Numerical Diffusion and its Impact on System-Identification for an Industrial Heating Process

Abstract

This paper deals with system-identification for a distributed parameter heating process where a solid substrate is moving through a spatially extended heating zone and heated up by applying hot air to its surface. The temperature distribution inside the substrate is modeled in a spatial plane, where heat conduction is considered in the direction, perpendicular to the direction of movement. In contrast to previous work, where scalar model parameters (e.g. the thermal parameters of the substrate) have been identified, here, the quantities for the heat transfer (heat transfer coefficient and air temperature) are identified as functions yielding a significantly improved fit to the measurement data. This improved system-identification is performed for two early-lumping modeling approaches, which differ in the way the advection term in the governing Partial Differential Equation is discretized: one uses Eulerian coordinates, where the computational grid is stationary, whereas the second employs Lagrangian coordinates where the grid is moving with the substrate. The differences of the two approaches are discussed with the main focus on numerical diffusion. Especially its impact on the system-identification is investigated: although the fit to the measurement is comparably good in both cases, very different solutions are obtained for the identified functions which, we argue, is due to the optimizer counteracting the smoothing effect of numerical diffusion.