Principal Component Analysis of low-frequency impedance spectra for hardness estimation in ferromagnetic materials
More details
Hide details
1
Department of Power Engineering and Turbomachinery, Faculty of Energy and Environmental Engineering, Silesian University of Technology, ul. Akademicka 2A, 44-100 Gliwice, Poland
2
Department of Machinery Engineering and Transport, Faculty of Mechanical Engineering and Robotics, AGH University of Krakow, al. A. Mickiewicza 30, 30-059 Krakow, Poland
3
The Institute of Technical Sciences and Aviation, The University College of Applied Sciences in Chelm, ul. Pocztowa 54, 22-100 Chełm, Poland
4
Center of Electromagnetic Fields Engineering and High-Frequency Techniques, Faculty of Electrical Engineering, West Pomeranian University of Technology: Szczecin, ul. Sikorskiego 37, 70-313 Szczecin, Poland
Corresponding author
Krzysztof Fryczowski
Department of Power Engineering and Turbomachinery, Faculty of Energy and Environmental Engineering, Silesian University of Technology, ul. Akademicka 2A, 44-100 Gliwice, Poland
KEYWORDS
TOPICS
ABSTRACT
This study presents a novel approach for the non-destructive evaluation of hardness in S235JR ferromagnetic steel using low-frequency impedance spectroscopy combined with advanced multivariate statistical analysis. The primary objective was to develop a correlation model enabling estimation of Vickers hardness (HV1) directly from complete electromagnetic response spectra without the need for equivalent circuit parameter identification. The experimental procedure included measurements of impedance components, namely resistance (R) and inductance (L), over a frequency range from 20 Hz to 200 kHz for specimens exhibiting various levels of strain hardening induced by plastic deformation. To reduce the dimensionality of the measurement dataset, consisting of 66 diagnostic parameters for each measurement point, Principal Component Analysis (PCA) was employed. The results demonstrated that the first four principal components (PC1 – PC4) accounted for more than 95% of the total variance of the electromagnetic response. While individual principal components exhibited limited predictive capability, a significant synergistic effect was observed when PC1 and PC2 were combined within a multiple linear regression (MLR) model. The resulting model achieved a coefficient of determination of R² = 0.855. The reliability of the proposed methodology was verified using an independent blind-test validation dataset, confirming the robustness and repeatability of the developed approach. The obtained results indicate that low-frequency impedance spectroscopy combined with PCA constitutes a promising tool for the non-destructive assessment of mechanical properties and structural condition monitoring of ferromagnetic construction steels.