Hybrid Analysis Method for Reliability-Based Design Optimization

Abstract

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the optimization process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the advanced mean value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the conjugate mean value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-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 the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the hybrid mean value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.

Possibility and Evidence-Based Reliability Analysis and Design Optimization

“…Recently, a multilevel-cut method has been developed to improve the accuracy of the vertex method for nonlinear structural design, but it is also very expensive to carry out PBDO. The PMA has been successfully applied with its advantages of numerical efficiency and stability in PBDO (Youn et al, 2003;Youn et al, 2004).…”

“…The Performance Measure Approach (PMA) is such a method satisfying the requirement, replacing the probabilistic constraint in Equation 53 with the performance measure under a specified reliability level Youn et al, 2003). Table 6.…”

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

“…When these works were published, design optimization with stochastic computational model was not still really possible for large scale multiscale computational models. The applications that have been published (see for instance [1,5,11,12,16,22,29] and also [35,54,57,68,70,72,80,99,96]) were devoted to optimization problems under uncertainties for which the computational models had a reasonable number of degrees of freedom, for which the optimizers were based on the use of relatively classical optimization algorithms and/or the introduction of approximations such as surface responses and surrogate models.…”

Recent methodologies for reliability-based design optimization

“…To overcome these difficulties, two points of view have been considered. From reliability view point, RBDO involves the evaluation of probabilistic constraints, which can be executed in two different ways: either using the Reliability Index Approach (RIA), or the Performance Measure Approach (PMA) (Tu et al [20]; Youn et al [22]). Recently, the enhanced hybrid mean value (HMV+) method is proposed by Youn et al [23], to improve numerical stability and efficiency in the Most Probable Point (MPP) search.…”