Monitoring Porcelain Insulator Condition Based on Leakage Current Characteristics

Insulator monitoring using leakage current characteristics is essential for predicting an insulator’s health. To evaluate the risk of flashover on the porcelain insulator using leakage current, experimental investigation of leakage current indices was carried out. In the first stage of the experiment, the effect of contamination, insoluble deposit density, wetting rate, and uneven distribution pollution were determined on the porcelain insulator under test. Then, based on the laboratory test results, leakage current information in time and frequency characteristics was extracted and employed as assessment indicators for the insulator’s health. Six indicators, namely, peak current indicator, phase shift indicator, slope indicator, crest factor indicator, total harmonic distortion indicator, and odd harmonics indicator, are introduced in this work. The obtained results indicated that the proposed indicators had a significant role in evaluating the insulator’s health. To evaluate the insulator’s health levels based on the extracted indicator values, this work presents the naïve Bayes technique for the classification and prediction of the insulator’s health. Finally, the confusion matrix for the experimental and prediction results for each indicator was established to determine the appropriateness of each indicator in determining the insulator’s health status.


Introduction
Outdoor insulators are important in electrical power transmission systems. However, the efficiency and health of the insulators are greatly impacted by numerous environmental factors, including wetness and contamination. Outdoor environmental factors, such as contamination and moisture, have a significant impact on insulator effectiveness. Moisture, such as rain and fog, in the presence of pollution reduces the surface resistance of insulators. Surface resistance lowering may result in higher leakage current flowing on the surface and dry band arcing. A large magnitude of leakage currents flowing on the surface over an extended length of time may produce insulator surface deterioration, which might eventually lead to flashover [1][2][3][4][5][6]. The unwanted discharge may result in a flashover phenomenon that leads to electrical grid disruption or even failure [7][8][9]. It is, therefore, crucial to monitor the status of the insulators to ensure that they are fit for purpose [10,11]. This would further strengthen the efficiency of the power grid and decrease its failure probability.
The evaluation of the performance of outdoor insulators continues to be a significant topic in the high-voltage community [12][13][14][15]. The use of the leakage current (LC) parameter in observing the performance of outdoor insulators has been popular and offers many advantages. This is because LC monitoring considers various environmental conditions, Regarding the classification and prediction of insulator health, the previous work in [33] introduces the support vector machine (SVM) for classifying the condition of the insulator under the effect of the different coating damage modes. The assessment of the contaminated insulators was performed using computer vision in [34] and k-nearest neighbors (k-NN) [35]. The results of these studies indicated that these techniques provide adequate efficiency and accuracy and that they are promising approaches since they are quick and easy to perform. Some researchers have evaluated the conditions of insulators using different artificial intelligence methods, as reported above. However, the application of the naïve Bayes method to estimate the insulator conditions based on the leakage current characteristics has not been investigated, and this will be discussed in our current work.
Our current work contributes to estimating the conditions of porcelain insulators, as follows: • Six indicators based on the measured LC characteristics in the time domain and frequency domain, namely, the peak current indicator, phase shift indicator, slope indicator, crest factor indicator, total harmonic distortion indicator, and odd harmonic indicator, were extracted by taking into consideration the significant effect of environmental factors on the performance of the overhead line insulators. Environmental factors, including the soluble deposit density, wetting rate, insoluble deposit density, and contamination ratio of the upper to the lower side of the insulator were taken into consideration while simulating the nature of insulators in service.

•
The classification of the state of insulators based on the proposed indicator values using the naïve Bayes approach was conducted.

•
The comparison of the performance of the proposed indicators using the confusion matrix for the actual insulator conditions and naïve Bayes prediction results was carried out.
The rest of this paper is structured as follows. Section 2 reviews the process of pollution of the insulators and discusses how LC is measured. Section 3 illustrates the proposed leakage current indicator expressions. Section 4 presents the experimental and modeling results. Finally, the conclusion is presented in Section 5.
The advantages of this study are: • The proposed indicators are useful to monitor the condition of overhead line insulators in real time. • Insulator condition estimation using LC indicators is simple, low cost, and accurate. • Applicable for any insulator type and any voltage level. • Monitoring insulator conditions on the transmission line (without removing the insulator and without interrupting the power line).

Test Sample
The porcelain insulators to be tested were collected from the transmission division of the national network in Malaysia. The selected insulators' main shape is portrayed in Figure 1. The insulators' actual specifications are tabulated as in Table 1. In this paper, a single disk of porcelain insulators and a string of three units of porcelain insulators were tested.

