基于阈值因子的结构可靠性解耦优化方法

A decoupling method of structural reliability optimization based on threshold factor

基于结构可靠性理论,引入阈值因子的概念,其物理意义为当前最优解满足可靠性约束需将阈值增减的幅度。随着迭代的进行,对于有效约束,阈值因子收敛于1,能够使得最可能失效点快速向满足可靠性约束的极限状态曲面靠拢,优化效率得以提升。解耦模型中,优化变量可为随机变量也可为非随机变量,当优化变量为随机变量时,采取优化变量拆解方式进行计算。数值算例表明,本文方法对优化变量拆解方式不敏感,对有效约束和非有效约束均能够获得满意的优化结果,且计算效率明显高于经典方法。

A concept of threshold factor is introduced based on the theory of structural reliability in this study.Its physical meaning is the magnitude of the threshold that must be adjusted so that the current optimal solution can satisfy the reliability constraints.The threshold factor approaches 1 for the active constraint with the progress of iterations,which can shift the most possible failure point to the limit state surface that satisfies the reliability constraints,and thus the optimization efficiency is improved.In the proposed method,the design variables can be random variables or non-random variables,and the decomposition method of design variables is used to solve the optimization model when design variables are random variables.Numerical results indicate that the proposed method is not sensitive to the decomposition method,satisfactory results can be obtained for both active and inactive constraints,and the computational efficiency of the proposed method is higher than that of the classical method.