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Article
Publication date: 26 November 2020

Armagan Karamanli

The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be…

156

Abstract

Purpose

The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be considered as a numerical tool for the engineering problems and used to obtain the trial solution and its derivatives without differentiating the basis functions for a meshless method. A meshless based on the CSRBF and Taylor series method has been developed for the solutions of engineering problems.

Design/methodology/approach

This paper is devoted to present a truly meshless method which is called a radial basis Taylor series method (RBTSM) based on the CSRBFs and Taylor series expansion (TSE). The basis function and its derivatives are obtained without differentiating CSRBFs.

Findings

The RBTSM does not involve differentiation of the approximated function. This property allows us to use a wide range of CSRBF and weight functions including the constant one. By using a different number of terms in the TSE, the global convergence properties of the RBTSM can be improved. The global convergence properties are satisfied by the RBTSM. The computed results based on the RBTSM shows excellent agreement with results given in the open literature. The RBTSM can provide satisfactory results even with the problem domains which have curved boundaries and irregularly distributed nodes.

Originality/value

The CSRBFs have been widely used for the construction of the basic function in the meshless methods. However, the derivative of the basis function is obtained with the differentiation of the CSRBF. In the RBTSM, the derivatives of the basis function are obtained by using the TSE without differentiating the CSRBF.

Details

Engineering Computations, vol. 38 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 5 June 2019

Ram Jiwari, Sanjay Kumar and R.C. Mittal

The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for…

Abstract

Purpose

The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for numerical simulation and to capture the shocks behavior of Burgers’ type problems.

Design/methodology/approach

The algorithms convert the problems into a system of ordinary differential equations which are solved by the Runge–Kutta method.

Findings

Two meshfree algorithms are developed and their stability is discussed. Numerical experiment is done to check the efficiency of the algorithms, and some shock behaviors of the problems are presented. The proposed algorithms are found to be accurate, simple and fast.

Originality/value

The present algorithms LRBF-DQM and GRBF-DQM are based on radial basis functions, which are new for Burgers’ type problems. It is concluded from the numerical experiments that LRBF-DQM is better than GRBF-DQM. The algorithms give better results than available literature.

Article
Publication date: 31 May 2013

Rajendra Machavaram and Shankar Krishnapillai

The purpose of this paper is to provide an effective and simple technique to structural damage identification, particularly to identify a crack in a structure. Artificial…

Abstract

Purpose

The purpose of this paper is to provide an effective and simple technique to structural damage identification, particularly to identify a crack in a structure. Artificial neural networks approach is an alternative to identify the extent and location of the damage over the classical methods. Radial basis function (RBF) networks are good at function mapping and generalization ability among the various neural network approaches. RBF neural networks are chosen for the present study of crack identification.

Design/methodology/approach

Analyzing the vibration response of a structure is an effective way to monitor its health and even to detect the damage. A novel two‐stage improved radial basis function (IRBF) neural network methodology with conventional RBF in the first stage and a reduced search space moving technique in the second stage is proposed to identify the crack in a cantilever beam structure in the frequency domain. Latin hypercube sampling (LHS) technique is used in both stages to sample the frequency modal patterns to train the proposed network. Study is also conducted with and without addition of 5% white noise to the input patterns to simulate the experimental errors.

Findings

The results show a significant improvement in identifying the location and magnitude of a crack by the proposed IRBF method, in comparison with conventional RBF method and other classical methods. In case of crack location in a beam, the average identification error over 12 test cases was 0.69 per cent by IRBF network compared to 4.88 per cent by conventional RBF. Similar improvements are reported when compared to hybrid CPN BPN networks. It also requires much less computational effort as compared to other hybrid neural network approaches and classical methods.

Originality/value

The proposed novel IRBF crack identification technique is unique in originality and not reported elsewhere. It can identify the crack location and crack depth with very good accuracy, less computational effort and ease of implementation.

