A Practical Application of a Maximum Entropy, Non-parametric Approach to Account for Epistemic Uncertainty Using Random Matrices

One major difficulty that exists in reconciling model predictions of a system with experimental measurements is assessing and accounting for the uncertainties in the system. There are several sources of uncertainty in model prediction of physical phenomena, the primary ones being: aleatoric uncertainty (i.e., uncertainty in the model parameters), epistemic uncertainty (i.e., uncertainty in the model itself), and model solution error. These forms of uncertainty can have insidious consequences for modeling if not properly identified and accounted for. In particular, confusion between aleatoric and epistemic uncertainty can lead to a fundamentally incorrect model being inappropriately fit to data such that the model seems to be correct. As a consequence, model predictions may be nonphysical or nonsensical outside of the regime for which the model was calibrated. This chapter presents a practical understanding of the method developed by Soize for incorporating estimates of epistemic uncertainty into parameter distributions used in structural dynamics analysis. Sample source code is provided in order to facilitate adoption of these techniques.