Transformer Paper Expected Life Estimation Using ANFIS Based on Oil Characteristics and Dissolved Gases ( Case Study : Indonesian Transformers )

This article presents an algorithm for modelling an Adaptive Neuro Fuzzy Inference System (ANFIS) for power transformer paper conditions in order to estimate the transformer’s expected life. The dielectric characteristics, dissolved gasses, and furfural of 108 running transformers were collected, which were divided into 76 training datasets and another 32 testing datasets. The degree of polymerization (DP) of the transformer paper was predicted using the ANFIS model based on using the dielectric characteristics and dissolved gases as input. These inputs were analyzed, and the best combination was selected, whereas CO + CO2, acidity, interfacial tension, and color were correlated with the paper’s deterioration condition and were chosen as the input variables. The best combination of input variables and membership function was selected to build the optimal ANFIS model, which was then compared and evaluated. The proposed ANFIS model has 89.07% training accuracy and 85.75% testing accuracy and was applied to a transformer paper insulation assessment and an estimation of the expected life of four Indonesian transformers for which furfural data is unavailable. This proposed algorithm can be used as a furfural alternative for the general assessment of transformer paper conditions and the estimation of expected life and provides a helpful assistance for experts in transformer condition assessment.


Introduction
A power transformer is a piece of equipment that is designed for years of usage and generally has good reliability, with a life expectancy up to 40 years or more.The condition of the transformer naturally decreases as it is operated because of the processes of aging.However, it may become damaged faster than normal.During operation, transformers experience things that accelerate aging such as increased water content, temperature, and oxidation [1].Without proper maintenance, the aging agents such as oxygen, heat, and moisture will cause acid formation and other materials that negatively impact cellulose insulation.Thus, these transformers may become unreliable and incapable of functioning as expected.The remaining life of a power transformer is an important aspect that the owner of the transformer needs to know.A good transformer assessment will give better insights on the condition of the transformer for maintenance purposes.This will result in better power transfer efficiency because of the smaller loss of opportunity resulting from power outages.
Aging power transformers have become a great concern for providers of electric power around the world, along with the growing needs of the power system.The oil-cellulose insulation in transformers will continue aging over a lifetime, and the cellulose insulation cannot be replaced.The aging of oil-immersed cellulose insulation decreases the mechanical strength and further limits the operation of the transformer [2].
Many data confirm that most of the damage to the transformer is related to the failure of the insulation system, while the life of the cellulose insulation is the life of the transformer [3].Failures of transformers that are operating are commonly dominated by events such as a short circuit or a lightning strike.Due to the aging on the transformer, the mechanical strength of the paper insulation will decrease, and short circuit events like this can cause the ultimate failure of the transformer.Due to their random occurrence, we cannot be certain when the final failure of the transformer is going to happen.However, if the strength of the latest paper insulation can be known, it is possible to make an estimation of when these events might occur [1].
Different methods of diagnosis have been used to estimate the insulation degradation rate, i.e., dissolved gas analysis (DGA) and the estimation of the aging based on the loading history.Furanic compounds have been a concern in the past 20 years because they offer measurement of specific chemical compounds that can be transformed directly into an indicator of the aging of the transformer's paper insulation [4].
Furfural testing data of transformers in Indonesia is limited, unlike DGA and dielectric characteristics.Therefore, it is necessary to find an alternative way to do transformer paper insulation condition assessments using other test parameters.This study collected 108 transformer testing datasets, consisting of dielectric characteristics, Dissolved Gas Analysis (DGA), and furfural (2FAL).
Several different approaches to paper insulation condition prediction have been reported such as a Fuzzy based method using interfacial tension and acidity as the input in [5], a Fuzzy Logic model using CO and CO 2 as the input in [6], a ML (Machine Learning) approach using CO 2 and acidity as the input in [7].The research in [8,9] shows the possibility of using neural networks to predict the furfural level.Another study uses the loading and temperature history to calculate and predict the degree of polymerization of the transformer paper, as reported in [10].
ANFIS has been used as estimator in several studies for many purposes.For transformer diagnosis purposes, various studies report the use of ANFIS to do dissolved gas analysis and complement the existing methods as shown in [11][12][13].For its good purpose as an ultimate estimator [14], this article presents the development of an ANFIS model to help the experts in transformer paper condition assessment using widely available data, dielectric characteristics, and dissolved gasses as the input variables when furfural data is unavailable.

