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In this work, we study estimation problems in nonlinear mechanical systemssubject to non-stationary and unknown excitation, which are common and criticalproblems in design and health management of mechanical systems.  A primary-auxiliary model scheduling procedure based on time-domaintransmissibilities is proposed and performed under switching linear dynamics:In addition to constructing a primary transmissibility family from thepseudo-inputs to the output during the offline stage, an auxiliarytransmissibility family is constructed by further decomposing the pseudo-inputvector into two parts. The auxiliary family enables to determine the unknownworking condition at which the system is currently running at, and then anappropriate transmissibility from the primary transmissibility family forestimating the unknown output can be selected during the online estimationstage. As a result, the proposed approach offers a generalizable andexplainable solution to the signal estimation problems in nonlinear mechanicalsystems in the context of switching linear dynamics with unknown inputs.  A real-world application to the estimation of the vertical wheel force in afull vehicle system are, respectively, conducted to demonstrate theeffectiveness of the proposed method. During the vehicle design phase, thevertical wheel force is the most important one among Wheel Center Loads (WCLs),and it is often measured directly with expensive, intrusive, andhard-to-install measurement devices during full vehicle testing campaigns.Meanwhile, the estimation problem of the vertical wheel force has not beensolved well and is still of great interest. The experimental results show goodperformances of the proposed method in the sense of estimation accuracy forestimating the vertical wheel force.

Primary-Auxiliary Model Scheduling Based Estimation of the Vertical Wheel Force in a Full Vehicle System