Real-Space Model Validation and Predictor-Corrector Extrapolation applied to the Sandia Cantilever Beam End-to-End UQ Problem~1

摘要

This paper describes and demonstrates the Real Space (RS) model validation approach and the Predictor-Corrector (PC) approach to extrapolative prediction given model bias information from RS validation assessments against experimental data. The RS validation method quantifies model prediction bias of selected output scalar quantities of engineering interest (QOIs) in terms of directional bias error and any uncertainty thereof. Information in this form facilitates potential bias correction of predicted QOIs. The PC extrapolation approach maps a QOI-specific bias correction and related uncertainty into perturbation of one or more model parameters selected for most robust extrapolation of that QOI's bias correction to prediction conditions away from the validation conditions. Such corrections are QOI dependent and not legitimate corrections or fixes to the physics model itself, so extrapolation of the bias correction to the prediction conditions is not expected to be perfect. Therefore, PC extrapolation employs both the perturbed and unperturbed models to estimate upper and lower bounds to the QOI correction that are scaled with extrapolation distance as measured by magnitude of change of the predicted QOI. An optional factor of safety on the uncertainty estimate for the predicted QOI also scales with the extrapolation. The RS-PC methodology is illustrated on a cantilever beam end-to-end uncertainty quantification (UQ) problem. Complementary "Discrete-Direct" model calibration and simple and effective sparse-data UQ methods feed into the RS and PC methods and round out a pragmatic and versatile systems approach to end-to-end UQ.