Deep learning–based surface contamination severity prediction of metal oxide surge arrester in power system

Abstract

This paper presents an advanced technique based on cross-Stockwell transform (XST) and sparse autoencoder to predict the surface contamination severity of metal oxide surge arrester (MOSA) employing leakage current signal. Generally, MOSAs in power system network are exposed to different environmental conditions where its condition may degrade due to accumulation of pollutants, which may cause premature failure of it. Hence, system reliability can get affected. Therefore, monitoring the surface condition of MOSA is very important. In this proposed technique, MOSA leakage current signals of different surface contamination severity have been cross-correlated with leakage current recorded at the clean surface in joint time-frequency plane through XST, which is an extended version of ST. Thereafter, sparse autoencoder, a deep learning framework, has been applied to extract potential deep feature from leakage current-converted XST matrices. The extracted deep features have been classified through different classifiers. It has been observed that the proposed technique yields satisfactory accuracy regarding the estimation of surface contamination severity of MOSA. Therefore, the proposed method can be implemented to monitor the surface condition of MOSA, and it may be applied for topologically similar problems.

1 INTRODUCTION

Metal oxide surge arresters (MOSAs) are used as an important device for power transmission and distribution system, as it absorbs energy associated with the switching and lightning surges. Normally, in any electrical power system network, switching or lightning surge can cause an explosion or catastrophic failure of several costly equipment [1-3]. This may affect the reliability of the system. Therefore, surge arresters have significant impact on insulation coordination of any power system network.

It should be noted that MOSA consists of stacked metal oxide varistors (normally ZnO varistor), which is covered by a housing. The number of varistors depends on the rated voltage level of MOSA. Generally, the housing may be porcelain or polymeric, which is used to protect the varistor from outer environmental pollution. In this work, polymeric-housed MOSA has been considered for experimental purpose. A simplified equivalent model of MOSA is shown in Figure 1. In this model, C denotes the capacitance of MOSA. R denotes the non-linear resistance of metal oxide blocks, and R_S refers to the external surface resistance of MOSA, which may vary because of the accumulation of pollutants on the MOSA surface.

FIGURE 1

Simplified MOSA model

The condition of MOSA surface may get significantly affected due to accumulation of polluted particles, that is, salt, sand, chemical pollutant [1]. The pollutant forms a contaminated layer on the surface of MOSA, which is a long-term process. It should be noted that the presence of salt and other contaminants forms a conduction path on the surface of MOSA when the surface is wet [4]. Consequently, the surface resistance R_S in Figure 1 decreases, which increases the magnitude of the leakage current through MOSA surface. Since the surface resistance R_S decreases with the increase in pollution severity, the leakage current flow through MOSA may get affected with the change in contamination degree. Due to the increased magnitude of surface leakage current, the current density at different points on the surface increases, which leads to power loss. This results in the formation of dry-bands, which leads to electric field enhancement at different points on the insulation surface. The consequence is the initiation of dry-band discharges, which further promotes erosion and tracking on the surface. These combined effects can trigger surface discharge, which introduces distortions in the leakage current waveform [1]. These distortions bring non-stationary characteristics in the leakage current waveform. Therefore, leakage current through MOSA follows non-linear dynamics with surface contamination. It is noteworthy that surface discharges at highly contaminated MOSA surface may overheat the MOSA and can cause irreversible damage to MOSA, which further induces premature failure of MOSA [1, 2]. Failure of MOSAs results in unwanted interruption in power supply and may affect the condition of other costly devices like transformer. Therefore, regular estimation of the surface contamination severity of MOSAs in service is necessary in order to maintain stable operation in a system.

Several methods can be used to monitor the surface condition of MOSA. Out of them, analysis-based leakage current, more specifically resistive leakage current, is one of the popular methods. Resistive leakage current signature has been used to estimate the condition of surge arrester [2, 4–6]. It is noteworthy that the accurate extraction of resistive leakage current requires an input voltage profile [2]. However, it is difficult to acquire the input voltage waveform precisely from the high-voltage side. Therefore, extraction of resistive leakage current may not be accurate all the time. It is noteworthy that the leakage current of MOSA becomes distorted under polluted condition. Hence, analysis based on harmonic components of leakage current does not always provide accurate information regarding the surface condition of the MOSA.