Methodology
This study used power transformer test data consisting of dielectric characteristics, dissolved gas analysis, and furfural.The transformers that were included in this study were 108 transformers with the nominal voltage of 150 and 500 kV and a capacity of 10 up to 100 MVA.There were 38 units under 30 MVA, 25 units between 30 and 60 MVA, and 45 units 60 MVA and more.All of the transformers used were mineral-oil immersed free breathing transformers with conservators.The transformers discussed in this article were already in operation for at least two years up to 53 years.These transformers underwent routine tests once a year and, if necessary, a few times a year.Dielectric characteristics and dissolved gas analysis tests are routinely performed, and the test datasets were collected.There are a lot of factors that influence transformer paper aging; the effects of nominal voltage, capacity, and the design of transformer on the aging of the paper are beyond the scope of this research and will further be ignored.Figure 1 shows one of the transformers included in the study.The ANFIS modelling process will be elaborated below.

Transformer Paper Deterioration Indicator
The degree of polymerization test is done in order to measure precisely the degradation of the paper insulation used in the transformer.Cellulose, which is used as solid transformer insulation, is a linear polymer molecule consisting of hundreds of glucose units.DP is the average number of glucose molecules that make cellulose chains.The DP value decreases by the time proportional to the broken cellulose molecule.The deterioration rate is highly dependent on the temperature.Based on IEEE C57 140 standard, DP values vary from about 1200 for new paper to at least 100 for aging paper.At DP 200, the paper has lost about 70% of the initial tensile strength.At this point, the paper becomes brittle and the transformer is considered at the end of its life because it has lost its mechanical strength.
Furans concentration is a very important aging indicator for the evaluation and life assessment of transformers in service [15,16].Furanic compounds are easier to get than DP and TS (Tensile Strength) because we only need to test an oil sample rather than taking paper samples of in service transformers.The furanic compound is one of the byproducts of the aging of oil-immersed cellulose paper and can be directly correlated to the degree of polymerization.Furfural (2FAL) is a compound that is tested to determine the aging rate of transformer paper.For non-upgraded kraft paper transformers, 2-Furaldehyde (2FAL), or so-called furfural, can be linked to the degree of polymerization by Chendong [17] Equation (1).

Adaptive Neuro-Fuzzy Inference System
The architecture and learning procedure underlying ANFIS (adaptive neuro fuzzy inference system) is a fuzzy inference system implemented in the framework of adaptive networks [13].By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy logic if-then rules) and stipulated input-output data pairs [18].
Two of the first parts of the process of fuzzy logic, the fuzzification of the input parameters and the use of the use of membership functions (MF), are used in ANFIS.The difference is in the output of the membership functions of Sugeno system, which can be either linear or constant.

Transformer Paper Deterioration Indicator
The degree of polymerization test is done in order to measure precisely the degradation of the paper insulation used in the transformer.Cellulose, which is used as solid transformer insulation, is a linear polymer molecule consisting of hundreds of glucose units.DP is the average number of glucose molecules that make cellulose chains.The DP value decreases by the time proportional to the broken cellulose molecule.The deterioration rate is highly dependent on the temperature.Based on IEEE C57 140 standard, DP values vary from about 1200 for new paper to at least 100 for aging paper.At DP 200, the paper has lost about 70% of the initial tensile strength.At this point, the paper becomes brittle and the transformer is considered at the end of its life because it has lost its mechanical strength.
Furans concentration is a very important aging indicator for the evaluation and life assessment of transformers in service [15,16].Furanic compounds are easier to get than DP and TS (Tensile Strength) because we only need to test an oil sample rather than taking paper samples of in service transformers.The furanic compound is one of the byproducts of the aging of oil-immersed cellulose paper and can be directly correlated to the degree of polymerization.Furfural (2FAL) is a compound that is tested to determine the aging rate of transformer paper.For non-upgraded kraft paper transformers, 2-Furaldehyde (2FAL), or so-called furfural, can be linked to the degree of polymerization by Chendong [17] Equation (1).

