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Strong averaging principles for a class of non-autonomous slow-fast systems of SPDEs with polynomial growth

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arXiv 2020年

In this work, we study a class of non-autonomous two-time-scale stochastic reaction-diffusion equations driven by Poisson random measures, in which the coefficients satisfy the polynomial growth condition and local Lipschitz condition. First, the existence and uniqueness of the mild solution are proved by constructing auxiliary equations and using the technique of stopping time. Then, consider that the time dependent of the coefficients, the averaged equation is redefined by studying the existence of time-dependent evolution family of measures associated with the frozen fast equation. Further, the slow component strongly converges to the solution of the corresponding averaged equation is verified by using the classical Khasminskii method. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Review of local mean decomposition and its application in fault diagnosis of rotating machinery

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Journal of systems Engineering and Electronics 2019年第4期30卷 799-814页

作者： LI Yongbo SI Shubin LIU Zhiliang LIANG Xihui MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an 710072China School of Mechanical and Electrical Engineering University of Electronic Science and Technology of ChinaChengdu 611731China Department of Mechanical Engineering University of ManitobaWinnipeg R3T 5V6Canada

Rotating machinery is widely used in the *** are vulnerable to many kinds of damages especially for those working under tough and time-varying operation *** detection of these damages is important,otherwise,they may lead to large economic loss even a *** signal processing methods have been developed for fault diagnosis of the rotating *** mean decomposition(LMD)is an adaptive mode decomposition method that can decompose a complicated signal into a series of mono-components,namely product functions(PFs).In recent years,many researchers have adopted LMD in fault detection and diagnosis of rotating *** give a comprehensive review of LMD in fault detection and diagnosis of rotating ***,the LMD is *** advantages,disadvantages and some improved LMD methods are ***,a comprehensive review on applications of LMD in fault diagnosis of the rotating machinery is *** review is divided into four parts:fault diagnosis of gears,fault diagnosis of rotors,fault diagnosis of bearings,and other LMD *** each of these four parts,a review is given to applications applying the LMD,improved LMD,and LMD-based combination methods,*** give a summary of this review and some future potential topics at the end.

关键词： local mean decomposition(LMD) signal processing gear rotor bearing

The central limit theorem for slow-fast systems with Lévy noise

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arXiv 2020年

作者： Yang, Xiaoyu Xu, Yong Wang, Ruifang Jiao, Zhe Department of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China

We consider a slow-fast stochastic differential system with Lévy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the *** Codes 70K70, 60G51, 60G46 Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

A hybrid model based on deep LSTM for predicting high-dimensional chaotic systems

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arXiv 2020年

作者： Lei, Youming Hu, Jian Ding, Jianpeng School of mathematics and statistics Northwestern Polytechnical University Xi'an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an710072 China

We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by superimposing multiple recurrent neural network layers and the hybrid model is trained with the Adam optimization algorithm. The statistical results of the Mackey-Glass system and the Kuramoto-Sivashinsky system are obtained under the criteria of root mean square error (RMSE) and anomaly correlation coefficient (ACC) using the singe-layer LSTM, the multi-layer LSTM, and the corresponding hybrid method, respectively. The numerical results show that the proposed method can effectively avoid the rapid divergence of the multi-layer LSTM model when reconstructing chaotic attractors, and demonstrate the feasibility of the combination of deep learning based on the gradient descent method and the empirical model. Copyright © 2020, The Authors. All rights reserved.

关键词： Long short-term memory

Current reversal and particle separation in Brownian transport

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Physical Review Research 2021年第3期3卷 033162-033162页

作者： Hai-Wei Hu Lin Du Liang-Hui Qu Zi-Lu Cao Zi-Chen Deng Ying-Cheng Lai School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China School of Aeronautics Northwestern Polytechnical University Xi'an 710072 China School of Electrical Computer and Energy Engineering Arizona State University Tempe Arizona 85287 USA Department of Physics Arizona State University Tempe Arizona 85287 USA

In transport of micro- or nanosized particles through a confined structure driven by thermal fluctuations and external forcing—a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile, such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerical results is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.

关键词： Brownian motion Classical transport Brownian dynamics Langevin equation Stochastic differential equations

Machine learning-integrated computational analysis on a blood-based ternary nanofluid flow in a stenosed artery with the artificial neural networks and modified finite difference approach

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Chaos, Solitons and Fractals 2025年 199卷

作者： Hussain, Mohib Lin, Du Waqas, Hassan Ali, Bagh Shah, Nehad Ali School of Mathematics and Statistics Northwestern Polytechnical University Xian710072 China MIIT Key Laboratory of Dynamics and Control Complex System Northwestern Polytechnical University Xi'an710072 China School of Naval Architecture Ocean and Energy Power Engineering Wuhan University of Technology Hubei Wuhan430063 China Department of Software Engineering Faculty of Science & Technology ILMA University 75190 Karachi Pakistan Department of Mechanical Engineering Sejong University Seoul05006 Korea Republic of

