Investigating the Capability of PD-Type Recognition Based on UHF Signals Recorded with Different Antennas Using Supervised Machine Learning

Abstract

The article presents research on the influence of the type of UHF antenna and the type of machine learning algorithm on the effectiveness of classification of partial discharges (PD) occurring in the insulation system of a power transformer. For this purpose, four antennas specially adapted to be installed in the transformer tank (UHF disk sensor, UHF drain valve sensor, planar inverted F-type antenna, Hilbert curve fractal antenna) and a reference log-periodic antenna were used in laboratory tests. During the research, the main types of PD, typical for oil-paper insulation, were generated, i.e., PD in oil, PD in oil wedge, PD in gas bubbles, surface discharges, and creeping sparks. For the registered UHF PD pulses, nine features in the frequency domain and four features in the wavelet domain were extracted. Then, the PD classification process was carried out with the use of selected methods of supervised machine learning. The study investigated the influence of the number and type of feature on the obtained classification results gained with the following machine-learning methods: decision tree, support vector machine, Bayes method, k-nearest neighbor, linear discriminant, and ensemble machine. As a result of the works carried out, it was found that the highest accuracies are gathered for the feature representing peak frequency using a decision tree, reaching values, depending on the type of antenna, from 89.7% to 100%, with an average of 96.8%. In addition, it was found that the MRMR method reduces the number of features from 13 to 1 while maintaining very high effectiveness. The broadband log-periodic antenna ensured the highest average efficiency (100%) in the PD classification. In the case of the tested antennas adapted to work in an energy transformer tank, the highest defect-recognition efficiency is provided by the UHF disk sensor (99.3%), and the lowest (89.7%) is by the UHF drain valve sensor.

1. Introduction

A defect in the insulation system is one of the main causes leading to a possible catastrophic failure of an electrical power device. Therefore, it is important that the condition of the insulation system is regularly verified during periodic tests or continuously using on-line partial discharge (PD) monitoring systems. Partial discharges are not only the main cause of damage to an insulation system but also a very reliable indicator of the formation of insulation defects in high-voltage electrical equipment [1,2].

The most frequently used methods of partial discharge detection, especially in field conditions, are the acoustic emission method and electromagnetic methods based on the registration of radio pulses in the HF, VHF, and UHF bands [3,4]. Moreover, in the case of devices with oil-paper insulation, the Dissolved Gas Analysis (DGA) method also plays an important role [5]. In the past decade, the UHF method in particular, has become the subject of numerous research and development activities. These works cover a wide range of issues such as: the development of new designs of UHF antennas [6,7,8], combined acoustic and electromagnetic PD sensors [9,10], new calibration methods for UHF partial discharge measurement [11], the use of UHF sensors to locate PD sources using time-difference of arrival (TDOA) [12], direction of arrival (DOA) [13,14], received signal strength indication (RSSI) [15,16], electromagnetic time reversal (EMTR) [17] and electromagnetic inverse filter (EMIF) [18] techniques, development of on-line PD monitoring systems [19], and automatic recognition of insulation defects based on advanced digital signal processing algorithms and machine learning methods [20]. The last issue is an important element of reliable diagnostics of electrical power devices because effective detection and identification of a defect (source of PD) can contribute to the prevention of a serious failure.

Most of the research works on the automatic classification of PD types focus on two issues, i.e., the selection and extraction of features describing PD signals and the implementation of machine learning (ML) methods. Among the numerous features describing PD, the most frequently selected and extracted are the statistical parameters (e.g., kurtosis, skewness, mean, variance, and cross-correlation factor) [21,22], two-dimensional phase-resolved partial discharge (PRPD) images [23], time-domain features (e.g., rise time, fall time, slew rate, pulse width) [24], frequency-domain features (e.g., mean amplitude of frequency, number of spectral peaks, root mean square value of frequency) [25], multifractal spectrum features [26], wavelet coefficients [27,28], and cross wavelet transform features [29].

The features mentioned above are used as input or training data in various PD pattern recognition methods, such as artificial neural network (ANN) classification [30,31], fuzzy clustering classification [32], distance-based classification [33], Fisher’s linear discriminant analysis (LDA) classification [34,35], classification based on the chaos theory [36], Bayesian classification [37], and support vector machine (SVM) classification [38].

In [39], the authors applied SVM for the classification of UHF signals emitted by PD occurring in gas-insulated switchgear (GIS). They achieved an average recognition rate of 90%, while using as features patterns based on chromatic parameters H, L, and S. In [40], the authors presented a design of a Hilbert fractal antenna applied for detecting and classifying PD types in an oil-paper insulated system. They used frequency components of the detected PD signal as features while considering the first 15 frequencies corresponding to the highest power peaks. They achieved a recognition rate of 95% when classifying the different PD types. In [41], the authors investigated defects of epoxy insulators using the UHF method. They extracted feature information from time-resolved partial discharge (TRPD) and PRPD analysis, while selecting them using minimal redundancy criterion (MRMR) and with SVM. They proposed a new algorithm for recognition reaching over 94% accuracy. In [42], the authors were involved in research using UHF measured with a wideband Horn antenna to detect and classify PD occurring on disc ceramic insulators. They applied ML techniques. As features they applied wavelet decomposition and statistical features. They used principal component analysis (PCA) and recursive feature elimination (RFE) for feature selection. In [43], the authors provided a review of various computational intelligence techniques applied for technical condition estimation in the field of power transformers. In addition, in a relatively recent study [44], the authors comprehensively summarized research on the area of detection, classification, and localization of UHF-recorded PD sources.

It must be admitted that a great deal of research has already been done, which confirms that there are a number of possibilities to classify PD types that were recorded with different types of antennas. Depending on the type of algorithm and the selected features, the authors have obtained efficiencies as high as 99.6%, as described in the review [44].

This article assesses the impact of the type of antenna used and the type of supervised ML algorithm on the effectiveness of PD classification in the insulation system of the power transformer. For this purpose, four antennas adapted for installation in the transformer tank were used in the research (UHF disk sensor, UHF drain valve sensor, Hilbert curve fractal antenna, and meandered planar inverted-F antenna). Additionally, a broadband log-periodic antenna was used, which was a reference for the other antennas. These antennas recorded the UHF signals generated by five types of PD occurring in the oil-paper insulation of the transformer, i.e., partial discharges in oil gap, partial discharges in oil, partial discharges in air bubbles in oil, surface discharges, and creeping discharges. For the recorded PD pulses, nine features in the frequency domain and four features in the wavelet domain were extracted. Among the available methods of supervised machine learning, six algorithms were selected, which are indicated frequently in the literature as promising: Bayes (BY), Tree (TREE), Ensemble (EN), K-Nearest Neighbor (KNN), Linear Discriminant (LD), and Support Vector Machine (SVM).

The most important contribution of the paper lies in the demonstration that there is no effect of antenna design on classification performance. Regardless of the type of antenna, an average efficiency above 89.7% was obtained. A second significant contribution to the knowledge of the UHF-recorded discharge diagnostics is that only the peak frequency needs to be computed in order to realize classification with high levels of accuracy, reaching the value of 99.7% for chosen defects.

This paper is organized as follows. Section 2 presents the types of tested defects (PD sources) and the parameters of the partial discharge measurement setup. This section also discusses the selection and extraction of features describing PD and the algorithms used for their classification. Section 3 presents the results obtained from single-feature analysis and feature analysis according to the MRMR algorithm. In this part, the obtained classification results were also assessed. General conclusions from the conducted research are included in Section 4.

2. Materials and Methods

2.1. Experimental Setup for Partial Discharge Measurements

As part of the experiment, five types of partial discharges were investigated, which most often occur in the oil-paper insulation system of power transformers, i.e., partial discharges in oil gap (PD1), partial discharges in oil (PD2), partial discharges in air bubbles (PD3), surface discharges (PD4) and creeping discharges (PD5). To generate PD pulses, electrode systems were used, the schematic diagrams and dimensions of which are shown in Figure 1. The electrode systems were placed in a cylindrical test chamber with a diameter of 150 mm and a height of 300 mm, made of organic glass and filled with TRAFO EN-type mineral oil (Orlen, Plock, Poland).

