Quantifying Model Uncertainty in Extrapolation from Tests to Prediction

Abstract

Computational simulations are used to predict the behavior of complex engineering systems where experimental data may be unavailable. A computational simulation is an imperfect representation of reality, though, with model uncertainty that affects prediction accuracy. Since experimental data of the full system is often unavailable, model uncertainty can be quantified and reduced using available sub-system experimental data, thus informing system-level predictions. This dissertation advances the state of the art in quantifying model uncertainty and develops methodologies for extrapolating experimental data from testing systems to correct predictions of full system behavior. First, model parameters and output discrepancy are estimated using Bayesian calibration with a robust and computationally efficient sampling algorithm, and high-dimensional spatiotemporal responses are included in the calibration after performing an eigen decomposition. Second, a reliability and relevance-based extrapolation confidence assessment is integrated into the uncertainty propagation framework to assess the confidence in extrapolating posterior distributions from testing to prediction systems. Third, instantaneous model discrepancy in model outputs is estimated for a dynamics system model using state estimation, and predictions at new input time histories are corrected using machine learning. Fourth, model inadequacy is addressed through state estimation of model form error in the governing equations, and predictions at new initial conditions and system configurations are corrected using machine learning. Finally, decision making with simulation predictions where uncertainty is quantified using extrapolation from test to application is discussed. The proposed methods are illustrated for several engineering systems including a thermal battery and an air cycle machine.