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Solving the transient response of the randomly excited dry friction system via piecewise RBF neural networks

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Science China(Technological Sciences) 2023年第5期66卷 1408-1416页

作者： QIAN JiaMin chen lincong SUN JianQiao College of Civil Engineering Huaqiao UniversityXiamen361021China Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province Huaqiao UniversityXiamen361021China Department of Mechanical Engineering School of EngineeringUniversity of CaliforniaMercedCA95343USA

Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction ***,an effective approach to capture the non-smooth transition behavior of such systems is still ***,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction *** the established framework,the transient probability density function of the dry friction system is expressed in a piecewise *** segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent *** time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint *** avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent *** on some numerical results,the proposed scheme effectively ***,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more ***,we can easily extend the proposed method to other types of non-smooth systems with piecewise response ***,the semi-analytical solution provides a valuable reference for system optimization.

关键词： dry friction system transient response semi-analytical solution piecewise RBF neural networks

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

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Applied Mathematics and Mechanics(English Edition) 2019年第12期40卷 1759-1776页

作者： lincong chen Haisheng ZHU J.Q.SUN College of Civil Engineering Huaqiao UniversityXiamen 361021Fujian ProvinceChina School of Engineering University of CaliforniaMercedCA 95343U.S.A

The vibroimpact systems with bilateral barriers are often encountered in ***,the dynamics of the vibroimpact system with bilateral barriers is full of *** closed-form solutions were *** this paper,we propose a novel method for random vibration analysis of single-degree-of-freedom(SDOF)vibroim-pact systems with bilateral barriers under Gaussian white noise excitations.A periodic approximate transformation is employed to convert the equations of the motion to a con-tinuous *** probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov(FPK)*** closed-form station-ary probability density function(PDF)of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability ***,the versatility of the proposed approach is demonstrated by its application to two typical *** that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

关键词： bilateral barrier vibroimpact system weighted residue method iterative random vibration

Stochastic averaging technique for SDOF strongly nonlinear systems with delayed feedback fractional-order PD controller

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Science China(Technological Sciences) 2019年第2期62卷 287-297页

作者： chen lincong LIANG Xiao ZHU WeiQiu ZHAO YaoBing College of Civil Engineering Huaqiao University Departments of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University

A stochastic averaging technique is proposed to study the randomly excited single-degree-of-freedom(SDOF) strongly nonlinear systems with delayed feedback fractional-order proportional-derivative(PD) controller. The delayed feedback fractional-order PD control force is approximated by an equivalent non-delay feedback control force combining with a quasi-linear elastic force and a quasi-linear damping force. The averaged It? stochastic differential equation for amplitude of the equivalent nonlinear system is derived by the generalized harmonic functions. The analytical stationary probability density function(PDF) is obtained with solving the reduced Fokker-Planck-Kolmogorov(FPK) equation. Two examples of van der Pol oscillator and RayleighDuffing oscillator are studied to illustrate the application and effectiveness of the proposed method. Numerical results display that the proposed method can yield to the high precision, and the time delay could ruin the control effectiveness, but also even amplifies the response of the system more than that of uncontrolled system. Furthermore, the study finds that the parameters of fractional-order α and time delay may cause the stochastic P-bifurcation. It is indicated that the delayed feedback fractional-order PD controller can offer a potentially effective tool for anti-control of stochastic bifurcation

关键词： αstochastic averaging strongly nonlinear system time delay fractional-order PD^a controller

Asymptotic stability with probability one of MDOF nonlinear oscillators with fractional derivative damping

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Science China(Physics,Mechanics & Astronomy) 2013年第11期56卷 2200-2207页

作者： chen lincong LI HaiFeng LI ZhongShen ZHU WeiQiu College of Civil Engineering Huaqiao University College of Mechanical Engineering and Automation Huaqiao University Department of Mechanics State Key Laboratory of Fluid Power Transmission and ControlZhejiang University

In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the *** an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of *** particular,the case of factional order more than 1 is studied for the first time.

关键词： fractional derivative damping nonlinear oscillator stochastic stability Lyapunov exponent

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

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Applied Mathematics and Mechanics(English Edition) 2020年第6期41卷 967-982页

作者： lincong chen J.Q.SUN College of Civil Engineering Huaqiao UniversityXiamen 361021Fujian ProvinceChina Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province Jimei Avenue 668Xiamen 361021Fujian ProvinceChina Department of Mechanical Engineering School of EngineeringUniversity of CaliforniaMercedCA 95343U.S.A.

Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical *** paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.

关键词： stationary response multi-degree-of-freedom(MDOF)nonlinear system Fokker-Planck-Kolmogorov(FPK)equation least square method

Random vibration of hysteretic systems under Poisson white noise excitations

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Applied Mathematics and Mechanics(English Edition) 2023年第2期44卷 207-220页

作者： lincong chen Zi YUAN Jiamin QIAN J.Q.SUN College of Civil Engineering Huaqiao UniversityXiamen 361021Fujian ProvinceChina Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province Xiamen 361021Fujian ProvinceChina Department of Mechanical Engineering School of EngineeringUniversity of CaliforniaMercedCA 95343U.S.A.

Hysteresis widely exists in civil structures,and dissipates the mechanical energy of *** on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is *** this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise *** solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution *** effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

关键词： random vibration Bouc-Wen hysteresis system non-Gaussian excitation Poisson white noise excitation radial basis function(RBF)neural network(RBF-NN)

Optimization for vibro-impact nonlinear energy sink under randomexcitation

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Theoretical & Applied Mechanics Letters 2022年第5期12卷 322-325页

作者： Jiamin Qian lincong chen College of Civil Engineering Huaqiao UniversityXiamen 361021China Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province Huaqiao UniversityJimei Avenue 668XiamenFujian361021China

As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available forthe design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effortto address this gap. Specifically, the approximate analytical solution of the system stochastic responseis obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Takingadvantages of this approximate solution, the variance of the system is defined and easily minimized tocalculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlatewith direct numeric simulations.

关键词： Vibration control Vibro-impact NES Stochastic averaging Optimization

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

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Acta Mechanica Solida Sinica 2009年第2期22卷 143-151页

作者： Ronghua Huan lincong chen Weiliang Jin Weiqiu Zhu Department of Mechanics Zhejiang University Hangzhou 310027 China College of Civil Engineering and Architecture Zhejiang University Hangzhou 310027 China

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.

关键词： nonlinear system random excitations optimal control partially observation actuator saturation

Stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative

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Science China(Physics,Mechanics & Astronomy) 2012年第12期55卷 2284-2289页

作者： chen lincong LOU Qun LI ZhongShen ZHU WeiQiu College of Civil Engineering Huaqiao University Xiamen 361021 China College of Mechanical Engineering and Automation Huaqiao University Xiamen 361021 China Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is ***,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic ***,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be *** effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.

关键词： fractional derivative damping Duffing oscillator stochastic averaging method stochastic stability