A global framework for active learning reliability in UQLab

Authors

M. Moustapha, S. Marelli and B. Sudret

Abstract

Since its introduction in the field of reliability analysis, active learning has been increasingly used for the solution of complex reliability problems at a manageable cost. The basic idea is to adaptively build an accurate approximation of the limit-state surface by sparsely covering the input space. In the early contributions, a metamodel, typically Kriging, was updated through a so-called learning function and then used for the estimation of the failure probability with Monte Carlo simulation. Popular methods include efficient global reliability analysis (EGRA) and active-Kriging Monte Carlo simulation (AK-MCS). More recently, a considerable number of methods that draw on this idea have been proposed by merely modifying one or more of these ingredients.

In this contribution, we first conduct a survey of active learning reliability methods available in the literature. We then identify the basic ingredients that make the backbone of these approaches. Drawing on their similarity, we propose a global framework for active learning reliability that combines non-intrusively four different blocks: metamodelling, reliability analysis, learning function and convergence criterion. By wisely choosing each element of the framework, a solution scheme that is tailored to a specific type of problems can be devised, e.g., problems with high-dimensional inputs or extremely rare events.

Using this framework, an active learning reliability module is implemented in UQLab, a Matlab-based framework for uncertainty quantification. In this paper, we show how such a framework is implemented, thus allowing users to easily build solution strategies by selecting independently each ingredient. The module is tested with 20 different limit state functions, and multiple combinations of the four ingredients, leading to more than 12,000 reliability analyses. These results are eventually aggregated to provide user-oriented recommendations.