Title: Time–frequency analysis of PD‐induced UHF signal in GIS and feature extraction using invariant moments
Abstract: IET Science, Measurement & TechnologyVolume 12, Issue 2 p. 169-175 Research ArticleFree Access Time–frequency analysis of PD-induced UHF signal in GIS and feature extraction using invariant moments Xi Li, Xi Li State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of China Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, 3010 AustraliaSearch for more papers by this authorXiaohua Wang, Corresponding Author Xiaohua Wang [email protected] State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorDingli Xie, Dingli Xie State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorXinqiao Wang, Xinqiao Wang State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorAijun Yang, Aijun Yang State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorMingzhe Rong, Mingzhe Rong State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this author Xi Li, Xi Li State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of China Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, 3010 AustraliaSearch for more papers by this authorXiaohua Wang, Corresponding Author Xiaohua Wang [email protected] State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorDingli Xie, Dingli Xie State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorXinqiao Wang, Xinqiao Wang State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorAijun Yang, Aijun Yang State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorMingzhe Rong, Mingzhe Rong State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this author First published: 01 March 2018 https://doi.org/10.1049/iet-smt.2017.0287Citations: 18AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The ultra-high-frequency (UHF) method is efficient in partial discharges (PDs) detection in gas-insulated switchgear (GIS). The features extraction of UHF signals is significant for propagation characteristics analysis and PD pattern classification. The PD-induced UHF signals are acquired by the internal UHF sensors in an actual 252 kV L-shaped GIS. The short-time Fourier transform method is applied to process UHF signals and describe the propagation characteristics in L-shaped GIS. Hu's invariant moments of energy density distribution are extracted as features in time–frequency plane. The features are utilised to discriminate different PD defect patterns in actual GIS model by the support vector machine classifier and achieve good results. Finally, a novel system of features extraction and classification of UHF signals is summarised. 1 Introduction Partial discharge (PD) monitoring is an efficient method to assess the insulate status of gas insulated switchgear (GIS). Nowadays, immense amounts of researches on insulation diagnosis have been carried out based on PD signals, especially the ultra-high-frequency (UHF) method. On the ground that UHF signal is highly sensitive, it is widely used to discover and eliminate the potential danger of insulation failure [1-5]. However, since UHF method is based on the electromagnetic (EM) wave induced from PD, it is essential to clarify the propagation properties and principles of EM wave in GIS. Meanwhile, UHF signals are practically applied to insulation diagnostic, so features of UHF signals need to be efficient and simple to classify. Considerable amount of works in the field of UHF signal feature extraction has been conducted [6-9]. There are three main different types of UHF signal features currently used for analysis, evaluation, and classification of PD. The number of PD pulses N of a certain phase position ϕ and a certain apparent charge q (ϕ–q–N) constitute the phase-resolved data [10-12]. Time-resolved data pattern displays the true shapes of the individual PD pulses [13, 14]. Data without phase/time pattern use the discharge magnitude at varying amplitudes of test voltage [15] or the frequency spectrum diagram of individual PD pulses [16]. Besides, frequency varies with time in the UHF signal which is non-stationary signal with stochastic properties, therefore, some studies focus on the features of UHF signal in time–frequency domain [4, 17, 18]. In recent years, based on patterns mentioned previously, UHF signal features such as statistical characteristics [19, 20], fractal features [21, 22], time–frequency features [23, 24], wavelet features [25-27], and spectral analysis [16, 28, 29] have been proposed for PD pattern recognition. These features represent UHF signals well and are quite