Pub Date : 2024-10-15DOI: 10.1016/j.matcom.2024.10.006
Rama Seck , Diene Ngom , Benjamin Ivorra , Angel M. Ramos
In this work, we formulate an age-structured model for studying the transmission of Malaria for both human and vector populations. First, we perform an analytical study of this model. To do so, we analyze the positivity and boundedness of solutions and study the stability of the Disease-Free Equilibrium (using a matrix-tree theorem). Then, we focus on the study of the Endemic Equilibrium. Applying a methodology grounded in graph theory, we prove that, under certain assumptions, the Endemic Equilibrium is both unique and globally asymptotically stable. We also conjecture that this result holds true even in cases where these assumptions are not met. While this conjecture remains unproven, it is supported by illustrative numerical experiments. Secondly, we illustrate the interest of our approach by considering real data from two specific areas in Senegal affected by Malaria, namely Dielmo and Ndiop. In particular, we estimate some of the model parameters for these zones and illustrate how the proposed model may help to estimate the behavior of Malaria outbreaks.
{"title":"An age-structured mathematical model for studying Malaria transmission dynamics: Applications to some areas of Senegal","authors":"Rama Seck , Diene Ngom , Benjamin Ivorra , Angel M. Ramos","doi":"10.1016/j.matcom.2024.10.006","DOIUrl":"10.1016/j.matcom.2024.10.006","url":null,"abstract":"<div><div>In this work, we formulate an age-structured model for studying the transmission of Malaria for both human and vector populations. First, we perform an analytical study of this model. To do so, we analyze the positivity and boundedness of solutions and study the stability of the Disease-Free Equilibrium (using a matrix-tree theorem). Then, we focus on the study of the Endemic Equilibrium. Applying a methodology grounded in graph theory, we prove that, under certain assumptions, the Endemic Equilibrium is both unique and globally asymptotically stable. We also conjecture that this result holds true even in cases where these assumptions are not met. While this conjecture remains unproven, it is supported by illustrative numerical experiments. Secondly, we illustrate the interest of our approach by considering real data from two specific areas in Senegal affected by Malaria, namely Dielmo and Ndiop. In particular, we estimate some of the model parameters for these zones and illustrate how the proposed model may help to estimate the behavior of Malaria outbreaks.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-12DOI: 10.1016/j.matcom.2024.10.009
B. Ducharne , G. Sebald
Analytical methods are recommended for rapid predictions of the magnetic core loss as they require less computational resources and offer straightforward sensitivity analysis. This paper proposes analytical expressions of the dynamic magnetic power loss under an alternating or rotating magnetic field. The formulations rely on fractional derivative analytical expressions of trigonometric functions. The simulation method is validated on extensive experimental data obtained from state-of-the-art setups and gathered in the scientific literature. Five materials are tested for up to at least 1 kHz in both alternating and rotating conditions. The relative Euclidean distance between the simulated and experimentally measured power loss is lower than 5 % for most tested materials and always lower than 10 %. In standard characterization conditions, i.e., sinusoidal flux density, the dynamic power loss contribution under a rotating magnetic field is shown to be precisely two times higher than an alternating one. The knowledge of electrical conductivity reduces the dynamic magnetic power loss contribution to a single parameter (the fractional order). This parameter has the same value for a given material's rotational and alternating contribution. This study confirms the viscoelastic behavior of the magnetization process in ferromagnetic materials and, consequently, the relevance of the fractional derivative operators for their simulation.
