• Journal of Astronomy and Space Sciences
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• 제15권1호
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• pp.229-234
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• 1998

We study on a terrain contour matching algorithm using Radial Basis Functions(RBFs) for aided inertial navigation system for position fixing aircraft, cruise missiles or re-entry vehicles. The parameter optimization technique is used for updating the parameters describing the characteristics of an area with modified Gaussian least square differential correction algorithm and the step size limitation filter according to the amount of updates. We have applied the algorithm for matching a sampled area with a target area supposed that the area data are available from Radar Terrain Sensor(RTS) and Reference Altitude Sensor(RAS)

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.951-969
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• 2012

In this paper, we propose a class of meshless collocation approaches for the solution of time dependent partial differential algebraic equations (PDAEs) in terms of a radial basis function interpolation numerical scheme. Kansa's method and the Hermite collocation method (HCM) for PDAEs are given. A sensitivity analysis of the solutions from different shape parameter c is obtained by numerical experiments. With use of the random collocation points, we have obtain the more accurate solution by the methods than those by the finite difference method for the PDAEs with index-2, i.e, we avoid the influence from an index jump of PDAEs in some degree. Several numerical experiments show that the methods are efficient.

• 한국CDE학회논문집
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• 제21권4호
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• pp.443-452
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• 2016

This paper proposes a method for expensive black box optimization using radial basis functions (RBFs). The proposed algorithm is a computational strategy that uses a RBF model approximating the expensive black box function to predict an optimum. First, a RBF-based approximation technique is introduced and a sampling plan for estimation of the black box function is described. Then the proposed algorithm is explained, which presents the pseudo-codes for implementation and the detailed description of each step performed in the optimization process. In addition, numerical experiments will be given to analyze the performance of the proposed algorithm, by investigating computation accuracy, number of function evaluations, and convergence history. Finally, geometric distance problem as application example will be also presented for showing the algorithm applicability to different engineering problems.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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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.

• Steel and Composite Structures
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• 제47권5호
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Structural Engineering and Mechanics
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• 제88권3호
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 하계종합학술대회 논문집
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• pp.482-485
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• 1999

In this paper we proposed a heterogeneous hidden layer consisting of both sigmoid functions and RBFs(Radial Basis Function) in multi-layered neural networks. Focusing on the orthogonal relationship between the sigmoid function and its derivative, a derived RBF that is a derivative of the sigmoid function is used as the RBF in the neural network. so the proposed neural network is called ONN(Orthogonal Neural Network). Identification results using a nonlinear function confirm both the ONN＇s feasibility and characteristics by comparing with those obtained using a conventional neural network which has sigmoid function or RBF in hidden layer

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 1999년도 추계종합학술대회
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• pp.214-217
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• 1999

본 논문에서는 시그모이드 함수와 시그모이드 함수의 도함수로 유도한 RBF의 직교관계에 착안하여 은닉충에 직교함수를 활성화함수로 갖는 신경회로망을 제안한다. 제안하는 신경회로망을 직교신경회로망(ONN)이라고 한다. 제안한 방식의 유용성을 확인하기 위하여 비선형 함수의 근사 시뮬레이션에 의해 사상능력을 검토하고, 각각의 단일함수만을 적용한 경우와 비교·검토한다.

• 전기학회논문지
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• 제58권2호
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• pp.399-406
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• 2009

In this study, Polynomial Radial Basis Function Neural Network(pRBFNN) based on Fuzzy Inference System is designed and its parameters such as learning rate, momentum coefficient, and distributed weight (width of RBF) are optimized by means of Particle Swarm Optimization. The proposed model can be expressed as three functional module that consists of condition part, conclusion part, and inference part in the viewpoint of fuzzy rule formed in 'If-then'. In the condition part of pRBFNN as a fuzzy rule, input space is partitioned by defining kernel functions (RBFs). Here, the structure of kernel functions, namely, RBF is generated from HCM clustering algorithm. We use Gaussian type and Inverse multiquadratic type as a RBF. Besides these types of RBF, Conic RBF is also proposed and used as a kernel function. Also, in order to reflect the characteristic of dataset when partitioning input space, we consider the width of RBF defined by standard deviation of dataset. In the conclusion part, the connection weights of pRBFNN are represented as a polynomial which is the extended structure of the general RBF neural network with constant as a connection weights. Finally, the output of model is decided by the fuzzy inference of the inference part of pRBFNN. In order to evaluate the proposed model, nonlinear function with 2 inputs, waster water dataset and gas furnace time series dataset are used and the results of pRBFNN are compared with some previous models. Approximation as well as generalization abilities are discussed with these results.

• 전기학회논문지
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• 제57권3호
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• pp.466-472
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• 2008

The paper concerns Fuzzy C-Means clustering based fuzzy neural networks (FCM-FNN) and the optimization of the network is carried out by means of hierarchal fair competition-based parallel genetic algorithm (HFCPGA). FCM-FNN is the extended architecture of Radial Basis Function Neural Network (RBFNN). FCM algorithm is used to determine centers and widths of RBFs. In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values directly rely on the computation of the relevant distance between data points by means of FCM. Also, as the consequent part of fuzzy rules extracted by the FCM-FNN model, the order of four types of polynomials can be considered such as constant, linear, quadratic and modified quadratic. Since the performance of FCM-FNN is affected by some parameters of FCM-FNN such as a specific subset of input variables, fuzzification coefficient of FCM, the number of rules and the order of polynomials of consequent part of fuzzy rule, we need the structural as well as parametric optimization of the network. In this study, the HFCPGA which is a kind of multipopulation-based parallel genetic algorithms(PGA) is exploited to carry out the structural optimization of FCM-FNN. Moreover the HFCPGA is taken into consideration to avoid a premature convergence related to the optimization problems. The proposed model is demonstrated with the use of two representative numerical examples.