Non-intrusive estimation of model error and discrepancy in dynamics models

Abstract

Errors in formulating the system physics model, due to inability to rigorously account for nonlinear behavior, boundary conditions, and multi-component and multi-physics interactions result in discrepancies between model predictions of system responses and the corresponding experimentally measured values. In our previous work, we have developed a Bayesian state estimation-based framework for the estimation of these model errors, and the subsequent prediction of model discrepancies at unmeasured locations, for untested inputs, and for untested configurations. In this approach, we represent model errors as external inputs in the dynamic system model, and estimate them using Bayesian state estimation. However, this approach is intrusive in the sense that it requires access to the governing system of equations, the ability to modify the system model by introducing an external system input, and the ability to represent system inputs and responses as probabilistic quantities. In this paper, we develop semi-intrusive and non-intrusive approaches to extend the model error estimation to black-box models. The semi-intrusive method does not need access to the governing equations, but requires the ability to interrupt the simulation at any time instant, update the system responses at that moment, and resume the simulation using the updated value of system responses. For situations where this is not permitted, we propose a fully non-intrusive approach where, a surrogate model is constructed and used in the Bayesian state estimation procedure. The proposed approaches are illustrated with three examples: structural deformation of a Timoshenko beam, heat transfer across a rigid bar, and deformation of a Timoshenko beam subjected to heating.