Power-Line Partial Discharge Recognition with Hilbert–Huang Transform Features

Abstract

Partial discharge (PD) has caused considerable challenges to the safety and stability of high voltage equipment. Therefore, highly accurate and effective PD detection has become the focus of research. Hilbert–Huang Transform (HHT) features have been proven to have great potential in the PD analysis of transformer, gas insulated switchgear and power cable. However, due to the insufficient research available on the PD features of power lines, its application in the PD recognition of power lines has not yet been systematically studied. In the present study, an enhanced light gradient boosting machine methodology for PD recognition is proposed; the HHT features are extracted from the signal and added to the feature pool to improve the performance of the classifier. A public power-line PD recognition contest dataset is introduced to evaluate the effectiveness of the proposed feature. Numerical studies along with comparison results demonstrate that the proposed method can achieve promising performances. This method which includes the HHT features contributes to the detection of PD in power lines.

1. Introduction

Partial discharge (PD) is an incomplete breakdown that may considerably shorten the service life of high-voltage equipment. If the local electric field is greater than the threshold, the surrounding dielectric breaks down, which leads to a short circuit. The initial tiny unidentified partial discharge may cause fires and explosions. PDs are transient in nature, characterized by pulsating currents with durations ranging from nanoseconds to microseconds [1]. PD intensity is not always proportional to its damage, as low PD intensity can rapidly lead to electrical tree growth [2]. Therefore, if the activity of a PD can be recognized and quantified before unacceptable damage occurs, the power department/enterprise can choose a reasonable time for the replacement of equipment in consideration of the economic effect and power-supply stability.

Powerful classifiers from machine learning make PD recognition results more accurate [2,3]. Deep convolutional neural network with convolutional and subsampling layers achieves a 12% improvement over support vector machines [4]. Convolutional neural network with convolution and pooling layers is applied to detect the extracted 33 features, including statistical features and wavelet transform (WT) features [1]. In [3], the deep belief network is introduced to apply the classification, and the maximum discharge, mean discharge and the number of PDs in different window lengths are chosen to be the features. Meanwhile, newly developed monitors that are generally about materials and physics research of sensors also provide assistance to the act of recognition [5,6,7]. The devices targeted by the PD recognition research contain transformer, gas insulated switchgear (GIS), cable and power line. The numbers of papers published about PD in different types of equipment are counted and shown in Figure 1. The statistics represent the numbers of papers obtained from the search results in IEEE Xplore. The key words were “partial discharge” combined with “transformer”, “GIS”, “cable” and “power line”. Most of the papers focused on the transformer PD as the equipment is much more expensive and the loss of disturbance is generally considerable. Approximately one quarter of the papers discussed GIS, while only less than one percent of the papers were associated with cables and power lines. This suggests that less attention was paid to the subjects of cable and power-line PD.

Nonetheless, cable and power-line PD recognition still matter. The great distances of medium power lines make them expensive to inspect manually. The occurrence of damage is minor, such as tree branches hitting the line, birds’ nests (presented in Figure 2) and flaws in the insulator, and do not immediately lead to a breakdown. Partial discharges gradually damage the power line, and they eventually cause power outages or start a fire if not repaired in time. Therefore, the increasing need for a high-quality power supply makes the detection of power-line PD necessary.

The PD of power lines is less discussed in the literature compared with other electrical devices, let alone their extracted features for recognition. Data augmentation was applied to bidirectional long short-term memory to increase the performance of medium-voltage power-line PD classifiers [8]. A text convolutional neural network and long short-term memory (LSTM) were combined and achieved a better performance [9]. The work presented in [8,9] concentrated on the algorithm, but did not clearly abstract the features. Feature extractions were presented in [10] and it was concluded that utilizing the Wavelet Transform (WT) method could improve the filtering process, and that the standard deviation, amplitude of the raw signal and amplitude of the denoised signal were effective features. Thus, the features of power-line PDs should be explored further.

