Abstract: Based on the weighted linear response surface (WLRS) method, an artificial neural network (ANN) method is presented to analyze the reliability of the implicit limit state equation. The formulation of the WLRS is very simple, and it is easy to be implemented. The important advantage of WLRS is the design point of the implicit limit state equation can be approximated very well. The disadvantage of WLRS is its inapplicability to the non-linear implicit state equation. Hence, WLRS in conjunction with the ANN is presented to analyze the reliability of the non-linear limit state equation, where the approximation to design point is guaranteed by WLRS and the approximation to non-linear limit state equation in vicinity of the design point is guaranteed by ANN. By use of the presented method to analyze the reliability, the computational effort is increased little in comparing with the WLRS, but the computational precision is significantly increased for the non-linear limit state equation, which is illustrated by the given examples.

Key words: response surface method, reliability, failure probability, implicit limit state equation, artificial neural network