Considering the aforementioned limitations, a methodology has been proposed in this work, which can sense the surface contamination of MOSA based on time-frequency characteristics of leakage current signal. As stated earlier, the contaminated layer on the surface of MOSA introduces distortion in the leakage current waveform [1, 2, 7]. Therefore, Stockwell transform (ST) can be an efficient technique to analyse the distorted characteristics of leakage current signals. ST is a method to analyse any non-stationary signals through joint time-frequency frame. It has to be noted that ST imposes several distinct advantages over traditional joint time-frequency analysis techniques (wavelet transform) such as its robustness against noise, ability to retain absolute phase information of the signal at each frequency [8-10]. Stockwell transformed-based feature extraction technique has been widely used in areas related to electrical, mechanical and biomedical engineering [9-12]. In this work, cross-ST (XST), which is an extended form of ST, has been implemented to bring out the change in non-stationary characteristics of leakage current with surface contamination. XST offers some advantages over generalised ST such as the two-time series signal can be cross-correlated through this method in both joint time-frequency space. Hence, XST-based analysis of leakage current signal has more potential in order to bring out the changes with surface contamination. After that, sparse autoencoder, an automated feature extraction technique based on deep learning framework, has been implemented in this study to extract suitable features from XST matrices. Thereafter, extracted features are statistically analysed through one-way ANOVA test and highly discriminant features are selected. Finally, the selected features are classified through several standard classifiers. Based on the result, it has been observed that the proposed method yields an accuracy level of 99% in order to estimate the surface contamination severity of polymeric-housed MOSA. A brief overview of the proposed module is represented in Figure 2.

FIGURE 2

Brief representation of the proposed technique

2 EXPERIMENTAL TESTS

2.1 Artificial surface contamination of MOSA

In this study, in field 11 kV polymeric-housed MOSAs have been imported from the local power utility. The technical specification of the samples is tabulated through Table 1. Here, the surface of the samples has been contaminated artificially through the ‘solid layer method’ as prescribed in IEC 60507 [2, 7, 13]. This method is well accepted and has been reported in many published literature [7, 14]. So this method has been adopted in this work for slurry deposition on the MOSA surface. For this purpose, different proportions of NaCl and kaolin has been mixed with deionised water to form a slurry, which has been coated on the MOSA surface. It is noteworthy here that kaolin is the insoluble compound, whereas (NaCl) is the soluble compound in this slurry. After that, coated MOSA has been allowed to dry for at least 24 h (at a humidity level of 75% and a temperature of 28°C). For the coating of slurry on the MOSA surface, a paintbrush is used.

TABLE 1. Technical specifications of sample

Property	Specification
Rated voltage (kVrms)	11
Housing type	Polymeric
Lightning impulse current 8/20 μs (kA)	5
No of varistor	3
Total creepage distance (mm)	320

It should be mentioned here that the samples have been thoroughly cleaned using deionised water and isopropyl alcohol prior to coating. An image of artificially surface-contaminated MOSA is presented in Figure 3. However, it may be observed from Figure 2 that the coating may not be uniformly deposited. The non-uniformity of coating happens because of the evaporation of water present in the NaCl-kaolin mixture. Moreover, practically speaking, in an outdoor environment, the deposition of contaminants will not be uniform all the time. Therefore, non-uniform coating is a more realistic scenario, compared to considering uniform coating. Thus, the real-life surface condition of MOSA has been better emulated in this study to assess the condition of MOSA surface.

FIGURE 3

Image of surface-contaminated MOSA

2.2 Leakage current measurement

Based on IEC 60507 [12], an experimental setup has been prepared in order to record leakage current of MOSA. Figure 4 shows the schematic diagram of the experimental setup along with a data acquisition system. In order to apply high voltage to the sample, a 500 V/250 kV, 50 Hz, 150 kVA testing transformer has been used in this setup. A water resistance of 180 kΩ has been connected between the high-voltage terminal of the testing transformer and the sample in order to limit high current flow during any accidental case. The leakage current flown through the sample can be recorded from the terminal of the current shunt of 10 kΩ using a digital oscilloscope (DSO). It is noteworthy that a protective circuit has been connected across the current shunt in order to protect the DSO from any kind of accidental flashover. Based on this setup, leakage current signature of MOSA has been acquired with a sampling frequency of 50 kHz at two voltage level, that is, 10 and 11 kVrms, respectively. In this work, the leakage current of MOSA has been recorded at a controlled environment chamber of Thermotron^® maintaining the relative humidity of 70%. Note that the initial part of the leakage current signal has been discarded to avoid transients at the start of the experiment. Therefore, steady part of leakage current signals has been selected for further analysis purpose.