{"title":"Analytical expressions of the dynamic magnetic power loss under alternating or rotating magnetic field","authors":"B. Ducharne , G. Sebald","doi":"10.1016/j.matcom.2024.10.009","DOIUrl":"10.1016/j.matcom.2024.10.009","url":null,"abstract":"<div><div>Analytical methods are recommended for rapid predictions of the magnetic core loss as they require less computational resources and offer straightforward sensitivity analysis. This paper proposes analytical expressions of the dynamic magnetic power loss under an alternating or rotating magnetic field. The formulations rely on fractional derivative analytical expressions of trigonometric functions. The simulation method is validated on extensive experimental data obtained from state-of-the-art setups and gathered in the scientific literature. Five materials are tested for up to at least 1 kHz in both alternating and rotating conditions. The relative Euclidean distance between the simulated and experimentally measured power loss is lower than 5 % for most tested materials and always lower than 10 %. In standard characterization conditions, i.e., sinusoidal flux density, the dynamic power loss contribution under a rotating magnetic field is shown to be precisely two times higher than an alternating one. The knowledge of electrical conductivity reduces the dynamic magnetic power loss contribution to a single parameter (the fractional order). This parameter has the same value for a given material's rotational and alternating contribution. This study confirms the viscoelastic behavior of the magnetization process in ferromagnetic materials and, consequently, the relevance of the fractional derivative operators for their simulation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.matcom.2024.10.008
Pham Thi Hoai
In this paper, we propose a new algorithm for solving monotone mixed variational inequality problems in real Hilbert spaces based on proximal gradient method. Our new algorithm uses a novel explicit stepsize which is proved to be increasing to a positive value. This property plays an important role in improving the speed of the algorithm. To the best of our knowledge, it is the first time such a kind of stepsize has been proposed for the proximal gradient method solving mixed variational inequality problems. We prove the weak convergence and strong convergence with R-linear rate of our new algorithm under standard assumptions. The reported numerical simulations for applications in sparse logistic regression and image deblurring reveal the significant efficacy performance of our proposed method compared to the recent ones.
本文提出了一种基于近似梯度法求解实希尔伯特空间中单调混合变分不等式问题的新算法。我们的新算法使用了一种新颖的显式步长，该步长被证明为正值递增。这一特性在提高算法速度方面发挥了重要作用。据我们所知，这是第一次为解决混合变分不等式问题的近似梯度法提出这种步长。我们证明了新算法在标准假设下的弱收敛性和具有 R 线性速率的强收敛性。报告中对稀疏逻辑回归和图像去模糊应用的数值模拟显示，与最近的方法相比，我们提出的方法具有显著的功效。
{"title":"A new proximal gradient method for solving mixed variational inequality problems with a novel explicit stepsize and applications","authors":"Pham Thi Hoai","doi":"10.1016/j.matcom.2024.10.008","DOIUrl":"10.1016/j.matcom.2024.10.008","url":null,"abstract":"<div><div>In this paper, we propose a new algorithm for solving monotone mixed variational inequality problems in real Hilbert spaces based on proximal gradient method. Our new algorithm uses a novel explicit stepsize which is proved to be increasing to a positive value. This property plays an important role in improving the speed of the algorithm. To the best of our knowledge, it is the first time such a kind of stepsize has been proposed for the proximal gradient method solving mixed variational inequality problems. We prove the weak convergence and strong convergence with R-linear rate of our new algorithm under standard assumptions. The reported numerical simulations for applications in sparse logistic regression and image deblurring reveal the significant efficacy performance of our proposed method compared to the recent ones.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.matcom.2024.09.034
Jiaxin Wang , Kun Wang , Zhen-Guo Yan , Xiaofeng He , Tiegang Liu
This paper implements the CUDA and hybrid CUDA/MPI parallel computation based on GPGPU heterogeneous parallel strategies for the direct discontinuous method (DDG) on 3D unstructured grids. The direct discontinuous Galerkin method inherits the compactness of the discontinuous Galerkin (DG) method, making it well-suited for large-scale parallelization. Firstly, we present the full single-GPU implementation of the three-dimensional (3D) DDG method with cell-level parallelism and face-level parallelism. Herein, all the numerical operators including volume integration, face integration (numerical fluxes), conservation variables calculation, and time iteration, are implemented by designing the corresponding kernel functions. Especially, we implement several key memory access optimization strategies, which are crucial for performance improvement. Operators merging and shared memory utilizing reduces the number of global access. Such memory Coalescing and data structure reconstruction apparently enhances the efficiency of global memory access. To align with data access pattern, we employ atomic operations to eliminate data race conditions. Furthermore, we propose a full hybrid GPU/CPU heterogeneous parallel strategy to implement multi-GPU parallelization of the DDG method, where asynchronization optimization is introduced to fully overlap communication and computation and basically eliminates the communication overhead. Finally, several numerical tests are conducted on Tesla V100 Cards to show performance of the parallelization. In addition, we utilize the NVIDIA performance testing tool, , to evaluate multiple metrics of the kernel functions and conduct a detailed analysis of the results. In the tests of parallel scalability, the weak scaling efficiency achieves 97% from 4 to 32 GPU cards, and the strong scaling efficiency is 90% from 1 to 8 GPU cards.