UHF sensors used in power transformers can be installed temporarily in standard oil drain valves, or permanently in specially adapted dielectric windows. The first type of sensor, due to the small diameter of the oil valve and the specific method of mounting, is, in most cases, a simple monopole antenna made in the shape of a straight rod, cone, or small disk [45,46,47]. The design of the second type of sensor is usually more sophisticated and is currently the subject of numerous research works aimed at developing a broadband UHF antenna that guarantees high sensitivity of PD detection and easy installation in a dielectric window. Apart from the first historically, but still popular (especially in commercial systems) narrowband disk antenna, broadband (or multiband) microstrip patch antennas are being implemented, e.g., the antipodal Vivaldi antenna [48], bio-inspired antennas [49,50], the Archimedean spiral antenna [51,52], the meander-line antenna [53], the spiral equiangular antenna [54,55], and various antennas based on fractal geometry, e.g., the Hilbert [56], Minkowski [57], and Peano fractal antennas [58].

In order to assess how the selection of a given antenna design affects the effectiveness of the PD classification process, the drain valve sensor and disk sensor type IC43 [59] (both produced by Qualitrol DMS, Glasgow, United Kingdom), Hilbert curve fractal antenna [60] and meandered planar inverted F-antenna [19] were selected for the purposes of the study. Additionally, the reference ultra-wideband log-periodic antenna type VULP 9118A (Schwarzbeck Mess-Elektronik OHG, Schönau, Germany) was used [61]. The parameters of the antennas used are summarized in

Table 1. Parameters of UHF antennas used in the research.

Label	Sensor Type	Measured Bandwidth (MHz)	Largest Dimension of the Antenna Aperture L [mm]	Sensor Mounting Method	Ref.
A1	Disk sensor type IC43	497–573; 1293–1427	150	Dielectric window	[59]
A2	Hilbert curve fractal antenna	397; 593–603; 664–676; 740–750 807–820; 870–884; 937–953; 1007–1027; 1070–1093; 1157–1173; 1477–1497	110	Dielectric window	[60]
A3	Log-periodic antenna type VULP 9118 A	160–1377 1	980	N/A	[61]
A4	Meandered planar inverted-F antenna	237–280	100	Dielectric window	[19]
A5	UHF drain valve sensor	527–533; 633–660	38	Oil drain valve	[59]

¹ The frequency range declared by the manufacturer is 180–1500 MHz.

, while the reflection coefficient S11 characteristics measured on the test stand using the vector network analyzer type KC901S (Deepace, Guangdong, China) are shown in Figure 2. In the remainder of this paper, references for each antenna are used as summarized in the left part of Table 1: A1–A5.

Measurement of PD in the UHF band was carried out in a shielded high-voltage hall with dimensions of 5390 × 2932 × 2499 mm, for which the theoretically determined main resonance frequencies for mode numbers m, n, p ∈ {0, 1, 2} are in the range from 58 MHz for transverse electric mode TE₁₀₁ to 158 MHz for transverse magnetic mode TM₂₂₀. For this reason, and the fact that the maximum operating frequency of the antennas used did not exceed 1500 MHz, the PD signals recorded by the antennas were filtered with a bandpass filter of 150 MHz to 1500 MHz. The antennas were placed at a distance of d = 2 m from the partial discharge source, thanks to which the far-field condition was fulfilled, such that d ≥ 2L²/λ where d is the distance from the source of UHF PD signals to the receiving antenna, L is the largest dimension of antenna aperture, and λ is the wavelength.

UHF pulses from PD were recorded with a digital oscilloscope of the MDO3104 type (Tektronix Inc., Beaverton, OR, USA) with a sampling rate of 5 GS/s. A high-frequency current transformer of the RFCT-4 type (Dimrus, Perm, Russia) was used to trigger the PD pulse acquisition process, installed on the grounding conductor of the electrode system. In addition, the intensity of PD and the level of their apparent charge q were monitored using a conventional partial discharge meter (PD-Smart, Doble Engineering Company, Marlborough, MA, USA) according to IEC 60270 standard [62]. All measurement system components are shown in Figure 3, while the basic parameters of the tested types of partial discharges are summarized in

Table 2. Parameters of the investigated types of partial discharges.

Label	PD Type	PD Inception Voltage Ui (kV)	Test Voltage Range Ut (kV)	Max. Value of PD Apparent Charge qmax (pC)	Mean Value of PD Apparent Charge qmean (pC)	Median Value of PD Apparent Charge qmed (pC)
PD1	PD in oil gap	14.3	14.3–27.0	16,286	4273	3004
PD2	PD in oil	24.1	24.1–30.2	2151	421	310
PD3	PD in air bubbles	10.7	10.7–20.8	834	306	102
PD4	Surface discharges	21.6	21.6–28.2	657	208	157
PD5	Creeping discharges	11.9	11.9–24.0	12,971	1777	1305

.

