p(t)MOR: Time-Varying Parametric Model Order Reduction and Applications for Moving Loads

In this contribution we investigate Model Order Reduction (MOR) for linear systems with time-varying parameters p(t). Such systems arise, for instance, in structural dynamics and multibody simulations when the position of an acting force on the physical structure varies with time. This behaviour is found in many industrial applications, e.g. in meshing gears, milling processes, bridge cranes or any system with moving load components. The varying load location can generally be considered as a parameter dependency of the systemmodel. Thus, a spatial discretization of such systems leads to large-scale linear parameter-varying (LPV) models, and model order reduction becomes necessary to enable a fast simulation keeping the computational expense and the storage requirements low. Our aim is to develop time-varying parametric model order reduction, which we call p(t)MOR, to obtain a reduced order model of a large-scale LPV system. After giving a review of standard pMOR by matrix interpolation to generate a reduced order model of a parametric LTI dynamical system, linear parameter-varying systems are examined in Section 3, where two different cases are presented: First, quasi-static parameter variations are considered, where the parameters are assumed to vary slowly with time. For this case, standard pMOR from Section 2 can be adapted and applied. Secondly, we consider the dynamic case where the parameters may change very quickly and present the challenges arising from this concern.