Applied Mathematics and Computation最新文献

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Remaining useful life estimation considering threshold epistemic uncertainty with uncertain differential equation

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-07 DOI: 10.1016/j.amc.2025.129340

Zhe Liu , Qingyuan Zhang

Remaining useful life (RUL) prediction is one of the key problems in equipment operation and maintenance. In some engineering practices, sufficient degradation observations can not be obtained due to limitations in cost, technology, and time. Under these situations, several degradation models are established using uncertain processes, and based on which the RULs are predicted under belief reliability theory. Although these methods showed advantages in dealing with small sample sizes, they all regarded the failure threshold as a known constant. However, as the system will be used by a diverse range of users, the failure threshold can vary appreciably with different using scenarios. Furthermore, due to the unclear understanding and insufficient collection of the actual operation process by users, the determination of the failure threshold is quite subjective. If the threshold is simply regarded as a known constant, it will cause inaccuracies in the reliability assessment and the scheduling of maintenance, which may further lead to unnecessary losses. Therefore, this work develops a method to estimate RUL with an uncertain failure threshold based on a degradation model constructed by the uncertain differential equation. Unknown parameters in the established degradation model are estimated by the method of moment based on residuals to alleviate the problem in which observation intervals are not close enough. The effectiveness of the proposed methodology is verified through a degradation data set.

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引用次数: 0

The supercloseness property and global superconvergence analysis for the transient conduction-convection equations

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-07 DOI: 10.1016/j.amc.2025.129342

Liuchao Xiao , Minghao Li , Zhenzhen Li , Hongru Chen

In this paper, we consider the implicit Euler scheme of the transient conduction-convection equations. The supercloseness properties and global superconvergence results are derived for two pairs of low order rectangular elements. Firstly, we obtain a prior estimate of finite element solutions. Then using the properties of the Stokes projection and Stokes operator, the derivative transforming skill and the

H^{- 1}

-norm estimate, we deduce the supercloseness properties of the velocity and temperature in

L^{\infty} (H^{1})

-norm, and the pressure in

L^{\infty} (L^{2})

-norm. Next, the global superconvergence results are obtained through the interpolation postprocessing technique. Finally, a numerical example is provided to confirm the theoretical analysis. Compared with previous results, the superconvergence analysis is more concise, a lower regularity of solutions is required, and no time step restriction is needed.

{"title":"The supercloseness property and global superconvergence analysis for the transient conduction-convection equations","authors":"Liuchao Xiao , Minghao Li , Zhenzhen Li , Hongru Chen","doi":"10.1016/j.amc.2025.129342","DOIUrl":"10.1016/j.amc.2025.129342","url":null,"abstract":"<div><div>In this paper, we consider the implicit Euler scheme of the transient conduction-convection equations. The supercloseness properties and global superconvergence results are derived for two pairs of low order rectangular elements. Firstly, we obtain a prior estimate of finite element solutions. Then using the properties of the Stokes projection and Stokes operator, the derivative transforming skill and the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-norm estimate, we deduce the supercloseness properties of the velocity and temperature in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span>-norm, and the pressure in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>-norm. Next, the global superconvergence results are obtained through the interpolation postprocessing technique. Finally, a numerical example is provided to confirm the theoretical analysis. Compared with previous results, the superconvergence analysis is more concise, a lower regularity of solutions is required, and no time step restriction is needed.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129342"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349953","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}

引用次数: 0

Set stabilization of Boolean control networks based on bisimulations: A dimensionality reduction approach

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-07 DOI: 10.1016/j.amc.2025.129338

Tiantian Mu , Jun-e Feng , Biao Wang

This paper exploits bisimulation relations, generated by extracting the concept of morphisms between algebraic structures, to analyze set stabilization of Boolean control networks with lower complexity. First, for two kinds of bisimulation relations, called as weak bisimulation and strong bisimulation relations, a novel verification method is provided by constructing the bisimulation matrices. Then the comparison for set stabilization of BCNs via two kinds of bisimulation methods is presented, which involves the dimensionality of quotient systems and dependency of the control laws on the original system. Moreover, the proposed method is also applied to the analysis of probabilistic Boolean control networks to establish the unified analysis framework of bisimulations. Finally, the validity of the obtained results is verified by the practical example.

引用次数: 0

A modification of Durán-type mesh for singularly perturbed problems

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-07 DOI: 10.1016/j.amc.2025.129339

G. Radojev , M. Brdar , Lj. Teofanov

A new approach to the Durán-type mesh is presented in order to improve the standard definition of this layer-adjusted mesh and eliminate some of its drawbacks. The construction of this graded mesh is provided for an elliptic convection-diffusion problem, a convection-diffusion-reaction problem, a third-order problem, and a convection-diffusion problem with a large shift. Our modification outperforms the standard Durán-type mesh both theoretically and numerically. Furthermore, the modified mesh is unique and allows for a fair comparison of numerical results obtained with other meshes of the Shishkin and Bakhvalov-types.

