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Performance measure approach of probability constraints assessment and its MATLAB achivement

LIU Zhen,YI Ping,ZHAO Xiuli(Faculty of Infrastructure Engineering,Dalian University of Technology,Dalian 116023,China)  
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.
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