| An incremental query learning algorithm is developed for generating an accurate representation of a surface defined in terms of a scalar function that can be nonlinear and computationally expensive to evaluate. The algorithm makes combined use of (1) an artificial neural network (ANN), as an efficient nonlinear mapping tool, to accurately map a complex surface represented by a set of training examples and (2) a genetic algorithm (GA), as a general optimization tool, to optimally locate new examples sequentially in untested regions of the surface. A training set, each point of which corresponds to a function evaluation, is constructed by optimizing an objective function, formulated to have maximum values at points both near the surface and far from existing points of the set.;The combined ANN-GA algorithm is used in quantifying the reliability of the passive containment cooling system (PCCS) of the Simplified Boiling Water Reactor. The performance of the PCCS, subject to a main steam line break inside containment, is modeled with the CONTAIN thermal-hydraulics code. The limit surface, separating the regions of PCCS success and failure in a space of five system variables, is generated with 130 points, each of which represents a CONTAIN run. The points were selected sequentially by the incremental learning algorithm and represent varying levels of component degradations. With an ANN approximation to the limit surface, we calculated the probability of the PCCS failing to maintain containment pressure within its design limit of 0.483 MPa, through Monte Carlo integrations of the probability density functions for the system variables. The representation of five concurrent system degradations, including the drywell-suppression chamber leakage, yields a two-fold increase in the PCCS unreliability over that accounting for the leakage alone. Although such an increase is generally expected, our study clearly illustrates the importance of explicitly accounting for multiple component degradations through a continuum limit surface representation.;Using the ANN-GA incremental learning algorithm, we were able to minimize the number of production CONTAIN runs needed to accurately represent the PCCS limit surface and quantify the performance reliability. The ANN-GA algorithm is general and should provide efficient unsupervised learning capability for the analysis of other complex nonlinear systems. |