FIGURE 4

Experiment setup for leakage current measurement of MOSA

2.3 Surface contamination severity measurement

According to the literature, the ratio of NaCl in the coated slurry directly affects the surface conductivity of MOSA [2, 4]. After acquiring the leakage current, the severity of each artificially coated surface has been measured through equivalent salt deposition density (ESDD). ESDD (expressed as weight of salt per unit area) has been used to measure the severity of contamination over an insulating surface [13]. In order to measure ESDD of each artificially coated MOSA surface, the procedure given in IEC 60815 has been adopted in this work [15]. For that purpose, the coated slurry has been collected from MOSA surface. After that, the collected slurry has been dissolved in 100 ml distilled water. Thereafter, the solution has been stirred and kept for 30 min, and the conductivity of the solution has been measured through a conductivity measuring device (shown in Figure 5). The measured conductivity is then converted to the conductivity at 20°C in Equation (1) [15]:

$${\sigma }_{20}={\sigma }_{\theta }\left[1-t\left(\theta -20\right)\right]$$(1)

FIGURE 5

Measurement of the surface conductivity of surface contaminated MOSA

In this equation, ${\sigma }_{20}$ is the conductivity of the solution in (μS/m) at 20°C, ${\sigma }_{\theta }$ is the conductivity at θ°C, and t is the constant whose value depends on the temperature [14]. Based on the conductivity at 20°C (${\sigma }_{20}$), the salinity of coated layer can be measured through the equation given as

$$S_m={(5.7{\sigma }_{20})}^{1.03}$$(2)

Based on the salinity, ESDD value can be determined as

$$ESDD=S_m\times \frac{V_m}{A_m}$$(3)

In this equation, A_m is the surface area of the MOSA, S_m is the salinity of the coated layer, and V_m refers to the volume of the solution. It is noteworthy that by varying the content of NaCl and kaolin in the coated slurry, a total of 275 artificial contamination profiles having different ESDD value have been created in this work.

As mentioned in Section 2.2, leakage current for each artificial contamination profile has been recorded at two voltage levels, that is, 10 and 11kVrms, respectively. Hence, a total of 550 leakage current signals have been acquired in this work. As ESDD value reflects the degree of contamination in MOSA surface, based on the ESDD range given in Table 2, recorded leakage current signals have been distributed into five classes. Hence, the number of leakage current signal for each class is 110. Detail description of ESDD range and corresponding surface contamination severity is shown in Table 2.

TABLE 2. Surface contamination severity categorisation based on the measured equivalent salt deposition density (ESDD) value

Class	ESDD range (mg/cm^2)	Severity of surface contamination
EA	0–0.05	Very low
EB	0.05–0.1	Low
EC	0.1–0.2	Average
ED	0.2–0.3	High
EE	> 0.3	Extreme

3 PROPOSED METHODOLOGY

3.1 Stockwell transform

Stockwell transform or S-transform provides a joint time-frequency distribution of a time series [8]. ST of a time series g(t) can be mathematically expressed as

$$S_g(\tau ,f)=\underset{-\infty }{\overset{+\infty }{\int }}g(t)w(t-\tau ,f)e^{-i2\pi ft}dt$$(4)

where $w(t,f)$ is normalised Gaussian window [8], which can be expressed as

$$w(t,f)=\frac{1}{\sigma (f)\sqrt{2\pi }}{e}^{\frac{-t^2}{2\sigma {(f)}^2}}$$(5)

Here, τ denotes translation of the window $w(t,f)$with a dilation σ, where $\sigma (f)$is the frequency-dependent standard deviation, which is inversely proportional to absolute frequency [16] and can be expressed as

$$\sigma (f)=\frac{1}{\left|f\right|}$$(6)

Through Equations (5) and (6), Equation (4) can be rewritten as

$$S_g(\tau ,f)=\frac{\left|f\right|}{\sqrt{2\pi }}\underset{-\infty }{\overset{+\infty }{\int }}{g(t)e}^{-i2\pi ft}\frac{(-{(t-\tau )}^2{f}^2)}{2}dt$$(7)