Test Facilities and Procedures
The IEC-507 standard, namely, "Artificial pollution tes and glass insulators to be used on AC systems" [36] was re the experimental setup. All experiments were carried out i with dimensions 50 cm × 50 cm × 75 cm in which the walls The chamber was installed with four inlet valves used for sp for the purpose of wetting. Figure 2a shows a schematic d polluted insulator experimental setup. A photograph of th ment used in the high-voltage laboratory is given in Figure  setup was composed of the following components: A is a tr

Test Facilities and Procedures
The IEC-507 standard, namely, "Artificial pollution tests on high-voltage ceramic and glass insulators to be used on AC systems" [36] was referred to while performing the experimental setup. All experiments were carried out in an artificial test chamber with dimensions 50 cm × 50 cm × 75 cm in which the walls were polycarbonate sheets. The chamber was installed with four inlet valves used for spraying insulators under test for the purpose of wetting. Figure 2a shows a schematic diagram for the high-voltage polluted insulator experimental setup. A photograph of the test setup and the equipment used in the high-voltage laboratory is given in Figure 2b. The experimental circuit setup was composed of the following components: A is a transformer (220 V/100 kV, 5 kVA, 50 Hz), B is a capacitive voltage divider, C is the test sample inside the chamber, D is a monitoring system to measure the leakage current, E is a resistive step-down divider (100:1) employed for the measurement of the LC and protection of the DAQ device, and F is a fog generator with a rate controller for wetting.

Wetting and Polluting
Prior to commencing the experiment, traces of grease and dirt were removed carefully for all specimens using alcohol liquid. Next, the insulators were dried for 24 h naturally. The contamination was then applied to the insulator surface based on the solid layer method [37][38][39][40]. The pollution was made up of two types of deposits: soluble deposit density (SDD), which is represented by sodium chloride salt (NaCl), and insoluble deposit density (NSDD), which was represented by kaolin. To prepare the SDD, the required amount of NaCl salt was mixed with 1000 mg of water to establish the pollution solution. Then, a conductivity meter was used to measure the conductivity of the polluted solution σσ at room temperature for three amounts of salt (10 g, 20 g, and 30 g) to compute three levels of SDD. Also, three amounts of kaolin (20 g, 40 g, and 60 g) were used to produce the NSDD levels listed in Table 2. Next, the conductivity of the pollution solution at 20 °C was calculated using Equation (1):

Wetting and Polluting
Prior to commencing the experiment, traces of grease and dirt were removed carefully for all specimens using alcohol liquid. Next, the insulators were dried for 24 h naturally. The contamination was then applied to the insulator surface based on the solid layer method [37][38][39][40]. The pollution was made up of two types of deposits: soluble deposit density (SDD), which is represented by sodium chloride salt (NaCl), and insoluble deposit density (NSDD), which was represented by kaolin. To prepare the SDD, the required amount of NaCl salt was mixed with 1000 mg of water to establish the pollution solution. Then, a conductivity meter was used to measure the conductivity of the polluted solution σ σ at room temperature for three amounts of salt (10 g, 20 g, and 30 g) to compute three levels of SDD. Also, three amounts of kaolin (20 g, 40 g, and 60 g) were used to produce the NSDD levels listed in Table 2. Next, the conductivity of the pollution solution at 20 • C was calculated using Equation (1): where σ 20 and σ σ , represent the solution conductivity at 20 • C, and the solution conductivity at the room temperature. θ is the temperature of the solution and b is a temperaturedependent factor that is determined to be 0.02 at = 27.5 • C using Equation (2) [36]. The SDD was calculated based on the IEC 60507 [36] and IEC 60815 [41] standards using Equation (3): where V and S represent the volume of pollution solution, and the insulator surface area, respectively. Meanwhile, Equation (4) was used to calculate NSDD according to the IEC-507 standard [36]: where w s and w i are the mass of the filter paper under contamination and under dry conditions, respectively. As shown in Table 2, three levels were determined for both SSD and NSDD: light, moderate, and high contamination. The sample was then polluted and hung in the test room and left drying for around 1 day to ensure that the polluted insulator was dried. The test room pressure remained constant throughout the experiment, matching the laboratory's ambient pressure. The temperature in the testing room was roughly 27.9 • C, which was about the same as the indoor temperature in the laboratory. The relative humidity inside the test room was set to 75% and monitored during the testing with the help of a humidity sensor. The spray technique was used to wet the insulator, with six nozzles regularly spaced around the test room wall. A control panel outside the test room was used to automatically calculate the fog flow rate. To achieve the moisture of insulators at different levels, three degrees of wetting rates Wt were applied, i.e., 3 mL/h, 6 mL/h, and 9 mL/h. Under both uniform and uneven contamination distributions, the porcelain was investigated. Also, three contamination ratios of the upper to the lower side of the insulator (P L /P u ), i.e., 1/3, 1/5, and 1/8, were selected in the uneven contamination case. The upper and lower surfaces of the insulator were polluted separately in the nonuniform pollution case to yield SDD u and SDD L , whereas the overall SDD can be met by Equation (5) [5,40]: where S u and S L are the area of the upper and lower surface of insulator, respectively. According to these selected pollution ratios, the SDD of the upper and lower sides (SDD u and SDD u ) can be satisfied by Equation (6):

