Line sampling method based on saddlepoint approximation for reliability analysis with non-normal random variables

For reliability analysis of non-linear limit state function with non-normal random variables, a novel line sampling method based on saddlepoint approximation (LS_SA) is presented. For the structural reliability problem with non-normal variables, traditional line sampling reliability analysis method requires the transformation from the original non-normal variable space into the equivalent standard normal space. This transformation is nonlinear, which tends to increase the nonlinearity of the performance function and difficulty of estimating the failure probability. The presented LS_SA method does not require this nonlinear transformation. By use of SA to estimate the probability distribution directly for the linear performance function with non-normal variables, and the traditional LS method expressing the failure probability of nonlinear performance function as the arithmetic average of a set of failure probabilities of the linear performance functions, the presented method can realize the high precision estimation of the failure probability of non-linear limit state function with non-normal variables. Before employing LS_SA method, the linear standardized transformation is needed to eliminate the dimensions of variables. The theoretical derivation verifies that the LS_SA method degenerates into traditional LS method when all the random variables are normally distributed. The results of the illustrations show that the presented method has higher precision than the direct SA for non-linear performance function reliability problem.