effective to PD classification. However, the features based on statistical characteristics discard the detail of original waveform in exchange for economy on hardware. Some works focus on the time domain and frequency domain separately. Researches concerning time–frequency [23, 24] achieve desirable results, but they use the artificial defect models outside GIS or transformer tank lacking field applications. The time–frequency features of UHF signal in actual GIS and derived classification approaches still need deeper investigation. The motivation of this paper is to extract a new group of features of PD energy density distribution in time–frequency domain, and study the UHF signal propagation characteristics in L-shaped GIS. Finally, the features are utilised for PD pattern recognition. In this paper, short-time Fourier transform (STFT) method is implemented to obtain the time–frequency distribution, and features are extracted using Hu's invariant moments in the field of figure processing. It is proofed that the features are representative and applied to discriminate different PD patterns accurately by the support vector machine (SVM) classifier. 2 Experimental setup A 252 kV single-phase type L-shaped GIS tank is designed for the experiment. The diameters of the central conductor and the tank are 90 and 320 mm, respectively. The insulation defect is installed in the chamber under the insulating bushing. A non-PD testing transformer (capacity: 30 kVA, maximum voltage: 150 kV) generates the applied voltage [30]. The internal UHF sensors used in the experiment are four planar equiangular spiral antennas [31], which are installed on the inside of the L-shaped tank in Fig. 1a. The plane where the antenna locates is parallel to the axis of the GIS axial direction. The four sensors are named UHF-A, UHF-B, UHF-C and UHF-D. Fig 1Open in figure viewerPowerPoint 252 kV GIS experimental platform (a) Placements of UHF sensors and defect, (b) Floating electrode defect The floating electrode defect is very common in GIS, which will lead to PD. In this paper, two adjacent copper nuts fixed on an insulated bolt are mounted on the high-voltage conductor as the floating electrode defect as Fig. 1b. The bolt is mounted in the same direction with the sensors, i.e. 0° position. The applied voltage is 49.8 kV. 3 Time–frequency analysis results 3.1 UHF signal in time and frequency domain Figs. 2a–d show the waveforms of UHF signals sampled by four sensors UHF-A to D and results of fast Fourier transform (FFT). Owing to the locations of four sensors, the delay of the waveforms in time domain can be easily observed. Fig 2Open in figure viewerPowerPoint Time-domain waveforms and spectrums (a) UHF-A, (b) UHF-B, (c) UHF-C, (d) UHF-D The cut-off frequency (CF) of each mode of the EM wave in the GIS with the similar structure to the coaxial waveguide can be obtained by [32, 33] (1) (2) where a is the radius of central conductor, b is the radius of the tank, and c is light velocity. In this experiment, a is 45 mm, and b is 160 mm. Based on the model size, the cut-off frequencies of transverse electric (TE) wave modes could be calculated as listed in Table 1. Table 1. Cut-off frequencies of TEm1 modes in GHz M 1 2 3 4 5 6 0.47 0.93 1.4 1.86 2.33 2.79 The high-frequency components attenuate obviously passing the L-branch (LB). The spectrums only indicate the frequency components distribution without time properties. The time–frequency analysis overcomes the shortage of FFT. 3.2 Short-time Fourier transform The time–frequency transform, such as STFT, is suited for signals with slow frequency changes, whereas the wavelet transform is suited for signals with rapid changes [34]. Energy distribution of time–frequency representation is useful signal feature and has been utilised in large number of applications [35]. The purpose of time–frequency analysis is to distribute the energy density of the signal over the time and frequency variables, respectively. STFT is very simple for implementation, while the constant window width limits time–frequency resolution. However, in this article, the features of energy distribution are not strict to the resolution actually. Consequently, STFT is chosen to extract the time–frequency information of UHF signals. STFT consists in pre-windowing the signal around a particular time t, calculating its Fourier transform, and doing that for each time instant t. STFT is defined by [4] (3) is the signal, is a short-time analysis window localised around and . The signal and the short-time window are