非线性结构动力学系统的首次穿越

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (4) : 163-166.

论文

非线性结构动力学系统的首次穿越

任丽梅，徐伟，李战国

作者信息 +

An importance sampling procedure for estimating failure probabilities of non-linear dynamic systems

Ren Limei，Xu Wei ，Li Zhanguo

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文章历史 +

摘要

在结构动力学系统的可靠性分析中，动力学系统的首次穿越失效一直是研究重点问题之一。在
基于重要抽样法基础上研究了非线性结构动力学系统的首次穿越。首先根据Rice公式，得到与非线性系统方程具有相同平均上穿率的等效线性化系统方程，利用此等效方程得到设计点的解析表达式来构造控制函数，最后将此控制函数运用到非线性系统中，利用重要抽样法估计非线性系统的首穿失效概率。文章以Duffing振子为例，模拟结果显示了方法的正确性与有效性，与原始蒙特卡罗模拟方法相比较，样本数量、计算所需时间都有明显减小。

Abstract

The failure probability is one of the most important reliability measures in structural reliability assessment of dynamical systems. This paper suggests a procedure for estimating failure probabilities of non-linear systems based on importance sampling technique. Firstly ,by used of Rice formula，the paper obtains the equivalent linear version of the non-linear systems. The paper uses design point of the equivalent linear systems to construct control function. Secondly, an importance sampling technique is used in order to estimate excursion probabilities for the non-linear system. Finally, the paper takes Duffing oscillator for example. The simulation results show the method of the paper to be correct and effective. The number of samples and the computational time are reduced significantly compared with direct Monte Carlo simulations.

导出引用

任丽梅;徐伟;李战国. 非线性结构动力学系统的首次穿越[J]. 振动与冲击, 2013, 32(4): 163-166

Ren Limei;Xu Wei;Li Zhanguo. An importance sampling procedure for estimating failure probabilities of non-linear dynamic systems[J]. Journal of Vibration and Shock, 2013, 32(4): 163-166