Qiqi Wang
Aerospace Computational Design Laboratory
Massachusetts Institute of Technology
Bldg 33 Rm 408
77 Massachusetts Avenue
Cambridge, MA 02139
Variance Reduction in Computational Risk Assessment using Reduced Order Models
Computational risk assessment uses mathematical models and
computational methods to estimate the probability of failure in an
engineering system, given uncertainty in the inputs, operating
condition, and other factors. When the probability of such events is
small, traditional Monte Carlo method requires evaluation of the
mathematical model on a very large number of random samples. When the
model is computationally expensive to evaluate, accurate risk
assessment is often computationally infeasible without methods of
reducing the number of required samples.
We present several methods for reducing the variance of Monte Carlo
method, thus the number of required samples, by using reduced order
models of computationally intensive models. These methods combine
reduced order models with methods widely used in statistics, including
control variates, importance sampling and stratified sampling. We
demonstrate these techniques in engineering risk assessment problems
involving unsteady hydrodynamics and hypersonic air breathing engines.
We show that our methods reduce the computation cost by an order of
magnitude, yet computes unbiased estimate of the probabilities of
failure.