Polynomial chaos-based parameter estimation methods applied to a vehicle system

Abstract

Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of uncertainties on the system response. This article compares two new computational approaches for parameter estimation based on the polynomial chaos theory for parameter estimation: a Bayesian approach, and an approach using an extended Kalman filter (EKF) to obtain the polynomial chaos representation of the uncertain states and the uncertain parameters. The two methods are applied to a non-linear 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. When using appropriate excitations, the results obtained with both approaches are close to the actual values of the parameters, and both approaches can work with noisy measurements. The EKF approach has an advantage over the Bayesian approach: the estimation comes in the form of a posteriori probability densities of the estimated parameters. However, it can yield poor estimations when dealing with non-identifiable systems, and it is recommended to repeat the estimation with different sampling rates in order to verify the coherence of the results with the EKF approach. The Bayesian approach is more robust, can recognize non-identifiability, and use regularization techniques if necessary.

Parameter identification study of frequency response data for a trilayer conjugated polymer actuator displacement model

“…The three uncertain parameters are the diffusion coefficient (D), the resistance (R), and the double-layer thickness (δ). The parameter estimation method used in this study was a Bayesian approach similar to the one developed by Blanchard et al [13,14] which has been proven to identify zones of nonidentifiability [13]. Since the full model used in [11] is not suitable for real-time control purposes, it is approximated by a reduced form (second-order) of the model [11].…”

“…6-8 (grids of 200x200x200) were between 15 and 30 minutes. With the polynomial chaos theory, results for a similar resolution would probably easily be obtained within a few seconds or even less [13,14], which would also enable the use of higher sample frequencies if needed.…”

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

“…computations take the form shown in (44) and defined in (23)- (24); the constants ܽ . These constraints represent the extreme rattle conditions from a standard deviation perspective.…”

“…Sandu and coworkers introduced its application to multibody dynamical systems in [27,28,[36][37][38][39][40]. Significant work has been done applying it as a foundational element in parameter [23][24][25][26][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] and state estimation [60,61], as well as system identification [62]. Relatively recent work has applied gPC to both classical and optimal control system design [41,63,64].…”

Real-Time Parameter Estimation Study for Inertia Properties of Ground Vehicles

“…Unfortunately, because they only include sprung mass dynamics [9,16] they have to run the system over relatively flat terrain where the pitch and roll dynamics are not heavily excited. Expansions to these methods are shown in [2,15] that add in either pitch or roll plane dynamics for the parameter estimation. These studies form the foundation of for this work, and motivate the expansion to include the roll dynamics of the vehicle for estimation of the roll inertia in an effort to be as thorough as possible.…”