scholarly journals Visualization Method for Arbitrary Cutting of Finite Element Data Based on Radial-Basis Functions

Information ◽  
2019 ◽  
Vol 10 (7) ◽  
pp. 229 ◽  
Author(s):  
Shifa Xia ◽  
Xiulin Li ◽  
Fuye Xu ◽  
Lufei Chen ◽  
Yong Zhang
Keyword(s):  
Finite Element ◽  
Basis Function ◽  
Experimental Studies ◽  
Basis Functions ◽  
Visualization Method ◽  
Interpolation Function ◽  
Element Data ◽  
Radial Basis ◽  
Arbitrary Section ◽  
Important Basis

Finite element data form an important basis for engineers to undertake analysis and research. In most cases, it is difficult to generate the internal sections of finite element data and professional operations are required. To display the internal data of entities, a method for generating the arbitrary sections of finite element data based on radial basis function (RBF) interpolation is proposed in this paper. The RBF interpolation function is used to realize arbitrary surface cutting of the entity, and the section can be generated by the triangulation of discrete tangent points. Experimental studies have proved that the method is very convenient for allowing users to obtain visualization results for an arbitrary section through simple and intuitive interactions.

scholarly journals Accurate radial basis functions technique for competitive and efficient solutions of non-linear Black-Scholes equations

2020 ◽  
Vol 20 (4) ◽  
pp. 60-83
Author(s):  
Vinícius Magalhães Pinto Marques ◽  
Gisele Tessari Santos ◽  
Mauri Fortes
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Efficient Solutions ◽  
Basis Functions ◽  
Adaptive Scheme ◽  
Call Options ◽  
Black Scholes ◽  
Non Linear ◽  
Radial Basis ◽  
Complex Models

ABSTRACTObjective: This article aims to solve the non-linear Black Scholes (BS) equation for European call options using Radial Basis Function (RBF) Multi-Quadratic (MQ) Method.Methodology / Approach: This work uses the MQ RBF method applied to the solution of two complex models of nonlinear BS equation for prices of European call options with modified volatility. Linear BS models are also solved to visualize the effects of modified volatility.  Additionally, an adaptive scheme is implemented in time based on the Runge-Kutta-Fehlberg (RKF) method.

scholarly journals The Conical Radial Basis Function for Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
J. Zhang ◽  
F. Z. Wang ◽  
E. R. Hou
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Computational Cost ◽  
Basis Functions ◽  
Simple Scheme ◽  
Collocation Points ◽  
Radial Basis ◽  
Radial Basis Function Method

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

Effects of sections added to multi-cell square tubes on crash performance

2020 ◽  
Vol 62 (5) ◽  
pp. 471-480 ◽  
Author(s):  
Emre İsa Albak
Keyword(s):  
Finite Element ◽  
Genetic Algorithms ◽  
Radial Basis Functions ◽  
Axial Loading ◽  
Basis Functions ◽  
Finite Element Analyses ◽  
Energy Absorber ◽  
Radial Basis ◽  
Crash Performance

Abstract In this study, the effects of sections added to multi-cell square tubes on crash performance are examined. Square, hexagonal and circular sections are added to multi-cell square tubes and their results are examined. Finite element analyses under axial loading are performed to examine the crash performance of the multi-cell tubes. Analyses show that by adding a section to the multi-cell square tubes. the crash behavior of the tubes is improved. According to the results, S5H multi-cell square tube reveals the best crash performance. The optimization of S5H is carried out by using genetic algorithms and radial basis functions. The S5H tube presents a good crashworthiness performance and could be used as an energy absorber.

Differential Evolution-Based Optimization of Kernel Parameters in Radial Basis Function Networks for Classification

2013 ◽  
Vol 4 (1) ◽  
pp. 56-80 ◽  
Author(s):  
Ch. Sanjeev Kumar Dash ◽  
Ajit Kumar Behera ◽  
Satchidananda Dehuri ◽  
Sung-Bae Cho
Keyword(s):  
Neural Networks ◽  
Differential Evolution ◽  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Basis Functions ◽  
Second Phase ◽  
Rbf Neural Networks ◽  
Radial Basis ◽  
Two Phases

In this paper a two phases learning algorithm with a modified kernel for radial basis function neural networks is proposed for classification. In phase one a new meta-heuristic approach differential evolution is used to reveal the parameters of the modified kernel. The second phase focuses on optimization of weights for learning the networks. Further, a predefined set of basis functions is taken for empirical analysis of which basis function is better for which kind of domain. The simulation result shows that the proposed learning mechanism is evidently producing better classification accuracy vis-à-vis radial basis function neural networks (RBFNs) and genetic algorithm-radial basis function (GA-RBF) neural networks.