Data Monitoring
As illustrated in the experimental setup in Figure 2, the input voltage values were obtained using a divider consisting of two capacitors with a ratio (C 1 to C 2 ) of 10,000:1. On the other side of the test chamber, the monitoring system consisted of a data acquisition (DAQ) card, oscilloscope, and a PC, which was used to measure LC. A resistive divider (100:1) was employed, since the DAQ's input voltage range is just 10 V. During the measurement, the LC data were captured from the divider and then transferred using a DAQ card to the PC. The captured data were saved in a CSV file after being displayed on a graphical user interface of the LabVIEW software. For measurement validation, the oscilloscope was utilized to compare with DAQ data reading. Finally, with the help of MATLAB software, the LC data saved were converted into the frequency domain using FFT.

Characteristic Parameter of Leakage Current
In this paper, six characteristics/indices were extracted in both the time and frequency domains of LC to predict the health of polluted insulators.

Leakage Current Indicators in Time Domain
The time and frequency domain signal of LC was used to derive all the leakage current indicator equations. The formulae presented in this section were used as the indicators of change in LC signal that was affected by the insulator conditions. In the time domain of LC, four indicators were selected. The first and second indicators, which were the peak of leakage current I m (denoted as x 1 ), found based on the absolute value of the current signal, and the phase shift φ between the applied voltage and LC (denoted as x 2 ) were extracted from the LC general equation, expressed as in Equation (7) [42]: where ω is the angular frequency equivalent to 2πf, with the value of frequency f in this study 50 Hz. As such, the first two characteristics can be defined as in Equations (8) and (9): Figure 3 illustrates how the phase difference φ between the applied voltage and LC can be determined for a clean and a polluted insulator. For a clean insulator, the phase difference φ between the applied voltage and LC appeared to be nearly 90 • (see Figure 3a). As the amount of pollution on the insulator increased, the phase difference φ between the applied voltage and LC decreased. Under heavily polluted circumstances, the phase difference φ between the applied voltage and LC became nearly zero (see Figure 3b).
The third indicator x 3 was extracted by calculating the slope of the line between two consecutive peaks of LC signal, expressed as in Equation (10): where ∆y n is the LC difference for adjacent peaks at the nth point for time and ∆x n is the time between these peaks. Figure 4a illustrates how the LC signal slope was calculated. The fourth indicator x 4 was obtained from the crest factor, which was calculated by dividing the peak value with the RMS value of the LC waveform, as shown in Figure 4b. As such, x 4 is expressed as in Equation (11): where RMS is root mean square, i i is each measured value, and n is the number of measurements.  The third indicator x3 was extracted by calculating the slope of the line between two consecutive peaks of LC signal, expressed as in Equation (10): where ∆yn is the LC difference for adjacent peaks at the nth point for time and ∆xn is the time between these peaks. Figure 4a illustrates how the LC signal slope was calculated. The fourth indicator x4 was obtained from the crest factor, which was calculated by dividing the peak value with the RMS value of the LC waveform, as shown in Figure 4b. As such, x4 is expressed as in Equation (11): where RMS is root mean square, ii is each measured value, and n is the number of measurements.   The third indicator x3 was extracted by calculating the slope of the line between two consecutive peaks of LC signal, expressed as in Equation (10) where ∆yn is the LC difference for adjacent peaks at the nth point for time and ∆xn is the time between these peaks. Figure 4a illustrates how the LC signal slope was calculated. The fourth indicator x4 was obtained from the crest factor, which was calculated by dividing the peak value with the RMS value of the LC waveform, as shown in Figure 4b. As such, x4 is expressed as in Equation (11): where RMS is root mean square, ii is each measured value, and n is the number of measurements.

Leakage Current Indicators in Frequency Domain
The frequency-domain signals of LC for polluted insulators have characteristic features at frequencies below 500 Hz. In this paper, the odd harmonic and total harmonic distortion (THD) of LC under 500 Hz were used to propose indicators for insulator condition assessment. The frequency characteristics of the LC are defined by the x 5 and x 6 indicators, as in Equations (13) and (14), respectively: where I n represent the nth harmonic and n is the odd-order harmonic number.

