  In this work, we study estimation problems in nonlinear mechanical systems
subject to non-stationary and unknown excitation, which are common and critical
problems in design and health management of mechanical systems.
  A primary-auxiliary model scheduling procedure based on time-domain
transmissibilities is proposed and performed under switching linear dynamics:
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 to determine the unknown
working condition at which the system is currently running at, and then an
appropriate transmissibility from the primary transmissibility family for
estimating the unknown output can be selected during the online estimation
stage. As a result, the proposed approach offers a generalizable and
explainable solution to the signal estimation problems in nonlinear mechanical
systems in the context of switching linear dynamics with unknown inputs.
  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. During the vehicle design phase, the
vertical wheel force is the most important one among Wheel Center Loads (WCLs),
and it is often measured directly with expensive, intrusive, and
hard-to-install measurement devices during full vehicle testing campaigns.
Meanwhile, the estimation problem of the vertical wheel force has not been
solved well and is still of great interest. The experimental results show good
performances of the proposed method in the sense of estimation accuracy for
estimating the vertical wheel force.
