The reliability sensitivity analysis based on saddlepoint approximation and its improved method

The saddlepoint approximation (SA) can directly estimate probability distribution of linear performance function in non-normal variables space and then calculate the failure probability of structure. Based on the property of SA, SA based reliability sensitivity analysis method is developed. For the nonlinear performance function, SA method needs the linearization of performance function firstly, but they neglect the influence of nonlinearity of performance function on the failure probability. So the reliability sensitivity analysis method based its improved method, named as SA based line sampling (LS), is presented. The reliability sensitivity can be estimated by the average of these partial derivatives of failure probabilities with respect to the distribution parameter of random variables, and the probabilities and sensitivities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn, (1) SA based reliability sensitivity method is only acceptable for the linear performance function. The error mostly results from the linearization of the performance functions. (2) The SA based LS method can obtain the estimators of failure probability and reliability sensitivity, which converge to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of performance function on the failure probability and reliability sensitivity; therefore it has the wide applicability.