Classification Model
The naïve Bayesian classifier is a classification algorithm based on Bayes's theorem. Its underlying idea and building approach are more straightforward and simpler than those of support vector machines and neural networks. Furthermore, compared to other algorithms, the naïve Bayesian classifier algorithm suits the approach of this work, and brought great accuracy in classifying the insulator situations. The naïve Bayesian classifier theorem, which is employed in the classification of the suggested LC indicators, is explained in this section. Figure 5 depicts the flowchart of the procedures involved in extracting and categorizing the recommended indicators.
where ( ) k P z represents the previous probability of the zk class that can be found from , Nk is the number of samples within zk class, N is data set size, and ( | ) k P y z   represent the class-conditional probability. The main aim of the naïve Bayesian classifier is to determine ( | ) k P y z   based on the training samples in the zk class. All features are assumed to be independent by the naïve Bayesian classifier. As a result, the class-conditional probability can be written as in Equation (16):

Naïve Bayesian Classifier
To understand the naïve Bayesian method, consider y to be a collection of samples. Each sample contains n condition characteristics that represent its special traits, as well as one class label. All LC features are assumed to be interrelated in this work, while the class label is assumed to be separated. Assume that all training examples are classified into m classifications and that the class label of each sample changes from {z 1 , z 2 , . . . , z m }. As a result, any sample can be shown as an n-dimensional vector. → y = (y 1 , y 2 , . . . , y n ) would be a piece of testing data whose class label has to be determined. A naïve Bayesian classifier may compute the posterior probabilities and decide the class label for the new sample based on the previous and class-conditional possibilities of the new sample. A naïve Bayesian classifier uses Equation (15) to characterize the new sample's class label [43]: where P(z k ) represents the previous probability of the z k class that can be found from P(z k ) = N k /N, N k is the number of samples within z k class, N is data set size, and P( → y|z k ) represent the class-conditional probability. The main aim of the naïve Bayesian classifier is to determine P( → y|z k ) based on the training samples in the z k class. All features are assumed to be independent by the naïve Bayesian classifier. As a result, the class-conditional probability can be written as in Equation (16): To find the class label of → y , the Naïve Bayesian classifier can substitute the classconditional probability with Equation (16) and yield the decision function in Equation (17).
where P(y f z k )(1 ≤ f ≤ n) is an essential factor in determining the class label of the new sample.

Leakage Current Results
The LC findings of uniformly polluted insulators in both time and frequency domains with various SDD levels but fixed NSDD of 0.15 mg/cm 2 and Wt of 3 mL/h are shown in Figures 6 and 7. Figure 6 indicates that increased pollution severity causes a considerable rise in LC under specific values of NSDD, Wt, and P u /P L . The LC increase can be explained by the increase in conductivity of the pollution layer on the insulator's surface once subjected to wetness. Consequently, the LC flowed from the high voltage terminal to the ground in the form of positively and negatively charged ions. Some spot arcs were observed on occasion under high-contamination conditions, particularly in the existence of moisture. During the flashover, the signal of the LC appeared to be severely distorted, as shown in Figure 6d. Furthermore, when LC increased, the THD and harmonic values increased (see Figure 7), while the phase angle between the current and voltage decreased. The decrease in phase angle between the LC and voltage is due to the resistive current increasing with constant capacitive current. Once the contamination level on the insulator surface was raised, a clear change in the odd harmonics (3rd, 5th, 7th, and 9th) was observed (see Figure 7). As seen in Figure 8, the 3rd harmonic will increase to surpass the 5th, 7th, and 9th harmonics, with a clear increase in the 7th and 9th harmonics. Furthermore, during discharge activity on the insulator's surface, the 3rd harmonic is often substantially high [44,45].
tude Im, harmonics, THD, and phase shift angle ϕ) for different pollution levels under uniform pollution distribution for all investigated conditions. Under the clean condition, the 5th and 7th harmonics were greater than the 3rd harmonic. Furthermore, there were no signs of flashover. The LC rose marginally as the wetting rate increased when the clean insulators were tested under a specific NSDD. This indicates that wetting the insulator surface caused the flow of the charges from the high-voltage terminal to the ground to rise noticeably.           Table 3 provides the test results of the LC harmonic components' values (magnitude I m , harmonics, THD, and phase shift angle φ) for different pollution levels under uniform pollution distribution for all investigated conditions. Under the clean condition, the 5th and 7th harmonics were greater than the 3rd harmonic. Furthermore, there were no signs of flashover. The LC rose marginally as the wetting rate increased when the clean insulators were tested under a specific NSDD. This indicates that wetting the insulator surface caused the flow of the charges from the high-voltage terminal to the ground to rise noticeably.  Table 3 also shows the results of the uniformly polluted insulators with the change in SDD, Wt, and NSDD. Table 3 shows that the LC on a clean insulator's surface is very low, approximately 1.81 mA for single disk and 1.78 for string insulators. This indicates that under clean circumstances, the performance of the insulators is capacitive. Because of the capacitive property of LC, the phase shift angle between current and voltage will be about 90 • . Under the clean and dry scenario, the 5th harmonic is higher than the 3rd harmonic. Generally, the LC component test results in Table 3 show that:

1.
Under dry conditions, surface conductivity was minimal. Therefore, the influence of increasing SDD and NSDD on LC and LC characteristics in this condition was minor.

