques such as GA and Neural Networks (NN) are used on the samples to optimise the interpolation methods and production of Digital Elevation Model (DEM). The aim of entire interpolation methods is to evaluate the accuracy of interpolation methods. Universal interpolation occurs in the entire neighbouring regions can be suggested for larger regions, which can be divided into smaller regions. The results obtained from applying GA and ANN individually, will be compared with the typical method of interpolation for creation of elevations. The resulting had performed that AI methods have a high potential in the interpolation of elevations. Using artificial networks algorithms for the interpolation and optimisation based on the IDW method with GA could be estimated the high precise elevations.
Kriging Interpolating Cosmic Velocity Field
Yu, Yu; Jing, Yipeng; Zhang, Pengjie
2015-01-01
[abridge] Volume-weighted statistics of large scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of uncertainties of galaxy density bias entangled in mass-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number $n_k$ of the nearby particles to interpolate and the density $n_P$ of the observed sample are investigated. (1) We find that Kriging induces $1\\%$ and $3\\%$ systematics at $k\\sim 0.1h{\\rm Mpc}^{-1}$ when $n_P\\sim 6\\times 10^{-2} ({\\rm Mpc}/h)^{-3}$ and $n_P\\sim 6\\times 10^{-3} ({\\rm Mpc...
Evaluation of various interpolants available in DICE
Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Reu, Phillip L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Crozier, Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-02-01
This report evaluates several interpolants implemented in the Digital Image Correlation Engine (DICe), an image correlation software package developed by Sandia. By interpolants we refer to the basis functions used to represent discrete pixel intensity data as a continuous signal. Interpolation is used to determine intensity values in an image at non - pixel locations. It is also used, in some cases, to evaluate the x and y gradients of the image intensities. Intensity gradients subsequently guide the optimization process. The goal of this report is to inform analysts as to the characteristics of each interpolant and provide guidance towards the best interpolant for a given dataset. This work also serves as an initial verification of each of the interpolants implemented.
An empirical RBF model of the magnetosphere parameterized by interplanetary and ground-based drivers
Tsyganenko, N. A.; Andreeva, V. A.
2016-11-01
In our recent paper (Andreeva and Tsyganenko, 2016), a novel method was proposed to model the magnetosphere directly from spacecraft data, with no a priori knowledge nor ad hoc assumptions about the geometry of the magnetic field sources. The idea was to split the field into the toroidal and poloidal parts and then expand each part into a weighted sum of radial basis functions (RBF). In the present work we take the next step forward by having developed a full-fledged model of the near magnetosphere, based on a multiyear set of space magnetometer data (1995-2015) and driven by ground-based and interplanetary input parameters. The model consolidates the largest ever amount of data and has been found to provide the best ever merit parameters, in terms of both the overall RMS residual field and record-high correlation coefficients between the observed and model field components. By experimenting with different combinations of input parameters and their time-averaging intervals, we found the best so far results to be given by the ram pressure Pd, SYM-H, and N-index by Newell et al. (2007). In addition, the IMF By has also been included as a model driver, with a goal to more accurately represent the IMF penetration effects. The model faithfully reproduces both externally and internally induced variations in the global distribution of the geomagnetic field and electric currents. Stronger solar wind driving results in a deepening of the equatorial field depression and a dramatic increase of its dawn-dusk asymmetry. The Earth's dipole tilt causes a consistent deformation of the magnetotail current sheet and a significant north-south asymmetry of the polar cusp depressions on the dayside. Next steps to further develop the new approach are also discussed.
Testing PSF Interpolation In Weak Lensing With Real Data
Lu, Tianhuan; Dong, Fuyu; Li, Yingke; Liu, Dezi; Fu, Liping; Li, Guoliang; Fan, Zuhui
2016-01-01
Reconstruction of the point spread function (PSF) is a critical process in weak lensing measurement. We develop a real-data based and galaxy-oriented pipeline to compare the performances of various PSF reconstruction schemes. Making use of a large amount of the CFHTLenS data, the performances of three classes of interpolating schemes - polynomial, Kriging, and Shepard - are evaluated. We find that polynomial interpolations with optimal orders and domains perform the best. We quantify the effect of the residual PSF reconstruction error on shear recovery in terms of the multiplicative and additive biases, and their spatial correlations using the shear measurement method of Zhang et al. (2015). We find that the impact of PSF reconstruction uncertainty on the shear-shear correlation can be significantly reduced by cross correlating the shear estimators from different exposures. It takes only 0.2 stars (SNR > 100) per square arcmin on each exposure to reach the best performance of PSF interpolation, a requirement ...