{"title":"GPGPU-based heterogeneous parallel implementation of direct discontinuous Galerkin methods","authors":"Jiaxin Wang , Kun Wang , Zhen-Guo Yan , Xiaofeng He , Tiegang Liu","doi":"10.1016/j.matcom.2024.09.034","DOIUrl":"10.1016/j.matcom.2024.09.034","url":null,"abstract":"<div><div>This paper implements the CUDA and hybrid CUDA/MPI parallel computation based on GPGPU heterogeneous parallel strategies for the direct discontinuous method (DDG) on 3D unstructured grids. The direct discontinuous Galerkin method inherits the compactness of the discontinuous Galerkin (DG) method, making it well-suited for large-scale parallelization. Firstly, we present the full single-GPU implementation of the three-dimensional (3D) DDG method with cell-level parallelism and face-level parallelism. Herein, all the numerical operators including volume integration, face integration (numerical fluxes), conservation variables calculation, and time iteration, are implemented by designing the corresponding kernel functions. Especially, we implement several key memory access optimization strategies, which are crucial for performance improvement. Operators merging and shared memory utilizing reduces the number of global access. Such memory Coalescing and data structure reconstruction apparently enhances the efficiency of global memory access. To align with data access pattern, we employ atomic operations to eliminate data race conditions. Furthermore, we propose a full hybrid GPU/CPU heterogeneous parallel strategy to implement multi-GPU parallelization of the DDG method, where asynchronization optimization is introduced to fully overlap communication and computation and basically eliminates the communication overhead. Finally, several numerical tests are conducted on Tesla V100 Cards to show performance of the parallelization. In addition, we utilize the NVIDIA performance testing tool, <span><math><mrow><mi>n</mi><mi>v</mi><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></math></span>, to evaluate multiple metrics of the kernel functions and conduct a detailed analysis of the results. In the tests of parallel scalability, the weak scaling efficiency achieves 97% from 4 to 32 GPU cards, and the strong scaling efficiency is 90% from 1 to 8 GPU cards.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.matcom.2024.10.012
Shi-Shun Chen, Xiao-Yang Li
Global sensitivity analysis (GSA) can provide rich information for controlling output uncertainty. In practical applications, segmented models are commonly used to describe an abrupt model change. For segmented models, the complicated uncertainty propagation during the transition region may lead to different importance rankings of different GSA methods. If an unsuitable GSA method is applied, misleading results will be obtained, resulting in suboptimal or even wrong decisions. In this paper, four GSA indices, i.e., Sobol index, mutual information, delta index and PAWN index, are applied for a segmented fire spread model (Dry Eucalypt). The results show that four GSA indices give different importance rankings during the transition region since segmented characteristics affect different GSA indices in different ways. We suggest that analysts should rely on the results of different GSA indices according to their practical purpose, especially when making decisions for segmented models during the transition region.
