Primary–auxiliary model scheduling based estimation of the vertical wheel force in a full vehicle system

In this work we study the estimation problem of the vertical wheel force in a vehicle system subject to non-stationary and unknown excitation, which is a common and critical problem in vehicle durability design. The vehicle system can be approximated by a linear time invariant system under each working condition. However, the working conditions are unknown during the estimation process. A primary–auxiliary model scheduling procedure based on time-domain transmissibilities is proposed and performed to identify the unknown working conditions and estimate the unknown vertical wheel force: In addition to constructing a primary transmissibility family from the pseudo-inputs to the output during the offline stage, an auxiliary transmissibility family is constructed by further decomposing the pseudo-input vector into two parts. The auxiliary family enables identifying the unknown working condition under which the system is currently running, and then an appropriate transmissibility from the primary transmissibility family for estimating the unknown output can be selected during the online estimation stage. Moreover, Finite Impulse Response (FIR) models, ridge regression, and Bayes classifiers are applied to realize the model scheduling procedure. A numerical example and a real-world application to the estimation of the vertical wheel force in a full vehicle system are, respectively, conducted to demonstrate the effectiveness of the proposed method. The results show that the estimates are in good agreement with reference measurements.