ST of a time series can alternatively express as

$$S_g(\tau ,f)=\underset{-\infty }{\overset{+\infty }{\int }}G(\alpha +f)W(\alpha ,f)e^{(i2\pi \alpha \tau )}d\alpha f\ne 0$$(8)

where $G(\alpha +f)$ is Fourier transform of time series g(t) and $W(\alpha ,f)=\exp (-\frac{2{\pi }^2{\alpha }^2}{f^2})$, Fourier transform of time-domain Gaussian window. As leakage current signal is discrete in nature, Equation (7) has been represented in discrete form replacing $\tau$ with jT and f with n/NT, where T is sampling time of time series. The discrete form of ST can be written as

$$\begin{array}{ccc}\hfill S_g(jT,\frac{n}{NT})& =& \sum _{p=0}^{N-1}G[\frac{p+n}{NT}]\exp \left(\frac{-2{\pi }^2{p}^{2}F}{a+{(b\times n^c)}^2}\right)\hfill \\ & & \exp \left(\frac{i2\pi nj}{N}\right)n\ne 0\hfill \end{array}$$(9)

The Gaussian window used in this work has been expressed as

$$W(p,n)=\exp \left(\frac{-2{\pi }^2{p}^{2}F}{a+{(b\times n^c)}^2}\right)$$(10)

It should be noted here that the shape of the Gaussian window depends on the parameters F, a, b and c, and for the analysis of leakage current signals of MOSA, the parameter values have been taken as 1, 0, 1.2 and 1.5, respectively. However, detail theoretical foundation of ST may be found in [8–10, 16, 17].

3.2 Analysis of leakage current signal using XST

The main motivation of the present work is to preserve local and non-stationary characteristics of leakage current signal of MOSA. Therefore, the ST has been applied to the leakage current signals that returns a P × Q complex 2-D array, namely, S-matrix, where P denotes the frequency of the leakage current signal, whereas Q denotes the sample point of the signal. After that, the S-matrices of the leakage current signals have been cross-correlated with a reference S-matrix. It is noteworthy here that S-matrix of leakage current signal at the clean surface has been taken as reference in this work. The mathematical form of XST between two-time series i(t) and r(t) can be expressed as

$$XS{T}_{ir}(jT,\frac{n}{NT})=S_i(jT,\frac{n}{NT})\times {\left\{S_r(jT,\frac{n}{NT})\right\}}^{\ast }$$(11)

Here, ${\{S_r(jT,\frac{n}{NT})\}}^{\ast }$ represents complex conjugate of S-matrix of the reference signal r(t).

The main motivation of XST is to compare two non-stationary time series in joint time-frequency space. XST can measure the degree of similarity of two signal in time-frequency space. In this work, MOSA leakage current signal of different surface contamination severity is cross-correlated with a reference leakage current signal (recorded at the clean surface). Implementation of XST in this work offer some advantages like the influence of capacitive leakage current in cross-correlogram of two non-stationary leakage current can be neutralised. XST can minimise the effect of random uncorrelated noise present in any two cross-correlated signals. It means that if two signals are contaminated with random uncorrelated noise, then the effect of that noise will not be reflected in the cross-correlogram of these two signals, as cross-correlation coefficient value for random uncorrelated noise is very small. Considering the fact, analysis of MOSA leakage current through XST can be a good choice to predict the surface contamination severity from leakage current signature.

3.3 Deep learning-based feature extraction employing autoencoder

Type of feature extraction from input data has a significant impact on the performance of any kind of classification task. Feature extraction through a supervised way may induce misclassification due to redundant feature variables [18]. Therefore, sparse autoencoder, an unsupervised feature extraction technique based on deep learning framework, has been introduced in this work in order to extract feature from XST matrices. An unsupervised feature extraction technique based on deep learning framework not only yields excellent feature extraction capability but also can overcome the problem of data labelling [19]. Normally, an auto-encoder model consists of an encoder, decoder and hidden layers [18-20]. The encoder encodes the input data into the best feature hidden layer representation through the hidden layer, approximating minimum error. The hidden layer compresses the input data in its lowest possible dimension. After that, the decoder reconstructs the encoded features in the original form [18, 19]. Therefore, in an autoencoder model, all information of input data can be preserved in the encoded features. Schematic diagram of autoencoder is shown in Figure 6.