Adaptive Neuro-Fuzzy Inference System
The architecture and learning procedure underlying ANFIS (adaptive neuro fuzzy inference system) is a fuzzy inference system implemented in the framework of adaptive networks [13].By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy logic if-then rules) and stipulated input-output data pairs [18].
Two of the first parts of the process of fuzzy logic, the fuzzification of the input parameters and the use of the use of membership functions (MF), are used in ANFIS.The difference is in the output of the membership functions of Sugeno system, which can be either linear or constant.
The structures of two input ANFIS models are shown in Figure 2. By using the input-output data sets, ANFIS makes a FIS (Fuzzy Inference System).The MF parameters are set by training using a hybrid algorithm, which is combination of backpropagation and least squares.This led to the ability of the FIS system to learn the training data.
The structures of two input ANFIS models are shown in Figure 2. By using the input-output data sets, ANFIS makes a FIS (Fuzzy Inference System).The MF parameters are set by training using a hybrid algorithm, which is combination of backpropagation and least squares.This led to the ability of the FIS system to learn the training data.At the first layer, all nodes are adaptive or the parameters can be changed by Equation (3).
With x (or y) as the input from the first node, while Ai or Bi is a linguistic label (high, low, medium), μ and μ are the membership functions of each node.
At the second layer, each node is labelled Π, which is non-adaptive.This is obtained by multiplying each input signal to generate an output signal using Equation (4).
Each output node represents the degree of activation.In the third layer, each node is non-adaptive, labelled N, and its function is to normalize the degree of activation by calculating the ratio of the first node of the previous layer to all layers of the previous output.Equation (5) is as follows.
In the fourth layer, each node is adaptive, by the following Equation (6).
f1 and f2 are fuzzy logic if-then functions, is the output of the third layer, and + + is an adaptive parameter.
In the fifth layer, each node in this layer is non-adaptive, labelled Σ; this node generates the output function of the ANFIS system by Equation (7).At the first layer, all nodes are adaptive or the parameters can be changed by Equation (3).
With x (or y) as the input from the first node, while A i or B i is a linguistic label (high, low, medium), µ A i and µ B i are the membership functions of each node.
At the second layer, each node is labelled Π, which is non-adaptive.This is obtained by multiplying each input signal to generate an output signal using Equation (4).
Each output node represents the degree of activation.In the third layer, each node is non-adaptive, labelled N, and its function is to normalize the degree of activation by calculating the ratio of the first node of the previous layer to all layers of the previous output.Equation ( 5) is as follows.
In the fourth layer, each node is adaptive, by the following Equation (6).
f 1 and f 2 are fuzzy logic if-then functions, w i is the output of the third layer, and (p i x + q i y + r i ) is an adaptive parameter.
In the fifth layer, each node in this layer is non-adaptive, labelled Σ; this node generates the output function of the ANFIS system by Equation (7).

Potential Input Variables
The dielectric characteristics and a dissolved gases test dataset of the transformers were collected and analyzed in this study.

Dielectric Characteristics
Temperature, water, and oxygen are the main agents of cellulose degradation as well as the oxidation of the oil.Insulation decomposition is a chemical phenomenon.The three mechanisms of degradation, namely, hydrolysis, pyrolysis, and oxidation, act simultaneously.Hydrolysis is the decomposition of a chemical compound by reaction with water.Pyrolysis is the decomposition or transformation of a compound caused by heat.Oxidation is the combination of a substance with oxygen [1].
When the transformer insulation undergoes degradation, the dielectric characteristics of the oil will change from the initial value.The dielectric characteristics parameters used in this article consist of According to [19] acidity, has a relationship with the DP value through the oxidation of insulation oil that degrades the insulation paper through a hydrolysis process.In a transformer, we expect that paper aging is the main source of low molecular weight acids.Oil acidity is measured as the sum of all acids and expressed as the total acid number [2].
Paper aging decomposition is also related to interfacial tension, which is sensitive to the presence of soluble polar contaminants from solid insulating material [3].The interfacial tension of oil in a transformer is the object of one of the tests done to assess the water content in solid insulation according to [1].As the time elapsed, the degradation of the oil as well as the paper was indicated by the darker color of the aged oils [20].

Dissolved Gas Analysis
Dissolved gas analysis (DGA) was used to identify the gasses released in the paper-oil composite insulation as the results of the thermal aging process [20].Normal operation will also result in the formation of some gases.In fact, it is possible for some transformers to operate throughout their useful life with substantial quantities of combustible gases present [21].
Operating a transformer with large quantities of combustible gas present is not a normal occurrence but it does happen, usually after some degree of investigation and an evaluation of the possible risk.
The concentration of gasses detected by the DGA test used in this article are: CO and CO 2 are a result of the thermal aging of paper insulation through an oxidation process [2,3,20].The amount of dissolved carbon monoxide and carbon dioxide in oil could be correlated with the degree of polymerization and the tensile strength of the paper.When insulating papers are degraded, their degree of polymerization decreases, and CO and CO 2 are generated.The higher the temperature, the more gasses are generated [22].

