A new approach for solving inverse reliability problems with implicit response functions

Abstract

The inverse first-order reliability method (FORM) is one of the most widely used methods in inverse reliability analysis. However, this method has two drawbacks in the solution of inverse reliability problems with implicit response functions. First, it requires the evaluation of the derivatives of the response functions with respect to the random variables. When these functions are implicit functions of the random variables, derivatives of these response functions are not readily available. Second, it usually involves repeated deterministic response analyses of complicated structures due to the variation of the basic variables, and therefore requires a relatively long computation time. To overcome these drawbacks of the inverse FORM, an artificial neural network (ANN)-based inverse FORM is proposed in this paper. In this method, an ANN model is used to approximate the structural response function so that the number of deterministic response analyses can be dramatically reduced. The explicit formulation of structural response is derived by using the parameters of the ANN model. After the explicit response function is determined, the inverse FORM is applied to solve the inverse reliability problem. The accuracy and efficiency of the proposed method is demonstrated through two numerical examples. Some important parameters in the proposed method are also discussed.