2.2. Selection of Features and Classification Method Applied

In the process of selecting features describing UHF PD pulses, both their high efficiency in applications related to automatic pattern recognition, as well as the possibility of their fast calculation with the use of FPGA technology were considered. This technology is more and more often implemented in modern systems of detection and online monitoring of PD [19,63,64,65,66]. Its popularity is due to the fact that it allows for processing signals and performing calculations in real time. Because of this, the online PD monitoring system is able to quickly detect and identify the type of defect and thus can reliably assess the threat and prevent a dangerous failure of the power electrical device. The latest FPGAs implement not only very efficient algorithms of the fast Fourier transform (FFT), but also more complex algorithms of digital signal processing, such as discrete wavelet decomposition [67,68,69]. For this reason and based on a literature search concerning classification problems in machine learning, we decided to select 9 features determined in the frequency domain (peak frequency, weighted peak frequency, spectral centroid, spectral roll-off frequency, spectral skewness, spectral kurtosis, and partial power determined for three frequency ranges) [70,71,72] and 4 features in the wavelet domain (energy of details coefficients at four decomposition levels) [73]. Descriptions of selected features along with references to mathematical formulas are summarized in

Table 3. List and description of selected features.

Label	Feature	Description	Unit	Ref.
F1	Peak Frequency	Frequency corresponding to the highest magnitude in the spectrum	Hz	[70]
F2	Spectral Centroid	Spectral centroid indicates where the center of mass of the frequency spectrum is located	Hz	[70]
F3	Weighted Peak Frequency	Geometric mean of the peak frequency and the spectral centroid	Hz	[70]
F4	Partial Power 1	This parameter specifies the percentage of the signal energy in the given frequency range (Partial Power 1: 150–250 MHz; Partial Power 2: 250–350 MHz; Partial Power 3: 350–1200 MHz)	%	[71]
F5	Partial Power 2
F6	Partial Power 3
F7	Spectral Skewness	Skewness of the frequency spectrum; this feature measures the symmetry of the spectrum around its arithmetic mean	–	[72]
F8	Spectral Kurtosis	Kurtosis of the frequency spectrum; this feature measures the intensity of the outlier values of the frequency spectrum distribution in relation to the intensity of the outlier values of the normal distribution curve	–	[72]
F9	Spectral Roll-Off Frequency	Frequency below which 85% of the accumulated magnitude of the spectrum is concentrated	Hz	[72]
F10	Energy of Detail Coefficients cD1	This parameter specifies the percentage of the details coefficients energy of the discrete wavelet transform (DWT) at the first, second, third, and fourth decomposition level, respectively	%	[73]
F11	Energy of Detail Coefficients cD2
F12	Energy of Detail Coefficients cD3
F13	Energy of Detail Coefficients cD4

, and Figure 4 shows their graphical representation.

In Figure 5 and Figure 6, selected sample scatter plots are presented along with box plots that encapsulate the basic information of descriptive statistics. The presented relationships illustrate the dependence of the feature F8 relative to F2 and F11 relative to F1, respectively; the UHF signal was measured using the A1 antenna. Different colors and markers were used to indicate the values obtained for each class PD1-PD5. The choice of visualization was made for two extreme cases: (1) the existence of visually distinct clusters while correlations between features exist, and (2) the absence of distinct clusters for all classes while no correlations between features exist. Box plots allowed us to determine the variability of values across groups. It is assumed that a large variation in box plots can be an indicator of the potential use of a feature, or set of features, for prediction. To enhance the process of analyzing all possibilities, the process was automated using scripts written in a MATLAB environment.

Based on the analysis of all possible combinations of each relationship, some features were found to correlate strongly, while others showed no correlation. The calculated features were examined for the existence of correlations between them before proceeding to classification. Pearson and Spearman correlation coefficients were calculated, providing very similar results. We then calculated how many times a feature was or was not correlated. In particular, results were grouped for highly correlated features (no HCF), where |r| > 0.7 and uncorrelated features (no UCF), where |r| < 0.3. The results are presented in Figure 7 and Figure 8 for the five considered antennas (as separate plots) and the various PD classes (in a different color).