FIGURE 6

Schematic diagram of the autoencoder model for deep feature extraction

The encoder maps the input data $x{}_i\in$ℝ^C into its hidden representation through a sigmoid activation function, which is expressed as

$$Y_i=f_e(x_i)=\sigma (W{x}_i+b)$$(12)

Here, σ is the sigmoid activation function, and W∈ℝ^C×F represents the weight matrix of the encoder having F no of features and b∈ℝ^C is the bias term of the encoder. Thereafter, hidden representation has been decoded through another activation function expressed as

$$z_i=\sigma (\widehat{W}{x}_i+\widehat{b})$$(13)

In this equation, $\widehat{w}$∈ℝ^C×F is the weight matrix of the decoder, whereas $\widehat{b}$∈ℝ^C is the bias vector of the decoder.

In sparse autoencoder model, the sparsity of hidden feature can be encouraged through adding a sparsity regulariser to the cost function. Sparsity regulariser attempts to enforce a constraint on the sparsity of the output from the hidden layer [19]. The sparsity regulariser penalises the hidden layer value in such a way that few of them have the value larger than the sparsity parameter (${\rho }_s$). The sparsity regularisation term can be expressed as

$${\mathrm{\Omega }}_{spar}=KL({\rho }_s\parallel {\widehat{\rho }}_s)={\rho }_s\log \frac{{\rho }_s}{{\widehat{\rho }}_s}+(1-{\rho }_s)\log \frac{1-{\rho }_s}{1-{\widehat{\rho }}_s}$$(14)

Note here that ${\widehat{\rho }}_s=\frac{1}{m}\sum {}_1^m{y}_i$ is the average activation value over the input data [19], whereas KL function is ‘Kullback–Leibler divergence’ [20].

The cost function for the sparse autoencoder model in order to extract deep feature has been expressed in Equation (15):

$$\begin{array}{ccc}\hfill C(W,b)& =& \frac{1}{m}\sum _{i=1}^m{\left(\frac{1}{2}‖x_i-z_i‖\right)}^2+\frac{\lambda }{2}\sum _{j=1}^h\sum _{l=1}^5\sum _{i=1}^m{‖W‖}^2\hfill \\ & & +\beta \ast {\mathrm{\Omega }}_{spar}\hfill \end{array}$$(15)

The first part of cost function C(W,b) is associated to minimise reconstruction error where x and z represent input and reconstructed XST matrices, respectively. The second part of the cost function refers to the L2 weight regulariser. It is noteworthy that limiting the autoencoder model from overfitting is very important in order to extract suitable deep features. Therefore, L2 regularisation technique has been employed in order to check the overfitting of sparse autoencoder model [17]. The weight of L2 regulariser has been controlled through a coefficient value (λ) assigned to the parameter named ‘L2 weight regularisation’ [18]. The third part of the cost function is related to the sparsity regularisation. The impact of the sparsity regularisation term can be controlled through the coefficient (β), which is assigned to the parameter ‘sparsity regularisation’ in the sparse autoencoder model [18].

The parameters of the sparse autoencoder model such as, ‘number of hidden layers’, ‘number of training epochs’, ‘L2 weight regularisation’, ‘sparsity regularisation’, ‘sparsity proportion’ and ‘learning rate of the model’ have been taken as 50, 200, 0.005, 4, 0.01 and 0.005, respectively. In this paper, the absolute of 2-D time-frequency XST matrices, that is, |XST| matrices obtained from the acquired leakage current signal have been subsequently fed as inputs to the sparse autoencoder network for deep feature extraction. Thereafter, the sparse autoencoder network has been trained using the aforenoted parameters. As the number of hidden layers in the autoencoder network has been taken as 50, each leakage current-converted time-frequency XST matrix has been encoded into 50 hidden layer representations, that is, 50 deep features. It is noteworthy here that these 50 encoded deep features can reflect the characteristics of the particular XST matrix, as decoder activation function can reconstruct the particular XST matrix using these deep features. The performance of the sparse autoencoder network used in this work is shown in Figure 6. According to Figure 7, the performance of the network is satisfactory, as the best achieved mean square error between the input and reconstructed XST matrices is less than 0.01. It is noteworthy that the best training performance of the network has been achieved at the epoch value of 200. After extraction of deep features, highly statically significant deep features have been fed as inputs into four classifiers, namely, k-nearest neighbour (kNN), Gaussian Naïve Bayes (GNB), Random Forest (RF) classifier and support vector machine (SVM) in order to classify different classes of leakage current waveforms.

