Efficient Surrogate Modeling for Reliability Analysis and Design

Abstract

Reliability analysis is critically important to a wide array of engineering fields that increasingly depend on computational models to predict system performance. However, previously available methods for performing this analysis either 1) require these models to be evaluated a large number of times leading to computational costs that are often unaffordable when the model is computationally expensive, or 2) provide potentially inaccurate reliability estimates due to simplifying approximations that reduce the cost of the analysis. Surrogate models can provide a practical alternative by replacing the computationally expensive model with one that is much less expensive to evaluate. This dissertation develops an efficient method for constructing Gaussian process surrogate models, specifically tailored for their use in reliability analysis, while simultaneously ensuring that the resulting surrogate is an accurate representation of the original computational model that it is intended to replace. This combination of efficiency and accuracy is achieved by using the uncertainty structure of Gaussian process models to guide the selection of training points, focusing them only in the region where accuracy is required, and only converging when the uncertainty in that region is sufficiently reduced. The resulting model is then used in a sampling-based reliability analysis method to provide accurate reliability estimates at a small fraction of the cost previously required to achieve this level of accuracy. This new method, named Efficient Global Reliability Analysis, was applied to a variety of test problems involving highly nonlinear and/or computationally expensive response functions with great success. Efficient Global Reliability Analysis (EGRA) was also applied to several classes of reliability problems that are historically difficult to solve either efficiently or accurately. 1. Reliability analysis with uncertainty on the input distributions. Because the limit state is modeled independently of the input distributions, it remains accurate for changes in those distributions, allowing EGRA to only build the surrogate model one time and then simply resampling it as the distributions change. 2. System-level reliability analysis. Through a slight modification of the EGRA algorithm, the method is able to focus only on the component responses that lead to system failure and “ignore” the others. This leads to substantial computational savings without sacrificing accuracy. 3. Reliability-based design optimization (RBDO). By combining EGRA with an efficient design optimizer and various formulations for combining surrogate models at the design and random variable levels, accurate RBDO solutions can be realized at a small fraction of their typical cost. These cost savings are especially dramatic when the design variables are distribution parameters. However, some work remains to make these RBDO methods feasible when applied to problems with a large number of design variables, due to the difficulty in finding suitable bounds for each variable to ensure that the Gaussian process model for the probabilistic constraint is smooth and continuous. Through these applications, new methods of accurately solving these classes of problems have been created that are far more efficient than previously available methods.