Comparative Study of Uncertainty Quantification Metrics via a Stochastic Method of Model Validation

Abstract

Uncertainty quantification metrics provide a quantitative measure of the agreement between predictions and observations. These metrics not only significantly influence the outcomes of model calibration but also provide a means of determining the desired level of fidelity for model validation. This manuscript evaluates the influence of these uncertainty quantification metrics on model validation focusing on Euclidian distance, i.e. the absolute geometric distance between two points; and Mahalanobis distance, i.e. the weighted distance between a point and a population that considers the correlations and Bhattacharyya distance, i.e. the weighted distance between two populations that considers the correlations. Discussions are provided on the use of these three metrics when comparing model predictions against observations in the context of model calibration and validation. These metrics are implemented and examined via a model validation method based on Monte Carlo and stochastic test-analysis correlation techniques. A finite element model of a frame structure with a set of uncertain parameters is provided in the simulated example to demonstrate these ideas.