Pub Date : 2022-05-30DOI: 10.1515/ijnsns-2021-0042
Ahmad Alalyani, S. Saber
Abstract The purpose of this article is to formulate a simplified nonlinear fractional mathematical model to illustrate the dynamics of the new coronavirus (COVID-19). Based on the infectious characteristics of COVID-19, the population is divided into five compartments: susceptible S(t), asymptomatic infection I(t), unreported symptomatic infection U(t), reported symptomatic infections W(T) and recovered R(t), collectively referred to as (SIUWR). The existence, uniqueness, boundedness, and non-negativeness of the proposed model solution are established. In addition, the basic reproduction number R 0 is calculated. All possible equilibrium points of the model are examined and their local and global stability under specific conditions is discussed. The disease-free equilibrium point is locally asymptotically stable for R 0 leq1 and unstable for R 0 > 1. In addition, the endemic equilibrium point is locally asymptotically stable with respect to R 0 > 1. Perform numerical simulations using the Adams–Bashforth–Moulton-type fractional predictor–corrector PECE method to validate the analysis results and understand the effect of parameter variation on the spread of COVID-19. For numerical simulations, the behavior of the approximate solution is displayed in the form of graphs of various fractional orders. Finally, a brief conclusion about simulation on how to model transmission dynamics in social work.
{"title":"Stability analysis and numerical simulations of the fractional COVID-19 pandemic model","authors":"Ahmad Alalyani, S. Saber","doi":"10.1515/ijnsns-2021-0042","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0042","url":null,"abstract":"Abstract The purpose of this article is to formulate a simplified nonlinear fractional mathematical model to illustrate the dynamics of the new coronavirus (COVID-19). Based on the infectious characteristics of COVID-19, the population is divided into five compartments: susceptible S(t), asymptomatic infection I(t), unreported symptomatic infection U(t), reported symptomatic infections W(T) and recovered R(t), collectively referred to as (SIUWR). The existence, uniqueness, boundedness, and non-negativeness of the proposed model solution are established. In addition, the basic reproduction number R 0 is calculated. All possible equilibrium points of the model are examined and their local and global stability under specific conditions is discussed. The disease-free equilibrium point is locally asymptotically stable for R 0 leq1 and unstable for R 0 > 1. In addition, the endemic equilibrium point is locally asymptotically stable with respect to R 0 > 1. Perform numerical simulations using the Adams–Bashforth–Moulton-type fractional predictor–corrector PECE method to validate the analysis results and understand the effect of parameter variation on the spread of COVID-19. For numerical simulations, the behavior of the approximate solution is displayed in the form of graphs of various fractional orders. Finally, a brief conclusion about simulation on how to model transmission dynamics in social work.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"24 1","pages":"989 - 1002"},"PeriodicalIF":1.5,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44323408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-26DOI: 10.1515/ijnsns-2021-0305
Kamel Mohamed, M. Abdelrahman
Abstract This paper considers the one-dimensional model of heat conduction in solids at low temperature, the so called phonon-Bose model. The nonlinear model consists of a conservation equation for the energy density e and the heat flux Q with ∣Q∣ < e. We present a simple and accurate class of finite volume schemes for numerical simulation of heat flow in arteries. This scheme consists of predictor and corrector steps, the predictor step contains a parameter of control of the numerical diffusion of the scheme, which modulate by using limiter theory and Riemann invariant, the corrector step recovers the balance conservation equation, the scheme can compute the numerical flux corresponding the real state of solution without relying on Riemann problem solvers and it can thus be turned to order 1 in the regions where the flow has a strong variation and to order 2 in the regions where the flow is regular. The numerical test cases demonstrate high resolution of the proposed finite volume scheme (modified Rusanov) and confirm its capability to provide accurate simulations for heat flow under flow regimes with strong shocks.
{"title":"The modified Rusanov scheme for solving the phonon-Bose model","authors":"Kamel Mohamed, M. Abdelrahman","doi":"10.1515/ijnsns-2021-0305","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0305","url":null,"abstract":"Abstract This paper considers the one-dimensional model of heat conduction in solids at low temperature, the so called phonon-Bose model. The nonlinear model consists of a conservation equation for the energy density e and the heat flux Q with ∣Q∣ < e. We present a simple and accurate class of finite volume schemes for numerical simulation of heat flow in arteries. This scheme consists of predictor and corrector steps, the predictor step contains a parameter of control of the numerical diffusion of the scheme, which modulate by using limiter theory and Riemann invariant, the corrector step recovers the balance conservation equation, the scheme can compute the numerical flux corresponding the real state of solution without relying on Riemann problem solvers and it can thus be turned to order 1 in the regions where the flow has a strong variation and to order 2 in the regions where the flow is regular. The numerical test cases demonstrate high resolution of the proposed finite volume scheme (modified Rusanov) and confirm its capability to provide accurate simulations for heat flow under flow regimes with strong shocks.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47672564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-23DOI: 10.1515/ijnsns-2021-0160
K. Karthikeyan, D. Tamizharasan, T. Abdeljawad, K. Nisar
Abstract This study investigates the functional abstract second order impulsive differential equation with state-dependent delay. The major result of this study is that the abstract second-order impulsive differential equation with state-dependent delay system has at least one solution and is unique. After that, the wellposed condition is defined. Following that, we look at whether the proposed problem is wellposed. Finally, some illustrations of our findings are provided.