{"title":"Comparison of global sensitivity analysis methods for a fire spread model with a segmented characteristic","authors":"Shi-Shun Chen, Xiao-Yang Li","doi":"10.1016/j.matcom.2024.10.012","DOIUrl":"10.1016/j.matcom.2024.10.012","url":null,"abstract":"<div><div>Global sensitivity analysis (GSA) can provide rich information for controlling output uncertainty. In practical applications, segmented models are commonly used to describe an abrupt model change. For segmented models, the complicated uncertainty propagation during the transition region may lead to different importance rankings of different GSA methods. If an unsuitable GSA method is applied, misleading results will be obtained, resulting in suboptimal or even wrong decisions. In this paper, four GSA indices, i.e., Sobol index, mutual information, delta index and PAWN index, are applied for a segmented fire spread model (Dry Eucalypt). The results show that four GSA indices give different importance rankings during the transition region since segmented characteristics affect different GSA indices in different ways. We suggest that analysts should rely on the results of different GSA indices according to their practical purpose, especially when making decisions for segmented models during the transition region.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.matcom.2024.10.004
E. Belenguer, J. Segarra-Tamarit, E. Pérez, R. Vidal-Albalate
Electricity market prices depend on various variables, including energy demand, weather conditions, gas prices, renewable generation, and other factors. Fluctuating prices are a common characteristic of electricity markets, making electricity price forecasting a complex process where predicting different variables is crucial. This paper introduces a hybrid forecasting model developed for the Spanish case. The model comprises four forecasting tools, with three of them relying on artificial neural networks, while the demand forecasting model employs a similar-day approach with temperature correction. This model can be employed by electrical energy trading companies to enhance their trading strategies in the day-ahead market and in derivative markets with a time horizon ranging from two to ten days. The results indicate that, with a forecasting horizon of two days, the price forecast has a rMAE of 8.18%. Furthermore, the model enables a market agent to accurately decide whether to purchase energy in the daily market or in the derivatives market in 69.9% of the days.
{"title":"Short-term electricity price forecasting through demand and renewable generation prediction","authors":"E. Belenguer, J. Segarra-Tamarit, E. Pérez, R. Vidal-Albalate","doi":"10.1016/j.matcom.2024.10.004","DOIUrl":"10.1016/j.matcom.2024.10.004","url":null,"abstract":"<div><div>Electricity market prices depend on various variables, including energy demand, weather conditions, gas prices, renewable generation, and other factors. Fluctuating prices are a common characteristic of electricity markets, making electricity price forecasting a complex process where predicting different variables is crucial. This paper introduces a hybrid forecasting model developed for the Spanish case. The model comprises four forecasting tools, with three of them relying on artificial neural networks, while the demand forecasting model employs a similar-day approach with temperature correction. This model can be employed by electrical energy trading companies to enhance their trading strategies in the day-ahead market and in derivative markets with a time horizon ranging from two to ten days. The results indicate that, with a forecasting horizon of two days, the price forecast has a rMAE of 8.18%. Furthermore, the model enables a market agent to accurately decide whether to purchase energy in the daily market or in the derivatives market in 69.9% of the days.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.matcom.2024.10.005
Lanlan Li , Zhuojia Fu , Ming Qin , Shuainan Liu , Weihong Zeng , Xiaoting Liu
This paper presents a meshless computational framework to simulate nonlinear water wave propagation behaviors of three-dimensional (3D) numerical wave tank containing submerged trapezoidal breakwaters. In the present computational framework, the localized method of fundamental solutions (LMFS) is used to spatial discretization, which is a localized meshless collocation method based on fundamental solutions and moving least square (MLS) technique, and fourth-order predictor-corrector scheme is used to temporal discretization. 3D numerical wave tanks containing single submerged trapezoidal breakwater and double submerged trapezoidal breakwaters are established by using LMFS. The LMFS results are compared with analytical results and experimental data through benchmarks. The effects of variations in incident wave parameters and shape parameters of the submerged trapezoidal breakwater on wave propagation are further analyzed. Additionally, the influence of double submerged trapezoidal breakwaters on the nonlinear water wave propagation behavior is investigated in comparison with the single submerged trapezoidal breakwater. Moreover, the effect of breakwater orientation on wave propagation is presented.
