非线性结构动力学系统的首次穿越  

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

作　　者：任丽梅[1] 徐伟[1] 李战国[1] 

机构地区：[1]西北工业大学理学院,陕西西安710072

出　　处：《振动与冲击》2013年第4期163-166,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10932009;11172233)

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。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,并用此解析式来构造控制函数,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。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。The failure probability is one of the most important reliability measures in structural reliability assessment of dynamical systems. Here, a procedure for estimating failure probabilities of non-linear systems based on the important sampling technique was presented. Firstly , by using Rice formula, the equivalent linear version of the non-linear systems was derived. Using the equivalent linear equation, the design point of the equivalent linear systems was used to construct control function. Secondly, an important sampling technique was used to estimate the first excursion probabilities for the non-linear system. Finally, a Duffing oscillator was taken for example. The simulation results showed that the proposed method is correct and effective ; the number of samples and the computational time are reduced significantly compared with those of direct Monte Carlo simulations.

关 键 词：首穿失效概率 重要样本法 平均上穿率 等效线性化 

分 类 号：O327[理学—一般力学与力学基础]