Incremental shifting vector and mixed uncertainty analysis method for reliability-based design optimization

Reliability-based design optimization (RBDO) is a powerful tool for addressing design problems involving variables with uncertainty characteristics. In practical engineering problems, there may not be sufficient information to build probabilistic distribution models for some crucial parameters. Evidence theory has emerged to deal with inaccuracies of parameters that lack information or knowledge. In this study, the incremental shifting vector and mixed uncertainty analysis method (ISVMUA) is proposed to improve the efficiency in dealing with RBDO problems with both aleatory and epistemic uncertainties based on probability and evidence theory. Higher efficiency is achieved in ISVMUA using the following strategies: (1) the result of the mixed uncertainty analysis is directly employed to update the deterministic optimization formulation by the incremental shifting vector; (2) a new allocation strategy is proposed to reasonably decompose the total target failure probability into all the focal elements of the epistemic uncertainties; and (3) a strategy of feasibility checking is employed to identify the inactive constraints among all the quasi-equivalent probabilistic constraints to simplify the deterministic optimization problem. Four examples are investigated to demonstrate the effectiveness and efficiency of the proposed method.