A cost-aware and sensitivity-based active learning algorithm for system reliability

The safety of structures is generally assessed using structural reliability analysis within a probabilistic framework. The parameters describing the system, which are affected by uncertainties, are represented by random variables and a set of so-called limit-state functions determine whether the system fails. The goal of the analysis is then to estimate the probability of failure of the system. Many techniques have been developed to achieve this goal and can be classified into approximation-, simulation- and surrogate-based methods. While approximation methods often lack of accuracy, simulation-based methods are computationally expensive. Surrogate-based methods, on the other hand, are an efficient alternative, especially when used in the so-called active learning framework. In active learning reliability, an inexpensive proxy of the limit-state function is built by sparsely evaluating the original limit-state function. This results in an experimental design that can be iteratively enriched so as to improve the accuracy of the approximated limit-state surface. Combined with an appropriate reliability estimation algorithm, this ultimately leads to accurately estimating the failure probability within a moderate computational cost. This idea has been largely investigated in the recent years and a plethora of active learning methods has been proposed in the literature as shown in recent reviews [1,2]. However, most of these contributions are limited to component reliability problems, i.e. when there is only a single limit-state function. System reliability, where there are multiple limit-state functions combined in a non-trivial way, is indeed more complex to solve. This is due to the presence of multiple (possibly disjoint) failure domains and their uneven contribution to system failure. In this work, we propose an active learning reliability method for system reliability problems. We devise a framework combining PC-Kriging and subset simulation. We make use of density-based clustering and Sobol’ sensitivity analysis to identify the most important points to add to the experimental design and the most relevant limit-states to refine. Furthermore, the proposed method is cost-sensitive, i.e., it factors in the relative cost of evaluating each limit-state function. The algorithm is illustrated and validated on a set of analytical functions and eventually applied to a network of transmission towers. References: [1] M Moustapha, S Marelli, and B Sudret. A generalized framework for active learning reliability: survey and benchmark. Structural Safety , 2022 (In press). [2] R. Teixeira, M. Nogal, and A. O’Connor. Adaptive approaches in metamodel-based reliability analysis: A review. Structural Safety, 89:102019, 2021