1. Introduction
SiFe electrical steel sheets are used in many technical solutions, including electric motors or transformers [
1,
2,
3,
4,
5]. There are two types of electrical sheets: non-grain oriented (NGO) and grain oriented (GO). The magnetic properties of NGO sheets do not depend on the direction [
6], thus they are used in applications where uniform magnetic flux distribution is required, e.g., in electric motors [
7]. The GO steels exhibit magnetic anisotropic properties. Therefore, this feature is mainly used in transformers cores. The GO sheets can be further divided into two types: conventional (CGO) and having super-oriented grain structure (High Grain Oriented—HGO) [
8,
9]. The HGO sheets are also referred to as high magnetic permeability steels (HiB) [
10]. The production process of GO sheets is complex and includes stages such as [
8,
10]: secondary recrystallization, heat treatment, hot rolling, cold rolling, annealing, coating the sheets with oxide layers. As a result of this process, a texture having a majority of grains oriented towards the (110) [001] direction (referred to as the Goss texture) is expected to be achieved, leading to low power loss and high permeability in the rolling direction. On the other hand, the large grains of the texture affect forming of large magnetic domains. That results in a higher demand for energy during domain walls’ movement taking place during magnetization. To obtain better magnetic parameters, the GO sheets are often subjected to the domain refinement (DR) processing methods, such as: laser scratching (LS), plasma jet irradiation, spark ablation, grove marking, chemical treatment, or coating stress [
8,
10]. Exemplary, through laser treatment, losses are reduced by reducing the width of the domains. This reduces the amount of energy necessary to reorganize the domain structure in the subsequent cycles of material magnetization [
10]. CGO sheets are characterized by a greater dispersion of grain orientation in relation to the rolling direction (so called tilt angle), reaching even 6–7°. In the case of HGO sheets, this angle is 2–3°. Due to such different grain structure, the anisotropic properties of those steels differ from each other. Therefore, in industrial applications, correct, non-invasive and relatively quick identification of GO steel properties becomes an important problem, requiring the introduction of methods that will quickly allow for controlled quality and verification of the properties of the tested electrical sheets.
In measurement practice, several different methods are used to study the magnetic anisotropic properties, including rotational method, torque measurement, magnetic hysteresis loop, and an induced magnetic field measurement [
11,
12,
13,
14,
15]. The magnetic Barkhausen noise (MBN) has also become an perspective testing method [
16,
17,
18,
19,
20,
21,
22,
23]. The MBN phenomenon is related to the stepwise nature of the domain structure reorganization process taking place during the magnetization of the material [
24]. The MBN signal is stochastic, non-stationary, and almost unique in each magnetization cycle [
25]. It is frequently used to study the damage and applied stress [
26,
27,
28,
29,
30,
31,
32,
33], residual stress [
22,
34], or microstructure [
35]. The anisotropic properties of electrical sheets were investigated with its application as well. In [
19], the MBN signals measured for the range of directions of the magnetizing field, from the TD (transverse direction) to RD (rolling direction) axis, were analyzed. The highest MBN activity was obtained for the RD consistent with the axis of easy magnetization. In another paper [
16], the authors investigated the influence of aspects such as texture, microstructure, and residual stress, confirming their importance for the anisotropic properties of steels. Also, the authors of [
23] noted that MBN can serve as a method for analysing the magnetic anisotropic properties and texture of ferritic cold-rolled sheets. In the mentioned works, the influence of various factors on the change of the angular characteristics of classical parameters, such as energy, rms, or number of impulses of the Barkhausen noise signal, was demonstrated. A change in MBN activity in various phases of the magnetisation process was also reported. It was shown that the sequential examination of the MBN signal allows for the analysis of the reorganization of the domain structure by linking the areas of activity occurring in the MBN signal [
20,
21,
36,
37]. In the works [
20,
21,
36], a detailed analysis in time domain of the course of the MBN phenomenon was performed. The three major activity regions referring to processes of nucleation of reverse domains, 180° and 90° DWs motion, depended on the given properties of materials, were then indicated. In [
37], to better observe the dynamics of changes in activity, a method of observation and parameterization of the MBN based on building the time–frequency characteristic (
TF) using the Short-Time Fourier Transform (STFT) has been proposed by the authors. The procedure of unambiguous division of the time–frequency space into sub-periods of MBN activity has been presented. The proposed
TF-based method made it possible to visualize not only the changes in dynamics or to determine the level of the background of the Barkhausen phenomenon during the entire magnetization period [
37], but also to identify any periodic disturbances constituting a constant contribution to the measured signal and disturbing the obtaining of information about the investigated anisotropy from the MBN signal [
38].