Analysis of the total number of UCF > 25 indicates that the following features might be used for classification: F1 and F13 for A1; F1, F8, F11, F12 for A2; F1, F5, F7, F8, F11, F12, F13 for A3; F1, F11 for A4; and only F1 for A5. In contrast, it can be shown based on Figure 8 that feature F1 does not correlate strongly with any other feature in most cases and for each antenna type. Furthermore, the value of HCF < 10 indicated that F4 does not correlate strongly for A2 and A3; F11 for A2 and A4; F12 for A2; and F13 for A1, A2, A4, and A5. To sum up, we can state that the best results should be obtained for F1 and possibly for individual antennas also: for F4, F11–F13.

Feature selection is one of the fundamental problems in classification issues that data scientists face. The feature selection process is primarily used to reduce the model size and dimensionality, secondly to prevent overfitting, and in tertiary but not last, to improve interpretability. These advantages should provide the best predictive power when modeling a given dataset.

There are a number of methods that are commonly used, such as independent component analysis (ICA) [74], principal component analysis (PCA) [44], minimum redundancy maximum relevance (MRMR) algorithm [75,76], and neighborhood component analysis (NCA) [77]. Many authors reduce feature sets to a few dimensions using some of the aforementioned methods, e.g., [78,79,80].

In order to determine which features are important in the classification process of our particular problem, the MRMR method was applied. Using the method, predictor importance score (PIS) values can be determined, with the highest values indicating the most optimal features. The PIS values calculated for individual antennas are visualized in the form of a bar chart in Figure 9. The MRMR algorithm is deterministic, and each time it is called it gives the same results.

The results obtained found that each time the first feature has a relatively significantly higher value than the second and subsequent features. For antenna A1, A2, A3, and A4, it was feature F1, while for antenna A5, it was feature F3. The second and subsequent positions were occupied by different features, depending on the type of antenna. For antenna A1, only two features obtained PIS values above 1, while for the other antennas, features with PIS factors above 1 were obtained by significantly more features. The above indicates that a single feature allows class prediction with high accuracy.

3. Results and Discussion

3.1. Single Feature Analysis

We tested the classification performance separately for each of the F1–F13 features in the first step. For the algorithms considered, the classification process was performed using cross-validation with a k-fold parameter value of 20. The performance values in the validation process are summarized as a stacked bar plot in Figure 10, where the values obtained for each antenna are shown in different colors and for different algorithms as separate drawings.

From the images shown, one can read the variation in classification performance when applied separately. In order to quantitatively assess the quality of prediction when using successive features separately, the average accuracy values obtained for each feature and the selected algorithms are summarized in

Table 4. Summary of averaged accuracy for five antennas for each feature applied individually.

	Averaged Accuracy Calculated for All Five Antennas
Algorithm	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12	F13
TREE	95.4	75.6	87.6	70.5	71.1	85.2	66.4	66.1	84.1	69.5	66.5	71.4	60.5
KNN	94.8	77.4	88.1	67.4	68.2	83.8	63.9	64.8	79.6	69.3	67.0	69.1	55.3
LD	75.1	72.9	72.2	60.4	69.5	70.2	63.7	53.4	74.3	54.5	66.6	66.3	43.3
EN	80.3	76.5	88.2	72.2	73.0	86.0	68.5	67.4	83.2	71.2	68.6	73.4	61.9
BY	84.6	75.8	75.0	64.9	70.3	79.0	66.6	57.0	79.0	69.1	67.0	67.7	48.6
SVM	85.8	76.3	82.3	67.9	72.4	82.9	66.8	64.6	80.9	68.7	67.8	73.1	55.3
Average	85.99	75.74	82.25	67.19	70.75	81.17	65.98	62.22	80.19	67.06	67.25	70.18	54.14

. Based on the tabulated data analysis, it was found that the use of feature F1 for the TREE and KNN algorithm allows for classifications with efficiencies exceeding 94%. On the other hand, features F3, F6 and F9 also receive relatively good results when applied alone, achieving accuracies exceeding 80%.