Article
Publication date: 1 September 1999

Th. Ebner, Ch. Magele, B.R. Brandstätter, M. Luschin and P.G. Alotto

Global optimization in electrical engineering using stochastic methods requires usually a large amount of CPU time to locate the optimum, if the objective function is…

Abstract

Global optimization in electrical engineering using stochastic methods requires usually a large amount of CPU time to locate the optimum, if the objective function is calculated either with the finite element method (FEM) or the boundary element method (BEM). One approach to reduce the number of FEM or BEM calls using neural networks and another one using multiquadric functions have been introduced recently. This paper compares the efficiency of both methods, which are applied to a couple of test problems and the results are discussed.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 18 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 4 November 2021

Jialiang Xie, Shanli Zhang and Ling Lin

In the new era of highly developed Internet information, the prediction of the development trend of network public opinion has a very important reference significance for…

Abstract

Purpose

In the new era of highly developed Internet information, the prediction of the development trend of network public opinion has a very important reference significance for monitoring and control of public opinion by relevant government departments.

Design/methodology/approach

Aiming at the complex and nonlinear characteristics of the network public opinion, considering the accuracy and stability of the applicable model, a network public opinion prediction model based on the bald eagle algorithm optimized radial basis function neural network (BES-RBF) is proposed. Empirical research is conducted with Baidu indexes such as “COVID-19”, “Winter Olympic Games”, “The 100th Anniversary of the Founding of the Party” and “Aerospace” as samples of network public opinion.

Findings

The experimental results show that the model proposed in this paper can better describe the development trend of different network public opinion information, has good stability in predictive performance and can provide a good decision-making reference for government public opinion control departments.

Originality/value

A method for optimizing the central value, weight, width and other parameters of the radial basis function neural network with the bald eagle algorithm is given, and it is applied to network public opinion trend prediction. The example verifies that the prediction algorithm has higher accuracy and better stability.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 15 no. 2
Type: Research Article
ISSN: 1756-378X

Keywords

Article
Publication date: 23 August 2022

Wafa' AlAlaween, Omar Abueed, Belal Gharaibeh, Abdallah Alalawin, Mahdi Mahfouf, Ahmad Alsoussi and Nibal Albashabsheh

The purpose of this research paper is to investigate and model the fused deposition modelling (FDM) process to predict the mechanical attributes of 3D printed specimens.

Abstract

Purpose

The purpose of this research paper is to investigate and model the fused deposition modelling (FDM) process to predict the mechanical attributes of 3D printed specimens.

Design/methodology/approach

By exploiting the main effect plots, a Taguchi L18 orthogonal array is used to investigate the effects of such parameters on three mechanical attributes of the 3D printed specimens. A radial-based integrated network is then developed to map the eight FDM parameters to the three mechanical attributes for both PEEK and PEKK. Such an integrated network maps and predicts the mechanical attributes through two consecutive phases that consist of several radial basis functions (RBFs).

Findings

Validated on a set of further experiments, the integrated network was successful in predicting the mechanical attributes of the 3D printed specimens. It also outperformed the well-known RBF network with an overall improvement of 24% in the coefficient of determination. The integrated network is also further validated by predicting the mechanical attributes of a medical-surgical implant (i.e. the MidFace Rim) as an application.

Originality/value

The main aim of this paper is to accurately predict the mechanical properties of parts produced using the FDM process. Such an aim requires modelling a highly dimensional space to represent highly nonlinear relationships. Therefore, a radial-based integrated network based on the combination of composition and superposition of radial functions is developed to model FDM using a limited number of data points.

Details

Rapid Prototyping Journal, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1355-2546

Keywords

Article
Publication date: 1 September 2003

Jean‐Louis Coulomb, Avenir Kobetski, Mauricio Caldora Costa, Yves Mare´chal and Ulf Jo¨nsson

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very…

Abstract

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 22 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 20 January 2021

Ram Jiwari and Alf Gerisch

This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical…

Abstract

Purpose

This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time.

