scholarly journals Solving the Nonlinear Heat Equilibrium Problems Using the Local Multiquadric Radial Basis Function Collocation Method

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1289 ◽  
Author(s):  
Weichung Yeih
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Equilibrium Problems ◽  
Collocation Point ◽  
Absolute Error ◽  
Algebraic Equations ◽  
Radial Basis ◽  
Residual Norm

In this article, the nonlinear heat equilibrium problems are solved by the local multiquadric (MQ) radial basis function (RBF) collocation method. The system of nonlinear algebraic equations is solved by iteration based on the residual norm-based algorithm, in which the direction of evolution is determined by a linear equation. In addition, the role of the collocation point and source point is clearly defined such that in our proposed method the field value of any interested point can be expressed. Six numerical examples are shown to check the performance of the proposed method. As the number of supporting points (mp) increases, the accuracy of numerical solution increases. Among all examples, mp = 50 can perform well. In addition, the selection of shape parameter, c, affects the accuracy. However, as c < 2 the maximum relative absolute error percentage is less than 1%.

scholarly journals Prediction of Peak Particle Velocity Caused by Blasting through the Combinations of Boosted-CHAID and SVM Models with Various Kernels

2021 ◽  
Vol 11 (8) ◽  
pp. 3705
Author(s):  
Jie Zeng ◽  
Panayiotis C. Roussis ◽  
Ahmed Salih Mohammed ◽  
Chrysanthos Maraveas ◽  
Seyed Alireza Fatemi ◽  
...  
Keyword(s):  
Radial Basis Function ◽  
Particle Velocity ◽  
Basis Function ◽  
Absolute Error ◽  
Peak Particle Velocity ◽  
Support Vector ◽  
Effective Parameters ◽  
Experimental Database ◽  
Interaction Detection ◽  
Radial Basis

This research examines the feasibility of hybridizing boosted Chi-Squared Automatic Interaction Detection (CHAID) with different kernels of support vector machine (SVM) techniques for the prediction of the peak particle velocity (PPV) induced by quarry blasting. To achieve this objective, a boosting-CHAID technique was applied to a big experimental database comprising six input variables. The technique identified four input parameters (distance from blast-face, stemming length, powder factor, and maximum charge per delay) as the most significant parameters affecting the prediction accuracy and utilized them to propose the SVM models with various kernels. The kernel types used in this study include radial basis function, polynomial, sigmoid, and linear. Several criteria, including mean absolute error (MAE), correlation coefficient (R), and gains, were calculated to evaluate the developed models’ accuracy and applicability. In addition, a simple ranking system was used to evaluate the models’ performance systematically. The performance of the R and MAE index of the radial basis function kernel of SVM in training and testing phases, respectively, confirm the high capability of this SVM kernel in predicting PPV values. This study successfully demonstrates that a combination of boosting-CHAID and SVM models can identify and predict with a high level of accuracy the most effective parameters affecting PPV values.

scholarly journals Comparative Study Between Radial Basis Function Neural Network and Random Forest Algorithm for Building Energy Estimation

2019 ◽  
Author(s):  
Che Munira Che Razali ◽  
Amrul Faruq
Keyword(s):  
Random Forest ◽  
Radial Basis Function ◽  
Basis Function ◽  
Comparative Studies ◽  
Computer Experiment ◽  
Absolute Error ◽  
Random Forest Algorithm ◽  
Energy Estimation ◽  
Wall Area ◽  
Radial Basis

Recently, a computer experiment is ubiquitous in modeling and engineering design. Estimation ofenergy building efficiency using computer experiment is widely used to improve performance andenergy consumption in the residential building. This paper proposed Radial Basis Function NeuralNetwork (RBFNN) for energy building consumption dataset and make comparative studies betweenthe Random Forest algorithm (RF) in previous work. This study using the experimental dataset in theliterature that consists of 768 experimental data with eight input variables and two outputparameters of estimation. The inputs variables are relative compactness, surface area, wall area, roofarea, overall height, orientation, glazing area, and glazing area distribution of a building, whileoutput variables include heating and cooling loads of the building. The analytical result of energybuilding performance shows RBFNN is better than RF algorithm in estimation based on errorvalidation calculation using Mean Square Error (MSE), Mean Absolute Error (MAE) and MeanRelative Error (MRE). The findings of this comparative studies found that RBFNN is good in estimationbased on accuracy performance, but the RF algorithm is suitable to determine irrelevant features inestimation by uses many decision trees simultaneously.

A novel local radial basis function collocation method for multi-dimensional piezoelectric problems

2021 ◽  
pp. 1045389X2110572
Author(s):  
Amir Noorizadegan ◽  
Der Liang Young ◽  
Chuin-Shan Chen
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Shape Parameter ◽  
Piezoelectric Medium ◽  
The Finite Element Method ◽  
Mechanical Field ◽  
Radial Basis ◽  
2D And 3D

The local radial basis function collocation method (LRBFCM), a strong-form formulation of the meshless numerical method, is proposed for solving piezoelectric medium problems. The proposed numerical algorithm is based on the local Kansa method using variable shape parameter. We introduce a novel technique for the determination of shape parameter in the LRBFCM, which leads to greater accuracy, and simplicity. The implemented algorithm is first verified with a 2D Poisson equation. Then, we employed LRBFCM in a numerical simulation for 2D and 3D piezoelectric problems involving mutual coupling of the electric field and elastodynamic equations for mechanical field. The presented meshless method is verified using corresponding results obtained from the finite element method and moving least squares meshless local Petrov–Galerkin method. In particular, the 2D piezoelectric problem is verified with an exact solution.

scholarly journals A Novel Meshfree Approach with a Radial Polynomial for Solving Nonhomogeneous Partial Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 270
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao ◽  
Chih-Yu Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Numerical Solutions ◽  
Polynomial Basis ◽  
Partial Differential ◽  
Minimum Order ◽  
Radial Basis

In this article, a novel radial–based meshfree approach for solving nonhomogeneous partial differential equations is proposed. Stemming from the radial basis function collocation method, the novel meshfree approach is formulated by incorporating the radial polynomial as the basis function. The solution of the nonhomogeneous partial differential equation is therefore approximated by the discretization of the governing equation using the radial polynomial basis function. To avoid the singularity, the minimum order of the radial polynomial basis function must be greater than two for the second order partial differential equations. Since the radial polynomial basis function is a non–singular series function, accurate numerical solutions may be obtained by increasing the terms of the radial polynomial. In addition, the shape parameter in the radial basis function collocation method is no longer required in the proposed method. Several numerical implementations, including homogeneous and nonhomogeneous Laplace and modified Helmholtz equations, are conducted. The results illustrate that the proposed approach may obtain highly accurate solutions with the use of higher order radial polynomial terms. Finally, compared with the radial basis function collocation method, the proposed approach may produce more accurate solutions than the other.

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