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Article
Publication date: 12 January 2024

Imtiyaz Ahmad Bhat, Lakshmi Narayan Mishra, Vishnu Narayan Mishra, Cemil Tunç and Osman Tunç

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in…

Abstract

Purpose

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

Design/methodology/approach

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Findings

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

Research limitations/implications

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

Practical implications

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

Social implications

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

Originality/value

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Open Access
Article
Publication date: 8 August 2022

Gopal Shruthi and Murugan Suvinthra

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

Abstract

Purpose

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

Design/methodology/approach

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Findings

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

Originality/value

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

Details

Arab Journal of Mathematical Sciences, vol. 30 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 10 November 2023

Yonghong Zhang, Shouwei Li, Jingwei Li and Xiaoyu Tang

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of…

Abstract

Purpose

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

Design/methodology/approach

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

Findings

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

Research limitations/implications

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

Practical implications

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Originality/value

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

Details

Grey Systems: Theory and Application, vol. 14 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 14 March 2024

Mustafa Altınel and Uğur Yalçın

This paper aims to examine the uniform diffracted fields from a perfectly magnetic conductive (PMC) surface with the extended theory of boundary diffraction wave (BDW) approach.

Abstract

Purpose

This paper aims to examine the uniform diffracted fields from a perfectly magnetic conductive (PMC) surface with the extended theory of boundary diffraction wave (BDW) approach.

Design/methodology/approach

Miyamoto and Wolf’s symbolic expression of the vector potential was used in the extended theory of BDW integral. This vector potential is applied to the problem, and the nonuniform field expression found was made uniform. Here, the expression is made uniform, using the detour parameter with the help of the asymptotic correlation of the Fresnel function. The BDW theory for the PMC surface extended the diffracted fields, and the uniform diffracted fields were calculated.

Findings

The field expressions obtained were interpreted with the graphs numerically for different aperture radii and observation distances. It has been shown that the BDW is continuous behind the diffracting aperture. There does not exist any discontinuity at the geometrically light-to-shadow transition boundary, as is required by the theory.

Originality/value

The results were graphically compared with diffracted fields for other surfaces. As far as we know, the uniform diffracted fields from the circular aperture on a PMC surface were calculated for the first time with the extended theory of the BDW approach.

Details

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

Keywords

Article
Publication date: 25 January 2024

Mauro Minervino and Renato Tognaccini

This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb…

Abstract

Purpose

This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.

Design/methodology/approach

Exact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).

Findings

Two total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.

Originality/value

No thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

Details

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

Keywords

Article
Publication date: 21 December 2023

Hongsen You, Mengying Gan, Dapeng Duan, Cheng Zhao, Yuan Chi, Shuai Gao and Jiansheng Yuan

This paper aims to develop a model that reflects the current transformer (CT) core materials nonlinearity. The model enables simulation and analysis of the CT excitation current…

Abstract

Purpose

This paper aims to develop a model that reflects the current transformer (CT) core materials nonlinearity. The model enables simulation and analysis of the CT excitation current that includes the inductive magnetizing current and the resistive excitation current.

Design/methodology/approach

A nonlinear CT model is established with the magnetizing current as the solution variable. This model presents the form of a nonlinear differential equation and can be solved discretely using the Runge–Kutta method.

Findings

By simulating variations in the excitation current for different primary currents, loads and core materials, the results demonstrate that enhancing the permeability of the BH curve leads to a more significant improvement in the CT ratio error at low primary currents.

Originality/value

The proposed model has three obvious advantages over the previous models with the secondary current as the solution variable: (1) The differential equation is simpler and easier to solve. Previous models contain the time differential terms of the secondary current and excitation flux or the integral term of the flux, making the iterative solution complicated. The proposed model only contains the time differential of the magnetizing current. (2) The accuracy of the excitation current obtained by the proposed model is higher. Previous models calculate the excitation current by subtracting the secondary current from the converted primary current. Because these two currents are much greater than the excitation current, the error of calculating the small excitation current by subtracting two large numbers is greatly enlarged. (3) The proposed model can calculate the distorted waveform of the excitation current and error for any form of time-domain primary current, while previous models can only obtain the effective value.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 43 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 18 January 2024

Zaihua Luo, Juliang Xiao, Sijiang Liu, Mingli Wang, Wei Zhao and Haitao Liu

This paper aims to propose a dynamic parameter identification method based on sensitivity analysis for the 5-degree of freedom (DOF) hybrid robots, to solve the problems of too…

Abstract

Purpose

This paper aims to propose a dynamic parameter identification method based on sensitivity analysis for the 5-degree of freedom (DOF) hybrid robots, to solve the problems of too many identification parameters, complex model, difficult convergence of optimization algorithms and easy-to-fall into a locally optimal solution, and improve the efficiency and accuracy of dynamic parameter identification.

