Parameter Estimation for Predictive Simulation of Oscillatory Systems with Model Discrepancy*

A Bayesian framework provides a methodology in which inferences from measurement data can be used to bound the uncertainties in the predictive simulation of a physical system. The accuracy of these bounds relies on the satisfaction of statistical assumptions on the measurement error. Discrepancies between the model and the true physics can invalidate these assumptions. We examine the effect of such model discrepancies in the context of an oscillating cantilever beam. First we illustrate the influence of discrepancies in a simplified model of purely periodic signals and then we observe how discrepancies affect the accuracy of prediction uncertainty bounds using Bayesian parameter inference on a Euler-Bernoulli beam model. Our study shows small changes in the inference setup can result in significant differences in prediction accuracy and calls attention to important considerations for the practical application of Bayesian parameter estimation.