动力可靠度约束下基于概率测度变换-全局收敛移动渐近线法的结构优化设计

Structural optimization under dynamic reliability constraints by synthesizing change of probability measure and globally convergent method of moving asymptotes

基于动力可靠度的结构优化是实现随机动力系统优化设计的重要途径。针对设计变量为系统中部分随机变量分布均值的情形,提出了一种基于动力可靠度的结构优化设计方法。在该方法中,通过概率密度演化理论实现了结构动力可靠度的高效分析。在此基础上,结合概率测度变换,可以在不增加任何确定性结构分析的前提下,实现动力可靠度对设计变量的灵敏度分析。进而,通过将上述概率密度演化-测度变换方法嵌入全局收敛移动渐近线法,实现了基于动力可靠度的结构优化设计问题的高效求解。数值算例的结果表明,所提方法可以显著降低结构分析次数,具有较高的效率与稳健性。

Dynamic-reliability-based design optimization is a reasonable framework for the optimization of stochastic dynamical systems.In the present paper,a method is proposed for solving dynamic-reliability-based design optimization problems where design variables are considered as the mean values of the probability density functions of part of the random variables involved in the system.In this method,the reliability of stochastic dynamical system is evaluated efficiently by the probability density evolution method(PDEM).Then,by performing the changes of probability measure(COM),the sensitivity of the dynamic reliability with respect to design variables can be efficiently estimated without any additional structural analysis.By incorporating the PDEM-COM synthesized method into a globally convergent version of the method of moving asymptote,dynamic-reliability-based design optimization problems can be solved efficiently.The effectiveness of the proposed method is verified by two numerical examples.The results of the numerical examples indicate that the proposed method is efficient and robust.