A new reliability-based design optimization (RBDO) approach is proposed based on saddlepoint approximation. An extension of the existing first-order saddlepoint approximation is proposed using a second-order Taylor expansion of the limit state function. This expansion utilizes curvature information from the Hessian matrix, resulting in a more accurate prediction of the probability of failure. The expansion is performed at the mean values of the random parameters increasing the efficiency of the so-called mean-value second-order saddlepoint approximation (MVSOSA) method. To improve computational efficiency, the implementation of MVSOSA in RBDO, estimates the exact Hessian matrix only at selected optimization cycles, based on how much the design changes from the previous iteration. The methodology is first demonstrated using two mathematical examples, and then applied to the reliability-based design optimization of two beams, minimizing their weight under probabilistic constraints. It is demonstrated that the proposed RBDO-MVSOSA method is more efficient than other methods in the literature, maintaining high-accuracy in estimating the probability of failure.
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