Hybrid Analysis Method for Reliability-Based Design

Reliability-based design optimization (RBDO) involves evaluation of probabilistic con-straints, which can be done in two different ways, the reliability index approach (RIA) andthe performance measure approach (PMA). It has been reported in the literature that RIAyields instability for some problems but PMA is robust and efficient in identifying aprobabilistic failure mode in the optimization process. However, several examples ofnumerical tests of PMA have also shown instability and inefficiency in the RBDO processif the advanced mean value (AMV) method, which is a numerical tool for probabilisticconstraint evaluation in PMA, is used, since it behaves poorly for a concave performancefunction, even though it is effective for a convex performance function. To overcomedifficulties of the AMV method, the conjugate mean value (CMV) method is proposed inthis paper for the concave performance function in PMA. However, since the CMV methodexhibits the slow rate of convergence for the convex function, it is selectively used forconcave-type constraints. That is, once the type of the performance function is identified,either the AMV method or the CMV method can be adaptively used for PMA during theRBDO iteration to evaluate probabilistic constraints effectively. This is referred to as thehybrid mean value (HMV) method. The enhanced PMA with the HMV method is com-pared to RIA for effective evaluation of probabilistic constraints in the RBDO process. Itis shown that PMA with a spherical equality constraint is easier to solve than RIA with acomplicated equality constraint in estimating the probabilistic constraint in the RBDOprocess. @DOI: 10.1115/1.1561042#