Even though the use of the proposed
TF analysis is a good expansion of classical methods and allows for a broad simultaneous analysis of many aspects [
37,
38], the correct interpretation of the MBN signal is still complex and often requires the analysis of many features describing the observed characteristics. Thus, in the context of developing automatic identification procedures for the state of the tested material few aspects remain. The problem of compiling the features vectors describing the studied signals, and then selecting their adequate representation, especially in the context of the analysis of the instantaneous dynamics of the MBN phenomenon, must be considered. The database of features ultimately has a decisive influence on the effectiveness of the entire method. The second problem is the selection of appropriate time ranges for MBN activity analysis under given anisotropic properties of material. The possible solution is to use an Artificial Neural Networks (ANN). They have been proven to be successful in various applications, i.e., in the use to Structural Health Monitoring (SHM) [
39] or to damage detection [
40]; however, they do not allow to fully avoid the described problematics. Recently, due to the innumerous extension of capabilities of computing machines, the deep learning methodology, that were created on the basis of ANN, brings new perspective and shows great potential to identification procedures’ automatization. The deep neural networks make it possible to create a system that enables the transition from expert to algorithmic description without defining the classification conditions, which allows for the elimination of possible human-based errors and the automation of the decision-making process [
41]. They are used in various industries. As well, they meet the rapidly growing interest in their application in non-destructive testing, for example, to control the condition of building structures [
42,
43], railway structures [
44], or testing the properties of materials [
45]. Deep networks based on autoencoders have also been successfully used to analyse the information contained in the time series of the Barkhausen noise signal for automatic and precise estimation of magnetocrystalline energy [
46]. Due to the possibilities of Deep Neural Networks (DNN) and their sensitivity to even subtle changes in the input data, it is possible to apply them to the analysis of the MBN signal obtained from electrical steel sheets. Moreover, considering the acquisition of time–frequency characteristics in the form of two-dimensional distributions, convolutional neural networks (CNNs) stand out with a high application potential [
41].
Therefore, to avoid the above described problems in this study, the new approach to MBN analysis based on STFT transformation and the use of deep convolutional neural networks (DCNN), to identify the type of GO sheet and to evaluate its magnetic directions, is proposed. The aim of the work is to investigate the possibility of building identification procedure sensitive to even subtle changes in the dynamics of the MBN signal. Thus, STFT spectrograms, allowing simultaneous consideration of MBN phenomenon dynamics expressed both in time and frequency, are proposed as input data of deep neural network model with the convolution layer. First, the structure of the DCNN was adjusted in preliminary experiments. Then, the DCNN was used to distinguish sheets with different anisotropic properties (obtained using different surface engineering methods) and to recognize the magnetic angles between the rolling and the perpendicular to the rolling directions. Additionally, the predations updating procedure, allowing improvement of the DCNN performance, was also introduced. Finally, the assessment of the proposed approach accuracy as a function of various angular resolutions applied during testing was carried out and the optimal conditions were discussed.
2. Measuring Samples and Characterization of Materials
Measurements were made for various types of SiFe grain-oriented steel sheet having different properties manufactured by two producers (marked as #1 and #2). The list of sheets with their parameters is presented in
Table 1.
To determine the influence of the GO electric steel type and various possible techniques for modelling their magnetic properties on the dynamics of the MBN phenomenon, two series of samples were investigated. In the case of the materials of the first producer, the experiments were carried out for a series of samples made of CGO sheets of different thickness. The set also contained the HGO sheet with a thickness corresponding to the thinnest CGO one in the set. In addition, this series of samples also included both CGO and HGO sheets subjected to domain refinement process using the laser scribing technique. In the case of the second series, the tests were carried out for three samples made of CGO sheet. The first represented the manufacturer’s base material. The second sample of this series was obtained by mechanical removing of (decoating) the oxide layer covering the steel surface. To compare the possibilities of modelling the anisotropic characteristics of electrical steels, the nitriding process was additionally carried out, thus obtaining the third sample of the series. The nitriding was conducted with a gas method in a mixture of ammonia (approximately 50 vol.%) and products of its dissociation at temperature of 570 °C for 3 h.
