High-Dimensional Reliability Analysis of Engineered Systems Involving Computationally Expensive Black-Box Simulations

Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit and unknown to the user. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to build a global surrogate model by adaptively tracking the important dimensions or regions. Then, the sequential exploration-exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function) with high prediction uncertainty. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions; (ii) capturing the interactive effects among variables on the performance function; and (iii) flexibility in choosing the locations of sample points. The performance of the proposed method is tested through two mathematical examples, the results of which suggest that the method can achieve accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables.