Adaptive single-loop reliability-based design optimization and post optimization using constraint boundary sampling

Abstract

The single-loop method (SLM) for reliability-based design optimization (RBDO) can be inaccurate when constraint functions are highly nonlinear because it uses gradient information calculated at the approximated most probable point (MPP) of the previous iteration. To overcome this limitation, this paper presents a new adaptive SLM (ASLM) that can automatically select the gradient at the approximate MPP of the previous iteration or the design point of the current iteration. If the design movement is large, the normalized gradient is calculated at the current design point, and the approximate MPP is calculated using the mean value method, and if small, the gradient is calculated at the approximate MPP of the previous iteration. In this study, a post optimization (PO) technique using constraint boundary sampling (CBS) is also proposed to improve the accuracy of ASLM. In the proposed method, ASLM is performed first, and then PO is applied to find a more accurate RBDO optimum using the Kriging model generated by samples accumulated during ASLM and sequentially added by CBS when the Kriging model is not accurate enough. Numerical studies show that the proposed ASLM is more efficient than the existing RBDO methods and the proposed PO improves its accuracy.