shown in Fig. 3. Fig 3Open in figure viewerPowerPoint UHF signal and Gaussian window For PD-induced UHF signal, the time and frequency resolution of STFT is enough to meet the requirements of the representation of energy density. Moreover, the energy density of the signal has the physical meaning that satisfies the global energy distribution. Therefore, it is easy to calculate the energy of specific duration and bandwidth. However, because of the Heisenberg–Gabor inequality, a signal cannot have simultaneously an arbitrarily small support in time and frequency. A trade-off needs to be made between time and frequency resolutions for the STFT. In this work, the Gaussian function with length of 115 points is chosen as the compromise between time and frequency resolutions. 3.3 Propagation characteristics examination in time–frequency domain Figs. 4a–d show the energy density distribution in the time–frequency plane of signals from UHF-A to UHF-D. Fig 4Open in figure viewerPowerPoint Three-dimensional energy density distribution of signals from UHF-A to UHF-D (a) UHF-A, (b) UHF-B, (c) UHF-C, (d) UHF-D The distribution corroborates the results obtained by the Fourier transform. In Figs. 4a and b, there is the highest peak proximity to 1.1 GHz. It can also be observed that the component at 1.1 GHz is concentrated in 25 ns or so after the signal is generated, and the energy density peaks of UHF-A and UHF-B signal are 0.048 and 0.033 J/(s·Hz), respectively. The UHF-A and UHF-B signals also have lower peaks of energy density at 500 MHz and the values are 0.014 and 0.007 J/(s·Hz). According to the result obtained by the FFT in Fig. 2, the energy at 500 MHz increases in the frequency spectrum, and exceeds the energy at 1.1 GHz after passing LB. It is in line with the result by time–frequency analysis shown in Figs. 4c and d. The energy density peaks of UHF-C and UHF-D signal are 0.013 and 0.005 J/(s·Hz), respectively, and the highest peaks are concentrated in 60 ns or so after the signal is generated. According to Fig. 4, the energy density of the two frequency bands 400–600 and 900 MHz–1.2 GHz is not distributed all over the time axis, nevertheless it is concentrate in a certain time range. The energy density of the UHF-A and UHF-B signals is more concentrated at the time axis, and the energy in the proximity of 1.1 GHz is concentrated in the range of 20 ns. Owing to the limitation of the time resolution and the distances between the two sensors before/after the LB <0.6 m, the delays between UHF-A and UHF-B/UHF-C and UHF-D are negligible. However, the energy density near the highest peaks at 500 MHz of the UHF-C and UHF-D signals are more diffuse comparing with the sensors before passing LB, and the energy density locates at the range of 60 ns. This phenomenon is caused by the reflection of EM-wave at the terminal of GIS tank and the velocity dispersion characteristics. The EM-wave propagates at different velocities depended on the frequency. The velocity of the TE mode shows by (4) where is the CF of the TE mode, and f is the frequency of the specific TE mode which is higher than . The energy distribution in different frequency bands over the time ranges from 0 to 102.4 ns is investigated in the following content. Fig. 5a shows the variation of the energy in the frequency band 400–600 MHz over the four sensors, and Fig. 5b shows the percentage of the total energy. Fig. 5c shows the variation of the energy in the frequency band 900 MHz to 1.2 GHz over the four sensors, and Fig. 5d shows the percentage of the total energy. Fig 5Open in figure viewerPowerPoint Variation of energy in specific frequency band (a) Variation of the energy in frequency band 400–600 MHz, (b) Percentage of the energy in frequency band 400–600 MHz of total energy, (c) Variation of the energy in frequency band 900 MHz to 1.2 GHz, (d) Percentage of the energy in frequency band 900 MHz to 1.2 GHz of total energy It can be seen in Fig. 5 that the energy in the frequency band 900 MHz to 1.2 GHz constitute about 57% of the total energy in the UHF-A and UHF-B signal, and the energy in the lower frequency band 400–600 MHz are about 24.5 and 18.0% of the total energy, respectively. In the actual detection, we are concerned about specific location of the PD point. Through the investigation in this paper, it can be seen that the energy density distribution of the UHF signal changes dramatically over the UHF sensors. The energy density in the frequency band 900 MHz to1.2 GHz attenuates strongly after passing the LB while the energy