A New Study on Reliability-Based Design Optimization

Abstract

This paper presents a general approach for the probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields singularity in some cases.

Enhanced sequential optimization and reliability assessment method for probabilistic optimization with varying design variance

“…R. The percentile performance g R is the value of the limit state function g that makes the integration area under the probabilistic distribution function of g for g ! g R exactly equal to the required reliability R. The concept of using percentile performance for feasibility assessment is identical to that used in the Performance Measure Approach (PMA) (Tu et al 1999). The original probabilistic constraint is written in the equivalent R-percentile formulation as…”

“…The SORA method decouples the probabilistic optimization problem in the form of a serial of sequential Deterministic Optimization (DO) followed by Reliability Assessments (RA). The SORA method achieves high efficiency by taking the following measures: the use of R-percentile formulation (Inverse Most Probable Point -IMPP concept) to evaluate constraint satisfaction only up to the required reliability level (R) (Tu et al 1999); the use of an efficient and robust IMPP search algorithm for reliability assessment (Du and Chen 2001); and the employment of a shifting vector for estimating IMPP in the DO formulation of a new cycle. Because the IMPP estimation of a new cycle is always based on the exact IMPP from the previous cycle, the method improves the accuracy in IMPP estimation, which is especially useful when there are multiple, local optimal solutions to IMPPs.…”

Iterative Kriging-Based Methods for Expensive Black-Box Models

“…DLM like Performance Measure Approach (PMA) [9] has a nested structure: The outer loop seeks for the optimum and the inner loop searches the Most Performance Target Point (MPTP) that maximize the constraint subject to a given reliability index.…”

Recent methodologies for reliability-based design optimization

“…The computational cost of this combined approach is higher than that of the nested RBDO model, i.e., it requires about 50% more computational effort to converge as compared with the classical RBDO approach. Der Kiureghian and Polak [1] and Tu et al [20] proposed several forms in order to satisfy the constraints and simplify the problem.…”

“…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.…”