Neural metamodels and transfer learning for induction heating processes (TEAM 36 problem)

Issue title: Deep learning for analysis and synthesis in electromagnetics

Guest editors: Maria Evelina Mognaschi

Article type: Research Article

Authors: Di Barba, Paolo^a | Dughiero, Fabrizio^b | Forzan, Michele^b | Lowther, David A.^c | Marconi, Antonio^b | Mognaschi, Maria Evelina^a; | Sykulski, Jan K.^d

Affiliations: [a] Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy | [b] Department of Industrial Engineering, University of Padova, Padova, Italy | [c] McGill University, Montreal, Canada | [d] Electronics and Computer Science, University of Southampton, Southampton, UK

Correspondence: [*] Corresponding author: M.E. Mognaschi, Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy. E-mail: eve.mognaschi@unipv.it

Abstract: The authors explore the possibility of applying a convolutional Naeural Network (CNN) to the solution of coupled electromagnetic and thermal problem, focusing on the classical problem of induction heating systems, traditionally solved by resorting to Finite Element (FE) models. In fact, FE modelling is widely used in the design of induction heating systems due its accuracy, even if the solution of a coupled nonlinear problem is expensive in terms of computational time and hardware resources, notably in 3D analysis. A model based on CNN could be an interesting alternative; in fact, CNN is a learning model selected for its excellent ability to converge, even when trained with a limited dataset. CNNs are able to treat images as input and they are used here as follows: given a temperature map in the workpiece, 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 the induction heating of a cylindrical steel billet, made of C45 steel, placed in a solenoidal inductor coil exhibiting the same axial length of the billet (TEAM 36 problem). A thorough heating process is usually applied before hot working of the billet, as in an extrusion process, but this methodology can be applied also in the design of induction hardening processes. First, a CNN has been trained from scratch by means of a dataset of FE solutions of coupled electromagnetic and thermal problems. For the sake of a comparison, a transfer learning technique is applied using GoogLeNet, i.e. a Deep Convolutional Neural Network able to classify images: starting from the pre-trained GoogLeNet, its training has been subsequently refined with the dataset of solutions from FE analyses. When the training dataset contains a limited number of samples, GoogleNet shows good accuracy in predicting the process parameters; in the case of a high number of samples in the training set, namely beyond a threshold like e.g. 1500, both CNNs show good accuracy of the result.

Keywords: Numerical modelling, coupled fields, neural network, induction heating, finite-element analysis

DOI: 10.3233/JAE-230087

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 73, no. 4, pp. 389-398, 2023