| 张峰,吕震宙,赵新攀.基于β面的截断重要抽样法[J].计算力学学报,2011,28(3):430~435 |
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| 基于β面的截断重要抽样法 |
| A novel β hyper-plane based importance sampling method |
| 投稿时间：2009-04-13 修订日期：2009-11-16 |
| DOI：10.7511/jslx201103022 |
| 中文关键词: 设计点 β截面 β面截断重要抽样法 失效概率 |
| 英文关键词:design point β hyper-plane β hyper-plane based importance sampling method failure probability |
| 基金项目:国家自然科学基金(50875213);航空基础基金(2007ZA53012);863计划课题(2007AA04Z401);西北工业大学基础研究基金(JC20100232)资助项目. |
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| 摘要点击次数: 1761 |
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| 中文摘要: |
| 提出一种基于β面的截断重要抽样法求解结构单失效模式的失效概率。该方法通过在设计点处作失效面的虚拟切面-β面,将变量空间分割成重要抽样区域R和非重要抽样区域S。在R和S区域分别建立相应的截断重要抽样密度函数hR(x)和hS(x),从hR(x)和hS(x)中抽取的样本量按照R和S区域对失效概率的贡献来分配,由迭代模拟计算得到。推导了基于β面截断重要抽样法的失效概率估计值的方差和变异系数计算公式,该方法还可推广应用到并联系统中。算例结果表明,在相同的计算精度下, 基于β面的截断重要抽样法所需的样本数比传统重要抽样法计算量少。 |
| 英文摘要: |
| A novel β hyper-plane based importance sampling method is presented to estimate failure probability of structure. Based on β section, a virtual hyper-plane tangent to the failure surface, the variable space is separated into the importance region R and the unimportance region S, on which the truncated importance sampling functions hR(x) and hS(x) are established respectively. The sampling numbers generated from hR(x) and hS(x) are dependent on the contributions of R and S to the failure probability, and they are determined by the iterative simulations. The formulae of the failure probability estimation, the variance and the coefficient of variation are derived for the presented β hyper-plane importance sampling method. The presented method is suitable for the failure probability estimation of both a single failure mode and multiple failure modes in parallel. The examples show that the presented method is more efficient than the traditional importance sampling method. |
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