WT features are usually applied to signal decompositions and their variants also contribute to PD recognition [1,10]. However, WT requires users to confirm the fundamental wavelet function, which leads to a lack of generalizability in different PD sources [11]. The Hilbert–Huang Transform (HHT) is often compared to WT. When the signal is nonstationary, the Hilbert representation produces a much sharper resolution in frequency and a more precise location in time [12]. The HHT and its improved version were applied in transformers [13], GIS [14] and cables [15,16], and resulted in improved performances. However, the HHT feature is rarely applied in power-line PD detection. In this paper, the main work and contributions are as follows:

• The possibility of HHT feature application in power-line PD recognition is explored. The HHT features were extracted from original signals and filtered.
• The filtered HHT feature was combined with peak features to train the light gradient boosting machine (LightGBM). The effectiveness of the HHT feature was then tested with the features used by the winner of a contest.
• An enhanced LightGBM methodology used for power-line PD recognition, based on HHT features, was constructed.

A public dataset obtained from a PD-recognition contest in Kaggle, held in 2019 [17], was introduced for the simulation tests. In terms of the classifier, LightGBM was applied by the winner of the contest [18]. In order to compare the performance of the proposed feature extraction method, LightGBM was selected as the classifier in this study.

The remainder of the paper is organized as follows. In Section 2, the basic HHT theory and LightGBM unique frames are introduced. In Section 3, details of filtering, feature extraction and training methods are illustrated. In Section 4, a contest case study is presented in order to verify the performance of the proposed method for power-line PD recognition. Section 5 concludes and presents the summary of the paper.

2. HHT and LightGBM Theories

2.1. HHT

All the variables in this paper and its descriptions are presented in

Table 1. Variables.

Variable	Description	Index Variable
$t$	Time	-
$X(t)$	An arbitrary time series	-
$Y(t)$	$\mathrm{Hilbert}\mathrm{transform}\mathrm{of}X(t)$	-
$Z(t)$	$\mathrm{The}\mathrm{analytic}\mathrm{signal}\mathrm{of}\mathrm{complex}\mathrm{conjugate}\mathrm{pair}X(t)$$\mathrm{and}Y(t)$	-
$a(t)$	Amplitude function of $\mathrm{analytic}\mathrm{signal}Z(t)$	$j$
$\theta (t)$	$\mathrm{Angle}\mathrm{function}\mathrm{of}\mathrm{analytic}\mathrm{signal}Z(t)$	$j$
$\omega (t)$	Instantaneous frequency	$j$
$i$	Imaginary	-
$n$	The number of intrinsic mode functions
RP	Real part	-
$X^{flatten}(t)$	Flattened signal	-
$X^{ref}$	Medium variable	-
$k$	Cycle count
$H(\omega ,t)$	Hilbert spectrum	-
$h(\omega )$	Hilbert marginal spectrum	-

.

For an arbitrary time series $X(t)$, it can be transformed into [12]:

$$Y(t)=\frac{1}{\pi }P\int \frac{X(t^{\prime })}{t-t^{\prime }}d{t}^{\prime }$$

(1)

where $P$ indicates the Cauchy principal value. With this definition, $X(t)$ and $Y(t)$ form a complex conjugate pair, so an analytic signal can be created. The analytic signal can be defined as [12]:

$$Z(t)=X(t)+Y(t)=a(t)e^{i\theta (t)}$$

(2)

where $a(t)={[X{(t)}^2+Y{(t)}^2]}^{1/2}$, $\theta (t)=\arctan (Y(t)/X(t))$.

The instantaneous frequency is expressed as

$$\omega (t)=\frac{d\theta (t)}{d(t)}$$

(3)

HHT contains two important parts: empirical mode decomposition (EMD) and Hilbert spectral analysis. EMD is used to decompose intrinsic mode functions (IMFs) that must meet certain constraints [12] from $X(t)$. Having obtained the IMF components, there is no difficulty in applying the Hilbert transform to each of these IMF components and computing the instantaneous frequency according to Equation (3). After performing the Hilbert transform on each IMF component, the original data can be expressed as the real part in the following form:

$$X(t)=RP{\displaystyle \sum _{j=1}^n{a}_j(t)e^i{\displaystyle \int {\omega }_j(t)dt}}$$

(4)

As a local and adaptive method in the frequency–time analysis, the HHT is especially sensitive to extracting low-frequency oscillations. Unlike WT, instantaneous frequency can still be localized in time, even for the longest period component, without spreading energy over wide frequency and long time ranges [12]. Thus, the HHT can offer more detailed information on PD signals.