引用次数: 0

Evolution of cooperation in a three-strategy game combining snowdrift and stag hunt games

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-07 DOI: 10.1016/j.amc.2025.129341

Hirofumi Takesue

This study aimed to investigate the evolutionary dynamics of a three-strategy game that combines snowdrift and stag hunt games. This game is motivated by an experimental study, which found that individual solution lowers cooperation levels. Agents adopting this option aim to address a problem to the extent necessary to prevent negative impact on themselves, although they do not free ride on cooperation effort provided by others. This property of the individual solution is similar to that of option defection in the stag hunt. Thus, the role of the interplay of defection in the snowdrift game and individual solution was examined in this study. The well-mixed population has two asymptotically stable rest points, one wherein the individual solution occupies the population, and the other wherein cooperation and defection coexist. The interactions on a square lattice enlarge the parameter region wherein cooperation survives, and the three strategies often coexist. The scrutinization of the evolutionary process shows that multiple mechanisms lead to the coexistence of the three strategies depending on parameter values. Our analysis suggests that considering the individual solution adds complexity to the evolutionary process, which might contribute to our understanding on the evolution of cooperation.

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引用次数: 0

Mode-based triggered protocol for synchronization of switched dynamic networks with semi-Markov kernel and its application

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-07 DOI: 10.1016/j.amc.2025.129336

Mengshen Chen , Derui Ding , Huaicheng Yan , Kun Liang

In this paper, the mean square synchronization is investigated for discrete-time dynamic networks with stochastic switching topologies via a semi-Markov kernel approach. A novel mode-based triggered protocol is developed to reduce the communication frequency, where the data between coupled nodes is only transmitted at the topology switching instants. Besides, a more general semi-Markov chain based on the semi-Markov kernel approach is first adopted to describe the stochastic switching process of network topologies, then the different types of probability density functions can coexist in any topological mode. Under the proposed triggering strategy, a mode-based distributed synchronization protocol is formed to deal with the controller design difficulty caused by the randomness of semi-Markov switching. Based on the Lyapunov function, some auxiliary inequalities in existing results are avoided and further the numerically testable criterion is obtained to ensure mean square synchronization of the dynamic networks. Finally, a practical example of power systems is presented to demonstrate the effectiveness of the proposed method.

{"title":"Mode-based triggered protocol for synchronization of switched dynamic networks with semi-Markov kernel and its application","authors":"Mengshen Chen , Derui Ding , Huaicheng Yan , Kun Liang","doi":"10.1016/j.amc.2025.129336","DOIUrl":"10.1016/j.amc.2025.129336","url":null,"abstract":"<div><div>In this paper, the mean square synchronization is investigated for discrete-time dynamic networks with stochastic switching topologies via a semi-Markov kernel approach. A novel mode-based triggered protocol is developed to reduce the communication frequency, where the data between coupled nodes is only transmitted at the topology switching instants. Besides, a more general semi-Markov chain based on the semi-Markov kernel approach is first adopted to describe the stochastic switching process of network topologies, then the different types of probability density functions can coexist in any topological mode. Under the proposed triggering strategy, a mode-based distributed synchronization protocol is formed to deal with the controller design difficulty caused by the randomness of semi-Markov switching. Based on the Lyapunov function, some auxiliary inequalities in existing results are avoided and further the numerically testable criterion is obtained to ensure mean square synchronization of the dynamic networks. Finally, a practical example of power systems is presented to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129336"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349948","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}

引用次数: 0

Optimal finite-horizon tracking control in affine nonlinear systems: A Stackelberg game approach with H2/H∞ framework

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-04 DOI: 10.1016/j.amc.2025.129276

Xu Dong , Huaguang Zhang , Zhongyang Ming , Yanhong Luo

In this paper, we address the finite-time optimal tracking control problem within the context of a Stackelberg game structure, characterized by the mixed

H_{2} / H_{\infty}

framework. This objective is accomplished through the innovative design and implementation of a novel Adaptive Dynamic Programming (ADP) algorithm. Initially, we establish a time-varying coupled Hamilton-Jacobi-Isaacs (HJI) equations, posing a significant challenge in deriving an analytical solution for the optimal leader. Subsequently, we elucidate the existence of Nash equilibrium points, confirming the algorithm's convergence and providing theoretical foundations for its practical application. Furthermore, we introduce a novel ADP algorithm that incorporates time-varying activation functions. The use of the Lyapunov direct method ensures the stability of the closed-loop affine nonlinear system under the ADP control scheme, thereby guaranteeing the system's uniformly ultimately bounded (UUB). Finally, the effectiveness of the aforementioned ADP-based control approach is validated through numerical simulations.

