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

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 mod-el,was decoupled into a simple one-step problem by using the HDMR.Based on the proposed sam-pling 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 pro-posed method has good efficiency and accuracy,and may calculate the reliability results with good ac-curacy at a little cost of calling the origin limit-state function.%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 H DMR 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。