Uncertainty Quantification and Output Prediction in Multi-level Problems

Abstract

The calibration of model parameters is essential to predict the output of a complicated system, but the lack of data at the system level makes it impossible to conduct this quantification directly. This situation drives analysts to obtain information on model parameters using experimental data at lower levels of complexity which share the same model parameters with the system of interest. To solve this multi-level problem, this paper first conducts model calibration using lower level data and Bayesian inference to obtain the posterior distribution of each model parameter. However, lower level models are not perfect; thus model validation is also needed to evaluate the model that was used in model calibration. In the model validation, this paper extends the model reliability metric by using a stochastic representation of model reliability, and model with multivariate output is also considered. Another contribution of this paper is the consideration of physical relevance through sensitivity analysis, in order to measure the extent to which a lower level test represents the physical characteristics of the actual system of interest so that the calibration results can be extrapolated to the system level. Finally all the information from calibration, validation and relevance analysis is integrated to quantify the uncertainty in the system level prediction.