In our opinion, the high efficiency obtained for the F1 feature results in the fact that it is the only one that does indicate a lack of correlation with the other features, while the other features, depending on the type of antenna, correlate with each other. It can also be deduced from Table 4 that by far the best results were obtained for the TREE and KNN algorithms.

In

Table 5. Average accuracies calculated for all features applied in classification.

Average Accuracies for All Features Applied Singularly
TREE	KNN	LD	EN	BY	SVM
74.62%	72.98%	64.79%	74.63%	69.59	72.67

, the averaged accuracies obtained for particular algorithms regardless of the feature applied are summarized.

3.2. Feature Analysis According to MRMR

In the next step, the classification process was carried out using a cumulative set of features, starting with the first one indicated by the MRMR method, then the first two, the first three, etc. Then the classification efficiencies were calculated for the six algorithms considered. The obtained results are included in Figure 11 in the form of a stacked bar plot, which illustrates the cumulative effectiveness values obtained for the successive antennas (marked with different colors) and the considered algorithms (subsequent figures).

Based on the gathered outcomes, very poor results were obtained for the EN algorithm for antenna A3. Worse results were also obtained for the LD algorithm, where weaker accuracies were calculated for antennas A4 and A5. Relatively good metrics were calculated for the other algorithms. From the relationships illustrated in Figure 11, it can also be concluded that after applying the first and subsequent features indicated by the MRMR method, there is no statistically significant difference in the obtained efficiencies. This clearly shows that applying only the first feature is sufficient to obtain almost the highest rates. In order to evaluate the quality of the classification and extract the best algorithm, the average efficiencies for all antennas were calculated, and these values are summarized in

Table 6. Average over accuracies calculated while using various No of features.

Alg.	Averages Accuracies [%] Dependent from the No of Features Applied for Classification
	1	2	3	4	5	6	7	8	9	10	11	12	13
TREE	96.7	96.8	96.7	96.8	96.8	96.7	96.7	96.8	96.8	96.8	96.8	96.7	96.7
KNN	96.3	96.2	96.3	96.2	96.3	96.3	96.3	96.3	96.3	96.3	96.3	96.3	96.3
LD	78.4	78.3	78.4	78.5	78.4	78.5	78.4	78.4	78.6	78.4	78.4	78.3	78.4
EN	81.9	81.8	81.9	81.9	81.9	81.8	81.8	81.9	81.9	81.9	81.9	81.9	81.9
BY	86.0	86.0	86.0	86.0	85.9	86.0	86.0	86.0	86.0	86.0	86.0	86.0	86.0
SVM	91.3	91.4	91.5	91.4	91.4	91.3	91.2	91.5	91.2	91.4	91.3	91.4	91.3

. It can be read from the table that, on average, the highest value, which was 96.8%, was obtained for the TREE algorithm when using two features. Slightly lower efficiencies characterized the KNN and SVM algorithm, which exceeded 90%. It should be noted that these results are not the same as in Table 4, because there the classifier predicted PD class based on the same feature, while here these, indicated by the MRMR, were applied. Hence, the average values are higher than those presented in Section 3.1.

The arithmetic means for the algorithms were also calculated regardless of the number of features used, and similar results were obtained for the same three algorithms. The values are summarized in

Table 7. Average over accuracies calculated for particular algorithms.

Averaged Accuracies for the Considered Algorithms
TREE	KNN	LD	EN	BY	SVM
96.75%	96.28%	78.40%	81.87%	85.99%	91.35%

. Again, the best results, above 90%, were obtained for the TREE, KNN, and SVM algorithms. Using two features during the prediction of the PD class resulted in a 1.4% improvement in accuracy.

3.3. Evaluation of Classification Performance

For classification performance evaluation, it is common to use various score metrics, e.g., accuracy (ACC) (1), precision, recall, or F₁-score (2), just to name the most popular ones, calculated based on the confusion matrix. However, these measures do not provide the complete picture of the performance and may give overly optimistic inflated results, especially in cases where the considered dataset is class-imbalanced [42]. The Matthews correlation coefficient (MCC) [81] (3) is a more reliable measure that estimates a high value only in cases when the classifier obtained appropriate scores for all the confusion matrix elements—true positives (TP), false negatives (FN), true negatives (TN), and false positives (FP)—proportionally both to the size of negative and positive elements in the dataset. The Cohen’s Kappa statistic [82] (4) is appropriate for both multi-class and class-imbalanced issues. This coefficient indicates how much better a classifier is performing compared to a simple classifier that simply guesses.

