色噪声激励下非线性阻尼动力系统的首次穿越分析

严惠云 1; 师义民 1; 苏剑 2

doi:10.7652/xjtuxb201704019

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色噪声激励下非线性阻尼动力系统的首次穿越分析

更新时间：2025-07-09

- 色噪声激励下非线性阻尼动力系统的首次穿越分析
- First-Passage Analysis for a Nonlinear Damping Dynamical Systems under Colored Noise Excitation
- 西安交通大学学报 2017年51卷第4期页码：122-127+154
- 作者机构：
  
  西北工业大学理学院,西安,710072
- 作者简介：
- 基金信息：
  
  : 2016-10-24。作者简介: 严惠云(1977—),女,讲师。基金项目: 国家自然科学基金资助项目(71571144,71401134,71171164);陕西省自然科学基础研究计划资助项目(2015JM1003)
- DOI：10.7652/xjtuxb201704019
  中图分类号： O313
- 网络首发：2017-04-10，
  
  纸质出版：2017
- 稿件说明：
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严惠云 1, 师义民 1, 苏剑 2. 色噪声激励下非线性阻尼动力系统的首次穿越分析[J]. 西安交通大学学报, 2017,51(4):122-127+154.

First-Passage Analysis for a Nonlinear Damping Dynamical Systems under Colored Noise Excitation[J]. 2017, 51(4): 122-127+154.
严惠云 1, 师义民 1, 苏剑 2. 色噪声激励下非线性阻尼动力系统的首次穿越分析[J]. 西安交通大学学报, 2017,51(4):122-127+154. DOI： 10.7652/xjtuxb201704019.

First-Passage Analysis for a Nonlinear Damping Dynamical Systems under Colored Noise Excitation[J]. 2017, 51(4): 122-127+154. DOI： 10.7652/xjtuxb201704019.

摘要

应用统一色噪声原理和随机平均法研究了色噪声激励下非线性阻尼动力系统的首次穿越问题。首先给出了条件可靠性函数满足的BK(Backward Kolmogorov)方程以及首次穿越时间条件矩满足的广义GP(General Pontryagin)方程

其次在规则边界条件和初始条件下得到了系统的条件可靠性函数、概率密度函数和首次穿越时间的数值解

最后通过数值模拟图分析了系统参数及外激励噪声对系统可靠性变化的影响。分析结果表明:增大系统参数可提高系统可靠性; 增大噪声强度会增大发生首次穿越的概率、降低系统的可靠性; 噪声自相关时间对系统可靠性的影响与系统参数有关

即在系统参数值较大时增大噪声相关时间会提高系统的可靠性

而当系统参数较小时增大噪声相关时间反而会降低系统的可靠性。该结果可为非线性系统的可靠性研究提供参考。

Abstract

By employing the unified colored-noise approximation approach and the stochastic averaging method

the first-passage is analyzed for a class of nonlinear damping dynamical systems under colored noise excitation. A backward Kolmogorov(BK)equation for the conditional reliability function and a generalized Pontryagin(GP)equation for the conditional moment of the first-passage time are established. Under the regular boundary conditions and initial conditions for BK and GP equations

the conditional reliability function

probability density function and numerical solution of the first-passage time of the systems are obtained

and the effects of system parameters and external excitation noise on system reliability are discussed via numerical simulation. The results show that the system reliability can be improved by increasing system parameters

and the probability of the first-passage rises and the system reliability lowers with the increasing excitation intensity. Moreover

the influence of noise autocorrelation time on the system reliability is related to the system parameters. The system reliability rises if the noise autocorrelation time for a large system parameter increases

but the system reliability lowers if the noise autocorrelation time for a small system parameter increases.

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