Discussion of Mathematical Models of Probabilistic Constraints Calculation in Reliability-Based Design Optimization
In a reliability-based design optimization (RBDO) problem, most of the computations are used for probabilistic constraints assessment, i.e., reliability analysis. Therefore, the effectiveness, especially the correctness of the reliability analysis is very important. If the probabilistic constraint is misjudged, the optimization iteration would have convergence problems or arrive at erratic solutions. The probabilistic constraint assessment can be carried out using either the conventional reliability index approach (RIA) or the performance measure approach (PMA). In this paper, the mathematical models to calculate the reliability index in RIA and to calculate the probabilistic performance measure (PPM) in PMA are discussed. In RIA, through estimating whether the mean-value point in safe domain or not, we should use a positive or negative reliability index respectively. In PMA, one should always minimize the performance measure to compute PPM whether the performance measure at the mean-value point is positive or negative, which puts right the wrong mathematical model in some literatures and makes it possible to produce effective and efficient approach for RBDO.
Chaohe Chen, Yong Huang and Guangfan Li
P. Yi "Discussion of Mathematical Models of Probabilistic Constraints Calculation in Reliability-Based Design Optimization", Advanced Materials Research, Vols. 243-249, pp. 5717-5726, 2011