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1 – 10 of 261
Article
Publication date: 16 August 2022

Zibo Li, Zhengxiang Yan, Shicheng Li, Guangmin Sun, Xin Wang, Dequn Zhao, Yu Li and Xiucheng Liu

The purpose of this paper is to overcome the application limitations of other multi-variable regression based on polynomials due to the huge computation room and time cost.

Abstract

Purpose

The purpose of this paper is to overcome the application limitations of other multi-variable regression based on polynomials due to the huge computation room and time cost.

Design/methodology/approach

In this paper, based on the idea of feature selection and cascaded regression, two strategies including Laguerre polynomials and manifolds optimization are proposed to enhance the accuracy of multi-variable regression. Laguerre polynomials were combined with the genetic algorithm to enhance the capacity of polynomials approximation and the manifolds optimization method was introduced to solve the co-related optimization problem.

Findings

Two multi-variable Laguerre polynomials regression methods are designed. Firstly, Laguerre polynomials are combined with feature selection method. Secondly, manifolds component analysis is adopted in cascaded Laguerre polynomials regression method. Two methods are brought to enhance the accuracy of multi-variable regression method.

Research limitations/implications

With the increasing number of variables in regression problem, the stable accuracy performance might not be kept by using manifold-based optimization method. Moreover, the methods mentioned in this paper are not suitable for the classification problem.

Originality/value

Experiments are conducted on three types of datasets to evaluate the performance of the proposed regression methods. The best accuracy was achieved by the combination of cascade, manifold optimization and Chebyshev polynomials, which implies that the manifolds optimization has stronger contribution than the genetic algorithm and Laguerre polynomials.

Details

Engineering Computations, vol. 39 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 22 May 2023

Yujie Zhang, Jing Cui, Yang Li and Zhongyi Chu

This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local…

Abstract

Purpose

This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.

Design/methodology/approach

Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.

Findings

Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.

Originality/value

The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

Details

Industrial Robot: the international journal of robotics research and application, vol. 50 no. 5
Type: Research Article
ISSN: 0143-991X

Keywords

Article
Publication date: 10 July 2020

Min Liu, Muzhou Hou, Juan Wang and Yangjin Cheng

This paper aims to develop a novel algorithm and apply it to solve two-dimensional linear partial differential equations (PDEs). The proposed method is based on Chebyshev neural…

Abstract

Purpose

This paper aims to develop a novel algorithm and apply it to solve two-dimensional linear partial differential equations (PDEs). The proposed method is based on Chebyshev neural network and extreme learning machine (ELM) called Chebyshev extreme learning machine (Ch-ELM) method.

Design/methodology/approach

The network used in the proposed method is a single hidden layer feedforward neural network. The Kronecker product of two Chebyshev polynomials is used as basis function. The weights from the input layer to the hidden layer are fixed value 1. The weights from the hidden layer to the output layer can be obtained by using ELM algorithm to solve the linear equations established by PDEs and its definite conditions.

Findings

To verify the effectiveness of the proposed method, two-dimensional linear PDEs are selected and its numerical solutions are obtained by using the proposed method. The effectiveness of the proposed method is illustrated by comparing with the analytical solutions, and its superiority is illustrated by comparing with other existing algorithms.

Originality/value

Ch-ELM algorithm for solving two-dimensional linear PDEs is proposed. The algorithm has fast execution speed and high numerical accuracy.

Details

Engineering Computations, vol. 38 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 April 2014

Jean Batina, Serge Blancher and Tarik Kouskou

Mathematical and numerical models are developed to study the melting of a Phase Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant and uniform…

Abstract

Purpose

Mathematical and numerical models are developed to study the melting of a Phase Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant and uniform temperature or heat flux, assuming that the rest of the cavity is completely adiabatic. The paper used suitable numerical methods to follow the interface temporal evolution with a good accuracy. The purpose of this paper is to show how the evolution of the latent energy absorbed to melt the PCM depends on the temperature imposed on the lower wall of the cavity.