{"title":"Three-dimensional numerical wave tank containing submerged breakwaters based on the localized method of fundamental solutions","authors":"Lanlan Li , Zhuojia Fu , Ming Qin , Shuainan Liu , Weihong Zeng , Xiaoting Liu","doi":"10.1016/j.matcom.2024.10.005","DOIUrl":"10.1016/j.matcom.2024.10.005","url":null,"abstract":"<div><div>This paper presents a meshless computational framework to simulate nonlinear water wave propagation behaviors of three-dimensional (3D) numerical wave tank containing submerged trapezoidal breakwaters. In the present computational framework, the localized method of fundamental solutions (LMFS) is used to spatial discretization, which is a localized meshless collocation method based on fundamental solutions and moving least square (MLS) technique, and fourth-order predictor-corrector scheme is used to temporal discretization. 3D numerical wave tanks containing single submerged trapezoidal breakwater and double submerged trapezoidal breakwaters are established by using LMFS. The LMFS results are compared with analytical results and experimental data through benchmarks. The effects of variations in incident wave parameters and shape parameters of the submerged trapezoidal breakwater on wave propagation are further analyzed. Additionally, the influence of double submerged trapezoidal breakwaters on the nonlinear water wave propagation behavior is investigated in comparison with the single submerged trapezoidal breakwater. Moreover, the effect of breakwater orientation on wave propagation is presented.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The study proposes a dynamic analysis regarding interactions between the resources provided by the forest, the wildlife present inside or in the proximity of that environment and visitors revolving around the before mentioned socioecological framework. The mathematical model is described by a nonlinear system with three differential equations. The discrete time delay is introduced to illustrate the entire past impact of tourists on forest resources and wildlife. The basic assumption is that the wildlife species which inhabit the area are relying entirely on forest resources to meet their needs for food, shelter, and to attract tourists. Also, there is a positive correlation between ecotourism activities and the presence of forest resources and wildlife. The equilibrium states are determined, and they are subjected to a stability and bifurcation analysis. The study employs a Hopf bifurcation analysis in the neighborhood of the equilibrium states by choosing the time delay as the bifurcation parameter. The critical values of the time-delay that lead to oscillatory behavior are determined. Numerical simulations are carried out to show the system’s qualitative behavior in the vicinity of the equilibria.
{"title":"A dynamic analysis of a tourism-based socioecological system","authors":"Andreea-Maria Ardeuan , Mihaela Neamţu , Adriana Loredana Tănasie","doi":"10.1016/j.matcom.2024.08.001","DOIUrl":"10.1016/j.matcom.2024.08.001","url":null,"abstract":"<div><div>The study proposes a dynamic analysis regarding interactions between the resources provided by the forest, the wildlife present inside or in the proximity of that environment and visitors revolving around the before mentioned socioecological framework. The mathematical model is described by a nonlinear system with three differential equations. The discrete time delay is introduced to illustrate the entire past impact of tourists on forest resources and wildlife. The basic assumption is that the wildlife species which inhabit the area are relying entirely on forest resources to meet their needs for food, shelter, and to attract tourists. Also, there is a positive correlation between ecotourism activities and the presence of forest resources and wildlife. The equilibrium states are determined, and they are subjected to a stability and bifurcation analysis. The study employs a Hopf bifurcation analysis in the neighborhood of the equilibrium states by choosing the time delay as the bifurcation parameter. The critical values of the time-delay that lead to oscillatory behavior are determined. Numerical simulations are carried out to show the system’s qualitative behavior in the vicinity of the equilibria.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-05DOI: 10.1016/j.matcom.2024.10.002
Dhabaleswar Mohapatra , S. Chakraverty
This article investigates type-2 fuzzy initial value problems and introduces a novel strategy that capitalises on granular differentiability. Incorporating type-2 fuzzy numbers to depict the problem’s uncertainty may be advantageous from a practical standpoint. This work employs triangularly perfect quasi type-2 fuzzy numbers (TPQT2FNs) and defines the granular differentiability of TPQT2FN-valued functions. In addition, the solution approach for initial value problems with type-2 fuzzy initial conditions is discussed in the context of granular differentiability by transforming the type-2 fuzzy problem into a type-1 fuzzy problem using the lower membership function (LMF) and upper membership function (UMF) concepts. A couple of numerical examples are then examined to determine the applicability of the proposed method, and comparisons are made with existing type-2 fuzzy results and, in a special case, type-1 fuzzy results. In order to aid readers’ comprehension and study the behaviour of the numerical solution, three-dimensional graphical results are also shown.
