Thermal neural networks: Lumped-parameter thermal modeling with state-space machine learning

With electric power systems becoming more compact with higher power density, the relevance of thermal stress and precise real-time-capable model-based thermal monitoring increases. Previous work on thermal modeling by lumped-parameter thermal networks (LPTNs) suffers from mandatory expert knowledge for their design and from uncertainty regarding the required power loss model. In contrast, deep learning-based temperature models cannot be designed with the low amount of model parameters as in a LPTN at equal estimation accuracy. In this work, the thermal neural network (TNN) is introduced, which unifies both, consolidated knowledge in the form of heat-transfer-based LPTNs, and data-driven nonlinear function approximation with supervised machine learning. The TNN approach overcomes the drawbacks of previous paradigms by having physically interpretable states through its state-space representation, is end-to-end differentiable through an automatic differentiation framework, and requires no material, geometry, nor expert knowledge for its design. Experiments on an electric motor data set show that a TNN achieves higher temperature estimation accuracies than previous white-/gray- or black-box models with a mean squared error of 3.18 K2 and a worst-case error of 5.84 K at 64 model parameters.