The prediction of mechanical breach in the Crash and Burn problem is important for designing the full system to minimize the probability of loss of containment. Due to uncertainties in the impact angle, material properties, and material models, it is not possible to define an exact critical impact speed at which the system breaches. Furthermore, the cost of running a large scale sampling study to determine the empirical probability of breach is prohibitive. In this work, surrogate models from machine learning, namely logistic regression and artificial neural networks, are introduced to predict binary classification of pass versus breach from a limited set of samples. The structure and calibration of these classifiers is discussed, and a set of metrics for describing the performance of the classifiers is introduced. The classifiers are used on the UUR version of the Crash model to attempt prediction of failure probability and perform variable sensitivity analysis. Where a single sample of the computational model can take hundreds of CPU-hours, training and evaluating a classifier can take seconds or less, thus giving high predictive power in a relatively short time.
The generalized linear Boltzmann equation is a recently developed framework based on non-classical transport theory for modeling the expected value of particle flux in an arbitrary stochastic medium. Provided with a non-classical cross-section for a given statistical description of a medium, any transport problem in that medium may be solved. Previous work has only considered one-dimensional media without finite boundary conditions and discrete binary mixtures of materials. In this work the solution approach for the GLBE in multidimensional media with finite boundaries is outlined. The discrete ordinates method with an implicit discretization of the pathlength variable is used to leverage sweeping methods for the transport operator. In addition, several convenient approximations for non-classical cross-sections are introduced. The solution approach is verified against random realizations of a Gaussian process medium in a square enclosure.