2.2. LightGBM

LightGBM is a framework for implementing the gradient-boosting algorithm. Compared with eXtreme Gradient Boosting (XGBoost), LightGBM has the following advantages: faster training speed, lower memory usage, better accuracy, parallel learning ability and capability of handling large-scaling data. A detailed comparison is shown in

Table 2. Comparison between XGBoost and LightGBM.

	Extreme Gradient Boosting	Light Gradient-Boosting Machine (LightGBM)
Tree growth algorithm	Level-wise	Leaf-wise with maximum depth limitation
Split search algorithm	Pre-sorted algorithm	Histogram algorithm
Memory cost	2*#feature*#data*4Bytes	#feature*#data*1 Bytes (8× smaller)
Calculation of split gain	O (#data* #features)	O (#bin *#features)

.

Gradient-based one-side sampling and exclusive feature bundling are innovative methods in LightGBM. Gradient-based one-side sampling discards sample gradients that are less helpful for training, to achieve a balance between data volume and accuracy. Exclusive feature bundling reduces the number of features and maintains the accuracy by greedy bundling and adding offset into bundles [19].

LightGBM received good reviews and was extensively applied in supervised learning. Therefore, it was chosen to detect PD from the proposed feature pool.

3. PD Recognition Method with HHT Features

The HHT feature was introduced to the PD recognition of power lines. The architecture of the proposed method is presented in Algorithm 1.

Algorithm 1. PD recognition method with Hilbert–Huang Transform (HHT) features.

Input: dataset

Output: prediction for testing set

Initialize: LightGBM characteristics

Step 1: Flatten the signals of training set.

Step 2: Perform empirical mode decomposition for training and testing sets.

Step 3: Extract HHT features and peak features from training and testing sets.

Step 4: Filter the HHT features.

Step 5: Train the models and perform prediction.

This section is divided into subsections, the headings of which provide concise and precise descriptions of the experimental results, their interpretations and part of the experimental conclusions.

3.1. Step 1: Flattening the Original Signal

The method presented in Algorithm 2 was applied to attenuate the sinusoidal signal amplitude. The signals (the length of the datum was 800,000) before (a) and after (b) flattening are presented in Figure 3. (The unit of the y-axis of the signal is not marked as it was not mentioned in the dataset of the contest. The signals were collected by newly developed sensors by the holder of contest). The fundamental sine signal was effectively removed.

Algorithm 2. Flatten the signal [20].

$\mathrm{Input}:\mathrm{Numeric}\mathrm{sequence}X(t)$

$\mathrm{Output}:X^{flatten}(t)$

$\mathrm{Initialize}:X^{flatten}(t)=X(t)\cdot 0$$,X^{ref}=X(0)$$,\alpha =50,\beta =1,k=1$

$\hspace{1em}\hspace{1em}\mathrm{while}k<len(X(t))$ $\hspace{1em}\hspace{1em}{X}^{ref}=X^{ref}\cdot \frac{\alpha -\beta }{\alpha }+X(k)\cdot \frac{\beta }{\alpha }$ $\hspace{1em}\hspace{1em}{X}^{flatten}(k)=X(k)-X^{ref}$ $\hspace{1em}\hspace{1em}k=k+1$

This method is simple and effective. The parameters can be adjusted according to various needs. It does not extract the fundamental sinusoidal electrical signal but directly calculates the PD signal and noise, and thus, avoids complex processing and contributes to real-time monitoring.

