Publications
Arguments for the Generality and Effectiveness of “Discrete Direct” Model Calibration and Uncertainty Propagation vs. Other Calibration-UQ Approaches
This paper describes and analyzes the Discrete Direct (DD) model calibration and uncertainty propagation approach for computational models calibrated to data from sparse replicate tests of stochastically varying phenomena. The DD approach consists of generating and propagating discrete realizations of possible calibration parameter values corresponding to possible realizations of the uncertain inputs and outputs of the experiments. This is in contrast to model calibration methods that attempt to assign or infer continuous probability density functions for the calibration parameters. The DD approach straightforwardly accommodates aleatory variabilities and epistemic uncertainties (interval and/or probabilistically represented) in system properties and behaviors, in input initial and boundary conditions, and in measurement uncertainties of experimental inputs and outputs. In particular, the approach has several advantages over Bayesian and other calibration techniques in capturing and utilizing the information obtained from the typically small number of replicate experiments in model calibration situations, especially when sparse realizations of random function data like force-displacement curves from replicate material tests are used for calibration. The DD approach better preserves the fundamental information from the experimental data in a way that enables model predictions to be more directly tied to the supporting experimental data. The DD methodology is also simpler and typically less expensive than other established calibration-UQ approaches, is straightforward to implement, and is plausibly more reliably conservative and accurate for sparse-data calibration-UQ problems. The methodology is explained and analyzed in this paper under several regimes of model calibration and uncertainty propagation circumstances.