Learning model discrepancy of an electric motor with Bayesian inference

Abstract

Uncertainty Quantification (UQ) is highly requested in computational modeling and simulation, especially in an industrial context. With the continuous evolution of modern complex systems demands on quality and reliability of simulation models increase. A main challenge is related to the fact that the considered computational models are rarely able to represent the true physics perfectly and demonstrate a discrepancy compared to measurement data. Further, an accurate knowledge of considered model parameters is usually not available. E.g. fluctuations in manufacturing processes of hardware components or noise in sensors introduce uncertainties which must be quantified in an appropriate way. Mathematically, such UQ tasks are posed as inverse problems, requiring efficient methods to solve. A popular approach for UQ in inverse problems is Bayesian inference. This work investigates the influence of model discrepancies onto the calibration of physical model parameters and further considers a Bayesian inference framework including an attempt to correct for model discrepancy by an additional term. A Markov Chain Monte Carlo (MCMC) method is utilized to approximate the posterior distribution. A polynomial expansion with unknown coefficients is used to approximate and learn model discrepancy and system parameters simultaneously. This work extends by discussion and specification of a guideline on how to define the model discrepancy term complexity, i.e. here the maximum polynomial degree, based on the available measurement data. Furthermore, the suggested method is applied to an electric motor model with synthetic measurement data and evaluated by comparing the results to the reference. The example illustrates the importance and promising perspective of the method by good approximation of discrepancy and parameters.