Data-driven discovery of the heat equation in an induction machine via sparse regression

Discovery of natural laws through input-output data analysis has been of considerable interest during the past decade. Various approach among which the increasingly growing body of sparsity-based algorithms have been recently proposed for the purpose of free-form system identification. There has however been limited discussion on the performance of these approaches when applied on experimental datasets. The aim of this paper is to study the capability of this technique for identifying the heat equation as the natural law of heat distribution from experimental data, obtained using a Totally-Enclosed-Fan-Cooled (TEFC) induction machine, with and without active cooling. The results confirm the usefulness of the algorithm as a method to identify the underlying natural law in a physical system in the form of a Partial Differential Equation (PDE).