• Title/Summary/Keyword: radial basis functions

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MESHLESS AND HOMOTOPY PERTURBATION METHODS FOR ONE DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM WITH NEUMANN AND ROBIN BOUNDARY CONDITIONS

  • GEDEFAW, HUSSEN;GIDAF, FASIL;SIRAW, HABTAMU;MERGIAW, TADESSE;TSEGAW, GETACHEW;WOLDESELASSIE, ASHENAFI;ABERA, MELAKU;KASSIM, MAHMUD;LISANU, WONDOSEN;MEBRATE, BENYAM
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.675-694
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    • 2022
  • In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

Meshless Local Petrov-Galerkin (MLPG) method for dynamic analysis of non-symmetric nanocomposite cylindrical shell

  • Ferezghi, Yaser Sadeghi;Sohrabi, Mohamadreza;Nezhad, Seyed Mojtaba Mosavi
    • Structural Engineering and Mechanics
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    • v.74 no.5
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    • pp.679-698
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    • 2020
  • In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

Effects of Latin hypercube sampling on surrogate modeling and optimization

  • Afzal, Arshad;Kim, Kwang-Yong;Seo, Jae-won
    • International Journal of Fluid Machinery and Systems
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    • v.10 no.3
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    • pp.240-253
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    • 2017
  • Latin hypercube sampling is widely used design-of-experiment technique to select design points for simulation which are then used to construct a surrogate model. The exploration/exploitation properties of surrogate models depend on the size and distribution of design points in the chosen design space. The present study aimed at evaluating the performance characteristics of various surrogate models depending on the Latin hypercube sampling (LHS) procedure (sample size and spatial distribution) for a diverse set of optimization problems. The analysis was carried out for two types of problems: (1) thermal-fluid design problems (optimizations of convergent-divergent micromixer coupled with pulsatile flow and boot-shaped ribs), and (2) analytical test functions (six-hump camel back, Branin-Hoo, Hartman 3, and Hartman 6 functions). The three surrogate models, namely, response surface approximation, Kriging, and radial basis neural networks were tested. The important findings are illustrated using Box-plots. The surrogate models were analyzed in terms of global exploration (accuracy over the domain space) and local exploitation (ease of finding the global optimum point). Radial basis neural networks showed the best overall performance in global exploration characteristics as well as tendency to find the approximate optimal solution for the majority of tested problems. To build a surrogate model, it is recommended to use an initial sample size equal to 15 times the number of design variables. The study will provide useful guidelines on the effect of initial sample size and distribution on surrogate construction and subsequent optimization using LHS sampling plan.

Approximate Optimization with Discrete Variables of Fire Resistance Design of A60 Class Bulkhead Penetration Piece Based on Multi-island Genetic Algorithm (다중 섬 유전자 알고리즘 기반 A60 급 격벽 관통 관의 방화설계에 대한 이산변수 근사최적화)

  • Park, Woo-Chang;Song, Chang Yong
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.20 no.6
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    • pp.33-43
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    • 2021
  • A60 class bulkhead penetration piece is a fire resistance system installed on a bulkhead compartment to protect lives and to prevent flame diffusion in a fire accident on a ship and offshore plant. This study focuses on the approximate optimization of the fire resistance design of the A60 class bulkhead penetration piece using a multi-island genetic algorithm. Transient heat transfer analysis was performed to evaluate the fire resistance design of the A60 class bulkhead penetration piece. For approximate optimization, the bulkhead penetration piece length, diameter, material type, and insulation density were considered discrete design variables; moreover, temperature, cost, and productivity were considered constraint functions. The approximate optimum design problem based on the meta-model was formulated by determining the discrete design variables by minimizing the weight of the A60 class bulkhead penetration piece subject to the constraint functions. The meta-models used for the approximate optimization were the Kriging model, response surface method, and radial basis function-based neural network. The results from the approximate optimization were compared to the actual results of the analysis to determine approximate accuracy. We conclude that the radial basis function-based neural network among the meta-models used in the approximate optimization generates the most accurate optimum design results for the fire resistance design of the A60 class bulkhead penetration piece.

An adaptive meshfree RPIM with improved shape parameter to simulate the mixing of a thermoviscoplastic material

  • Zouhair Saffah;Mohammed Amdi;Abdelaziz Timesli;Badr Abou El Majd;Hassane Lahmam
    • Structural Engineering and Mechanics
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    • v.88 no.3
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    • pp.239-249
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    • 2023
  • The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

A Study on Hybrid Structure of Semi-Continuous HMM and RBF for Speaker Independent Speech Recognition (화자 독립 음성 인식을 위한 반연속 HMM과 RBF의 혼합 구조에 관한 연구)

