概率约束评估的功能度量法及其MATLAB实现

Performance measure approach of probability constraints assessment and its MATLAB achivement

基于可靠性的结构优化通常表述为在概率约束下最小化目标函数,其中概率约束的评定可以通过两种方法进行——传统的可靠指标法和最近被提出的功能度量法。本文简单介绍了功能度量法,明确概率功能度量的求解表述为许可可靠指标下功能函数极小值的优化问题。然后利用MATLAB强大的优化功能求解该优化模型,从而得到概率功能度量。最后给出算例,证明了可靠指标法与功能度量法在评价概率约束时的等效性,同时验证了功能度量法比可靠指标法更稳定,较少依赖于随机变量的概率分布类型。可靠指标求解的正确性都用Monte-Carlo模拟进行了验证。

In reliability-based structural optimization,the uncertainties are typically captured as probabilistic constraints. The evaluation of probabilistic constraints can be carried out in two ways. One is the conventional reliability index approach （RIA） and the other is the more recently proposed performance measure approach （PMA）. In this paper, we introduce PMA briefly and clarify the mathematical optimal model of probabilistic constraints calculation in PMA. That is one should always minimize the performance measure to compute the probabilistic performance measure （PPM）. Then,the procedure of calculating PPM using MATLAB optimizing tool is described in detail. Finally, five examples verify the consistence of PMA and RIA in the sense of evaluation of probabilistic constraints and show that PMA is more efficient, stable, and less dependent on probabilistic distribution types than RIA. The correctness of reliability indexes calculation is always verified by Monte-Carlo simulation.