{"title":"Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay","authors":"K. Karthikeyan, D. Tamizharasan, T. Abdeljawad, K. Nisar","doi":"10.1515/ijnsns-2021-0160","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0160","url":null,"abstract":"Abstract This study investigates the functional abstract second order impulsive differential equation with state-dependent delay. The major result of this study is that the abstract second-order impulsive differential equation with state-dependent delay system has at least one solution and is unique. After that, the wellposed condition is defined. Following that, we look at whether the proposed problem is wellposed. Finally, some illustrations of our findings are provided.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"24 1","pages":"1355 - 1368"},"PeriodicalIF":1.5,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45545899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-23DOI: 10.1515/ijnsns-2021-0007
Daoling Chen, Pengpeng Cheng
Abstract In order to understand consumers’ perceptual cognition of Zhangpu paper-cut patterns and grasp the innovative application direction. The four design elements of paper-cut patterns were extracted by morphological analysis, and representative perceptual vocabulary were selected using Kansei engineering theory and factor analysis, then the design elements and perceptual evaluation scores of representative words are used as the input and output data of the GWO-BP neural network, respectively, to establish an intelligent model that can predict consumers’ perceptual cognition of paper-cut patterns. To verify the superiority of the model, the predicted result of BP and FA-BP are compared with GWO-BP neural network. The results show that although the convergence speed of the GWO-BP model is slightly lower than that of the FA-BP model, its prediction accuracy is significantly better than other algorithms. Designers can use the model to quickly redesign the paper-cut pattern to better meet the aesthetic needs of modern consumers.
{"title":"Perceptual evaluation for Zhangpu paper-cut patterns by using improved GWO-BP neural network","authors":"Daoling Chen, Pengpeng Cheng","doi":"10.1515/ijnsns-2021-0007","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0007","url":null,"abstract":"Abstract In order to understand consumers’ perceptual cognition of Zhangpu paper-cut patterns and grasp the innovative application direction. The four design elements of paper-cut patterns were extracted by morphological analysis, and representative perceptual vocabulary were selected using Kansei engineering theory and factor analysis, then the design elements and perceptual evaluation scores of representative words are used as the input and output data of the GWO-BP neural network, respectively, to establish an intelligent model that can predict consumers’ perceptual cognition of paper-cut patterns. To verify the superiority of the model, the predicted result of BP and FA-BP are compared with GWO-BP neural network. The results show that although the convergence speed of the GWO-BP model is slightly lower than that of the FA-BP model, its prediction accuracy is significantly better than other algorithms. Designers can use the model to quickly redesign the paper-cut pattern to better meet the aesthetic needs of modern consumers.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"24 1","pages":"1249 - 1264"},"PeriodicalIF":1.5,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47076378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-20DOI: 10.1515/ijnsns-2021-0231
Mian Muhammad Farooq, Muhammad Mohsin, M. Farman, A. Akgül, M. Saleem
Abstract In many life time scenarios, life of one component or system nested in other components or systems. To model these complex structures some so called nested models are required rather than conventional models. This paper introduces the generalization of the method of generating continuous distribution proposed by N. Eugene, C. Lee, and F. Famoye, “Beta-normal distribution and its applications,” Commun. Stat. Theor. Methods, vol. 31, no. 4, pp. 497–512, 2002 and A. Alzaatreh, C. Lee, and F. Famoye, “A new method for generating families of continuous distributions,” Metron, vol. 71, no. 1, pp. 63–79, 2013 which nest one model in other to cope with complex systems. Some important characteristics of the proposed family of generalized distribution have been studied. The famous Beta, Kumaraswami and Gamma generated distributions are special cases of our suggested procedure. Some new distributions have also been developed by using the suggested methodology and their important properties have been discussed as well. A variety of real life data sets are used to demonstrate the efficacy of new suggested distributions and illation is made with baseline models.