{"title":"Type-2 fuzzy initial value problems under granular differentiability","authors":"Dhabaleswar Mohapatra , S. Chakraverty","doi":"10.1016/j.matcom.2024.10.002","DOIUrl":"10.1016/j.matcom.2024.10.002","url":null,"abstract":"<div><div>This article investigates type-2 fuzzy initial value problems and introduces a novel strategy that capitalises on granular differentiability. Incorporating type-2 fuzzy numbers to depict the problem’s uncertainty may be advantageous from a practical standpoint. This work employs triangularly perfect quasi type-2 fuzzy numbers (TPQT2FNs) and defines the granular differentiability of TPQT2FN-valued functions. In addition, the solution approach for initial value problems with type-2 fuzzy initial conditions is discussed in the context of granular differentiability by transforming the type-2 fuzzy problem into a type-1 fuzzy problem using the lower membership function (LMF) and upper membership function (UMF) concepts. A couple of numerical examples are then examined to determine the applicability of the proposed method, and comparisons are made with existing type-2 fuzzy results and, in a special case, type-1 fuzzy results. In order to aid readers’ comprehension and study the behaviour of the numerical solution, three-dimensional graphical results are also shown.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-05DOI: 10.1016/j.matcom.2024.09.007
Phuong Nam Dao, Quang Phat Nguyen, Manh Hung Vu
In this article, we study the unification of coordination control problem between two sides and optimal control effectiveness for an unknown Bilateral Teleoperators (BTs) under variable time delays in communication between two sides and external disturbance. We proposed the control frame of Actor/Critic strategy and the Robust Integral of the Sign of the Error (RISE), in which the synchronization effectiveness is discussed in two sections with different conditions. The sliding variable is given to transform a BT dynamic model into order reduction model, which can be designed more favourable. By fully analysing optimization problem in designing the training weights of Actor/Critic structure based on the property of Hamiltonian term, Reinforcement Learning (RL) control scheme in each side is proposed for a BT system. Consequently, we incorporate the RISE term into proposed control frame to mathematically prove that the tracking errors asymptotically converge to zero. Furthermore, the proposed control strategy can also guarantee the convergence of learning process. Simulation results and the comparisons demonstrate the performance of the proposed control framework.
本文研究了在双方通信时间延迟可变和外部干扰的情况下，双方协调控制问题的统一性和未知双边远程操作员（BTs）的最优控制效果。我们提出了 "行动者/批评者"（Actor/Critic）策略和 "误差符号的稳健积分"（Robust Integral of the Sign of the Error，RISE）的控制框架，并在其中分两部分讨论了不同条件下的同步有效性。给出了滑动变量，将 BT 动态模型转化为阶次减少模型，从而更有利于设计。通过全面分析基于哈密顿项的演员/批评者结构训练权重设计的优化问题，为 BT 系统提出了各边的强化学习（RL）控制方案。因此，我们在提议的控制框架中加入了 RISE 项，从数学上证明了跟踪误差渐近收敛为零。此外，所提出的控制策略还能保证学习过程的收敛性。仿真结果和比较证明了所提控制框架的性能。
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