Stochastic Lookup Tables - A Method for the Integration of Parametric Uncertainties in Non-Linear Simulation Models

摘要

Integration of uncertainties in flight physical simulation models opens up a variety of stochastic analysis methods, which can provide highly valuable confidence statements about the computed results. However, embedding random variables in non-linear simulation models of aerospace vehicles is by no means straightforward. They usually contain precomputed results in form of multi-dimensional data arrays, e.g. lookup tables for aerodynamic coefficients. The given variance within those tables is generally not constant, e.g. the confidence about the linear region in aerodynamic coefficients is much higher than for the post-stall behavior. The present study suggests and compares two methods for the low parametric inclusion of uncertainties in lookup tables with non-constant variance. One method injects the uncertainty at sparsely placed pivot points whereas the other one makes use of a principal component decomposition. We conducted Monte Carlo experiments and found that both methods are able to reproduce the demanded uncertainty variation in the sampled lookup table realizations. The eigenvalue method is superior in terms of variance distribution fitting and model order reduction.