Post optimization for accurate and efficient reliability-based design optimization using second-order reliability method based on importance sampling and its stochastic sensitivity analysis

In this study, a post optimization technique for a correction of inaccurate optimum obtained using first-order reliability method (FORM) is proposed for accurate reliability-based design optimization (RBDO). In the proposed method, RBDO using FORM is first performed, and then the proposed second-order reliability method (SORM) is performed at the optimum obtained using FORM for more accurate reliability assessment and its sensitivity analysis. In the proposed SORM, the Hessian of a performance function is approximated by reusing derivatives information accumulated during previous RBDO iterations using FORM, indicating that additional functional evaluations are not required in the proposed SORM. The proposed SORM calculates a probability of failure and its first-order and second-order stochastic sensitivity by applying the importance sampling to a complete second-order Taylor series of the performance function. The proposed post optimization constructs a second-order Taylor expansion of the probability of failure using results of the proposed SORM. Because the constructed Taylor expansion is based on the reliability method more accurate than FORM, the corrected optimum using this Taylor expansion can satisfy the target reliability more accurately. In this way, the proposed method simultaneously achieves both efficiency of FORM and accuracy of SORM. Copyright (c) 2015 John Wiley & Sons, Ltd.