Identification of Complex Models
Jan Peter Hessling · SIAM/ASA Journal on Uncertainty Quantification · 2014
A general noninvasive method for identification of uncertain parametric models is proposed. It can be applied to a broad range of calculations and simulations, e.g., for finite element models of electromagnetism, fluids and mechanical structures, dynamic modeling and signal processing, or even econometric models. The model statistics are represented by a small and hence efficient deterministic ensemble containing samples of parameter sets, which is the object of identification. In contrast to random ensembles, deterministic ensembles are calculated with definite rules and hence are well-defined and completely reproducible, i.e., possible to calibrate. Upon identification, the prior ensemble is calibrated to a posterior ensemble with Bayesian inference. For model inversion, a surrogate model is found by linear regression. To maximize its quality, the regression points of the surrogate model can be optimized to match the sampling points of the deterministic ensemble by means of fixed-point iterations. Identification with surrogate model optimization is illustrated for a Wiener filter equivalent to a steady-state Kalman filter, contained in a rudimentary inertial navigation system.