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Mean-Value Second-Order Saddlepoint Approximation for Reliability Analysis
ISSN: 1946-391X, e-ISSN: 1946-3928
Published March 28, 2017 by SAE International in United States
Citation: Papadimitriou, D. and Mourelatos, Z., "Mean-Value Second-Order Saddlepoint Approximation for Reliability Analysis," SAE Int. J. Commer. Veh. 10(1):73-80, 2017, https://doi.org/10.4271/2017-01-0207.
A new second-order Saddlepoint Approximation (SA) method for structural reliability analysis is introduced. The Mean-value Second-order Saddlepoint Approximation (MVSOSA) is presented as an extension to the Mean-value First-order Saddlepoint Approximation (MVFOSA). The proposed method is based on a second-order Taylor expansion of the limit state function around the mean value of the input random variables. It requires not only the first but also the second-order sensitivity derivatives of the limit state function. If sensitivity analysis must be avoided because of computational cost, a quadrature integration approach, based on sparse grids, is also presented and linked to the saddlepoint approximation (SGSA - Sparse Grid Saddlepoint Approximation). The SGSA method is compared with the first and second-order SA methods in terms of accuracy and efficiency. The proposed MVSOSA and SGSA methods are used in the reliability analysis of two examples.