Inverse Uncertainty Quantification in Material Parameter Calibration Using Probabilistic and Interval Approaches

In model calibration, the identification of the unknown parameter values themselves, but also the uncertainty of these model parameters, due to uncertain measurements or model outputs might be required. The analysis of parameter uncertainty helps us understand the calibration problem better. Investigations on the parameter sensitivity and the uniqueness of the identified parameters could be addressed within uncertainty quantification. In this paper, we investigate different probabilistic approaches for this purpose, which identify the unknown parameters as multivariate distribution functions. However, these approaches require accurate knowledge of the model output covariance, which is often not available. In addition, we investigate interval optimization methods for the identification of parameter bounds. The correlation or interaction of the input parameters can be modeled with a convex feasible domain that belongs to a feasible solution of the model output within given bounds. We introduce a novel radial line-search procedure that can identify the boundary of such a parameter domain for arbitrary nonlinear dependencies between model input and output.