Comparative Study of Model Order Reduction for Linear Parameter-Variant Thermal Systems

Thermal modeling using finite element analysis with spatially fine discretization frequently leads to large scaled state space systems of differential equations. Hence, model order reduction can be inevitable to meet real-time requirements e.g. in model-based process control. In addition to large system orders, dealing with temperature-dependent boundary conditions, including convection and thermal radiation, when reducing the model order is challenging, since classical projection based reduction approaches are merely applicable for linear systems. Thus, the system description is divided into a dominant linear part and an additive piece-wise constant function, which is frequently updated. Reduction methods are compared regarding considered cooling model whereby discrepancies between the approximation of transmission behaviour and overall state reconstruction of initial and forced dynamic are elaborated. Finally suitable reduction strategies facing corresponding purposes are proposed. For a good approximation in transfer behaviour, Iterative Rational Krylov Algorithm for initial dynamic and Balanced Truncation for external load dynamic are proper choices. If an overall state reconstruction is required, Tangential Interpolation and Rational Krylov are favourable.