**Michal Maciusowicz \* and Grzegorz Psuj \***

Department of Electrical and Computer Engineering, Faculty of Electrical Engineering, West Pomeranian University of Technology, ul. Sikorskiego 37, 70-313 Szczecin, Poland

**\*** Correspondence: michal.maciusowicz@zut.edu.pl (M.M.); gpsuj@zut.edu.pl (G.P.);

Tel.: +4891-449-4967 (M.M.); +4891-449-4727 (G.P.)

Received: 10 June 2020; Accepted: 28 July 2020; Published: 31 July 2020

**Abstract:** The paper presents a new approach to non-destructive evaluation of easy/hard magnetization axis in grain-oriented SiFe electrical steels based on the Barkhausen phenomenon and its time-frequency (*TF*) characteristics. Anisotropy in steels is influenced by a number of factors that formulate the global relationship and affect the Barkhausen effect. Due to the observed high variability in the dynamics of magnetic Barkhausen noise (MBN) over time, obtained for various directions in grain-oriented steel, it becomes justified to conduct MBN signal analyses in the time-frequency domain. This representation allows not only global information from MBN signal over entire period to be expressed, but also detailed relationships between properties in time and in frequency to be observed as well. This creates the opportunity to supplement the information obtained. The main aspect considered in the work is to present a procedure that allows an assessment of the resultant angular characteristics in steel. For this purpose, a sample of a conventional grain-oriented SiFe sheet was used. Measurements were made for several angular settings towards the rolling and transverse directions. A data transformation procedure based on short-time Fourier transform (STFT) as well as quantitative analysis and synthesis of information contained in the *TF* space was presented. Angular characteristics of selected *TF* parameters were shown and discussed. In addition, an analysis of the repeatability of information obtained using the proposed procedure under various measurement conditions was carried out. The relationship between the selection of calculation parameters used during transformation and the repeatability of the obtained *TF* distributions were demonstrated. Then the selection of the final values of the calculation parameters was commented upon. Finally, the conclusions of the work carried out were discussed.

**Keywords:** non-destructive testing; magnetic Barkhausen noise; magnetic anisotropy; grain oriented steel; time-frequency representation; signal processing; data mining methods
