基于广义子集模拟和自适应Kriging模型的非线性随机动力系统的时变可靠性分析

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (21) : 47-54.

论文

唐和生1,2，郭雪媛1，薛松涛1

作者信息 +

Time-varying reliability analysis of nonlinear stochastic dynamic systems based on generalized subset simulation and adaptive Kriging model

TANG Hesheng1,2, GUO Xueyuan1, XUE Songtao1

Author information +

文章历史 +

摘要

针对非线性随机动力系统在非平稳高斯随机过程激励下的时变可靠性问题，提出一种广义子集模拟（GSS）和主动学习Kriging模型结合Monte Carlo的自适应更新（AK-MCS）高效计算方法（GSS-AK-MCS）。基于全概率定理，将非线性随机动力系统的时变可靠性转化为一个双层嵌套问题：内层通过GSS算法解决非平稳随机激励下累积失效概率的计算；外层自适应地构建系统随机参数与累积失效概率之间的Kriging代理模型，基于代理模型实现随机系统的可靠性分析。以两个非线性结构系统的时变可靠性分析为例，验证所提出方法的可行性。数值算例结果表明：GSS-AK-MCS方法不受非平稳随机激励的频谱特征的影响，与传统的MCS和Kriging模型方法比较，显著提高了非线性随机动力系统的时变可靠性计算效率。

Abstract

A GSS-AK-MCS method, which combines the generalized subset simulation algorithm (GSS) with the adaptive Kriging model(AK-MCS), is proposed for the time-variant reliability analysis of nonlinear stochastic dynamic systems excited by non-stationary Gaussian stochastic processes. Based on the total probability theorem, the time-variant reliability problem is transformed into a two-layer nested time-invariant problem. In the inner layer, the cumulative probability of failure under non-stationary random excitation is calculated by the GSS algorithm. In the outer layer, a Kriging model is constructed for the nonlinear relationship between random parameters and cumulative probability of failure. The feasibility of the proposed method is verified by two numerical case studies. The numerical results indicate that the GSS-AK-MCS method is not affected by the spectral characteristics of non-stationary random excitation and shows good accuracy. The proposed method improves the computational efficiency of time-variant reliability analysis significantly.

导出引用

唐和生1,2，郭雪媛1，薛松涛1. 基于广义子集模拟和自适应Kriging模型的非线性随机动力系统的时变可靠性分析[J]. 振动与冲击, 2021, 40(21): 47-54

TANG Hesheng1,2, GUO Xueyuan1, XUE Songtao1. Time-varying reliability analysis of nonlinear stochastic dynamic systems based on generalized subset simulation and adaptive Kriging model[J]. Journal of Vibration and Shock, 2021, 40(21): 47-54

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