A framework for structural reliability analysis based on conjugate sensitivity factor and saddlepoint approximation

A new structural reliability analysis framework is developed to extend the performance of first-order reliability method, which is low robustness and poor accuracy when dealing with highly nonlinear functions. Initially, an improved conjugate sensitivity factor method is proposed to find the most probable point. The method enhances its robustness of convergence by introducing a conjugate gradient direction based sensitivity factor technique and improves its computational efficiency by putting forward a hybrid conjugate gradient factor and an adaptive step length strategy. Subsequently, the dimension reduction-based saddlepoint approximation method is developed, which uses the dimension reduction approach to construct the limit state function as the additive univariate quadratic functions and applies saddlepoint approximation to obtain the result with higher precision. A comparison analysis from five mathematical and structural examples illustrates that the proposed method is better than most existing methods in terms of robustness, efficiency and accuracy for estimating the failure probability of structures.