2.
The LC magnitude grew substantially as the contamination severity of SDD, NSDD, and Wt increased.

3.
As SDD, NSDD, and Wt increased and P u /P L decreased, odd harmonic values and THD increased. In contrast, the phase angle decreased. 4.
When the Wt was changed for a clean insulator under a specific NSDD, the LC value varies somewhat, as do the temporal and frequency characteristics of the LC. Figure 9 shows the LC indices of a clean (0.00 mg/cm 2 of SDD) insulator under different Wt and NSDD. Each indicator demonstrates a unique behavior when the wetting rate and NSDD were changed. Of note, there is no significant difference between different NSDD under the same Wt. The x 1 , x 3 , x 4 , and x 5 indices increased with the rise in both the

Indicators Trends under Different SDD
The leakage current indices x1, x3, x4, and x5 under different SDD, NSDD, Wt, and Pu/PL for single and string insulators are presented in Figure 10 and Table 4. The LC indicators of insulators under test increased with the increase in SDD under specific NSDD, Wt, and Pu/PL. On the contrary, the indices x2 and x6 of insulators decreased with the increase in SDD under the same conditions. For example, under NSDD of 0.25 mg/cm 2 , Wt of 6 mL/h and Pu/PL of 1/3, when SDD was 0.05, 0.1 and 0.2 mg/cm 2 , the x1 for the single disk insulator corresponded to 12.2, 15.4, and 26.6 mA, respectively. The x1 also increased by 26.2% and 118.03% when the SDD increased from 0.05 to 0.1 mg/cm 2 and from 0.1 to 0.2 mg/cm 2 , respectively. For x6, when the SDD was 0.05, 0.1 and 0.2 mg/cm 2 , x6 corresponded to 2.69, 1.31, and 0.63 mA, respectively. The LC indicators showed a similar trend and performance for the insulator string under 33 kV with minor variations, as illustrated in Table 5.  In contrast, the x 2 and x 6 decreased with the increase in both the Wt and NSDD. For example, when the Wt increased from 3 mL/h to 9 mL/h under NSDD = 0.15 mg/cm 2 , the x 2 decreased from 87.2 to 86.01 and x 6 decreased from 5.9 to 4.7.

Indicators Trends under Different SDD
The leakage current indices x 1 , x 3 , x 4 , and x 5 under different SDD, NSDD, Wt, and P u /P L for single and string insulators are presented in Figure 10 and Table 4. The LC indicators of insulators under test increased with the increase in SDD under specific NSDD, Wt, and P u /P L . On the contrary, the indices x 2 and x 6 of insulators decreased with the increase in SDD under the same conditions. For example, under NSDD of 0.25 mg/cm 2 , Wt of 6 mL/h and P u /P L of 1/3, when SDD was 0.05, 0.1 and 0.2 mg/cm 2 , the x 1 for the single disk insulator corresponded to 12.2, 15.4, and 26.6 mA, respectively. The x 1 also increased by 26.2% and 118.03% when the SDD increased from 0.05 to 0.1 mg/cm 2 and from 0.1 to 0.2 mg/cm 2 , respectively. For x 6 , when the SDD was 0.05, 0.1 and 0.2 mg/cm 2 , x 6 corresponded to 2.69, 1.31, and 0.63 mA, respectively. The LC indicators showed a similar trend and performance for the insulator string under 33 kV with minor variations, as illustrated in Table 5.

Indicator Trends under Different NSDD
The differences in the indicators are comparable to the previous case (pollution variation), and changes in the amount of increment/or decrement can be detected. The test findings in Table 5 demonstrate that under constant SDD, Wt, and Pu/PL, increasing the NSDD increases the x1, x3, x4, and x5, but decreases the x2 and x6. To further understand the relationship between NSDD and the suggested indices, Figure 11 displays the x1, x3, x4, x5, and x6 vs. NSDD curves with SDD of 0.2 mg/cm 2 , Wt of 6 mL/h, and Pu/PL of 1/1.   The differences in the indicators are comparable to the previous case (pollution variation), and changes in the amount of increment/or decrement can be detected. The test findings in Table 5 demonstrate that under constant SDD, Wt, and Pu/PL, increasing the NSDD increases the x 1 , x 3 , x 4 , and x 5 , but decreases the x 2 and x 6 . To further understand the relationship between NSDD and the suggested indices, Figure 11 displays the x 1 , x 3 , x 4 , x 5 , and x 6 vs. NSDD curves with SDD of 0.2 mg/cm 2 , Wt of 6 mL/h, and P u /P L of 1/1.