3.2. Step 2: EMD with Segmentation and Parallel Computing

EMD is an important and the time-consuming part of the HHT, consuming over 99% of the total computing time. If the amount of data is large, this method tends to be very slow, since IMFs must meet the constraints described in Section 2.

The changing trend of the mean running time for a single segmentation of $X(t)$ with different segmentations is presented in

Table 3. Segmentation part and single computation time.

Seg/Parts	104	103	400	200	160	100	80	50	20	1
One time/s	0.0099	0.0100	0.0103	0.0110	0.0125	0.0125	0.0438	0.32	2.25	1876

and Figure 4. The computing time for the single segmentation decreased, as the two constraints for the EMD addressed in Section 2.1 were easier to realize with a smaller amount of data. As shown in the left-hand section of Table 3, segmentation over 100 meant that the data amount for a single segmentation was less than 8000, and the single HHT processing time decreased no more than 21% compared with more detailed segmentation. However, on the right-hand side, the single computing time abruptly decreased from 1876s to 0.0125s when the segmentation increased from 1 to 100. Correspondingly, the left part of the curve illustrated in Figure 4 is steady, while the right part is steep.

To obtain a suitable point for the segmentation, the relationship between the total computing time and different segmentations was recorded and is presented in Figure 5. Two requirements for the segmentation were determined: (a) the segmentation had to be a factor of the data length and (b) the segmentation had to be divisible by 4. The first requirement makes segmentation convenient. The second corresponds to the four quadrants of the original data. Since the computing time for a single segmentation slowly decreased when the segmentation exceeded 100, the increase in the number of segmentations became a dominant factor. As a result, when the segmentation exceeded 100, the trendline on the right-hand side of Figure 5 was similar to a straight line.

With a multi-core processor, the time-consumption problem can be solved by splitting the signals into segmentations and parallel operations. The number of segmentations chosen was 160, in consideration of the speed and future application in LSTM. Under the same computing power, the total operation time of the proposed method described in Steps 1–3 was reduced to 31.5% for the general EMD method. The IMFs obtained from EMD in one segmentation (1/160 period) are presented in Figure 6.

Ensemble EMD(EEMD) can achieve this task more rapidly, but its accuracy cannot meet the requirements. Complementary and complete EEMDs with adaptive noise offer more options with sufficient accuracy and speed. The parallel computing presented in Step 2 is designed to process features with time characteristics which can be handled by models with time sequences, such as LSTM. Simultaneously, faster HHT variation algorithms, such as complementary and complete EEMDs with adaptive noise, can always replace normal EMD in parallel computing.

3.3. Step 3: Obtaining the Hilbert Spectrum

Following Step 2, several IMFs were decomposed from the original signal. The flattened signal can be expressed as shown in Equation (4), which contains the amplitude and frequency of each IMF as a function of time and which is the Hilbert amplitude spectrum. The frequencies were split into 1050 bins. A Hilbert-spectrum fragment representation of 5000 points (1/16 period) is presented in Figure 7.

With the Hilbert spectrum, the marginal spectrum can be defined as

$$h(\omega )={\displaystyle {\int }_0^{T}H(\omega ,t)dt}$$

(5)

The energy contribution of each frequency interval can be accumulated via Equation (5). By summing over the time axis of the joint distribution, we can obtain the marginal Hilbert spectrum. This represents the cumulated energy of each bin of frequencies over the entire data time span, as shown in Figure 8. Generally speaking, the right-hand side of the spectrum is less useful than the left-hand side since the high-frequency bins often come from the noise.

The peak features were extracted from all the peaks in the flattened signal from Step 1. The label features (1–9) presented in

Table 4. Feature pool.

Label	Feature
0	Hilbert–Huang Transform (HHT) features from Steps 1–3
1	The total number of peaks
2	The number of peaks in quarters 0 and 2
3	The number of peaks in quarters 1 and 3
4	The std height in quarters 0 and 2
5	The mean “sawtooth” root mean square error (RMSE) value in quarters 0 and 2
6	The mean height in quarters 0 and 2
7	The mean value of the ratio with the previous data point feature in quarters 0 and 2
8	The mean value of the ratio with the next data point feature in quarters 0 and 2
9	The mean value of the absolute distance to the opposite polarity maximum

were calculated from each signal according to [18]. In the remainder of this paper, the labels of the features conform with those in Table 4.

