随机变量和非独立区间变量下的可靠性序列迭代算法

针对机械系统中输入变量存在随机变量和区间变量混合的情况，考虑区间变量的非独立性，提出高效混合可靠性分析方法。区间变量使可靠性分析问题变为双层优化问题。为降低双层优化和非独立区间变量对可靠性计算效率的影响，提出了高效序列迭代计算策略，基于椭球模型描述的非独立区间变量，提出将非独立区间变量转换为独立区间变量的方法，并利用二次泰勒近似方法，将区间分析问题转换为易求解的二次规划问题。算例结果表明，所提出的可靠性序列迭代算法具有较高的计算效率和精度；可靠性分析结果受区间变量独立性假设的影响，区间变量独立可导致较保守的可靠性分析结果。

A Sequential Iteration Algorithm for Reliability Analysis with Random and Dependent Interval Variables

Focusing on  the  mixed conditions  of both random  variables and dependent interval variables,an efficient hybrid reliability analysis method was   proposed.Interval variables made the reliability analysis problem become  a  double-loop  optimization problem.In order to reduce the impacts  on the reliability analysis  efficiency by the double-loop optimization and dependent interval variables,   an efficient  sequentially iterative strategy was  proposed,and   a   formula  to  transform the dependent interval variables modelled by  ellipsoid model  was  developed  into independent interval variables,and   the limit-state  function  was  approximated  during the inner loop in the second order form to make the optimization  problem become a more solvable quadratic programming problem.The results show that the proposed sequential iteration algorithm has good efficiency and   accuracy, and that the reliability analysis results are affected by the assumption of dependence between interval variables; results under the assumption of independence between interval variables can be  more conservative than that of  dependence.