  • 문연주;전선도;강철호
    • The Journal of the Acoustical Society of Korea
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    • v.18 no.8
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    • pp.94-99
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    • 1999
  • It is the hybrid structure of HMM and neural network(NN) that shows high recognition rate in speech recognition algorithms. And it is a method which has majorities of statistical model and neural network model respectively. In this study, we propose a new style of the hybrid structure of semi-continuous HMM(SCHMM) and radial basis function(RBF), which re-estimates weighting coefficients probability affecting observation probability after Baum-Welch estimation. The proposed method takes account of the similarity of basis Auction of RBF's hidden layer and SCHMM's probability density functions so as to discriminate speech signals sensibly through the learned and estimated weighting coefficients of RBF. As simulation results show that the recognition rates of the hybrid structure SCHMM/RBF are higher than those of SCHMM in unlearned speakers' recognition experiment, the proposed method has been proved to be one which has more sensible property in recognition than SCHMM.

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A Performance Study of Gaussian Radial Basis Function Model for the Monk's Problems (Monk's Problem에 관한 가우시안 RBF 모델의 성능 고찰)

  • Shin, Mi-Young;Park, Joon-Goo
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.43 no.6 s.312
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    • pp.34-42
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    • 2006
  • As art analytic method to uncover interesting patterns hidden under a large volume of data, data mining research has been actively done so far in various fields. However, current state-of-the-arts in data mining research have several challenging problems such as being too ad-hoc. The existing techniques are mostly the ones designed for individual problems, so there is no unifying theory applicable for more general data mining problems. In this paper, we address the problem of classification, which is one of significant data mining tasks. Specifically, our objective is to evaluate radial basis function (RBF) model for classification tasks and investigate its usefulness. For evaluation, we analyze the popular Monk's problems which are well-known datasets in data mining research. First, we develop RBF models by using the representational capacity based learning algorithm, and then perform a comparative assessment of the results with other models generated by the existing techniques. Through a variety of experiments, it is empirically shown that the RBF model has not only the superior performance on the Monk's problems but also its modeling process can be controlled in a systematic way, so the RBF model with RC-based algorithm might be a good candidate to handle the current ad-hoc problem.

A Rule Merging Method for Fuzzy Classifier Systems and Its Applications to Fuzzy Control Rules Acquisition

  • Inoue, Hiroyuki;Kamei, Katsuari
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2003.09a
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    • pp.78-81
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    • 2003
  • This paper proposes a fuzzy classifier system (FCS) using hyper-cone membership functions (HCMFs) and rule reduction techniques. The FCS can generate excellent rules which have the best number of rules and the best location and shape of membership functions. The HCMF is expressed by a kind of radial basis function, and its fuzzy rule can be flexibly located in input and output spaces. The rule reduction technique adopts a decreasing method by merging the two appropriate rules. We applay the FCS to a tubby rule generation for the inverted pendulum control.

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Nonlinear Approximation in High-Dimensional Spaces Using Tree-Structured Intelligent Systems (수목구조 지능시스템을 이용한 고차원 공간 위에서의 비선형 근사)

  • 길준민;정창호;강성훈;박주영;박대희
    • Journal of the Korean Institute of Intelligent Systems
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    • v.6 no.3
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    • pp.25-36
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    • 1996
  • Conventional radial-basis-function networks and fuzzy systems have serious problems in dealing with the non1inea:r approximations on high-dimensional spaces due to the explosive increase of the number of hidden nodes or fuzzy IF-THEN rules. In order to avoid such problems, this paper proposes a tree-structured intelligent system in which semi-local basis functions form its basic elements, and develops a training algorithm for the proposed system based on the modified genetic algorithm and LMS rule. Theoretical analysis is performed on the approximation capability of the proposed system, together with experimental studies which demonstrate the effectiveness of the developed methodology.

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A Novel Kernel SVM Algorithm with Game Theory for Network Intrusion Detection

  • Liu, Yufei;Pi, Dechang
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.11 no.8
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    • pp.4043-4060
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    • 2017
  • Network Intrusion Detection (NID), an important topic in the field of information security, can be viewed as a pattern recognition problem. The existing pattern recognition methods can achieve a good performance when the number of training samples is large enough. However, modern network attacks are diverse and constantly updated, and the training samples have much smaller size. Furthermore, to improve the learning ability of SVM, the research of kernel functions mainly focus on the selection, construction and improvement of kernel functions. Nonetheless, in practice, there are no theories to solve the problem of the construction of kernel functions perfectly. In this paper, we effectively integrate the advantages of the radial basis function kernel and the polynomial kernel on the notion of the game theory and propose a novel kernel SVM algorithm with game theory for NID, called GTNID-SVM. The basic idea is to exploit the game theory in NID to get a SVM classifier with better learning ability and generalization performance. To the best of our knowledge, GTNID-SVM is the first algorithm that studies ensemble kernel function with game theory in NID. We conduct empirical studies on the DARPA dataset, and the results demonstrate that the proposed approach is feasible and more effective.