|
|
Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly
2017 Vol.18 No.2 P.83-91
Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump
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.
Key words: Nonlinear system, Continuous-time Markov jump, Stochastic excitation, Stochastic averaging
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。
关键词组：
References:
Open peer comments: Debate/Discuss/Question/Opinion
<1>
DOI:
10.1631/jzus.A1600176
CLC number:
O324
Download Full Text:
Downloaded:
2576
Download summary:
<Click Here>Downloaded:
1974Clicked:
5327
Cited:
0
On-line Access:
2017-01-24
Received:
2016-02-23
Revision Accepted:
2016-08-04
Crosschecked:
2017-01-05