$$ACC=\frac{no of correct prediction}{total no of predictions},$$

(1)

$$F_{1}score=\frac{2·TP}{2·TP+FP+FN},$$

(2)

$$MCC=\frac{TP·TN-FP·FN}{\sqrt{\left(TP+FP\right)·\left(TP+FN\right)·\left(TN+FP\right)·\left(TN+FN\right)}},$$

(3)

$$Kappa=\frac{p_0-p_{\mathrm{e}}}{1-p_{\mathrm{e}}},$$

(4)

where: TP, TN, FP, FN is the No of correct or incorrect classified samples, $p_0$—observed agreement, $p_{\mathrm{e}}$—expected agreement.

Figure 12 shows the confusion matrices for each antenna obtained for the TREE algorithm, which obtained the best results, when applying the first feature according to the MRMR method. From the matrix, it can be seen which classes of discharges performed better and which performed worse in the classification process. It was found that efficiencies above 99.7% were obtained for class PD1 recorded with antennas A1 and A3 and class PD2 with antennas A1, A2 and A3, and class PD5 was 100% effective regardless of the type of antenna. Discharges of type PD3 and PD4 only for antenna A3 received a high efficiency ratio. Based on the matrix analysis, it is also clear that the highest efficiency was obtained for signals recorded with antenna A3, then A1, A2, and A4. The classification results for data obtained with antenna A5 were the lowest but also relatively high, exceeding 89%.

Table 8. Goodness parameters of the TREE algorithm applied to first MRMR feature.

Antenna	ACC	F1-Score	MCC	Kappa
A1	0.993	0.993	0.991	0.977
A2	0.975	0.974	0.968	0.922
A3	1.000	1.000	1.000	1.000
A4	0.972	0.973	0.966	0.912
A5	0.897	0.897	0.873	0.679

comparatively summarizes the F1-score, MCC and Kappa parameter values calculated for the classification process using the TREE algorithm with a single feature, according to the MRMR method. It can be seen that the ACC values are almost identical to the F1-score values. The MCC values are slightly smaller, in the range of 0.002 to 0.024. In contrast, as compared to MCC, the Kappa values are significantly lower, in the range of 0.014 to 0.194. The worst predictions were obtained for the feature set calculated from the signals recorded with the A5 antenna, for which the Kappa is only 0.68. The best predictions were gathered for the A3 antenna, reaching the highest score values of 1.

4. Conclusions

As part of the research work, the results of which are presented in this paper, UHF signals were measured with five types of antennas. The UHF signals were emitted in systems modeling partial discharges of five different types. The study attempted to extract features that were used for classification using supervised learning methods. The most crucial conclusions, which were stated based on the analyses performed, are as follows:

• Relatively high scores of efficiency measures were calculated for the feature representing peak frequency (F1). When applied as a predictor using the TREE and KNN algorithm, it allowed for classifications with accuracy exceeding 94%.
• Application of features F3, F6, and F9 resulted in accuracies exceeding 80%.
• Application of the MRMR method enabled reduction of the number of features from 13 to 1 while maintaining very high effectiveness. Best scores were achieved for two features.
• The highest efficiency (100%) was obtained for the broadband log-periodic antenna intended for research purposes. Comparably high efficiency of defect recognition was obtained for antennas installed in the dielectric window of the transformer tank. For these types of antennas, the efficiency was 99.3% for the UHF disk antenna, 97.5% for the Hilbert curve fractal antenna, and 97.2% for the meandered planar inverted-F antenna, respectively. Slightly lower efficiency (89.7%) was obtained for the monopole antenna installed in the oil drain valve.
• The high values of both ACC and MCC and Kappa coefficients indicate that the data set was well-balanced.
• Accuracies above 99.7% were obtained for the PD1 recorded with A1 and A3, and for PD2 recorded with A1, A2, and A3.
• Classification of PD5 was performed with 100% accuracy regardless of the type of antenna.

In future works, the authors plan to expand the software layer of the developed on-line partial discharge monitoring system [19] with the function of automatic defect recognition. Additionally, it is planned to investigate the influence of narrow- and broadband electromagnetic disturbances on the efficiency of PD classification.