scholarly journals Upset Prediction in Friction Welding Using Radial Basis Function Neural Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wei Liu ◽  
Feifan Wang ◽  
Xiawei Yang ◽  
Wenya Li
Keyword(s):  
Neural Network ◽  
Finite Element ◽  
Radial Basis Function ◽  
Basis Function ◽  
Welded Joints ◽  
Friction Welding ◽  
Rbf Neural Network ◽  
Finite Element Simulations ◽  
Welding Parameters ◽  
Radial Basis

This paper addresses the upset prediction problem of friction welded joints. Based on finite element simulations of inertia friction welding (IFW), a radial basis function (RBF) neural network was developed initially to predict the final upset for a number of welding parameters. The predicted joint upset by the RBF neural network was compared to validated finite element simulations, producing an error of less than 8.16% which is reasonable. Furthermore, the effects of initial rotational speed and axial pressure on the upset were investigated in relation to energy conversion with the RBF neural network. The developed RBF neural network was also applied to linear friction welding (LFW) and continuous drive friction welding (CDFW). The correlation coefficients of RBF prediction for LFW and CDFW were 0.963 and 0.998, respectively, which further suggest that an RBF neural network is an effective method for upset prediction of friction welded joints.

Multilevel RBF collocation method for the fourth-order thin plate problem

2020 ◽  
pp. 2050079
Author(s):  
Lanling Ding ◽  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Fourth Order ◽  
Basis Function ◽  
Research Method ◽  
Meshfree Method ◽  
Basis Functions ◽  
Radial Basis

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s [Formula: see text] and [Formula: see text] functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

scholarly journals Applying models of spatial interpolation for the approximation of responses in the refinement of parameters of finite element models

2018 ◽  
Vol 212 ◽  
pp. 01021
Author(s):  
Anatoly Pikhalov ◽  
Anton Zabelin
Keyword(s):  
Finite Element ◽  
Radial Basis Functions ◽  
Element Model ◽  
Optimization Method ◽  
Latin Squares ◽  
Basis Functions ◽  
Finite Element Models ◽  
Radial Basis ◽  
High Level ◽  
Parameter Values

The numerical experiment on refining the parameters of the finite element model of the beam by the method of approximating the responses is presented in the article. As mathematical models of joint-stock companies are used: linear combinations of radial-basis functions, and Kriging-models. These models are generated in the work on the basis of Latin squares and depend on the parameters to be refined (the moduli of elasticity of finite element groups of the beam). To obtain optimal values of the parameters, a genetic optimization method was used. The results of solving the optimization problem showed a high level of coincidence of the parameter values with a combination of response models obtained from dynamic and static types of calculations. It was also shown that when solving the problems of finite element models, it is sufficient to use models constructed only on the basis of radial-basis functions.

Radial basis function surrogate model-based optimization of guardrail post embedment depth in different soil conditions

2019 ◽  
Vol 234 (2-3) ◽  
pp. 739-761
Author(s):  
Sedat Ozcanan ◽  
Ali Osman Atahan
Keyword(s):  
Finite Element ◽  
Radial Basis Function ◽  
Basis Function ◽  
Computational Cost ◽  
Critical Parameters ◽  
Crash Test ◽  
Soil Conditions ◽  
Embedment Depth ◽  
Element Analysis ◽  
Radial Basis

For guardrail designers, it is essential to achieve a crashworthy and optimal system design. One of the most critical parameters for an optimal road restraint system is the post embedment depth or the post-to-soil interaction. This study aims to assess the optimum post embedment depth values of three different guardrail posts embedded in soil with varying density. Posts were subjected to dynamic impact loads in the field while a detailed finite element study was performed to construct accurate models for the post–soil interaction. It is well-known that experimental tests and simulations are costly and time-consuming. Therefore, to reduce the computational cost of optimization, radial basis function–based metamodeling methodology was employed to create surrogate models that were used to replace the expensive three-dimensional finite element models. In order to establish the radial basis function model, samples were derived using the full factorial design. Afterward, radial basis function–based metamodels were generated from the derived data and objective functions performed using finite element analysis. The accuracy of the metamodels were validated by k-fold cross-validation, then optimized using multi-objective genetic algorithm. After optimum embedment depths were obtained, finite element simulations of the results were compared with full-scale crash test results. In comparison with the actual post embedment depths, optimal post embedment depths provided significant economic advantages without compromising safety and crashworthiness. It is concluded that the optimum post embedment depths provide an economic advantage of up to 17.89%, 36.75%, and 43.09% for C, S, and H types of post, respectively, when compared to actual post embedment depths.

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