Structural identifiability analysis of a heat transfer system

Excessive energy consumption is currently a big deal for society. Part of the solution to this problem is to improve the efficiency of extensive use systems, particularly thermal systems. One way to address this is through the building of energy improvement oriented models. These models depend on a priori unknown parameters that must be estimated. In this sense, identifiability is an essential property to be analyzed in any parametric estimation process. In this paper, we present a lumped-parameter model of a thermal system. Then, we analyze its identifiability using the local isomorphism theorem. Finally, we discuss two scenarios depending on the measured variables. In the first o ne we have measurements of the complete state and we show that the model is identifiable, while in the second one we have partial measurements and the model turns out to be non-identiafiable. Finally, we propose an additional analysis in which we determine the minimum set of variables to be measured for the model to be identifiable.