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

Abstract

Dynamic systems with time-varying parameters arise in numerous industrial applications, e.g. in structural dynamics or systems with moving loads. A spatial discretization of such systems often leads to high-dimensional linear parameter-varying models, which need to be reduced in order to enable a fast simulation. In the following we present time-varying parametric model order reduction (p(t)MOR) based on matrix interpolation and apply this novel framework to a system with moving load. Model Reduction:• p(t)MOR by Matrix Interpolation applied• Order of locally reduced systems:Further study:• Interpretation of the new matrix Projective pMOR: Choose appropriate projection matrices to approximate the state-vector by . Application for Systems with Moving Loads Projective p(t)MOR:Analogously, we aim to approximate the state-vector by Systems with Moving Loads:• position of the acting load varies with time

Model Reduction of Linear Time-Varying Systems with Applications for Moving Loads

“…Note that moving load and sensor problems can be represented as LPV systems with only parameter-varying input and/or output matrices, if the load and sensor location are considered as time-dependent parameters of the system model. Due to the time-dependency of the parameters, in the next subsection we derive a projectionbased, time-varying parametric model order reduction approach called p(t)MOR, to obtain a reduced-order model of a LPV system [5,6]. Based on that, we then adapt the pMOR approach by matrix interpolation [14] to the parameter-varying case, whereby new time derivative terms emerge [6,7].…”

“…Thereby any parametric model order reduction (pMOR) approach [4] can be applied to the resulting parametric LTI system. In some other recent publications [18,5,6,7] the time variation of the parameter is taken into account, whereby new time derivative terms emerge during the time-dependent parametric model reduction process. This paper deals with different time-varying model reduction techniques for systems with moving loads.…”

“…Since moving loads represent particular LTV systems, we then introduce some straightforward reduction approaches for the resulting special cases in section 3. In the second part of the paper, we focus on LPV systems and present a timedependent parametric model reduction approach by matrix interpolation [5,7] in section 4. Some numerical results for the reduction of systems with moving loads applying the proposed methods are finally reported and discussed in section 5.…”