Heart failure and stroke continue to be the most common cause of global death, with atherosclerosis artery stenosis becoming a significant contributor. Although prior research has progressed in comprehending blood circulation behaviour, however, the incorporation of artificial intelligence (AI) and machine learning (ML) in the examination of ternary nanofluids for stenosed arterial diseases signifies a notable breakthrough in this domain. We proposes an integration of ML technique with computational fluid dynamics (CFD) to analyse the non-linear dynamics of thermal characterization in blood-based tri-hybrid nano-fluid flow, influenced by thermal radiation, variable heat sources and sinks, and aligned magnetic field effects within a blood artery exhibiting cosine stenosis. The investigation is based on AI approach, the Levenberg–Marquardt algorithm (LMA), with back propagation Artificial Neural Network (ANN-BP). The mathematical model is developed in the form of partial differentia equations and transformed into ordinary differential equation by similarity scaling, and then numerically evaluated by a modified finite difference approach, the Keller-Box method. The suggested ANN-LMA accuracy is compared to the ML solution for boundary layer flow. Regression values indicate an excellent fit between the predictions and the real data. It is observed that the inclined magnetic angle affects the drag force and heat transfer rate. There is a 27.9% increase in the heat transfer rate for ternary nano-fluid. Conclusively, the non-linear interaction between the magnetic field and nanofluid flow may significantly enhance heat transfer rates, which could have potential applications in biomedical sciences. © 2025 Elsevier Ltd

关键词： Magnetic levitation

CONVERGENCE on A SYMMETRIC ACCELERATED STOCHASTIC ADMM with LARGER STEPSIZES

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arXiv 2021年

作者： Bai, Jianchao Han, Deren Sun, Hao Zhang, Hongchao School of Mathematics and Statistics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710129 China LMIB of the Ministry of Education School of Mathematical Sciences Beihang University Beijing100191 China School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710129 China Department of Mathematics Louisiana State University Baton RougeLA70803-4918 United States

In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly nonsmooth convex function and an average function of many smooth convex functions. Our proposed algorithm combines both ideas of ADMM and the techniques of accelerated stochastic gradient methods possibly with variance reduction to solve the smooth subproblem. One main feature of SAS-ADMM is that its dual variable is symmetrically updated after each update of the separated primal variable, which would allow a more flexible and larger convergence region of the dual variable compared with that of standard deterministic or stochastic ADMM. This new stochastic optimization algorithm is shown to have ergodic converge in expectation with O(1/T) convergence rate, where T is the number of outer iterations. Our preliminary experiments indicate the proposed algorithm is very effective for solving separable optimization problems from big-data applications. Finally, 3-block extensions of the algorithm and its variant of an accelerated stochastic augmented Lagrangian method are discussed in the appendix. © 2021, CC BY.

关键词： Convex optimization

Slowing down critical transitions via Gaussian white noise and periodic force

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Science China(Technological Sciences) 2019年第12期62卷 2144-2152页

作者： MA JinZhong XU Yong XU Wei LI YongGe KURTHS Jirge Department of Applied Mathematics Northwestern Polytechnical UniversityXi'an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversiyXi'an 710072China Center for Mathematical Sciences&School of Mathematics and Statistics Huazhong University of Science and TechmologyWuhan 430074China Potsdam Institute for Climate Impact Research Potsdam 14412Germany Department of Physics Humboldt UniversityBerlin 12489Germany

Stochastic perturbations and periodic excitations are generally regarded as sources to induce critical transitions in complex systems. However, we find that they are also able to slow down an imminent critical transition. To illustrate this phenomenon, a periodically driven bistable eutrophication model with Gaussian white noise is introduced as a prototype class of real *** residence probability(RP) is presented to measure the possibility that the given system stays in the oligotrophic state versus Gaussian white noise and periodic force. Variations in the mean first passage time(MFPT) and the mean velocity(MV) of the first right-crossing process are also calculated respectively. We show that the frequency of the periodic force can increase the MFPT while reduce the MV under different control parameters. Nevertheless, the noise intensity or the amplitude may result in an increase of the RP only in the case of control parameters approaching the critical values. Furthermore, for an impending critical transition, an increase of the RP appears with the interaction between the amplitude and noise intensity or the combination of the noise intensity and frequency, while the interaction of the frequency and amplitude leads to an extension of the MFPT or a decrease of the MV. As a result, an increase of the RP and MFPT, and a decrease of the MVobtained from our results claim that it is possible to slow down an imminent critical transition via Gaussian white noise and periodic force.

关键词： critical transition slowing down bistable eutrophication model Gaussian white noise periodic force residence probability mean first passage time mean velocity

Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

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arXiv 2020年

作者： Zhang, Xiaoyu Xu, Yong Liu, Qi Kurths, Jürgen Department of Applied Mathematics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xian710072 China Potsdam Institute for Climate Impact Research Potsdam14412 Germany

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs. When the parameter varies within a certain time scale, the rate will affect the tipping behaviors. These behaviors are undesirable in thermoacoustic systems, which are widely used in aviation, power generation and other industries. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises. Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method. Then, the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions. Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption, which is called as a rate-dependent tipping-delay phenomenon. Besides, the influences of the initial values, the rate, the changing time of the parameters, and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines. Copyright © 2020, The Authors. All rights reserved.

关键词： White noise