Quantitative functional failure analysis of a thermal–hydraulic passive system by means of bootstrapped Artificial Neural Networks

The estimation of the functional failure probability of a thermal–hydraulic (T–H) passive system can be done by Monte Carlo (MC) sampling of the epistemic uncertainties affecting the system model and the numerical values of its parameters, followed by the computation of the system response by a mechanistic T–H code, for each sample. The computational effort associated to this approach can be prohibitive because a large number of lengthy T–H code simulations must be performed (one for each sample) for accurate quantification of the functional failure probability and the related statistics.In this paper, the computational burden is reduced by replacing the long-running, original T–H code by a fast-running, empirical regression model: in particular, an Artificial Neural Network (ANN) model is considered. It is constructed on the basis of a limited-size set of data representing examples of the input/output nonlinear relationships underlying the original T–H code; once the model is built, it is used for performing, in an acceptable computational time, the numerous system response calculations needed for an accurate failure probability estimation, uncertainty propagation and sensitivity analysis.The empirical approximation of the system response provided by the ANN model introduces an additional source of (model) uncertainty, which needs to be evaluated and accounted for. A bootstrapped ensemble of ANN regression models is here built for quantifying, in terms of confidence intervals, the (model) uncertainties associated with the estimates provided by the ANNs.For demonstration purposes, an application to the functional failure analysis of an emergency passive decay heat removal system in a simple steady-state model of a Gas-cooled Fast Reactor (GFR) is presented. The functional failure probability of the system is estimated together with global Sobol sensitivity indices. The bootstrapped ANN regression model built with low computational time on few (e.g., 100) data examples is shown capable of providing reliable (very near to the true values of the quantities of interest) and robust (the confidence intervals are satisfactorily narrow around the true values of the quantities of interest) point estimates.