3.4. Step 4: Filtering Features

The training set was used to test the validity of extracted features in different frequencies. A total of 1050 bins exposed to different frequencies meant resulted in 1050 additional features. However, most of the features were useless, such as the high-frequency features located on the right-hand side of Figure 8.

All the 1059 features extracted in Step 3 were trained in the models to verify the most useful frequency bin. The decision-tree gain was selected to be the judging rule. The 4th frequency bin was the most effective HHT feature that is highlighted in black box, as shown in Figure 9. Meanwhile, the original features (Labels 1–9) performed well. The gains for the top 15 features are presented, and the final HHT feature was locked as the 4th bin frequency feature. Here, we used only the most effective HHT feature, while the others were abandoned.

3.5. Final Training

The final feature pool included 10 features similar to those presented in Table 4, except that the Label 0 feature was replaced by the filtered feature in Step 4. These were sent to the LightGBM for training of the models.

4. Experiments and Results

The experiments were based on a PD contest. Proposed HHT features were added to the feature pools and tested on the contest dataset to evaluate the effectiveness of the proposed features. All the code was written in Python and realized on a PC with Intel(R) Core(TM) i7 CPU @ 2.60 GHz.

4.1. Contest and Dataset Description

The VSB power-line fault detection contest was held by the ENET Centre to challenge competitors to realize detecting partial discharge patterns in signals, with a prize of USD 25,000. The signals were acquired from these power lines with a new meter designed by the ENET Centre at VSB. Effective classifiers using these data will make it possible to continuously monitor power lines for faults. The training datum was the original signal and its callout. There were 2904 groups of signals and each group contained three power-line phases. The length of signal data collected for each phase was 800,000. The testing data comprised the other 6779 groups of signals. This is the most popular public dataset used for power-line PD. The competitors were required to submit their results file in the specified format. The final list was ranked by a Matthews correlation coefficient (MCC) of 43% of the testing data results.

4.2. Experiment and Test

4.2.1. Extracting the Features

After the steps in Section 3, we obtained the energy contribution of every frequency bin. In addition, the best decision-tree gain for HHT features was obtained from the 4th frequency bin, presented in Figure 9. The detailed features are described in Section 3.5.

4.2.2. Verifying the Effectiveness of the Features

To verify the effectiveness of the HHT features, they were added to the feature pool. Three perspectives were proposed to demonstrate the effectiveness of the HHT features. The first was a comparison between the nine original features and ten proposed features. The second was the changes in the performances of models when one of the proposed 10 features was removed from the feature pool. The third was the decision-tree gain.

4.2.3. Training with All 10 Features

After adding the HHT feature, the prediction results were well improved, as presented in Figure 10. From the analysis presented in

Table 5. Prediction result with 9 features and 10 features.

	Predict 0 9 Features	Predict 0 10 Features	Predict 1 9 Features	Predict 1 10 Features
Actual 0	19,497	19,496	186	187
Actual 1	192	127 (−33.8%)	462	527 (+14.1%)

, it can be observed that the main changes are the decrease in the number of false negative and the increase in that of true positive. The HHT feature helped the classifier avoid classifying signals with PD as non-PD. The MCC score was the final standard of the contest; it increased from 0.700 to 0.7632. The proposed HHT feature helped the feature increase by 9.02% in the MCC score. A detailed comparison in other performance evaluations between models with the original nine features and proposed ten features are reported in Figure 10.

4.2.4. Leave-One-Out Experiment

In this experiment, one feature was removed from the ten proposed features each time and the decreases in performance were detected. The labels of the features presented in Figure 11 are consistent with those in Table 4. The accuracy was always over 98% no matter which feature was absent, meanwhile the decrease in accuracy was always less than 0.36%. The F1 and MCC scores show similar trends, while the precision and recall present less regularity. When the HHT feature was removed, the decreases in accuracy, precision, recall, F1 and MCC scores ranked 4th, 3rd, 4th, 3rd and 3rd, respectively.