density at 500 MHz increases obviously, which can avoid the potential defect and provide a basis for locating the source position of PD. 4 Hu's invariant moments An essential issue in the field of image analysis is the feature extraction. Hu's invariant moments have been widely applied as features for digital image recognition, since which were proposed in 1962 [36]. Hu's invariant moments feature the image as a whole, and the moments describe features of the image such as the sum of horizontal and vertical directed variance [36, 37]. The moments work well for the time–frequency representation because the issue we focus on is the energy density distribution with the time axis and the frequency axis, and the relative position of energy density peaks in the plane. Hu's invariant moments are efficient to extract features in image processing. Pattanachai [38] proposed a method to recognise a tooth in dental X-ray images using Hu's moment invariants. Jin [37] used Hu's invariant moments to identify people's palm print. Xu [39] used surface moment invariants as shape descriptors for the shape retrieval of 3D face models. Good results are obtained by using the moment invariants. A brief review of Hu's invariant moments is presented in this chapter. Two-dimensional geometric moments of a digital time–frequency representation image (M × N) that has energy density distribution function (x = 1,…, M, y = 1, …, N) are given as (5) The function can be the result of STFT or any other time–frequency representations. The zero-order moment is the mass of the image. The (p + q)-order central moments are defined as (6) where . is the coordinates of the centroid. Central moments are given as (7)–(15) in terms of the geometric moments: (7) (8) (9) (10) (11) (12) (13) (14) (15) To eliminate effects of image scaling, the normalised(p + q)-order central momentis given by (16) This paper proposes to extract features of energy densitydistribution by using Hu's invariant moments. Hu's moment invariants are applied asa shape descriptor in image processing. The theory of algebraic invariants is thesource of Hu's invariant moments. The basic idea is to describe images by a set ofmeasurable quantities called invariants and its invariant features on imagetranslation, scaling and rotation [38]. A setof seven Hu's invariant moments is as (17) (18) (19) (20) (21) (22) (23) 5 Field applications 5.1 SVM classification via resultant moment vector Hu's moments describe key characteristics of the UHF signal. However, owing to the invariants of Hu's moment, the images cannot be distinguished if they have the relationship of translation, scaling or rotation. Meanwhile, geometric moments carry out the distribution of the image refers to the origin and time, frequency axes of the coordinate. Therefore, the feature vector is the combination of Hu's moments and geometric moments. The resultant moment vector is defined as (24) where , . Classification is the final stage of the PD signal processing, and the PD pattern or relative sensor position is assigned to a category. The SVM is a popular machine learning method for classification, regression, and other learning tasks [40]. Zhang studied the mechanical prediction algorithm for high-voltage circuit breakers (HVCBs) based on SVM, which could predict the mechanical condition of HVCBs successfully [41]. Hao used SVM to distinguish different PD sources [42]. Sharkawy introduces the use of SVM to classify the dimensions and composition of contaminating particles in transformer mineral oils [20]. The kernel function of SVM maps the feature vector into the higher dimensional space to find a linear separator in this new space [43]. The Gaussian radial basis function (Gaussian-RBF) kernel is chosen in this paper, which is defined as (25) where is the kernel parameter controlling the flexibility of classifiers [43]. In order to obtain the best classification results, cost penalty parameters C and is optimised using the cross-validation. In this work, the optimised C and are 0.5664 and 3.4822, respectively. As mentioned before, ten groups of UHF signals are sampled in this experiment, five groups are the training dataset, and others are test dataset. Conclusively, 20 UHF signals are used for the SVM model test in total. Fig. 6 shows the classification results of the SVM model. Only one UHF-B signal is identified as class A incorrectly, and the whole classification accuracy is 95%. The classification results indicate that invariant moments and geometric moments represent features of UHF signals