A Comparison of Response Surface Methods for Reliability Analysis using Directional Simulation

摘要

Complex systems, such as those found in aerospace engineering are often subject to a large number of uncertainties. By taking such uncertainties into account, engineers can design more reliable systems while also reducing conservatism in the design, leading to reduced costs and increased performance. However accurately and efficiently estimating the probability of failure of such systems remains a difficult task because the analysis of such systems is computationally expensive. This paper explores and extends the application of a recently-proposed method, the Adaptive Directional Importance Sampling (ADIS) method, for the estimation of probabilities of failure. The performance of linear and quadratic polynomial, Gaussian process, and artificial neural network response surfaces for both the limit state function and the distance to the limit state are compared for a variety of problems within the ADIS framework, including a realistic multiphysics supersonic nozzle application with up to 40 random variables. Our exploration reveals some of the difficulties encountered in using the ADIS algorithm but also shows that in certain cases probabilities of failure around 10~(-5) can be estimated efficiently with ~ 100 exact function evaluations.