A new chance reliability-based design optimization approach considering aleatory and epistemic uncertainties

Aleatory and epistemic uncertainties, which coexist widely in the preliminary design phase of engineering structures, should be appropriately controlled for safety purposes. A methodology of hybrid reliability analysis and optimization based on chance theory is proposed in this paper. Random variables are adopted to describe aleatory uncertainty with sufficient statistical data. On the other hand, uncertain variables are used to quantify epistemic uncertainty with objective limited information or subjective expert opinions. More specifically, a metric termed chance measure is introduced to formulate a chance reliability indicator (CRI) for modeling structural reliability in the presence of hybrid uncertainty. Then, two CRI estimation methods denoted as crisp equivalent model and uncertain random simulation (URS) methods, are developed for the mixed reliability assessment. Furthermore, an efficient CRI-based design optimization (CRBDO) model is established under prescribed chance reliability constraints. Two solving strategies, including crisp mathematical programming and URS combined with genetic algorithm strategies, are presented to solve the CRBDO model and obtain optimal results. Finally, the performance of the constructed analysis model, as well as the feasibility of the corresponding solution technique, is verified by four engineering applications.