Radial basis function approximations: comparison and applications

Majdisova, Zuzana; Skala, Václav

doi:10.1016/j.apm.2017.07.033

Cited by 128 publications

(55 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where is the shape parameter of the radial basis function [11]. Application of global RBFs usually leads to ill-conditioned system, especially in the case of large data sets with a large span [27], [39]. The "local" RBFs were introduced in [45] as compactly supported RBF (CSRBF) and satisfy the following condition:…”

Section: Radial Basis Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Large scattered data interpolation with radial basis functions and space subdivision

Smolik¹,

Skala²

2017

ICA

Self Cite

View full text Add to dashboard Cite

We propose a new approach for the radial basis function (RBF) interpolation of large scattered data sets. It uses the space subdivision technique into independent cells allowing processing of large data sets with low memory requirements and offering high computation speed, together with the possibility of parallel processing as each cell can be processed independently. The proposed RBF interpolation was tested on both synthetic and real data sets. It proved its simplicity, robustness and the ability to handle large data sets together with significant speed-up. In the case of parallel processing, speed-up was experimentally proved when 2 and 4 threads were used.

show abstract

Section: Radial Basis Functionsmentioning

confidence: 99%

“…Another approach using virtual points for approximation is used in [25] and [42]. Of course, there are other meshless techniques than RBF, such as discrete smooth interpolation (DSI) [28], which avoids explicitly computing a function defined everywhere and produces values only at the grid points instead.…”

Section: Introductionmentioning

confidence: 99%

Large scattered data interpolation with radial basis functions and space subdivision

Smolik¹,

Skala²

2017

ICA

Self Cite

View full text Add to dashboard Cite

show abstract

“…The method guarantees convergence. Majdisova and Skala [25,26] discussed the applications of RBFs for big geo data as well as finding the best basis for function approximations. A good survey on scattered data interpolation using meshfree methods and other methods can be found in Lodha and Franke [24], Franke and Nielson [10,11], and Franke [9].…”

Section: Introductionmentioning

confidence: 99%

“…Even though the study on interpolation based on Bézier and Ball representation is already thirty years old, many researchers are still focusing on how to improve both representations by adding more flexibility to the control point to control the shape of curves or surfaces. For instance, [26] constructed an explicit parametric curve to be taken as the limitation curve of progressive iteration approximation (PIA) which can interpolate some scattered data points by using normalized totally positive (NTP) basis by specially choosing two kinds of NTP bases, Said-Bézier type generalized Ball (SBGB) basis and DP basis. Their results avoid the tedious calculation of the inverse matrix and hence will gain extensive application in reverse engineering.…”

Section: Introductionmentioning

confidence: 99%

Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

et al. 2020

Self Cite

View full text Add to dashboard Cite

This paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bézier-like triangular basis function controlled by three shape parameters. This is an advantage compared with the existing schemes since it gives more flexibility for the shape design in geometric modeling. By choosing some suitable value of the parameters, this new triangular basis is reduced to the cubic Ball and cubic Bézier triangular patches, respectively. In order to apply the proposed bases to general scattered data, firstly the data is triangulated using Delaunay triangulation. Then the sufficient condition for C 1 continuity using cubic precision method on each adjacent triangle is implemented. Finally, the interpolation scheme is constructed based on a convex combination between three local schemes of the cubic Bézier-like triangular patches. The detail comparison in terms of maximum error and coefficient of determination r 2 with some existing meshfree methods i.e. radial basis function (RBF) such as linear, thin plate spline (TPS), Gaussian, and multiquadric are presented. From graphical results, the proposed scheme gives more visually pleasing interpolating surfaces compared with all RBF methods. Based on error analysis, for all four functions, the proposed scheme is better than RBFs except for data from the third function. Overall, the proposed scheme gives r 2 value between 0.99920443 and 0.99999994. This is very good for surface fitting for a large scattered data set.

show abstract

“…However, due to money and/or time costs, it is practically infeasible to experiment or numerically simulate every feasible design point; thus, based on obtained results, different techniques to predict the outcome at a specified point have been developed, among which, one of the most widely used types is surrogate models, such as polynomial response surfaces [8], Kriging, gradient-enhanced Kriging (GEK) [9], radial basis function [10], support vector machine [11] et al With the constructed approximation models, an optimization procedure is consequently used to find the optimal result. Optimization methods arise from optimal objectives, and they are becoming essential in every field of research.…”

Section: Introductionmentioning

confidence: 99%

Layout Optimization Design of Two Vortex Induced Piezoelectric Energy Converters (VIPECs) Using the Combined Kriging Surrogate Model and Particle Swarm Optimization Method

Song

Mao

et al. 2018

Energies

View full text Add to dashboard Cite

Abstract:The layout configuration of Vortex Induced Piezoelectric Energy Converters (VIPECs) is essential to improve its overall performance. Based on the formations of migrating geese, the configuration is characterized by two nondimensionalized layout parameters. A number of sampled points for different configurations are simulated with the two-dimensional Computation Fluid Dynamics (CFD) method. The influence of layout configurations on VIPECs' lift force and wake structure is investigated and the generated open circuit output voltage is obtained through the derived output voltage equation. The response surface model of the output voltage of both the leading VIPEC and the following VIPEC and their summation are established using the Kriging surrogate model based on the obtained simulation results. Then, optimal layout parameters are found through the Particle Swarm Optimization (PSO) algorithm, and its predicted result is compared with that of the CFD simulation. The simulation and optimization results reveal that the output voltage is not always consistent with the lift force on the plate. When VIPECs are placed in parallel with a certain spacing, their overall performance increases. The summation of output voltage is predicted to improve by approximately 63.7% compared to two single VIPECs when they are placed at the optimal layout parameters.

show abstract

Radial basis function approximations: comparison and applications

Cited by 128 publications

References 6 publications

Large scattered data interpolation with radial basis functions and space subdivision

Large scattered data interpolation with radial basis functions and space subdivision

Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

Layout Optimization Design of Two Vortex Induced Piezoelectric Energy Converters (VIPECs) Using the Combined Kriging Surrogate Model and Particle Swarm Optimization Method

Contact Info

Product

Resources

About