色噪声激励下非线性阻尼动力系统的首次穿越分析

发布时间：2018-12-29 13:11

【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]:The first crossing problem of nonlinear damped dynamical system under colored noise excitation is studied by using the unified chromatic noise principle and the stochastic averaging method. In this paper, the BK (Backward Kolmogorov) equation of conditional reliability function and the generalized GP (General Pontryagin) equation of first-pass time condition moment are given. Secondly, the conditional reliability function of the system is obtained under the regular boundary condition and initial condition. The probabilistic density function and the numerical solution of the first traversing time are given. Finally, the effects of system parameters and external excitation noise on the reliability of the system are analyzed by numerical simulation. The results show that the reliability of the system can be improved by increasing the parameters of the system, the probability of the first crossing will be increased by increasing the noise intensity, and the reliability of the system will be reduced. The effect of noise autocorrelation time on the system reliability is related to the system parameters, that is, increasing the noise correlation time increases the reliability of the system. When the system parameters are small, increasing the noise correlation time will reduce the reliability of the system. The results can provide a reference for the reliability study of nonlinear systems.
【作者单位】：西北工业大学理学院;西安交通大学数学与统计学院;
【基金】：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)
【分类号】：O19

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