The robust optimization of engineering systems generally involves the use of complex numerical models that take as input both design variables and random variables that model the uncertainties. The numerous simulations required by such analyses can become computationally very expensive. Moreover, some input conditions can lead to simulation failures or instabilities, 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 hidden constraint may be as costly as a feasible simulation, we seek to learn the feasible set of inputs and thus target areas without simulation failure before further analysis. In this context, we propose an adaptive Gaussian Process Classifier method to learn the feasible domain. The proposed methodology is based on a Stepwise Uncertainty Reduction strategy on random sets in the classification setting with Gaussian Process Classifiers. The performance of this strategy on different hidden-constrained problems will be presented in particular on an application in wind turbine reliability analysis.