Design/methodology/approach

The problem is written with non-homogeneous boundary conditions. Momentum and energy equations are numerically solved in space by a spectral collocation method especially oriented to this situation. A Crank-Nicolson scheme permits the resolution in time.

Findings

The results clearly show the evolution of multicellular regime during the process of fusion and the kinetics of phase change depends on the boundary condition imposed on the bottom cell wall. Thus the charge and discharge processes in energy storage cells can be controlled by varying the temperature in the cell PCM. Substantial modifications of the thermal convective heat and mass transfer are highlighted during the transient regime. This model is particularly suitable to follow with a good accuracy the evolution of the solid/liquid interface in the process of storage/release energy.

Research limitations/implications

The time-dependent physical properties that induce non-linear coupled unsteady terms in Navier-Stokes and energy equations are not taken into account in the present model. The present model is actually extended to these coupled situations. This problem requires smoother geometries. One can try to palliate this disadvantage by constructing smoother approximations of non-smooth geometries. The augmentation of polynomials developments orders increases strongly the computing time. When the external heat flux or temperature imposed at the PCM is much greater than the temperature of the PCM fusion, one must choose carefully some data to assume the algorithms convergence.

Practical implications

Among the areas where this work can be used, are: buildings where the PCM are used in insulation and passive cooling; thermal energy storage, the PCM stores energy by changing phase, solid to liquid (fusion); cooling and transport of foodstuffs or pharmaceutical or medical sensitive products, the PCM is used in the food industry, pharmaceutical and medical, to minimize temperature variations of food, drug or sensitive materials; and the textile industry, PCM materials in the textile industry are used in microcapsules placed inside textile fibres. The PCM intervene to regulate heat transfer between the body and the outside.

Originality/value

The paper's originality is reflected in the precision of its results, due to the use of a high-accuracy numerical approximation based on collocation spectral methods, and the choice of Chebyshev polynomials basis in both axial and radial directions.

Article
Publication date: 27 September 2021

Arzu Turan Dincel and Sadiye Nergis Tural Polat

Multi-term variable-order fractional differential equations (VO-FDEs) are powerful tools in accurate modeling of transient-regime real-life problems such as diffusion phenomena…

Abstract

Purpose

Multi-term variable-order fractional differential equations (VO-FDEs) are powerful tools in accurate modeling of transient-regime real-life problems such as diffusion phenomena and nonlinear viscoelasticity. In this paper the Chebyshev polynomials of the fourth kind is employed to obtain a numerical solution for those multi-term VO-FDEs.

Design/methodology/approach

To this end, operational matrices for the approximation of the VO-FDEs are obtained using the Fourth kind Chebyshev Wavelets (FKCW). Thus, the VO-FDE is condensed into an algebraic equation system. The solution of the system of those equations yields a coefficient vector, the coefficient vector in turn yields the approximate solution.

Findings

Several examples that we present at the end of the paper emphasize the efficacy and preciseness of the proposed method.

Originality/value

The value of the paper stems from the exploitation of FKCWs for the numerical solution of multi-term VO-FDEs. The method produces accurate results even for relatively small collocation points. What is more, FKCW method provides a compact mapping between multi-term VO-FDEs and a system of algebraic equations given in vector-matrix form.

Article
Publication date: 3 December 2018

Avadh Pati and Richa Negi

The stability and input voltage saturation is a common problem associated with an active magnetic bearing (AMB) system. The purpose of this paper is to design a control scheme…

Abstract

Purpose

The stability and input voltage saturation is a common problem associated with an active magnetic bearing (AMB) system. The purpose of this paper is to design a control scheme that stabilizes the single degree of freedom AMB system and also tackle the problem of input voltage saturation in the AMB system.

Design/methodology/approach

The proposed control technique is a combination of two separate control schemes. First, the Backstepping control scheme is designed to stabilize and control the AMB system and then Chebyshev neural network (CNN)-based compensator is designed to tackle the input voltage saturation when the system control action is saturated.

