Reliability analysis of frame structures using radial basis function neural networks

Abstract

In this study, a hybrid reliability methodology via Monte Carlo simulation techniques with radial basis function neural network (RBFNN) is presented. Monte Carlo simulation is a powerful tool, simple to implement, and capable of solving a broad range of reliability problems. However, its use for the evaluation of very low probabilities of failure implies a great number of analyses, and the computational time highly increases. In practice, the size of a design problem can be very large and the limit state functions (LSFs) are usually implicit in terms of the random variables. A hybrid method consisting of Monte Carlo simulation and RBFNN is proposed in the present study to approximate the LSF or failure function of the structure. Therefore, the computational burden of Monte Carlo simulation decreases significantly. A distinctive feature of this method is the introduction of an explicit approximate LSF. Using the parameters of the RBFNN, the explicit formulation of the LSF is derived. By introducing the derived approximate LSF, the failure probability can be easily estimated. In order to assess the effectiveness of the proposed methodology, some illustrative examples including frame structures are considered, and the numerical results are verified.