Table 6. Rank of decrease for every feature.

Feature	Accuracy	Precision	Recall	F1_score	MCC	Sum	Rank
HHT	4	3	4	3	3	17	3
1	3	6	1	1	1	12	1
2	7	8	5	6	6	32	6
3	1	1	9	4	4	19	4
4	9	9	6	8	8	40	8
5	5	5	3	5	5	23	5
6	2	4	2	2	2	12	1
7	10	10	7	9	9	45	10
8	8	7	8	10	10	43	9
9	6	2	10	7	7	32	6

presents more detailed information on the rank of each performance decrease. Each column shows the rank of the decrease in each feature on the performance evaluation (ranks 1–10). For each feature, the higher the rank, the greater the decrease in the performance evaluation, which means that the features are more essential for the model. The rightmost column is the comprehensive rank according to the sum of the other performance evaluations. The HHT feature ranked third and Labels 1 and 6 tied in first place.

4.2.5. Decision-Tree Gain Analysis

The decision-tree gain is demonstrated in this section. The gain for the HHT feature ranked third out of the ten features, as presented in Figure 12. The Label 5 feature presented in Table 4 (the mean “sawtooth” root mean square error value in quarters 0 and 2) contributed to most of the gain. These two features are highlighted in black box.

Although the Label 5 feature was ranked first, when it was removed from the 10 features, the HHT feature had the greatest gain that is highlighted in black box, as shown in Figure 13. Furthermore, as shown in Figure 11, when the HHT feature was removed, the decreases in five evaluation indicators all exceeded that of when the Label 5 feature was removed. This means that the HHT feature had more influence over the model. Figure 14 shows the detailed information about the performance evaluations. It is obvious that the model without the HHT feature performed worse than that without the Label 5 feature, which further proves the effectiveness of the proposed HHT feature for PD recognition.

4.3. Final Description of Experiment

There are definitions of the physical appearance of the IMFs and the Hilbert spectrum [12]; the frequency bin offers abundant information for power-line PD. The three perspectives present the filtered frequency bin as being effective for power-line PD recognition. Other HHT features in different frequency bins are helpful, but were not applied in this paper; this issue was described in Section 5. The application of LightGBM resulted in this model only consuming 333 MB of memory during training (including 260 MB of training data) and the trained models utilized less than 4 MB of disk space. Lightweight LightGBM makes the proposed method easy to use and implement, which could also make online inspection available.

5. Conclusions

This paper proposed an enhanced LightGBM methodology for PD recognition. The HHT feature was extracted from the collected signal and added to the feature pools to improve the classifier. A published power-line PD-recognition contest dataset was introduced to evaluate the effectiveness of the feature. With the HHT features, the winning algorithm in the contest achieved a much better performance with a 9.02% increase in MCC score. The comparison demonstrates that the HHT features contributed to the performance of the classifier. Compared with the deep learning method, LightGBM consumes less time and memory. The HHT spectrum has a clear physical definition, which will help researchers explore PD principles further. The dataset used in this paper was based on a newly developed sensor in [17]. With this hardware, the HHT features can improve the effectiveness and efficiency of PD detections.

There are several shortcomings and limitations to the method proposed in this paper. Although the process of HHT feature extraction was accelerated, it tended to be slightly slower than other statistical features extracted from the peaks. The replacement with other quicker improved EMDs, as described in Section 3.2, may overcome this issue to some extent. Limited by the absence of experimental equipment, a theoretical explanation of the HHT feature and hardware-based physical modeling were absent. Furthermore, the HHT features were filtered in a simple way and only one remained: other more sophisticated filter methods and the combinations of several bins should be explored. In addition to the above weaknesses and related future works, the development of PD-positioning algorithms is a future research direction, provided that a more abundant dataset can be obtained. Meanwhile, the performance of HHT features in a time-series model, such as LSTM, should be tested.