A Polynomial Chaos Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems – Part II: Applications to Vehicle Systems

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Department of Computer Science, Virginia Polytechnic Institute & State University

This is the second part of a two-part article. In the first part, a new computational approach for parameter estimation was proposed based on the application of the polynomial chaos theory. The maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. In this part, the new parameter estimation method is illustrated on a nonlinear four-degree-of-freedom roll plane model of a vehicle in which an uncertain mass with an uncertain position is added on the roll bar. The value of the mass and its position are estimated from periodic observations of the displacements and velocities across the suspensions. Appropriate excitations are needed in order to obtain accurate results. For some excitations, different combinations of uncertain parameters lead to essentially the same time responses, and no estimation method can work without additional information. Regularization techniques can still yield most likely values among the possible combinations of uncertain parameters resulting in the same time responses than the ones observed. When using appropriate excitations, the results obtained with this approach are close to the actual values of the parameters. The accuracy of the estimations has been shown to be sensitive to the number of terms used in the polynomial expressions and to the number of collocation points, and thus it may become computationally expensive when a very high accuracy of the results is desired. However, the noise level in the measurements affects the accuracy of the estimations as well. Therefore, it is usually not necessary to use a large number of terms in the polynomial expressions and a very large number of collocation points since the addition of extra precision eventually affects the results less than the effect of the measurement noise. Possible applications of this theory to the field of vehicle dynamics simulations include the estimation of mass, inertia properties, as well as other parameters of interest.

Numerical analysis