Indicator Trends under Different NSDD
The differences in the indicators are comparable to the previous case (pollution variation), and changes in the amount of increment/or decrement can be detected. The test findings in Table 5 demonstrate that under constant SDD, Wt, and Pu/PL, increasing the NSDD increases the x1, x3, x4, and x5, but decreases the x2 and x6. To further understand the relationship between NSDD and the suggested indices, Figure 11 displays the x1, x3, x4, x5, and x6 vs. NSDD curves with SDD of 0.2 mg/cm 2 , Wt of 6 mL/h, and Pu/PL of 1/1.

Indicator Trends under Different Wt
The relationship between the proposed indices x1-x6 and Wt for porcelain insulator under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and Pu/PL of 1/1 and different Wt is demonstrated in Figure 12. It is worth noting that when Wt increases, the x2 and x6 fall while the x1, x3, x4, and x5 increase. For example, under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and Pu/PL of 1/1, the x1 increased by 13.4% and 15.4% when Wt increased from 3 to 6 mL/h and from 3 to 9 mL/h, respectively, whereas under the same conditions, the x2 decreased by 72.1% and 57.2% when Wt increased from 3 to 6 mL/h and from 6 to 9 mL/h, respectively.

Indicator Trends under Different Wt
The relationship between the proposed indices x 1 -x 6 and Wt for porcelain insulator under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and Pu/PL of 1/1 and different Wt is demonstrated in Figure 12. It is worth noting that when Wt increases, the x 2 and x 6 fall while the x 1 , x 3 , x 4 , and x 5 increase. For example, under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and P u /P L of 1/1, the x 1 increased by 13.4% and 15.4% when Wt increased from 3 to 6 mL/h and from 3 to 9 mL/h, respectively, whereas under the same conditions, the x 2 decreased by 72.1% and 57.2% when Wt increased from 3 to 6 mL/h and from 6 to 9 mL/h, respectively.

Indicator Trends under Different Nonuniform Pollution Distribution (Pu/PL)
The relationship between proposed indices x1-x6 and nonuniform pollution distribution Pu/PL for a polluted porcelain insulator under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and Wt of 9 mL/h and different Pu/PL as an example is shown in Figure 13. It can be observed that an increase in Pu/PL causes an increase in the x2 and x6 and a decrease in the x1, x3, x4, and x5. This means that the sample under uniform contamination conditions is more dangerous in terms of flashover incidence than the sample under nonuniform pollution levels. The relationship between proposed indices x 1 -x 6 and nonuniform pollution distribution Pu/PL for a polluted porcelain insulator under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and Wt of 9 mL/h and different Pu/PL as an example is shown in Figure 13. It can be observed that an increase in Pu/PL causes an increase in the x 2 and x 6 and a decrease in the x 1 , x 3 , x 4 , and x 5 . This means that the sample under uniform contamination conditions is more dangerous in terms of flashover incidence than the sample under nonuniform pollution levels.
The relationship between proposed indices x1-x6 and nonuniform pollution distribution Pu/PL for a polluted porcelain insulator under SDD of 0.2 mg/cm 2 , NSDD of 0.35 mg/cm 2 , and Wt of 9 mL/h and different Pu/PL as an example is shown in Figure 13. It can be observed that an increase in Pu/PL causes an increase in the x2 and x6 and a decrease in the x1, x3, x4, and x5. This means that the sample under uniform contamination conditions is more dangerous in terms of flashover incidence than the sample under nonuniform pollution levels.

Insulator Condition Classification Based on Test Preparation
In this section, the ranges of the indicators corresponded to the level of SDD, NSDD, Wt, and Pu/PL are classified. The experimental data indicated that the values of x1, x3, x4, and x5 increased in proportion to an increase in SDD, NSDD, and Wt, but a decrease in Pu/PL. Meanwhile, the indicators x2 and x6 decreased with an increase in SDD, NSDD, and Wt, and decrease in Pu/PL. The proposed index values in the normal range were observed under the clean and low-pollution cases with Wt less than 4 mL/h and NSDD less than 0.2 mg/cm 2 . In this case, the possibility of discharge occurrence is almost nonexistent. According to indicator results in Table 5, the insulator was in an abnormal state under low contamination (0.05 mg/cm 2 ) with heavy wetting Wt (9 mL/h) and medium and high NSDD (0.25 and 0.35 mg/cm 2 ) for all contamination distribution (Pu/PL), except when Pu/PL = 1/8. In addition, the insulator under examination displayed an abnormal condition in the presence of moderate pollution (0.12 mg/cm 2 ) under moderate wetting Wt of 6 mL/h, NSDD of 0.25 mg/cm 2 , and Pu/PL of 1/1 and 1/5. The probability of a discharge occurring in these conditions is low, except in cases of extreme wetting, where the possibility of flashover increases. Meanwhile, the critical condition of the in- Figure 13. The impact of P u /P L on indicator shift.