Design/methodology/approach

In a method of lines setting, a meshless method for their discretization in space is proposed. This discretization is based on a DQ approach, and RBFs are used as test functions. A local approach is followed where only selected RBFs feature in the computation of a particular DQ weight.

Findings

The proposed method is applied on four reaction-diffusion models: Huxley’s equation, a linear reaction-diffusion system, the Gray–Scott model and the two-dimensional Brusselator model. The method captured the various patterns of the models similar to available in literature. The method shows second order of convergence in space variables and works reliably and efficiently for the problems.

Originality/value

The originality lies in the following facts: A meshless method is proposed for reaction-diffusion models based on local RBFs; the proposed scheme is able to capture patterns of the models for big time T; the scheme has second order of convergence in both time and space variables and Nuemann boundary conditions are easy to implement in this scheme.

Details

Engineering Computations, vol. 38 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Book part
Publication date: 6 September 2019

Vivian M. Evangelista and Rommel G. Regis

Machine learning methods have recently gained attention in business applications. We will explore the suitability of machine learning methods, particularly support vector…

Abstract

Machine learning methods have recently gained attention in business applications. We will explore the suitability of machine learning methods, particularly support vector regression (SVR) and radial basis function (RBF) approximation, in forecasting company sales. We compare the one-step-ahead forecast accuracy of these machine learning methods with traditional statistical forecasting techniques such as moving average (MA), exponential smoothing, and linear and quadratic trend regression on quarterly sales data of 43 Fortune 500 companies. Moreover, we implement an additive seasonal adjustment procedure on the quarterly sales data of 28 of the Fortune 500 companies whose time series exhibited seasonality, referred to as the seasonal group. Furthermore, we prove a mathematical property of this seasonal adjustment procedure that is useful in interpreting the resulting time series model. Our results show that the Gaussian form of a moving RBF model, with or without seasonal adjustment, is a promising method for forecasting company sales. In particular, the moving RBF-Gaussian model with seasonal adjustment yields generally better mean absolute percentage error (MAPE) values than the other methods on the sales data of 28 companies in the seasonal group. In addition, it is competitive with single exponential smoothing and better than the other methods on the sales data of the other 15 companies in the non-seasonal group.

Details

Advances in Business and Management Forecasting
Type: Book
ISBN: 978-1-78754-290-7

Keywords

Article
Publication date: 20 July 2010

Francisco Bernal and Manuel Kindelan

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary…

Abstract

Purpose

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The purpose of this paper is to address the solution of the Motz problem using the radial basis function (RBF) method, which is a truly meshfree scheme.

Design/methodology/approach

Both the global RBF collocation method (also known as Kansa's method) and the recently proposed local RBF‐based differential quadrature (LRBFDQ) method are considered. In both cases, it is shown that the accuracy of the solution can be significantly increased by using special functions which capture the behavior of the singularity. In the case of global collocation, the functional space spanned by the RBF is enlarged by adding singular functions which capture the behavior of the local singular solution. In the case of local collocation, the problem is modified appropriately in order to eliminate the singularities from the formulation.

Findings

The paper shows that the exponential convergence both with increasing resolution and increasing shape parameter, which is typical of the RBF method, is lost in problems containing singularities. The accuracy of the solution can be increased by collocation of the partial differential equation (PDE) at boundary nodes. However, in order to restore the exponential convergence of the RBF method, it is necessary to use special functions which capture the behavior of the solution near the discontinuity.

Practical implications

The paper uses Motz's problem as a prototype for problems described by elliptic partial differential equations with boundary singularities. However, the results obtained in the paper are applicable to a wide range of problems containing boundaries with conditions which change from Dirichlet to Neumann, thus leading to singularities in the first derivatives.

Originality/value

The paper shows that both the global RBF collocation method and the LRBFDQ method, are truly meshless methods which can be very useful for the solution of elliptic problems with boundary singularities. In particular, when complemented with special functions that capture the behavior of the solution near the discontinuity, the method exhibits exponential convergence both with resolution and with shape parameter.

Details

Engineering Computations, vol. 27 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

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