A new hybrid inverse reliability method for searching MPTP and its application in reliability-based design optimization

Reliability-based Design Optimization (RBDO) is a nested optimization approach. This paper emphasizes the importance of improving computational efficiency by reducing the number of evaluations of the performance function, which is the bottleneck for practical engineering applications. Aim at this issue, the paper proposes to reduce the function evaluation number caused by gradient calculations as the important direction for improving RBDO's efficiency, as it takes up the majority of the total evaluation number of RBDO. Within the above important direction, the paper introduces a new hybrid inverse reliability method for searching the minimum performance target point (MPTP). It integrates the traditional Advanced Mean Value (AMV) with an innovative MPTP-searching approach, where the new format of gradient computation is dependent on one variable other than muliti-ones. This can effectively eliminate a drawback of conventional gradient computation, whose evaluation number is influenced by the dimensionality of random variables. Furthermore, its operational simplicity is highlighted by the absence of chaos control factors, making it more convenient for real engineering applications compared to methods like Chaos Control (CC) or Modified Chaos Control (MCC). Lastly, the numerical examples are investigated to validate the accuracy and efficiency of the proposed method.