Samples for metallographic examinations were precisely cut than mounted in a conductive resin (Polyfast, Struers, Ballerup, Denmark) and mechanically ground and polished using a 0.25-µm diamond suspension. This was followed by polishing using a fine silica suspension. Low angle (7°) argon ion milling (Flat Milling System IM-3000, Hitachi, Naka, Japan) was the final stage of the sample preparation procedure for EBSD (electron backscattered diffraction) and X-ray microanalysis.
The samples were examined using an FE-SEM (Field Emission Scanning Electron Microscopy) SU-70 microscope (Hitachi, Naka, Japan) equipped with EDS (energy dispersive spectrometry) X-ray microanalysis UltraDry X-ray detector and EBSD (Electron Backscattering Diffraction) QuasOr. The EDS and EBSD components were integrated under the NORAN™ System 7 from Thermo Fisher Scientific (Madison, WI, USA).
EBSD crystal orientation and EDS measurements were acquired at an accelerating voltage of 20 and 15 kV, respectively.
The X-ray diffraction (XRD) phase analysis was conducted using X-ray tube CuKα, operating at the voltage of 35 kV, current 45 mA and a Bragg–Brentano geometry (X’Pert–PRO, Panalytical, Almelo, The Netherlands). The applied step of the goniometer was 0.05°, and the acquisition time was 200 s. The data was processed using X’Pert HighScore (v. 2.2.1) software provided by Panalytical.
All results obtained during the conducted by authors material characterization were presented in following figures and tables of this section.
The EBSD results showed that the samples H
23#1 and H
23LS#1 were characterized by the smallest deviations from the ideal Goss texture (
Figure 1,
Table 2) in the beta angle (tilt angle).
The silicon content in all tested materials was similar and amounted to approximately 3 wt.%. (
Table 3).
The measured thickness of the surface oxide layers (
Figure 2 and
Table 4) was varied and ranged from about 3 to 9 µm depending on the sheet manufacturer. The microstructure of the oxide layers of the examined steel sheets (see
Figure 2) was similar for all samples and was typical for modern electrical sheets [
47]. For all samples, the outer zone of the oxide layers was rich in aluminium, silicon and phosphorus. The inner zone contained mainly magnesium and oxygen (
Figure 3).
The diffraction patterns for all tested samples were similar (
Figure 4). XRD tests of the sheets carried out after the removal of the oxide layers showed a significantly increased intensity of the diffraction peak from the planes (110), which is typical for steel with a Goss texture. A significantly higher intensity of the peak assigned to planes (110) was observed for sample H
23#1, what is consistent with the EBSD result, where the smallest misorientation angle γ was measured (
Table 2). X-ray diffraction examinations of the nitrided sample (
Figure 5) showed a 2-phase structure. The presence of γ’—Fe
4N and ε—Fe
3N nitrides has been identified. The ferrite peak was not observed, which proves the nitriding to entire thickness of the sheet.
3. Measuring System and Measurements Results Processing
The diagram visualizing the configuration of the system along with the measuring procedure is presented in
Figure 6. The measurements were made for 51 angular settings of the MBN measuring transducer. The transducer rotation angle was ranging from 0° to 90° at a resolution (angular rotation step) of 1.8°, where 0° corresponds to a situation where the transducer magnetizes the sample along the TD direction. The measurements were performed using an automated positioning system and a signal acquisition system controlled by a computer. Data acquisition was carried out by a personal computer equipped with a DAQ card (NI-PCI-6251). The sine-shaped excitation signal having a frequency of 10 Hz was utilized. The resulting current amplitude value was 0.37 mA, which corresponded to a field strength of 1.6 kA/m. The sampling frequency was equal to 250 kHz. The unit of combined low and high pass filters created a pass band ranging from 2 kHz to 100 kHz. The detailed description of the transducer, system and measurement parameters as well can be found in the previous papers [
27,
37,
38].