{"title":"Optimal finite-horizon tracking control in affine nonlinear systems: A Stackelberg game approach with H2/H∞ framework","authors":"Xu Dong , Huaguang Zhang , Zhongyang Ming , Yanhong Luo","doi":"10.1016/j.amc.2025.129276","DOIUrl":"10.1016/j.amc.2025.129276","url":null,"abstract":"<div><div>In this paper, we address the finite-time optimal tracking control problem within the context of a Stackelberg game structure, characterized by the mixed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> framework. This objective is accomplished through the innovative design and implementation of a novel Adaptive Dynamic Programming (ADP) algorithm. Initially, we establish a time-varying coupled Hamilton-Jacobi-Isaacs (HJI) equations, posing a significant challenge in deriving an analytical solution for the optimal leader. Subsequently, we elucidate the existence of Nash equilibrium points, confirming the algorithm's convergence and providing theoretical foundations for its practical application. Furthermore, we introduce a novel ADP algorithm that incorporates time-varying activation functions. The use of the Lyapunov direct method ensures the stability of the closed-loop affine nonlinear system under the ADP control scheme, thereby guaranteeing the system's uniformly ultimately bounded (UUB). Finally, the effectiveness of the aforementioned ADP-based control approach is validated through numerical simulations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129276"},"PeriodicalIF":3.5,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137452","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}

引用次数: 0

Analysis of a stabilized element-free Galerkin method for magnetohydrodynamic flow at very large Hartmann numbers

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-04 DOI: 10.1016/j.amc.2025.129334

Xiaolin Li , Haiyun Dong

A stabilized element-free Galerkin (EFG) method is designed to simulate magnetohydrodynamic (MHD) flow at very large Hartmann numbers. By transforming the MHD flow to two decoupled convection-diffusion problems, residual-based formulas are devised to improve the performance of the standard EFG method damaged by large Hartmann numbers. Error of the stabilized EFG method is discussed in theory. Numerical examples show that this meshless method can produce efficacious solutions for MHD problems with very large Hartmann numbers such as 10¹⁶.

引用次数: 0

Stabilization of hybrid stochastic neutral-type systems with non-differentiable delays under high nonlinearity via discrete-time feedback control

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-04 DOI: 10.1016/j.amc.2025.129333

Yueli Huang , Yuan Lv , Quanxin Zhu

In this paper, we discuss a kind of unstable hybrid neutral stochastic systems with non-differentiable delays, whose coefficients satisfy polynomial growth conditions. The key purpose of this paper is to develop a controller based on discrete-time observations for both modes and states to achieve stability of the controlled system. We establish some new stability criteria for hybrid neutral-type stochastic systems with non-differentiable delay under high nonlinearity. The sufficient stability criteria of asymptotic stability, exponential stability and

H_{\infty}

stability are established. Finally, an example is given to verify our theoretical results.

引用次数: 0

Coupled diffusion dynamics of competitive information and green behaviors on multiplex networks under policy intervention

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-02-04 DOI: 10.1016/j.amc.2025.129328

Zhishuang Wang , Yicong Wan , Qian Yin , Zhiyong Hong , Qiuxia Xu , Chengyi Xia

In addition to reducing greenhouse gas emissions from industrial production, individual green behaviors also play a significant role in alleviating the climate crisis. To quantitatively analyze the dynamic properties of the coupled diffusion of positive and negative information and green behaviors under policy intervention, we constructed a model based on a two-layer complex networks framework. Positive information promotes individual adoption of green behaviors, while negative information reduces individual willingness to engage in green behaviors, and policy intervention affects the probability of individuals abandoning green behaviors. We also considered the influence of individual hesitancy psychology in the competitive dissemination process of the two types of information. Utilizing compartmental models commonly used in infectious disease transmission, we characterized the diffusion processes of both types of information and green behaviors and described the transition mechanism of individual states using probability transition trees based on the coupled diffusion mechanism. Combining the topological structure of the two-layer complex networks, we further formalized the coupled propagation model into coupled diffusion dynamic equations. Based on the steady-state coupled diffusion dynamic equations, we derived the outbreak threshold expression for green behaviors in the proposed coupled diffusion model, indicating that both the density of information propagation and the intensity of policy intervention directly influence the diffusion threshold of green behaviors in the population. Extensive computer simulation results were used to further analyze the dynamic properties of coupled diffusion, showing that when the propagation rate of positive information exceeds that of negative information, it is conducive to the outbreak and diffusion of green behaviors. Policy intervention has a better promotional effect when negative information spreads widely. Moreover, the diffusion threshold of green behaviors may undergo a sudden change with the variation in the propagation rates of the two types of information.

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引用次数: 0

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