Sequential optimization and moment-based method for efficient probabilistic design

To increase the range of applicability of decoupling strategies for reliability-based design optimization (RBDO), a sequential optimization and moment-based reliability assessment (SOMRA) is proposed. In this approach, a moment method based on the univariate dimension reduction method (UDRM) and probability density function (PDF) estimation is employed. Meanwhile, a corresponding mathematical model and a PDF-based method of calculating the shifting scalar are developed to decouple the reliability assessment from the optimization process. The shifting scalar is corrected according to the nonlinear degree of the limit state surface of the performance function before reconstructing the mathematical model for the next iteration of optimization. This approach uses statistical moments to check whether the constraints are active, and rather than assessing the reliability and calculating the shifting scalars for all constraints, only the active constraints are considered for the PDF estimation and shifting scalar calculation. Three numerical examples and an automobile crashworthiness lightweight design problem are presented to demonstrate the effectiveness of the proposed method.

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