COMPARISON BETWEEN A POLYNOMIAL-CHAOS-BASED BAYESIAN APPROACH AND A POLYNOMIAL-CHAOS-BASED EKF APPROACH FOR PARAMETER ESTIMATION WITH APPLICATION TO VEHICLE DYNAMICS

摘要

Many parameters in mechanical systems cannot be measured physically with good accuracy, which results in parametric and external excitation uncertainties. This paper compares two new computational approaches for parameter estimation. The first approach is a polynomial-chaos based Bayesian approach in which maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. The second one uses an Extended Kalman Filter (EKF) to obtain the polynomial chaos representation of the uncertain states and the uncertain parameters. The two methods are illustrated on a nonlinear four degree of freedom roll plane vehicle model, where an uncertain mass with an uncertain location is added on the roll bar.rnBoth approaches can work with noisy measurements and yield results close to the actual values of the parameters, except when different combinations of uncertain parameters lead to essentially the same time response than the measured response. In that case, the aposteriori probability densities of the estimated parameters obtained with the EKF approach cannot be trusted. The Bayesian approach identifies that problem since the Bayesian cost function has an entire region of minima, and can use regularization techniques to yield most likely values in that region based on apriori knowledge.