Estimation of simulation failure set with active learning based on Gaussian Process classifiers and random set theory

A wide range of industrial applications require numerous time-consuming simulations across various input sets, such as for optimization, calibration, or reliability assessments. In that context, some simulation failures or instabilities can be observed, due for instance, to convergence issues of the numerical scheme of complex partial derivative equations. Most of the time, the set of inputs corresponding to failures is not known a priori and thus may be associated to a hidden constraint. Since the observation of a simulation failure regarding this unknown constraint may be as costly as a feasible expensive simulation, we seek to learn the feasible set of inputs and thus target areas without simulation failure before further analysis. In this classification context, we propose to learn the feasible domain with a new adaptive Gaussian Process Classifier. The proposed methodology is a batch-mode active learning classification strategy that reduces uncertainty step by step, using a random set paradigm and a Gaussian Process Classifiers. The performance of this strategy is demonstrated on several hidden-constrained problems, particularly in the context of a wind turbine simulator-based reliability analysis.