Structural Reliability Analysis for Implicit Performance with Legendre Orthogonal Neural Network Method

In order to evaluate the failure probability of a complicated structure, the structural responses usually need to be estimated by some numerical analysis methods such as finite element method (FEM). The response surface method (RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However, the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network (LONN)-based RSM to estimate the structural reliability. In this method, the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method, i.e. first-order reliability methods (FORM) to calculate the failure probability of the structure. Numerical examples show that the proposed approach is applicable to structural reliability analysis, as well as the structure with implicit performance functions.