Discrete-Direct Model Calibration and Propagation Approach Addressing Sparse Replicate Tests and Material, Geometric, and Measurement Uncertainties

This paper introduces the “Discrete Direct” (DD) model calibration and uncertainty propagation approach for computational models calibrated to data from sparse replicate tests of stochastically varying systems. The DD approach generates and propagates various 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-which incorporates unjustified information in the calibration and propagation problem. The DD approach straightforwardly accommodates aleatory variabilities and epistemic uncertainties in system properties and behaviors, in input initial and boundary conditions, and in measurement uncertainties in the experiments. The approach appears to have several advantages over Bayesian and other calibration approaches for capturing and utilizing the information obtained from the typically small number of experiments in model calibration situations. In particular, the DD methodology better preserves the fundamental information from the experimental data in a way that enables model predictions to be more directly traced back to the supporting experimental data. The approach is also presently more viable for calibration involving sparse realizations of random function data (e.g. stress-strain curves) and random field data. The DD methodology is conceptually simpler than Bayesian calibration approaches, and is straightforward to implement. The methodology is demonstrated and analyzed in this paper on several illustrative calibration and uncertainty propagation problems.