High Dimensional Stochastic Simulation and Electric Ship Models

Determination of statistical moments requires the numerical computation of integrals, but as the number of random dimensions increases, computational cost grows dramatically. There is great interest in the large scale complex systems encountered in the all-electric ship, and to deal with the large dimension, we present the sparse grid technique based on Smolyak's algorithm for evaluating mid-dimensional integrals. We compare its performance with collocation (full grid) and Monte Carlo methods, first focusing on a now standard package of six test integrals proposed by Genz. We then apply these methods to a validated electric ship model to compute mean and variance behaviors, given variation in physical parameters, both individually and in ranked sets.