Design/methodology/approach

First, the dynamic parameter identification model of the 5-DOF hybrid robot was established based on the principle of virtual work. Then, the sensitivity of the parameters to be identified is analyzed by Sobol’s sensitivity method and verified by simulation. Finally, an identification strategy based on sensitivity analysis was designed, experiments were carried out on the real robot and the results were verified.

Findings

Compared with the traditional full-parameter identification method, the dynamic parameter identification method based on sensitivity analysis proposed in this paper converges faster when optimized using the genetic algorithm, and the identified dynamic model has higher prediction accuracy for joint drive forces and torques than the full-parameter identification models.

Originality/value

This work analyzes the sensitivity of the parameters to be identified in the dynamic parameter identification model for the first time. Then a parameter identification method is proposed based on the results of the sensitivity analysis, which can effectively reduce the parameters to be identified, simplify the identification model, accelerate the convergence of the optimization algorithm and improve the prediction accuracy of the identified model for the joint driving forces and torques.

Details

Industrial Robot: the international journal of robotics research and application, vol. 51 no. 2
Type: Research Article
ISSN: 0143-991X

Keywords

Article
Publication date: 12 March 2024

Salma Benharref, Vincent Lanfranchi, Daniel Depernet, Tahar Hamiti and Sara Bazhar

The purpose of this paper is to propose a new method that allows to compare the magnetic pressures of different pulse width modulation (PWM) strategies in a fast and efficient way.

Abstract

Purpose

The purpose of this paper is to propose a new method that allows to compare the magnetic pressures of different pulse width modulation (PWM) strategies in a fast and efficient way.

Design/methodology/approach

The voltage harmonics are determined using the double Fourier integral. As for current harmonics and waveforms, a new generic model based on the Park transformation and a dq model of the machine was established taking saturation into consideration. The obtained analytical waveforms are then injected into a finite element software to compute magnetic pressures using nodal forces.

Findings

The overall proposed method allows to accelerate the calculations and the comparison of different PWM strategies and operating points as an analytical model is used to generate current waveforms.

Originality/value

While the analytical expressions of voltage harmonics are already provided in the literature for the space vector pulse width modulation, they had to be calculated for the discontinuous pulse width modulation. In this paper, the obtained expressions are provided. For current harmonics, different models based on a linear and a nonlinear model of the machine are presented in the referenced papers; however, these models are not generic and are limited to the second range of harmonics (two times the switching frequency). A new generic model is then established and used in this paper after being validated experimentally. And finally, the direct injection of analytical current waveforms in a finite element software to perform any magnetic computation is very efficient.

Details

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

Keywords

Open Access
Article
Publication date: 7 June 2022

Manoj Kumar

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

Abstract

Purpose

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

Design/methodology/approach

The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).

Findings

The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.

Originality/value

The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

Details

Arab Journal of Mathematical Sciences, vol. 30 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 22 March 2024

Shahin Alipour Bonab, Alireza Sadeghi and Mohammad Yazdani-Asrami

The ionization of the air surrounding the phase conductor in high-voltage transmission lines results in a phenomenon known as the Corona effect. To avoid this, Corona rings are…

Abstract

Purpose

The ionization of the air surrounding the phase conductor in high-voltage transmission lines results in a phenomenon known as the Corona effect. To avoid this, Corona rings are used to dampen the electric field imposed on the insulator. The purpose of this study is to present a fast and intelligent surrogate model for determination of the electric field imposed on the surface of a 120 kV composite insulator, in presence of the Corona ring.

Design/methodology/approach

Usually, the structural design parameters of the Corona ring are selected through an optimization procedure combined with some numerical simulations such as finite element method (FEM). These methods are slow and computationally expensive and thus, extremely reducing the speed of optimization problems. In this paper, a novel surrogate model was proposed that could calculate the maximum electric field imposed on a ceramic insulator in a 120 kV line. The surrogate model was created based on the different scenarios of height, radius and inner radius of the Corona ring, as the inputs of the model, while the maximum electric field on the body of the insulator was considered as the output.

Findings

The proposed model was based on artificial intelligence techniques that have high accuracy and low computational time. Three methods were used here to develop the AI-based surrogate model, namely, Cascade forward neural network (CFNN), support vector regression and K-nearest neighbors regression. The results indicated that the CFNN has the highest accuracy among these methods with 99.81% R-squared and only 0.045468 root mean squared error while the testing time is less than 10 ms.

Originality/value

To the best of the authors’ knowledge, for the first time, a surrogate method is proposed for the prediction of the maximum electric field imposed on the high voltage insulators in the presence Corona ring which is faster than any conventional finite element method.

Details

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

Keywords

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