Findings

The mathematical and simulation results are presented to validate the effectiveness of proposed methodology for single-degree freedom AMB system.

Originality/value

This paper introduces a CNN-based compensator with Backstepping control strategy to stabilize and tackle the problem of input voltage saturation in the 1-DOF AMB systems.

Details

World Journal of Engineering, vol. 15 no. 6
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 15 May 2009

J. Batina, M. Batchi, S. Blancher, R. Creff and C. Amrouche

The purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is…

Abstract

Purpose

The purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature.

Design/methodology/approach

The problem is written with classical homogeneous boundary conditions. We use a shift operator to impose non‐homogeneous boundary conditions. Consequently, this method introduces source terms in the Galerkin formulation. The momentum equations and the energy equation which govern this problem are numerically solved in space by a spectral Galerkin method especially oriented to this situation. A Crank‐Nicolson scheme permits the resolution in time.

Findings

From the temperature field, the heat transfer phenomenon is presented, discussed and compared to those obtained in straight cylindrical pipes. This study showed the existence of zones of dead fluid that locally have a negative influence on heat transfer. Substantial modifications of the thermal convective heat transfer are highlighted at the entry and the minimum duct sections.

Practical implications

Pulsated flows in axisymmetric geometries can be applied to medical industries, mechanical engineering and technological processes.

Originality/value

One of the original features of this study is the choice of Chebyshev polynomials basis in both axial and radial directions for spectral methods, combined with the use of a shift operator to satisfy non‐homogeneous boundary conditions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 April 2020

Jing-Kui Zhang, Miao Cui, Ben-Wen Li and Ya-Song Sun

The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial…

157

Abstract

Purpose

The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer.

Design/methodology/approach

The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method.

Findings

The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step.

Research limitations/implications

It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer.

Practical implications

The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes.

Originality/value

The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 September 2005

S.S. Motsa and P. Sibanda

A detailed investigation of the effects of surface flexibility on the inviscid instability of boundary‐layer flow over a horizontal flat plate with heat transfer when the fluid…

Abstract

Purpose

A detailed investigation of the effects of surface flexibility on the inviscid instability of boundary‐layer flow over a horizontal flat plate with heat transfer when the fluid buoyancy is large is undertaken. The aim of this study is to determine whether the inviscid disturbances that arise at this limit are stabilized or destabilized by surface compliancy.

Design/methodology/approach

For large positive buoyancy numbers, the motion of the disturbances is governed by the Taylor‐Goldstein (TG) equation. Using the Chebyshev collocation spectral method, the eigen‐solutions of the TG equation are obtained and compared with known results from boundary‐layer flow over rigid flat plates.

Findings

The numerical results show that the effects of surface compliancy are important for small wave numbers and that for the inviscid modes, increasing surface parameters has the effect of destabilizing the flow. For large compliancy parameters the flow structure is indistinguishable from that which obtains in boundary layer flow over rigid surfaces.

Research limitations/implications

The multiplicity of the compliant wall parameters makes a full parametric study that should show the effect of varying the compliance of the boundary surface on the stability of the flow mathematically intractable. In this study only a brief parametric study, for selected parameters is presented.

Originality/value

It is believed that this paper would be of immense value to applied mathematicians and engineers working in the areas of boundary layer stability and natural convection flows. In the last four decades there has been overwhelming interest shown by researchers in convective boundary‐layer flow. This has largely stemmed from the numerous applications of such flows in geophysics and engineering problems. Many of these applications, for example, polymer and food processing involve the flow of a fluid over a flexible surface. This research aims to bring the dynamics of the surface as a possible mechanism to stabilize convective boundary layer flows and prevent separation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 August 2017

Velinda Calvert and Mohsen Razzaghi

This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD…

Abstract

Purpose

This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain.

Design/methodology/approach

The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations.

Findings

The method is computationally very attractive and gives very accurate results.

Originality/value

Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 261