在许多生命周期场景中，一个组件或系统的生命周期嵌套在其他组件或系统中。为了对这些复杂的结构进行建模，需要一些所谓的嵌套模型，而不是传统的模型。本文介绍了N. Eugene, C. Lee和F. Famoye在“beta -正态分布及其应用”中提出的生成连续分布方法的推广。统计理论的。方法，第31卷，第5期。A. Alzaatreh、C. Lee和F. Famoye，“连续分布族生成的一种新方法”，《数学学报》，第71卷，第1期。1, pp. 63 - 79,2013，其中一个模型嵌套在另一个模型中以应对复杂系统。本文研究了广义分布族的一些重要特征。著名的Beta、Kumaraswami和Gamma生成的分布是我们建议的过程的特殊情况。使用所建议的方法还开发了一些新的分布，并讨论了它们的重要性质。各种现实生活数据集被用来证明新的建议分布的有效性，并与基线模型进行了验证。
{"title":"Generalization method of generating the continuous nested distributions","authors":"Mian Muhammad Farooq, Muhammad Mohsin, M. Farman, A. Akgül, M. Saleem","doi":"10.1515/ijnsns-2021-0231","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0231","url":null,"abstract":"Abstract In many life time scenarios, life of one component or system nested in other components or systems. To model these complex structures some so called nested models are required rather than conventional models. This paper introduces the generalization of the method of generating continuous distribution proposed by N. Eugene, C. Lee, and F. Famoye, “Beta-normal distribution and its applications,” Commun. Stat. Theor. Methods, vol. 31, no. 4, pp. 497–512, 2002 and A. Alzaatreh, C. Lee, and F. Famoye, “A new method for generating families of continuous distributions,” Metron, vol. 71, no. 1, pp. 63–79, 2013 which nest one model in other to cope with complex systems. Some important characteristics of the proposed family of generalized distribution have been studied. The famous Beta, Kumaraswami and Gamma generated distributions are special cases of our suggested procedure. Some new distributions have also been developed by using the suggested methodology and their important properties have been discussed as well. A variety of real life data sets are used to demonstrate the efficacy of new suggested distributions and illation is made with baseline models.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"67 ","pages":"1327 - 1353"},"PeriodicalIF":1.5,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41315777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-20DOI: 10.1515/ijnsns-2021-0349
M. Gaballah, R. El-Shiekh, L. Akinyemi, H. Rezazadeh
Abstract As Davey–Stewartson system is considered one of the most important models in optics, quantum physics, plasmas, and Bose–Einstein condensates. In this study, we have solved the Davey–Stewartson system using a modified Jacobi elliptic function methodology, and therefore many novel Jacobi elliptic wave function solutions were obtained, which degenerated to hypergeometric functions and periodic functions. The results obtained in this paper are novel in addition, contain other results achieved before in literatures. Moreover, some dynamic behavior for the periodic, kink type, and soliton wave propagation is demonstrated.
{"title":"Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method","authors":"M. Gaballah, R. El-Shiekh, L. Akinyemi, H. Rezazadeh","doi":"10.1515/ijnsns-2021-0349","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0349","url":null,"abstract":"Abstract As Davey–Stewartson system is considered one of the most important models in optics, quantum physics, plasmas, and Bose–Einstein condensates. In this study, we have solved the Davey–Stewartson system using a modified Jacobi elliptic function methodology, and therefore many novel Jacobi elliptic wave function solutions were obtained, which degenerated to hypergeometric functions and periodic functions. The results obtained in this paper are novel in addition, contain other results achieved before in literatures. Moreover, some dynamic behavior for the periodic, kink type, and soliton wave propagation is demonstrated.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42449389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-17DOI: 10.1515/ijnsns-2021-0333
Safoura Rezaei Aderyani, R. Saadati, D. O’Regan
Abstract In this paper, we apply the Cădariu–Radu method derived from the Diaz–Margolis theorem to investigate existence, uniqueness approximation of Ξ-Hilfer fractional differential equations, and Hypergeometric stability for both finite and infinite domains. An example is given to illustrate the main result for a fractional system.
{"title":"The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations","authors":"Safoura Rezaei Aderyani, R. Saadati, D. O’Regan","doi":"10.1515/ijnsns-2021-0333","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0333","url":null,"abstract":"Abstract In this paper, we apply the Cădariu–Radu method derived from the Diaz–Margolis theorem to investigate existence, uniqueness approximation of Ξ-Hilfer fractional differential equations, and Hypergeometric stability for both finite and infinite domains. An example is given to illustrate the main result for a fractional system.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41578276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-17DOI: 10.1515/ijnsns-2021-0299
Shiwei Li
Abstract In this paper, a class of strictly hyperbolic systems of conservation laws which arises in connection with enhanced oil recovery is studied. The Riemann problem is solved analytically. The Riemann solutions with two kinds of different structures involving the delta-shock are obtained. For delta-shock, the generalized Rankine–Hugoniot relations and over-compressive delta-entropy condition are clarified. Further, the existence and uniqueness of delta-shock are established. The theoretical analysis is tested accurately by the numerical results.
