First order control variates algorithm for reliability analysis of engineering structures

Abstract

• Indicator of linearized limit state function served as control variates of original indicator. • First order failure probability regulated by control variates technique using few samples. • 50 benchmark reliability problems gathered and solved by proposed method. • Accuracy close to simulations and efficiency close to first order reliability method . • Method is suitable for nonlinear/high-dimensional problems with small probability. This study introduces an efficient method for safety evaluation of the structures with small failure probability. The proposed approach reformulates basic failure probability formula based on control variates method and suggests to firstly substitute the nonlinear limit state function with a linear limit state function for taking the advantages of linear problems during reliability process. Reliability analysis of linear problems would be fully accurate and dimension insensitive. Subsequently, the control variates method imposes the effect of limit state function nonlinearity on the obtained first-order failure probability by using a very small sampling size simulation. The result is a new reliability formulation that is highly suitable for solving nonlinear and high dimension problems. The capabilities of the method examined by solving several benchmarks numerical/engineering problems involving non-normal random variables, complex/noisy limit state functions, and nonlinear high dimension problems. Compared with mainstream reliability methods, for all solved problems, it is demonstrated that the proposed approach presents accuracy close to Monte Carlo simulation while the required number of performance function valuation is close to first-order reliability method.