非独立区间变量和随机变量下的单步可靠性计算方法

摘要/Abstract

摘要： 随机变量和非独立区间变量往往共存,两种变量共存不仅导致出现双层优化问题,而且会降低可靠性的计算效率。为解决双层优化问题和提高可靠性计算效率,基于椭球模型描述的非独立区间变量,利用高维模型表示方法（HDMR）解耦随机变量和非独立区间变量,转换双层优化问题为简单的单步求解问题,基于提出的采样方法,利用二次多项式近似HDMR展式,将隐式的单步求解问题转化为显式问题,提出了一种混合型单步可靠性计算方法。算例结果表明,所提出的单步可靠性计算方法具有较高的计算效率和精度;该方法仅需少量的极限状态函数调用次数,即可获得较高精度的计算结果。

关键词: 椭球模型, 非独立区间变量, 高维模型表示方法, 快速可靠性方法

Abstract: Random variables and dependent interval variables often coexisted, and this made the reliability analysis problem into a double-loop optimization problem and reduces the efficiency of the reliability analysis. So an one-step reliability analysis method was proposed. Specifically, the double-loop optimization problem where the dependent interval variables were modelled by the ellipsoid model, was decoupled into a simple one-step problem by using the HDMR. Based on the proposed sampling strategy, a quadratic polynomial was applied to approximate each of the HDMR expression, making the implicit one-step problem into the explicit one. The example results show that the proposed method has good efficiency and accuracy, and may calculate the reliability results with good accuracy at a little cost of calling the origin limit-state function.

Key words: ellipsoid model, dependent interval variable, high dimensional model representation(HDMR), rapid reliability analysis method

中图分类号:

TH122

潘柏松, 谢少军, 蒋立正. 非独立区间变量和随机变量下的单步可靠性计算方法[J]. 中国机械工程.

Pan Baisong, Xie Shaojun, Jiang Lizheng. An One-step Reliability Analysis Method with Random and Dependent Interval Variables[J]. China Mechanical Engineering.

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