Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non...Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In 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 excitations.The 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 process.The 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.展开更多
The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural e...The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.展开更多
The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed fo...The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itp differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.展开更多
The stationary probability density function (PDF) solution to nonlinear ship roll motion excited by Poisson white noise is analyzed. Subjected to such random excitation, the joint PDF solution to the roll angle and an...The stationary probability density function (PDF) solution to nonlinear ship roll motion excited by Poisson white noise is analyzed. Subjected to such random excitation, the joint PDF solution to the roll angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the exponential-polynomial closure (EPC) method is adopted. With the EPC method, the PDF solution is assumed to be an exponential-polynomial function of state variables. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. The problem of determining the unknown parameters in the approximate PDF finally results in solving simultaneous nonlinear algebraic equations. Both slight and high nonlinearities are considered in the illustrative examples. The analysis shows that when a second-order polynomial is taken, the result of the EPC method is the same as the one given by the equivalent linearization (EQL) method. The EQL results differ significantly from the simulated results in the case of high nonlinearity. When a fourth-order or sixth-order polynomial is taken, the results of the EPC method agree well with the simulated ones, especially in the tail regions of the PDF. This agreement is observed in the cases of both slight and high nonlinearities.展开更多
In this paper,stochastic dynamics of a single degree‐of‐freedom quasi‐linear system with multitime delays and Poisson white noises are investigated using an approximate procedure based on the stochastic averaging m...In this paper,stochastic dynamics of a single degree‐of‐freedom quasi‐linear system with multitime delays and Poisson white noises are investigated using an approximate procedure based on the stochastic averaging method.The simplified equations,including the averaged stochastic differential equation and the averaged generalized Fokker–Planck–Kolmogorov equation,are obtained to calculate the probability density functions(PDFs)to explore stationary responses.The expression of the Lyapunov exponent is presented to examine the asymptotic stochastic Lyapunov stability.An illustrative example of a quasi‐linear oscillator with two Poisson white noises controlled by two time‐delayed feedback forces is worked out to demonstrate the validity of the proposed method.The approximate stationary PDFs of stochastic responses and asymptotic stochastic stability are demonstrated numerically and theoretically.The results show that the Gaussian white noise has a stronger influence on the dynamics than the Poisson white noise with a small mean arrival rate.Moreover,the influence of the time delay and noise parameters on stochastic dynamics is investigated.It is found that the PDFs under the Poisson white noise approach those under Gaussian white noise as the mean arrival rate increases.The time delay can induce stochastic P‐bifurcation of the system.It is also found that the increase of time delay and the mean arrival rates of the Poisson white noises will broaden the unstable parameter region.The comparison between numerical and theoretical results shows the effectiveness of the proposed method.展开更多
Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is...Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.展开更多
基金the National Natural Science Foundation of China(No.12072118)the Natural Science Funds for Distinguished Young Scholar of Fujian Province of China(No.2021J06024)the Project for Youth Innovation Fund of Xiamen of China(No.3502Z20206005)。
文摘Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In 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 excitations.The 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 process.The 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.
基金supported by the National Natural Science Foundation of China(10932009,11072212,11272279,and 11321202)
文摘The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10932009)
文摘The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itp differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.
基金supported by the National Natural Science Foundation of China (Grant No. 51008211)
文摘The stationary probability density function (PDF) solution to nonlinear ship roll motion excited by Poisson white noise is analyzed. Subjected to such random excitation, the joint PDF solution to the roll angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the exponential-polynomial closure (EPC) method is adopted. With the EPC method, the PDF solution is assumed to be an exponential-polynomial function of state variables. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. The problem of determining the unknown parameters in the approximate PDF finally results in solving simultaneous nonlinear algebraic equations. Both slight and high nonlinearities are considered in the illustrative examples. The analysis shows that when a second-order polynomial is taken, the result of the EPC method is the same as the one given by the equivalent linearization (EQL) method. The EQL results differ significantly from the simulated results in the case of high nonlinearity. When a fourth-order or sixth-order polynomial is taken, the results of the EPC method agree well with the simulated ones, especially in the tail regions of the PDF. This agreement is observed in the cases of both slight and high nonlinearities.
基金This study was supported by the National Natural Science Foundation of China under Grant Nos.11872306,11702214,12072264the Natural Science Basic Research Plan in Shaanxi Province 2020JQ‐108+1 种基金Yong Xu was partially supported by the Key International(Regional)Cooperative Research Projects of the National Natural Science Foundation of China(Grant 12120101002)the Fundamental Research Funds for the Central Universities(Grant D5000220035).
文摘In this paper,stochastic dynamics of a single degree‐of‐freedom quasi‐linear system with multitime delays and Poisson white noises are investigated using an approximate procedure based on the stochastic averaging method.The simplified equations,including the averaged stochastic differential equation and the averaged generalized Fokker–Planck–Kolmogorov equation,are obtained to calculate the probability density functions(PDFs)to explore stationary responses.The expression of the Lyapunov exponent is presented to examine the asymptotic stochastic Lyapunov stability.An illustrative example of a quasi‐linear oscillator with two Poisson white noises controlled by two time‐delayed feedback forces is worked out to demonstrate the validity of the proposed method.The approximate stationary PDFs of stochastic responses and asymptotic stochastic stability are demonstrated numerically and theoretically.The results show that the Gaussian white noise has a stronger influence on the dynamics than the Poisson white noise with a small mean arrival rate.Moreover,the influence of the time delay and noise parameters on stochastic dynamics is investigated.It is found that the PDFs under the Poisson white noise approach those under Gaussian white noise as the mean arrival rate increases.The time delay can induce stochastic P‐bifurcation of the system.It is also found that the increase of time delay and the mean arrival rates of the Poisson white noises will broaden the unstable parameter region.The comparison between numerical and theoretical results shows the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(Nos. 60674048,60772053, 60672142,and 60932005)the National Key Basic Research and Development (973) Program of China (Nos.2007CB307100 and 2007CB307105)
文摘Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.
