A PDF-based performance shift approach for reliability-based design optimization

Abstract A probability density function (PDF)-based performance shift approach (PPSA) is proposed for sequential reliability-based design optimization (RBDO) in this paper, which provides an effective tool for complex engineering design with consideration of uncertainties associated with design variables and simulation models. It converts the double-loop probabilistic optimization into a serial of cycles of reliability assessment and deterministic optimization through a performance shift strategy. The approach further proceeds by calculating the performance shift scalar and then solving a deterministic design optimization at each cycle, and eventually converges to the optimum design solution. The novelty of the proposed approach lies in two main aspects. First, the shift scalar is deducted for each probabilistic constraint in the response space, rather than in the design variable space, through which the violated constraints are moved towards the reliable region and the design solutions are improved progressively. Second, reliability analysis methods that calculate the moments or probability density functions, rather than most probable points or reliability indexes, are able to be integrated in the sequential RBDO framework, through which we could enhance the performance of existing sequential RBDO methods, especially the computational efficiency. Three numerical examples are investigated to demonstrate the effectiveness of the proposed approach, and the proposed approach is further utilized to perform crashworthiness design of a vehicle side impact problem.