{"title":"Delta-shock for a class of strictly hyperbolic systems of conservation laws","authors":"Shiwei Li","doi":"10.1515/ijnsns-2021-0299","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0299","url":null,"abstract":"Abstract In this paper, a class of strictly hyperbolic systems of conservation laws which arises in connection with enhanced oil recovery is studied. The Riemann problem is solved analytically. The Riemann solutions with two kinds of different structures involving the delta-shock are obtained. For delta-shock, the generalized Rankine–Hugoniot relations and over-compressive delta-entropy condition are clarified. Further, the existence and uniqueness of delta-shock are established. The theoretical analysis is tested accurately by the numerical results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42390475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-17DOI: 10.1515/ijnsns-2021-0126
Zehra Pinar Izgi
Abstract Crystallization problem is one of the popular problems in wide area of science. The first principles are not used to design a crystallizer in which complicated processes include nucleation, crystal growth, attrition and agglomeration of crystals. It is modeled by the population balance model, which is one of the important models of mathematical biology and engineering, is a nonlinear partial integro-differential equation and examines the exchange of particles and the production of new particles in a system of particles. For the crystallization problem, one-dimensional and multi-dimensional models are considered and semi-analytical solutions are obtained via the linear separation method.
{"title":"Simulation of the crystallization processes by population balance model using a linear separation method","authors":"Zehra Pinar Izgi","doi":"10.1515/ijnsns-2021-0126","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0126","url":null,"abstract":"Abstract Crystallization problem is one of the popular problems in wide area of science. The first principles are not used to design a crystallizer in which complicated processes include nucleation, crystal growth, attrition and agglomeration of crystals. It is modeled by the population balance model, which is one of the important models of mathematical biology and engineering, is a nonlinear partial integro-differential equation and examines the exchange of particles and the production of new particles in a system of particles. For the crystallization problem, one-dimensional and multi-dimensional models are considered and semi-analytical solutions are obtained via the linear separation method.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45393171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-16DOI: 10.1515/ijnsns-2020-0031
N. Rokbani, Raghvendra Kumar, A. Alimi, Pham Huy Thong, Ishaani Priyadarshini, Viet-Ha Nhu, Phuong Thao Thi Ngo
Abstract In this paper, an investigation is conducted in order to understand impacts of Particle Swarm Optimization (PSO) parameters on the convergence and the quality of the inverse kinematics solutions provided by the IK-PSO (inverse kinematics solver using PSO) – a heuristic inverse kinematics solver algorithm. Over a large panel of parameters investigations, a statistical proof of convergence is provided for 5 links to 60 links articulated system. A recommended set of parameters intervals are presented for this class of IK problems. Investigations are based on the standard inertia weight PSO, and concerned the impact of the inertia weight, the swarm size and the maximum iteration number. For a given set of parameters, the existence of a solution with a given position error is also proved. All tests were conducted over 100 times. The density of probability function, PDF, is used to approximate and analyze the fineness functions, which are the square of the position error. Results showed IK-PSO is an interesting IK solver when a set of good parameters are used. For these parameters, the algorithm showed a statistical proof of convergence with a high resolution, by mean of error position. The algorithm also showed time-effectiveness compared to CCD method, which is assumed to be a real-time IK heuristic solver used in gaming.
{"title":"Impacts of heuristic parameters in PSO inverse kinematics solvers","authors":"N. Rokbani, Raghvendra Kumar, A. Alimi, Pham Huy Thong, Ishaani Priyadarshini, Viet-Ha Nhu, Phuong Thao Thi Ngo","doi":"10.1515/ijnsns-2020-0031","DOIUrl":"https://doi.org/10.1515/ijnsns-2020-0031","url":null,"abstract":"Abstract In this paper, an investigation is conducted in order to understand impacts of Particle Swarm Optimization (PSO) parameters on the convergence and the quality of the inverse kinematics solutions provided by the IK-PSO (inverse kinematics solver using PSO) – a heuristic inverse kinematics solver algorithm. Over a large panel of parameters investigations, a statistical proof of convergence is provided for 5 links to 60 links articulated system. A recommended set of parameters intervals are presented for this class of IK problems. Investigations are based on the standard inertia weight PSO, and concerned the impact of the inertia weight, the swarm size and the maximum iteration number. For a given set of parameters, the existence of a solution with a given position error is also proved. All tests were conducted over 100 times. The density of probability function, PDF, is used to approximate and analyze the fineness functions, which are the square of the position error. Results showed IK-PSO is an interesting IK solver when a set of good parameters are used. For these parameters, the algorithm showed a statistical proof of convergence with a high resolution, by mean of error position. The algorithm also showed time-effectiveness compared to CCD method, which is assumed to be a real-time IK heuristic solver used in gaming.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"23 1","pages":"833 - 858"},"PeriodicalIF":1.5,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49237353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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