Active-learning-based system reliability analysis with budget constraints

Abstract

Ensuring the safety of structures is a crucial task in engineering design. Structural reliability analysis provides practitioners with tools to estimate the probability of failure of various engineering systems. Failure is assumed to occur when the system operates beyond its nominal range. The latter is characterized using a so-called limit-state function that takes as input a set of random variables describing the system and accounting for uncertainties, e.g., design parameters (with variability due to manufacturing tolerance), material properties or loading.

Due to the complexity of engineering systems, multiple limit-state functions are generally necessary to define the reliability of a structure. The problem is known as system reliability, as opposed to component reliability, for which only a single limit-state is considered. Many methods have been developed for the latter and can be classified into approximation (e.g., first-order reliability method (FORM)), simulation-based (e.g., crude Monte Carlo simulation) and surrogate-based methods.

Surrogate models, which act as proxies of the computational model used to evaluate the limit-state function, have been widely used in the context of reliability analysis and are among the most efficient methods when used in an active learning scheme. In this context, a surrogate model is built by sequentially enriching the experimental design so as to accurately approximate the limit-state surface (boundary between failed and safe states). A computationally intensive but accurate reliability estimation algorithm can then be used to estimate the probability of failure using the surrogate in lieu of the original model.

Research efforts have mainly been devoted to component reliability analysis. Extensions or adaptations to system reliability have been proposed but they lack efficiency. This is because they do not account for specific aspects of system problems, such as the presence of multiple and possibly disjoint and uneven failure domains or do require assumptions about the system configuration (e.g., series or parallel).

In this work, we propose an active learning scheme for solving system reliability problems in an arbitrary configuration while accounting for the difference in evaluation costs of the various limit-state functions. We use Sobolﾒ sensitivity analysis and clustering to identify the relevant limit-state functions to update at each iteration. Furthermore, we formulate a discrete optimization problem that allows us to account for the computational budget constraints and each limit-state evaluation cost. The proposed method is validated on two mathematical examples and applied on a finite element-based truss problem.