In the paper, authors explore the possibility of applying convolutional Neural Network (CNN) to the solution of coupled electromagnetic and thermal problem, i.e. the classical modeling of induction heating systems, traditionally solved by resorting to Finite Element Models. In fact, finite Element modeling is widely used for the design of induction heating systems also in industrial production, even if the solution of a coupled nonlinear problem, that usually arises for the design of induction heating devices, is still expensive in terms of computational time and hardware resources, notably in 3D analysis.
CNN is a learning model selected for its excellent ability of convergence, also when trained with a limited dataset. CNNs are able to treat images as input and they are here used as follows: given a temperature map, identify the corresponding vector of current, frequency and process heating time; this mapping is a model of the inverse induction heating problem. Specifically, we consider as an example a classical problem, i.e. the induction heating of a cylindrical steel billet, made of C45 steel, placed in a solenoidal inductor coil exhibiting the same axial length. The thermal process is usually applied before hot working of the billet, like in extrusion processes, but this methodology can be applied also in the design of induction hardening processes.
Two different neural networks, a CNN trained from scratch and GoogleNet, i.e. a Deep Convolutional Neural Network able to classify images, have been trained by means of a dataset of FE solutions of coupled Electromagnetic and Thermal problems. The training dataset has been built by solving a linearized weakly coupled model, namely a low fidelity modelling. When the training dataset contains a limited number of samples, only GoogleNet shows a good accuracy in predicting the process parameters, while in the case of high number of samples in the training set, namely more than e.g. 1500, both CNNs show a good accuracy in the result.
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