Fast convergence reliability-based design optimization method considering random and evidence variables

Abstract

[Abstract:] An efficient approximate reliability-based design optimization method under both aleatory and epistemic uncertainty is presented. As stated by the unified uncertainty analysis based on the first-order reliability method (FORM-UUA), it is possible to merge the probability and evidence theory to quantify the belief and plausibility of a specific performance function under mixed uncertainty. When the number of evidence variables and the number of intervals increase, the number of evaluations grows dramatically. As a result, if the hybrid reliability analysis is included in an optimization problem, usually referred to as nested hybrid reliability-based design optimization (HRBDO), it becomes unmanageable due to its high computational cost. The strategy proposed allows to avoid the computation of the subplausibilities for each focal element as required in the FORM-UUA. This strategy decouples the nested HRBDO into an iterative process with a deterministic optimization and a reliability analysis phase consisting of two separate but connected reliability analyses that handle separately the random and evidence variables. Then, the optimum design obtained is checked and adjusted through the FORM-UUA method. One analytical and one numerical problem are presented to validate the proposed method.