The STFT was used to transform the MBN signal from the time domain into the time–frequency one in the form of spectrograms
SBN(t, f). In the transformation process, the Kaiser function with a size of 512 points was used, which resulted into a resolution in time of 512 µs and in frequency of 488 Hz. Details of the STFT transformation procedure for the analysis of the MBN phenomenon have been described by the authors in their previous papers [
26,
37,
38]. Since the highest activity of MBN was observed in the lower ranges of the spectrograms, the utilized frequency band was limited. Considering that the variance for the 0–72 kHz range is approximately 30-times greater than the variance for the remaining range, the 72 kHz was chosen as the high frequency limit of the band. Hence, the applied limitation does not affect the loss of important information while allows a significant reduction in training time and the operation of the entire procedure in further stages. Finally, the spectrograms amplitude distributions |
SBN(
t,
f)|
2 matrix, representing the described frequency range was used as the input data to the designing neural network.
Figure 7 presents exemplary amplitude of the STFT spectrograms |
SBN(
t, f)|
2 obtained for all tested samples and for three magnetization directions: 0, 45, and 90 degrees. All results were shown in the common range and the colour map was expressed in logarithmic scale. As it can be seen, the highest spectral power density values over the entire magnetizing period were obtained for the HGO sheet (H
23#1). Significant activity is visible not only for the 90° angle, as is the case of the rest of the samples, but also for the 0° and 45° angles as well. In the case of CGO sheets (C
23#1, C
27#1, C
30#1) it can be noticed that for the C
23#1 the spectral power density, within the highest MBN activity areas, achieves generally lower values ranges on the spectrograms than for the C
27#1 and C
30#1. It can also be seen that for the thicker sheets (C
27#1 and C
30#1), the MBN activity is more concentrated near the centre of the magnetizing period and encompasses higher frequency bands. It can be explained in the context of highest rate of dispersion of grain orientation of sample C
23#1. The misorientation results in deterioration of the bulk magnetic properties of electrical steels (i.e., decrease of magnetic permeability and increase of coercivity) [
48]. Thus, generally the lowest activity can be noticed for steel C
23#1. In the case of CGO sheets subjected to laser scribing, higher values of power density and a larger area of the highest activity are observed for the thinner sheet (C
27LS#1) than for the thicker one (C
30LS#1). In the case of the C
27#2 sheet, the removing of the insulating oxide layer (decoating) resulted in general increase of spectral power level in successive activity areas concentrated around
t = 0.02 s and
t = 0.03 s. The decoating affects the increase in average 180° domain width being a result of stress release, which was introduced to the steel by a coating process. In consequence, the higher rate of change in magnetization is obtained, affecting the increase in MBN activity [
49]. However, there is a clear change in the
TF characteristics for the sample obtained in the nitriding process (C
27N#2). For the 0° angle, the activity in the
TF space is mostly concentrated from about 0.025 to 0.035 s. Then, for the 45° angle, there is a visible shift and an increase in activity from about 0.02 to 0.04 s. For the 90° angle, a compact area (from about 0.02 to 0.03 s) with very high spectral power density values was obtained. Considering steel having the same thickness (C
23#1, H
23#1 and H
23LS#1), it can also be noticed that for laser scribed HGO (H
23LS#1) sheet the three areas of activity can be distinguished [
37,
38], while compared to the CGO (C
23LS) and the HGO (H
23#1) the lowest values of the power density regardless of the magnetization angle was obtained for it as well. The scribing process introduces local stress and further results in reduction of 180° domains width and population of 90° ones as well. This lead to lower rate of change in magnetisation and thus lower MBN activity [
48,
50].
Based on the given distributions of |SBN(t, f)|2, one can clearly see differences in the course of the instantaneous dynamics and the level of activity of the MBN depending on the steel grade and machining technique. Observation of the course of MBN with the use of time–frequency spectrograms enables the visualization of various stages of the changes taking place in a broader sense. A detailed interpretation of the changes in the domain structure taking place during the process of magnetization requires further sequential analysis. However, in the approach proposed in this paper, due to the properties of the deep neural network, the adequate definition of the human-chose features characterizing the spectrograms and reflecting different properties of the examined material is not the aim of the work, as the features are being autonomously coded in training process of the neural network.