Impedance-Based Temperature Estimation in Induction Hardening Using a UKF with FEM-Trained Hybrid Surrogate Models

Abstract

This paper presents a method for estimating the internal temperature field of a cylindrical workpiece during an induction hardening process using an Unscented Kalman Filter (UKF). Since the internal temperature distribution cannot be measured online, the estimator infers this field by exploiting its direct physical effect on the measurable inductor impedance. The proposed framework is built upon experimental measurements, which are used to calibrate a model based on the finite element method (FEM). Data generated from this validated FEM simulation are subsequently used to train computationally efficient hybrid surrogate models: a hybrid linear-neural model for the heat-transfer dynamics and a neural network observer for the inductor impedance. The hybrid architecture effectively captures the non-linear magnetic and thermal behavior while preserving the fundamental thermodynamic consistency. Experimental results confirm the proposed impedance-based UKF accurately reconstructs the internal spatiotemporal temperature profile. Ultimately, real-time tracking of critical metallurgical variables, such as the Curie temperature depth, establishes a strong foundation for advanced closed-loop control.