A sequential single-loop reliability optimization and confidence analysis method

Abstract

In practical engineering problems, it is frequently challenging to collect sufficient data to construct high-precision probabilistic models. In this case, probabilistic models typically contain cognitive uncertainty and may be biased. Confidence-based design optimization (CBDO) is an effective tool for solving optimization problems with insufficient input data. Therein, epistemic uncertainty is taken into account, and its propagation is quantified by the confidence level of reliability. However, the coupling of reliability analysis and confidence analysis (CA) results in low calculation accuracy and an unacceptable rise in computational cost. To improve the performance of CBDO, a sequential single-loop reliability optimization and confidence analysis method (SROCA) is proposed in this paper. Specifically, a decoupling strategy with a serial of cycles of complete single-loop method (CSLM) and CA is established. In each cycle, CSLM and CA are decoupled from each other. Therein, the CSLM integrates both the reliability and confidence constraints into the deterministic optimization loop, and the performance functions are not required to be evaluated in CA due to the application of a semi-analytic sensitivity method. Additionally, update strategies for both the reliability and confidence indexes are employed to neutralize the linear approximation errors based on the dimension reduction method. Finally, four mathematical and one engineering example are adopted to demonstrate the performance of the proposed SROCA. The results show that the efficiency and accuracy of implementing CBDO achieve significant improvement by the proposed method.