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CLC number: O324

On-line Access: 2017-01-24

Received: 2016-02-23

Revision Accepted: 2016-08-04

Crosschecked: 2017-01-05

Cited: 0

Clicked: 1886

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Rong-hua Huan

http://orcid.org/0000-0003-4648-3805

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Journal of Zhejiang University SCIENCE A 2017 Vol.18 No.2 P.83-91

http://doi.org/10.1631/jzus.A1600176


Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump


Author(s):  Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan

Affiliation(s):  Department of Mechanics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   rhhuan@zju.edu.cn

Key Words:  Nonlinear system, Continuous-time Markov jump, Stochastic excitation, Stochastic averaging


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Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan. Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump[J]. Journal of Zhejiang University Science A, 2017, 18(2): 83-91.

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Abstract: 
An approximate method for predicting the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump is proposed. By using the stochastic averaging method, the original system is reduced to one governed by a 1D averaged Itô equation for the total energy with the Markov jump process as parameter. A Fokker-Planck-Kolmogorov (FPK) equation is then deduced, from which the approximate stationary probability density of the response of the original system is obtained for different jump rules. To illustrate the effectiveness of the proposed method, a stochastically excited Markov jump Duffing system is worked out in detail.

The method of stochastic averaging is applied to predict the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump. The method itself has been validated with many nonlinear stochastic systems. The current work is yet another extension of the method to a new system with Markov jump.

随机激励下连续时间马尔科夫跳变非线性系统的平稳响应研究

目的:提出一种预测随机激励下连续时间马尔科夫跳变非线性系统的平稳响应的近似方法。
创新点:1. 得到了含有马尔科夫跳变参数的关于能量的平均Itô方程;2. 建立了含有马尔科夫跳变参数的平均Itô方程相应的FPK方程。
方法:1. 将一个随机激励的马尔科夫跳变非线性系统由状态方程转化为等价的Itô方程,并根据Itô微分法则给出哈密顿量(系统总能量)的Itô方程;2. 通过随机平均法,得到关于系统能量的平均Itô方程;3. 推导并求解相应的FPK方程。
结论:1. 跳变规律对马尔科夫跳变非线性系统随机响应具有重要影响;2. 理论结果与数字模拟结果吻合验证了理论方法的准确性。

关键词:非线性系统;连续时间马尔科夫跳变;随机激励;随机平均

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