Identifiability of Cauer thermal networks

Abstract

Compact thermal models replace computationally prohibitive alternatives in electrothermal simulation of power electronic systems. The Cauer network is particularly attractive because its two-port topology preserves physical heat flow between material layers and enables composition of separately characterized subsystems. However, the inverse problem of inferring its parameters from thermal impedance data is ill-conditioned. Thermal diffusion limits how many layers can be resolved from a step response, whether the parameters are obtained by deconvolution, direct fitting, or any other estimation method. Models that exceed the resolution limit can fit the impedance curve well yet contain unphysical capacitances that produce unreliable heat flow predictions at the boundary. We propose using profile likelihood to determine how many Cauer layers are identifiable from the data. Expert judgment then enters through interpretable quantities, such as a tolerance on the confidence intervals of the network values, rather than through qualitative choices. In the widely used deconvolution approach, these include the smoothing settings, the truncation of the structure function, its visual partition into sections, etc. We integrated this test into an automated algorithm in PLECS and validated it on synthetic and measured data. It selects ladders that reproduce the impedance curve while also predicting through-power accurately.