at different detect positions, which can be utilised for localisation of the PD source. Fig 6Open in figure viewerPowerPoint Classification results of different sensors 5.2 PD defects pattern recognition The goal of feature extraction of UHF signals is to distinguish different PD defect patterns. Large quantities of researchers have worked on this issue which are mentioned in Section 1. In this paper, new features derived from invariant moments and geometric moments are applied for defect patterns recognition. The UHF signal is represented by a 13-dimension vector. In order to verify the recognition algorithm, three kinds of common PD defects are installed, respectively. They are floating electrode, metal protrusion and particle on the spacer surface as shown in Fig. 7. Fig 7Open in figure viewerPowerPoint Typical PD defect patterns (a) Floating electrode, (b) Metal protrusion, (c) Particle on the spacer surface One hundred groups of UHF signal are recorded in each situation, and only signals of UHF-A are used to recognise different defect patterns by SVM. Resultant moment defined by (24) is the characteristics vector. Fifty groups of signals are the training set, and the rest are the test set. Finally, the classification results of the SVM model based on Hu's moments and geometric moments are listed in Table 2. The global accuracy is 87%. Table 2. Recognition results of SVM model PD patterns Number of recognition Accuracy, % floating electrode 49 98 metal protrusion 45 90 particle on the spacer surface 36 72 total 130 87 5.3 A novel system of feature extraction and classification A novel system of feature extraction and classification of UHF signals is proposed in this paper. UHF signals acquired by UHF sensors are processed by STFT. The energy density distribution is treated as a digital image. Then geometric moments and Hu's invariant moments are extracted as the characteristics of UHF signals from the time–frequency representation image. Next, the feature vector of UHF signal is normalised and the parameters are optimised, before the vector is input to the SVM model for pattern classification. The flowchart shown in Fig. 8 summarises the procedure mentioned before. Fig 8Open in figure viewerPowerPoint Flowchart of feature extraction and classification of UHF signal 6 Conclusion In this paper, the time–frequency analysis method and Hu's invariant moments are proposed to study the feature extraction and UHF signal propagation characteristics in L-shaped GIS. Then the features are utilised for PD pattern recognition. The conclusions are summarised as follows. The principles of propagation characteristics in L-shaped GIS in time–frequency domain are revealed. For an L-shaped GIS, the energy density is concentrated at 1.1 GHz, and the aggregation of the time axis is better before passing the LB. After passing LB, the energy density at 1.1 GHz attenuates remarkably while the energy density at 500 MHz increases obviously. However, the time aggregation of the energy distribution at 500 MHz becomes worse and several peaks appear in the time–frequency plane. Hu's invariant moments are used as characteristics of UHF signal energy density distribution, which are proofed to be efficient and simple to describe the UHF signal in time–frequency domain. The accuracy is up to 95% discriminating UHF signals of different sensor positions using the SVM classifier, which is helpful for localisation of the PD source. The approach is also applied to the PD pattern recognition in the actual 252 kV GIS tank. The features are efficient to classify three typical PD defect patterns. A novel system of feature extraction and classification is summarised conclusively. 7 Acknowledgments This work was supported by China Scholarship Council (CSC, grant no: 201606280066), the National Natural Science Foundation of China (grant no. 51521065), the National Key Basic Research Program (‘973’ Program) of China (grant no. 2015CB251001), and Program for New Century Excellent Talents in University. 8 References 1Hikita, M., Ohtsuka, S., Matsumoto, S.: ‘Recent trend of the partial discharge measurement technique using the UHF electromagnetic wave detection method’, IEEJ Trans. Electr. Electron. Eng., 2007, 2, (5), pp. 504– 509 2Judd, M.D., Farish, O., Hampton, B.F.: ‘The excitation of UHF signals by partial discharges in GIS’, IEEE Trans. Dielectr. Electr. 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Publication Year: 2017
Publication Date: 2017-10-12
Language: en
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