On Double Interpolation in Polar Coordinates
Antoniu Nicula
2009-10-01
Full Text Available Interpolation is an important tool in numerical modeling of real-life systems. The Lagrange interpolation is frequently used, due to particular advantages in implementation. The bi-dimensional version may be implemented with Cartesian or with polar coordinate system. Choice of the coordinate system is important in order to obtain accurate results. The polar case has particular properties that can be exploited to minimize some of the common disadvantages of polynomial interpolation.
3D Hail Size Distribution Interpolation/Extrapolation Algorithm
Lane, John
2013-01-01
Radar data can usually detect hail; however, it is difficult for present day radar to accurately discriminate between hail and rain. Local ground-based hail sensors are much better at detecting hail against a rain background, and when incorporated with radar data, provide a much better local picture of a severe rain or hail event. The previous disdrometer interpolation/ extrapolation algorithm described a method to interpolate horizontally between multiple ground sensors (a minimum of three) and extrapolate vertically. This work is a modification to that approach that generates a purely extrapolated 3D spatial distribution when using a single sensor.
Hermite interpolation of scattered data based on the assistant surface
WANG Quan-wei; LI Xue-yi; LI Bin; WANG Xiao-chun
2006-01-01
An assistant surface was constructed on the base of boundary that being automatically extracted from the scattered data. The parameters of every data point corresponding to the assistant surface and their applied fields were calculated respectively. In every applied region, a surface patch was constructed by a special Hermite interpolation.The final surface can be obtained by a piecewise bicubic Hermite interpolation in the aggregate of applied regions of metrical data. This method avoids the triangulation problem.Numerical results indicate that it is efficient and accurate.
MULTI-EPIPOLAR LINES MATCHING-BASED RAY-SPACE INTERPOLATION FOR FREE VIEWPOINT VIDEO SYSTEM
Fan Liangzhong; Jiang Gangyi; Yu Mei; Yong-deak Kim
2008-01-01
Ray-space based arbitrary viewpoint rendering without complex object segmentation or model construction is the main technology to realize Free Viewpoint Video(FVV) system for complex scenes.Ray-space interpolation and compression are two key techniques for the solution.In this paper,correlation among multiple epipolar lines in ray-space data is analyzed,and a new method of ray-space interpolation with multi-epipolar lines matching is proposed.Comparing with the pixel-based matching interpolation method and the block-based matching interpolation method,the proposed method can achieve higher Peak Signal to Noise Ratio(PSNR)in interpolating rayspace data and rendering arbitrary viewpoint images.
Approaches for Constrained Parametric Curve Interpolation
ZHANG CaiMing(张彩明); YANG XingQiang(杨兴强); WANG JiaYe(汪嘉业)
2003-01-01
The construction of a GC 1 cubic interpolating curve that lies on the same side of agiven straight line as the data points is studied. The main task is to choose appropriate approachesto modify tangent vectors at the data points for the desired curve. Three types of approaches forchanging the magnitudes of the tangent vectors are presented. The first-type approach nodifiesthe tangent vectors by applying a constraint to the curve segment. The second one does the workby optimization techniques. The third one is a modification of the existing method. Three criteriaare presented to compare the three types of approaches with the existing method. The experimentsthat test the effectiveness of the approaches are included.
Research on Data Mining Based on RBF Neural Network%基于RBF神经网络的数据挖掘研究
徐晓
2014-01-01
This paper discusses the principle and related methods of data mining technology based on data warehouse, and introduces the principle and characteristics of RBF neural network. Aiming at the characteristics of RBF neural network such as strong nonlinear mapping ability and high-speed learning, this paper introduces the data cleaning, pretreatment and regularization steps of data mining method based on RBF neural network. With the distributed information storage feature, the neural network can use a large number of connections between neurons and the analysis of connection weights to limit specific information. The network system built by this idea will not lead to an overall paralysis, even if the local network is damaged..%探讨了基于数据仓库的数据挖掘技术的原理与相关方法，介绍了RBF神经网络的原理与特点。针对RBF神经网络非线性映射能力强和学习速度快等特点，介绍了基于RBF神经网络的数据挖掘方法的数据清洗、预处理和正则化等操作步骤。神经网络具有分布式存储信息的特点，能够利用大量神经元间的连接，以及连接权值的分析，来限定特定信息。使用这种思想构建的网络系统，即使在局部的网络损坏，也不会导致整体的瘫痪。
High degree interpolation polynomial in Newton form
Tal-Ezer, Hillel
1988-01-01
Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.
COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS
檀结庆
2003-01-01
As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.
Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.
Craciunescu, O I; Das, S K; Poulson, J M; Samulski, T V
2001-04-01
It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.
Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline
Cheng-ming Liu; Ze-kun Wang; Hai-bo Pang; Jun-xiao Xue
2017-01-01
Image interpolation is a basic operation in image processing. Lots of methods have been proposed, including convolution-based methods, edge modeling methods, point spread function (PSF)-based methods or learning-based methods. Most of them, however, present a high computational complexity and are not suitable for real time applications. However, fast methods are not able to provide artifacts-free images. In this paper we describe a new image interpolation method by using scanning line algorit...
Hurkmans, R.T.W.L.; Bamber, J.L.; Sørensen, Louise Sandberg
2012-01-01
. In those areas, straightforward interpolation of data is unlikely to reflect the true patterns of dH/dt. Here, four interpolation methods are compared and evaluated over Jakobshavn Isbræ, an outlet glacier for which widespread airborne validation data are available from NASA's Airborne Topographic Mapper...
Werner-Type Matrix Valued Rational Interpolation and Its Recurrence Algorithms
顾传青; 王金波
2004-01-01
In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem isprovided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the in-terpolants, an efficient forward recurrence algorithm is obtained.
Yoo, Yeon Hwa; Kim, Hak Sun; Lee, Young Han [Dept. of Radiology, Gangnam Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of); and others
2015-10-15
To assess whether multi-echo Dixon magnetic resonance (MR) imaging with simultaneous T2{sup *} estimation and correction yields more accurate fat-signal fraction (FF) measurement of the lumbar paravertebral muscles, in comparison with non-T2{sup *}-corrected two-echo Dixon or T2{sup *}-corrected three-echo Dixon, using the FF measurements from single-voxel MR spectroscopy as the reference standard. Sixty patients with low back pain underwent MR imaging with a 1.5T scanner. FF mapping images automatically obtained using T2{sup *}-corrected Dixon technique with two (non-T2{sup *}-corrected), three, and six echoes, were compared with images from single-voxel MR spectroscopy at the paravertebral muscles on levels L4 through L5. FFs were measured directly by two radiologists, who independently drew the region of interest on the mapping images from the three sequences. A total of 117 spectroscopic measurements were performed either bilaterally (57 of 60 subjects) or unilaterally (3 of 60 subjects). The mean spectroscopic FF was 14.3 ± 11.7% (range, 1.9-63.7%). Interobserver agreement was excellent between the two radiologists. Lin's concordance correlation between the spectroscopic findings and all the imaging-based FFs were statistically significant (p < 0.001). FFs obtained from the T2*-corrected six-echo Dixon sequences showed a significantly better concordance with the spectroscopic data, with its concordance correlation coefficient being 0.99 and 0.98 (p < 0.001), as compared with two- or three-echo methods. T2{sup *}-corrected six-echo Dixon sequence would be a better option than two- or three-echo methods for noninvasive quantification of lumbar muscle fat quantification.
Automatic Image Interpolation Using Homography
Chi-Tsung Liu
2010-01-01
Full Text Available While taking photographs, we often face the problem that unwanted foreground objects (e.g., vehicles, signs, and pedestrians occlude the main subject(s. We propose to apply image interpolation (also known as inpainting techniques to remove unwanted objects in the photographs and to automatically patch the vacancy after the unwanted objects are removed. When given only a single image, if the information loss after the unwanted objects in images being removed is too great, the patching results are usually unsatisfactory. The proposed inpainting techniques employ the homographic constraints in geometry to incorporate multiple images taken from different viewpoints. Our experiment results showed that the proposed techniques could effectively reduce process in searching for potential patches from multiple input images and decide the best patches for the missing regions.
