Low-cost finite element method-based reliability analysis using adjusted control variate technique

Reliability analysis is used to evaluate the safety of engineering structures subject to uncertainties. Finite element method (FEM) is a popular engineering tool used to evaluate the reliability of complex engineering structures. In general, FEM−based reliability analysis of engineering structures is influenced by the mesh density of the model and the accuracy of the results requires the use of a very fine mesh density in the analysis. However, it is often impractical for reliability analysis complex structures, especially those with low failure probabilities. Hence, a new method is proposed to address this issue, which provides an accurate estimate of the failure probability at low computational cost. In this method, the control variate technique is used in conjunction with the FEM-based reliability analysis, where the failure probability integral is broken down into two separate integral terms. The first term provides a low-cost estimate of the failure probability using a model with coarse mesh density, whereas the second term regulates the failure probability based on fewer finite element analyses with fine mesh density. The adjusted correction factors are also presented in this paper in order to improve the efficiency of the proposed approach. The proposed approach is used to estimate the reliability index of four engineering structures and the results show that the method is efficient and practical for FEM-based reliability analysis of engineering structures.