Insulator Condition Classification Based on Test Preparation
In this section, the ranges of the indicators corresponded to the level of SDD, NSDD, Wt, and P u /P L are classified. The experimental data indicated that the values of x 1 , x 3 , x 4 , and x 5 increased in proportion to an increase in SDD, NSDD, and Wt, but a decrease in P u /P L . Meanwhile, the indicators x 2 and x 6 decreased with an increase in SDD, NSDD, and Wt, and decrease in P u /P L . The proposed index values in the normal range were observed under the clean and low-pollution cases with Wt less than 4 mL/h and NSDD less than 0.2 mg/cm 2 . In this case, the possibility of discharge occurrence is almost nonexistent. According to indicator results in Table 5, the insulator was in an abnormal state under low contamination (0.05 mg/cm 2 ) with heavy wetting Wt (9 mL/h) and medium and high NSDD (0.25 and 0.35 mg/cm 2 ) for all contamination distribution (Pu/PL), except when P u /P L = 1/8. In addition, the insulator under examination displayed an abnormal condition in the presence of moderate pollution (0.12 mg/cm 2 ) under moderate wetting Wt of 6 mL/h, NSDD of 0.25 mg/cm 2 , and P u /P L of 1/1 and 1/5. The probability of a discharge occurring in these conditions is low, except in cases of extreme wetting, where the possibility of flashover increases. Meanwhile, the critical condition of the insulator under test was found under two circumstances: first, under medium contamination conditions with Wt of 9 mL/h, NSDD of 0.35 mg/cm 2 , and all contamination distribution P u /P L cases; and second, when SDD is high under medium and heavy levels for Wt, NSDD, and all P u /P L cases. The flashover possibility occurring in these conditions is high, especially under high wetting and high NSDD.

Insulator Condition Classification Based on Proposed Indicators
To develop a statistical technique for identifying diagnostic indicator borders based on the x 1 , x 2 , x 3 , x 4 , x 5 , and x 6 inputs, the naïve Bayes classification algorithm [46] was trained with the experimental data to predict the insulator's state. In this study, MATLAB's Deep Learning Toolbox was employed to develop the classification model. In the classification procedure, 952 data sets for each indicator were used in the classification process using the naïve Bayes classifier algorithm, where 70% of the data (666 data) were chosen for the model training, 15% of the data (143 data) were utilized for the model performance verification, and the other 15% of the data (143 data) were selected for the model testing, as shown in Figure 14. The boundary classification results of indicators x 1 , x 2 , x 3 , x 4 , x 5 , and x 6 based on naïve Bayes classification are also shown in Figure 14.
In the classification procedure, 952 data sets for each indicator were used in the classifi-cation process using the naïve Bayes classifier algorithm, where 70% of the data (666 data) were chosen for the model training, 15% of the data (143 data) were utilized for the model performance verification, and the other 15% of the data (143 data) were selected for the model testing, as shown in Figure 14. The boundary classification results of indicators x1, x2, x3, x4, x5, and x6 based on naïve Bayes classification are also shown in Figure  14.  Figure 15 depicts the limitations of the suggested indicators for diagnosing insulator conditions (normal, abnormal, and critical). Taking indicator x1 as an example, the insulator condition is normal when the x1 value is less than 7.59 mA, abnormal when it is about 20.88 mA, and critical when it is more than 46.6 mA. Of note, the restriction was set at 75% of each level's data in the box plot ( Figure 14). Therefore, the insulator state is normal when x1 is less than 9.33 and abnormal when x1 is between 15.9 mA and 25.3 mA; otherwise, the insulator condition is critical.  Figure 15 depicts the limitations of the suggested indicators for diagnosing insulator conditions (normal, abnormal, and critical). Taking indicator x 1 as an example, the insulator condition is normal when the x 1 value is less than 7.59 mA, abnormal when it is about 20.88 mA, and critical when it is more than 46.6 mA. Of note, the restriction was set at 75% of each level's data in the box plot ( Figure 14). Therefore, the insulator state is normal when x 1 is less than 9.33 and abnormal when x 1 is between 15.9 mA and 25.3 mA; otherwise, the insulator condition is critical.

