Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions

TLDR

Engineering systems often involve expensive, nonlinear implicit response functions, complicating reliability analysis. The study proposes an efficient method to accurately characterize the limit state across the random variable space. The method builds a Gaussian process surrogate from few samples, adaptively refines it near the limit state, and then uses multimodal adaptive importance sampling to estimate failure probability, enabling accurate modeling of complex, nonlinear limit states with few true evaluations. The resulting method is accurate for arbitrarily shaped limit states and computationally efficient even for expensive response functions, as demonstrated on example problems including a challenging microelectromechanical system device.

Abstract

Many engineering applications are characterized by implicit response functions that are expensive to evaluate and sometimes nonlinear in their behavior, making reliability analysis difficult. This paper develops an efficient reliability analysis method that accurately characterizes the limit state throughout the random variable space. The method begins with a Gaussian process model built from a very small number of samples, and then adaptively chooses where to generate subsequent samples to ensure that the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex and nonlinear limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e., in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally efficient even for expensive response functions. This new method is applied to a collection of example problems including one that analyzes the reliability of a microelectromechanical system device that current available methods have difficulty solving either accurately or efficiently.