| 张凯,李刚.基于改进降维法的可靠度分析[J].计算力学学报,2011,28(2):187~192 |
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| 基于改进降维法的可靠度分析 |
| Reliability analysis based on the improved dimension reduction method |
| 投稿时间：2009-10-09 修订日期：2010-05-05 |
| DOI：10.7511/jslx201102006 |
| 中文关键词: 可靠度 降维法 基于矩的积分法 Pearson系统 |
| 英文关键词:reliability dimension reduction method Moment Based Quadrature Rule (MBQR) pearson system |
| 基金项目:973计划课题(2006CB705403);国家自然科学基金(90815023 和10721062)资助项目. |
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| 中文摘要: |
| 单变量维数缩减法可以高效、准确地进行结构响应矩的分析。与传统的一阶可靠度算法FORM (First Order Reliability Method),二阶可靠度算法SORM (Second Order Reliability Method)相比,该方法不需要响应的导数,也不需要迭代搜索最可能失效点。然而近期的研究发现,该方法中基于矩的积分方法MBQR(Moment Based Quadrature Rule)在积分点增加之后求解线性方程组时,会出现系数矩阵的奇异性并导致数值结果不稳定,从而影响了该方法的效率和精度。提出了归一化的基于矩的积分方法,有效地解决了数值求解过程中的不稳定问题。利用降维法求解结构响应统计矩,并通过Pearson系统计算响应的概率密度函数,从而获得失效概率。算例表明了本文方法的计算效率和精度。 |
| 英文摘要: |
| The Univariate Dimension Reduction Method (DRM) can be used to calculate the moments of response efficiently and accurately. Compared to the FORM (First Order Reliability Method) and SORM (Second Order Reliability Method), the DRM does not need the derivative of the response and the iteration searching for the MMP. However, in some recent researches, the Moment Based Quadrature Rule (MBQR) in the DRM was found to be numerically instable when solving a system of linear equations after increasing the integration points. A Normalized Moment Based Quadrature Rule (IMBQR) is proposed to solve this problem and the Pearson system is taken to generate the probability density function (PDF) of the response. The failure probability is calculated with the PDF obtained by Pearson system. Numerical examples demonstrate the accuracy and efficiency of the proposed approach. |
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