基于重要样本法的结构动力学系统的首次穿越

任丽梅; 徐伟; 肖玉柱; 王文杰

doi:10.6052/0459-1879-2012-3-20120324

基于重要样本法的结构动力学系统的首次穿越

1.
西北工业大学理学院, 西安 710072
2. 长安大学理学院, 西安 710064

基金项目: 国家自然科学基金资助项目(10872165, 10932009, 11172233).

详细信息

中图分类号: O324
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出版历程
- 收稿日期: 2011-10-18
- 修回日期: 2011-12-27
- 刊出日期: 2012-05-17

FIRST EXCURSION PROBABILITIES OF DYNAMICAL SYSTEMS BY IMPORTANCE SAMPLING

1.
Collegeof Science Northwestern Polytechnical University, Xi'an 710072, China
2. College of Science Chang'an University, Xi'an 710064, China

Funds: The project was supported by the National Natural Science Foundation of China (10872165,10932009,11172233)

摘要

摘要: 基于Gisranov定理, 提出一种估计稳态高斯白噪声激励的结构动力学系统首穿失效概率的重要样本法. 文章重点是构造控制函数, 控制函数促使随机响应尽量集中在样本空间中最易导致首次穿越发生的部分. 利用设计点构造控制函数, 在线性系统场合, 结合时不变系统的结构可靠性理论, 通过解有约束的优化问题得到设计点; 在非线性系统场合, 利用Heonsang Koo提出的设计点激励, 通过镜像法得到设计点. 最后给出例子, 将所提方法与原始蒙特卡罗法相比较, 模拟结果显示方法的正确性与有效性.
- 首穿失效概率 /
- 重要抽样法 /
- 设计点激励 /
- 镜像法
Abstract: Based on the Girsanov transformation, this paper develops a method for estimating the first excursion probability of dynamical systems with stationary gauss white noise. The focus is to construct control function that concentrates on the samples paths in the “most important part” of the sample space, to achieve the purpose of variance reduction. The paper uses design point to construct control function. For linear systems, the present approach combines with the time-invariant structure reliability theory to get design points by solving the problem of the optimization. For non-linear systems, the paper uses mirror-images method to get design points. Finally the paper gives two examples. The results show the method of this paper to be correct and effective by comparing with the primitive Monte Carlo method.
- first excursion probability /
- importance sampling /
- design-point excitation /
- mirror-image method

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参考文献(18)

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