Determination of Indices' Performance
To determine the performance of the proposed indices precisely, the ability of the indicators to accurately estimate the insulator state taken from the data set of 952 tests observation was examined. The sensitivity, precision, and accuracy of these indices were calculated using the confusion matrix shown in Figure 16 during the assessment based on the naïve Bayes classification. The parameters of the confusion matrix were specified based on the insulator condition preparation. The decision of test results and proposed indices are defined as:

1.
True positive (TP) represents the number of insulator tests that have been properly classified using the indicators to have pollution, meaning they have the pollution.

2.
True negative (TN) represents the number of correctly classified insulator tests using the indicators as clean and it in fact is clean.

3.
False positive (FP) represents the number of misclassified insulator tests using the indicators as polluted, but in fact they are polluted.

4.
False negative (FN) represents the number of insulator tests misclassified using the indicators as polluted, but in fact are not polluted. classified using the indicators to have pollution, meaning they have the pollution. 2. True negative (TN) represents the number of correctly classified insulator tests using the indicators as clean and it in fact is clean. 3.
False positive (FP) represents the number of misclassified insulator tests using the indicators as polluted, but in fact they are polluted. 4.
False negative (FN) represents the number of insulator tests misclassified using the indicators as polluted, but in fact are not polluted. Experimentally, 905 test results out of 952 total tests reflected the insulator condition correctly, whereas 47 test results provided negative results. The explanation for the erroneous test results is a lack of implementation of pollutants on the insulator surface in a proper way or measuring-device error. In comparison to the total number of test outcomes, the number of prediction results for each indicator varied.
The variation in the prediction results may assist in determining which indicators are the best. It can be observed that the indices with a high number of correct prediction results are the best and will achieve high accuracy.
According to the indicator-prediction output, the greatest number of correct predicted results was observed for indicator x6 (906), followed by x3 (894), x4 (890), x1 (883), x5 (879), and x2 (873). As a result, the highest indicator accuracy is x6, followed by x3, x4, x1, x5, and x2 accordingly, as shown in Table 6. Meanwhile, the greatest sensitivity was in indicator x3, followed by x6, x4, x1, x5, and x2 accordingly. Moreover, the "best" performance is that where the variance between sensitivity and specificity is the least [47]. According to Table 5, the smallest difference between sensitivity and specificity is shown with the indicator x6, followed by x3, x4, x1, x5 and x2 accordingly. The sensitivity, precision, and accuracy of these indices were calculated using the confusion matrix shown in Figure 16 during the assessment.  Experimentally, 905 test results out of 952 total tests reflected the insulator condition correctly, whereas 47 test results provided negative results. The explanation for the erroneous test results is a lack of implementation of pollutants on the insulator surface in a proper way or measuring-device error. In comparison to the total number of test outcomes, the number of prediction results for each indicator varied.
The variation in the prediction results may assist in determining which indicators are the best. It can be observed that the indices with a high number of correct prediction results are the best and will achieve high accuracy.
According to the indicator-prediction output, the greatest number of correct predicted results was observed for indicator x 6 (906), followed by x 3 (894), x 4 (890), x 1 (883), x 5 (879), and x 2 (873). As a result, the highest indicator accuracy is x 6 , followed by x 3 , x 4 , x 1 , x 5 , and x 2 accordingly, as shown in Table 6. Meanwhile, the greatest sensitivity was in indicator x 3 , followed by x 6 , x 4 , x 1 , x 5 , and x 2 accordingly. Moreover, the "best" performance is that where the variance between sensitivity and specificity is the least [47]. According to Table 5, the smallest difference between sensitivity and specificity is shown with the indicator x 6 , followed by x 3 , x 4 , x 1 , x 5 and x 2 accordingly. The sensitivity, precision, and accuracy of these indices were calculated using the confusion matrix shown in Figure 16 during the assessment.

Conclusions
This paper reports on an experimental investigation of leakage current indices to determine the stability of polluted insulators. Porcelain insulators of 11 kV and 33 kV distribution lines under different levels of contamination (SDD), wetting rate (Wt), insoluble deposit density (NSDD), and nonuniform distribution pollution (Pu/PL) were investigated. The temporal and frequency characteristics of the leakage current were then derived from the laboratory test results and used as assessment indicators for the insulators' physical properties. The leakage current indication ranges were classified using the naïve Bayes technique into three levels of insulator health status. The suggested indicator's performance was evaluated using the confusion matrix approach. The indicators used in this study are all useful in detecting the pollution levels of the insulators. According to the confusion matrix study, the odd harmonic indicator x 6 , slope indicator x 3 , and crest factor indicator x 4 perform better than the others in terms of accuracy, with 0.918, 0.901, and 0.892, respectively.