FIGURE 7

Performance of sparse autoencoder network

3.4 ANOVA test-based feature selection

Feature selection in any classification work has a significant impact as it finds out meaningful features from extracted feature variables. Hence, it can enhance the classifier performance as well as reduce the computational burden. In this work, the extracted features from XST matrix has been analysed through one-way ANOVA test. ANOVA is a statistical tool normally used to figure out the discriminative capability among the extracted feature variables. The ANOVA test uses F-test to compare the means between the groups to see how much the group means differ from each other. The outcome of the ANOVA test gives a probability (p) value. If the ‘p’ value is very low, it indicates high discriminative capability between the classes [20, 21].

4 RESULTS AND DISCUSSIONS

This work is aimed at estimating surface contamination severity of MOSA through leakage current signal. For this purpose, a total number of 550 leakage current signals has been acquired at different surface contamination profile of MOSA. Among the 550 leakage current signals, five signals recorded at 11 kVrms are portrayed in Figures 8 (a) to (e) with associated ESDD value of 0.01453, 0.07684, 0.1456, 0.27543 and 0.35298, respectively.

FIGURE 8

Leakage current waveforms at different surface contamination severity (a) very low, (b) low, (c) average, (d) high, and (e) extreme

It may be observed from Figure 7 that the magnitude of leakage current has been increased with ESDD value or the severity of surface contamination. According to Figure 8, it is evident that distortion in the leakage current increases at higher ESDD value. Presence of distortion introduces non-stationary behaviour in the leakage current waveform. Considering the above issue, in this study, XST has been implemented to bring out the changes in non-stationary characteristics of leakage current signal through cross-correlation in joint time-frequency space. For this purpose, all 550 leakage current signals have been transformed to S-matrix, which represents joint time-frequency characteristics of leakage current signal. The time-frequency spectrum of leakage current signal obtained from leakage current transformed S-matrices at low, high and extreme surface contamination severity is presented in Figures 9(a) to (c).

FIGURE 9

Time-frequency spectrum of leakage current at surface contamination severity (a) low, (b) high, and (c) extreme

Thereafter, obtained leakage current waveforms have been initially converted to time-frequency frame using XST taking leakage current at the clean surface as reference (using Equation 11). It is noteworthy that the total of 550 XST matrices has been produced in this study from the 550 recorded leakage current signals. The obtained time-frequency XST matrices of different leakage current waveforms have been subsequently fed as inputs to the sparse autoencoder network for deep feature extraction. Total 50 features have been extracted for each XST matrices through the sparse autoencoder network using the parameter setting mentioned in Section 3.3. After that, the extracted deep features have been statistically analysed through one-way ANOVA test in order to find the relevant features. It should be mentioned that threshold p-value for the ANOVA test has been taken as 0.000001. In addition, the false discovery rate (FDR) correction has been performed on the extracted deep features having p-value less than 0.000001 in ANOVA analysis. It is noteworthy that the FDR correction of the extracted features has been done in order to control false positive in classification result [17]. Finally, after FDR correction, highly correlated and statistically significant 10 deep features for each XST matrix features have been used for the purpose of classification.

The classifier task has been performed with 7:3 train-test ratio, that is, the classifier model is trained with the selected deep features of 70% XST matrices, whereas selected deep features from rest of the XST matrices have been used to evaluate the classifier model. Four standard classifiers, namely, SVM [22-24], kNN [25], GNB [26] and RF classifier [16] have been employed in order to classify the leakage current signal based on the selected deep features. To evaluate the performance of the proposed method, four statistical parameters, namely, accuracy, precision, specificity and sensitivity have been calculated from the respective confusion matrices. Note that classification task for all classifiers has been repeated for 20 times having 20 different combinations of train-test feature set. Hence, the classification parameters are taken as the mean of each iteration. The classification results are reported in Table 3.