Comparison of Three Interpolation Schemes for Six Parameters
Kolbe, Christine; Rehfeldt, Kira; Ziese, Markus; Rustemeier, Elke; Krähenmann, Stefan; Becker, Andreas
2017-04-01
The European Commission set up the Copernicus Emergency Management Service (EMS), which up to now includes the European Flood Awareness System (EFAS) and the European Forest Fire Information System (EFFIS). Within this framework, the Meteorological Data Collection Center (Copernicus MDCC) collects data from European data providers and supplies regularly gridded and station related analyses as input data for the EMS's EFAS and EFFIS. To identify the optimum interpolation scheme for the six EMS relevant parameters (precipitation total, maximum temperature, minimum temperature, mean vapor pressure, daily mean wind speed, daily total radiation) a comparison of three different interpolation methods using European station observation data on a daily basis covering May 2014 had been conducted. This month featured high precipitation amounts in some areas of Europe, especially in the Balkan states and Italy. Such periods of high precipitation amounts across topographically structured terrain are a challenge for interpolation schemes to represent the entire variability actually taking place, thus most suitable for the comparison. We compared inverse distance weighting (Ntegeka et al., 2013), Spheremap (Willmott et al., 1985) and ordinary kriging (Krige, 1966). Furthermore, the uncertainty information of the gridded product is provided. A leave-one-out cross validation was utilized to assess the quality of the interpolation schemes and different error metrics were calculated, as they focus on different aspects of uncertainties. Yamamoto's approach was used to determine the uncertainty of the gridded fields in order to find the best interpolation scheme (Yamamoto, 2000). This analysis revealed that IDW is the best performing scheme regarding the computational effort. However, Spheremap is more robust against locally higher density of input data and grids generated by Spheremap are more reliable and the overall uncertainty is lower than in the other tested interpolation schemes
Image interpolation by two-dimensional parametric cubic convolution.
Shi, Jiazheng; Reichenbach, Stephen E
2006-07-01
Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] x [-2, 2] with constraints for biaxial symmetry, diagonal (or 90 degrees rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.
Knowledge base interpolation of path-dependent data using irregularly spaced natural neighbors
Hipp, J.; Keyser, R.; Young, C.; Shepard-Dombroski, E.; Chael, E.
1996-08-01
This paper summarizes the requirements for the interpolation scheme needed for the CTBT Knowledge Base and discusses interpolation issues relative to the requirements. Based on these requirements, a methodology for providing an accurate and robust interpolation scheme for the CTBT Knowledge Base is proposed. The method utilizes a Delaunay triangle tessellation to mesh the Earth`s surface and employs the natural-neighbor interpolation technique to provide accurate evaluation of geophysical data that is important for CTBT verification. The natural-neighbor interpolation method is a local weighted average technique capable of modeling sparse irregular data sets as is commonly found in the geophysical sciences. This is particularly true of the data to be contained in the CTBT Knowledge Base. Furthermore, natural neighbor interpolation is first order continuous everywhere except at the data points. The non-linear form of the natural-neighbor interpolation method can provide continuous first and second order derivatives throughout the entire data domain. Since one of the primary support functions of the Knowledge Base is to provide event location capabilities, and the seismic event location algorithms typically require first and second order continuity, this is a prime requirement of any interpolation methodology chosen for use by the CTBT Knowledge Base.
李军成
2011-01-01
The traditional method for constructing identical slope surface is under the premise that exact expression of lead curve is known. But in practical engineering, the exact expression of lead curve is hard to obtain, and only some measured data points of the lead curve are given. For solving that problem, a method of constructing the identical slope surface in engineering is presented in this paper. Firstly, cubic parametric spline interpolation curve is constructed according to the measured data points, which is regarded as the lead curve. Then, the parametric equation of identical slope gradient surface is constructed based on the forming principle of that surface. Lastly, an example is presented to show the method is feasible and effectual.%传统的同坡曲面构造方法都是在导线方程为已知的前提下进行的.然而在实际工程中,导线方程往往是很难得到的,只能通过测量得知导线通过一列数据点.针对这一问题,给出了一种实际工程中同坡曲面的构造方法,该法首先根据测量数据点,利用三次参数样条曲线插值方法构造出同坡曲面的导线方程,然后再从同坡曲面的形成原理入手建立其参数方程,最后通过实例表明该方法是可行有效的.