TABLE 3. Classification report for different classification technique

Classification technique	Accuracy (ACC)(%)	Sensitivity (SEN)(%)	Specificity (SPE)(%)	Precision (PRC)(%)
k-Nearest neighbour classifier	98.75	98.81	98.88	98.79
Gaussian Naïve Bayes	98.84	98.95	98.98	99.02
Random Forest classifier	98.93	98.91	99.18	99.26
Support vector machine	99.03	99.17	99.35	99.32

According to Table 4, it may be observed that all the benchmark classifiers returned reasonably high accuracy indicating the robustness of the proposed technique. Based on the classification result, it is also pointed out that SVM classifier outperforms rest of the classifiers. It is noteworthy that the one-against-all (OAA) approach has been incorporated in this work for multiclass classification through SVM. In this approach, the classifier is trained to find the feature vector of a particular class against the feature vector of the remaining class [24]. In the SVM model, selection of kernel function is very important because it affects the model performance. In this work, the Gaussian radial basis function is selected as the kernel function. It should be noted that the hyper-parameters of the SVM model, that is, penalty factor γ and Gaussian kernel parameter σ have been optimised in order to get accurate prediction. The penalty factor is used to balance the model complexity and training error, whereas the kernel parameter reflects the distribution characteristics of training data [23]. Several optimisation techniques are used to tune the hyper-parameters. However, in this work, Grid search method [27] has been used to optimise the hyper-parameters. In this method, accuracy value has been taken as the objective function to optimise the hyper-parameters. However, the theoretical background of all the classification techniques has been given in [16, 22–26]. The detail classification performance of the proposed method using SVM classifier is presented in Table 4.

TABLE 4. Classification performance of the proposed scheme

Class	ACC (%)	SEN (%)	SPE (%)	PRC (%)
EA	98.78	98.98	99.11	99.19
EB	98.96	99.05	99.18	99.15
EC	98.94	99.11	99.08	99.19
ED	99.13	99.16	99.54	99.38
EE	99.32	99.48	99.78	99.71

The classification performance for SVM and RF classifier based on extracted deep feature from XST is compared with other time-frequency analysis technique like ST, continuous wavelet transform (CWT). According to Figure 10, it may be observed that the performance of both SVM and RF classifier utilizing XST based deep features is better than utilizing CWT and ST based deep features. It can be explained as XST correlates two-leakage current signal in joint time-frequency space and measure the similarity between them. Also, in XST, a reference signal is required to which all the recorded leakage current is compared. Due to the fact, XST based deep features are more effective compared to other time-frequency method in estimating the surface contamination severity of MOSA employing total leakage current.

FIGURE 10

Comparison with other time-frequency method (a) using support vector machine (SVM) classifier and (b) using Random Forest (RF) classifier

The performance of the proposed method has been compared with some published method in the literature. The main advantage of this method is that features are extracted automatically through the sparse autoencoder. There is no need of feature labelling in this work, whereas existing techniques are based on handcrafted features. According to Table 5, it is also observed that the proposed technique in this paper delivered better performance in monitoring the operating condition of MOSA.

TABLE 5. Performance comparison with published method

Reference	Extracted Feature	ACC (%)
[28]	Handcrafted	98.03
[2]	Handcrafted	98.78
This work	Automated	99.03

5 CONCLUSION

In this paper, an advanced technique based on deep learning framework has been proposed in order to predict the surface contamination severity of MOSA. For this purpose, leakage current signal of contaminated MOSA sample are cross-correlated with a reference leakage current (captured at the clean surface) in the time-frequency domain using XST. XST minimises the effect of uncorrelated random noise and also neutralises the effect of the capacitive component. In order to extract feature from XST cross-correlogram, the sparse autoencoder has been employed, which is a deep learning-based automated feature extraction technique. Investigation revealed that deep features extracted from XST returned the best performance with SVM classifier after one-way ANOVA test and FDR correction. However, other classification techniques have also returned satisfactory performance, which reflects the robustness of the extracted deep features from XST matrices. It has been also revealed that XST-based deep features yield better classification accuracy, compared with other time-frequency analysis technique like ST and CWT. A comparative study with published method also indicates that the proposed framework yields better performance. Therefore, the proposed deep learning framework can be potentially applied for surface contamination severity prediction of MOSA.