Modelling ANFIS for Transformer Paper Condition
The proposed algorithm for building an ANFIS model for transformer paper condition estimation is shown in Figure 3 Energies 2017, 10, 1135 6 of 18 • C2H2 (acetylene) • Tdcg (Total Dissolved Combustible Gas) CO and CO2 are a result of the thermal aging of paper insulation through an oxidation process [2,3,20].The amount of dissolved carbon monoxide and carbon dioxide in oil could be correlated with the degree of polymerization and the tensile strength of the paper.When insulating papers are degraded, their degree of polymerization decreases, and CO and CO2 are generated.The higher the temperature, the more gasses are generated [22].

Modelling ANFIS for Transformer Paper Condition
The proposed algorithm for building an ANFIS model for transformer paper condition estimation is shown in Figure 3   (1) Data Preparation: In the first stage, DP is estimated from 2FAL using Equations ( 1) and (2).
The correlation of estimated DP and potential variables consists of dielectric characteristics, and the dissolved gases of transformer oil are analysed.The best combination of input variables for predicting DP is selected.The data from 108 transformers are then divided into training and testing datasets.76 datasets will be used for training, and 32 datasets will be used to evaluate the proposed model.(2) ANFIS Modelling: The training dataset is used for building the ANFIS model.The next step is to find the optimal combination of the Membership Function (MF).The number and type of MF for each input variable is selected, the model of each combination is trained using the training dataset, and each model is tested to find the satisfactory combination.(3) Accuracy Evaluation: The proposed model is tested using the testing datasets, and then the error is calculated both from training and testing.

Prediction Accuracy and Evaluation
There are several criteria that can be used to do the performance evaluation of a transformer paper condition model.The accuracy of the proposed model has been evaluated using these different methods.

Mean Absolute Error (MAE)
This error evaluation criterion measures the difference between the estimated DP and the target DP.
Equation ( 8) calculates MAE where f i and t i are respectively the average difference of the estimated and target DP values of the i transformer, whereas N is the amount of DP predicted [23].

Symmetric Mean Absolute Percentage Error (SMAPE)
This criterion evaluates the prediction error as a percentage of the actual or target DP value using Equation (9) [24,25].
Provided that the data are strictly positive, a better measure of relative accuracy can be obtained based on the log of the accuracy ratio, log (Ft/At).This measure is easier to analyze statistically and has valuable symmetry and unbiasedness properties [26].

Root Mean Squared Error (RMSE)
RMSE is a measure of accuracy to compare the forecasting errors of different models for a particular variable and not between variables, as it is scale-dependent [27].This is a criterion that minimizes the variance of the error distribution.For a target sequence t and forecast sequence f with N time steps, it is calculated by Equation (10).

Transformer Paper Expected Life Estimation
The result of the ANFIS model is DP prediction.This DP value indicates the condition of the transformer paper.The life of the paper insulation is the life of the transformer [3].Estimated percentage remaining life (%Eprl) can then be calculated using Equation (11).%Eprl = 100 − Log 10 (DP) − 2.903 −0.00602 (11) The DP value of cellulose decreases from its initial value (DP 0 ) due to cellulosic chain termination.The relationship between chain scission (η) and measured DP is calculated using Equation (12).
The Arrhenius Equation ( 13) about the aging of paper is shown below.
R is the molar gas constant (8.314J/mole/K), T is the absolute temperature in Kelvin, and Ea is the activation energy in kilojoules per mole.A is a constant that is dependent on the chemical conditions.
The chemical degradation of cellulose can be described, as above, by the above equation, which can be reconstituted into the equation below to determine the residual life of the transformer.In order to calculate expected life estimation of the transformer in years, Equation ( 14) is used.
Equation ( 15) is completed with coefficients that are needed.
Remnant Life = A is a constant using the results of [28,29], which are 2 × 10 8 for non-upgraded kraft paper and 0.67 × 10 8 for thermally upgraded paper.HST is the hot spot temperature rise from the hot spot of the winding.The standard HST in Indonesia is 68 K from IEC (International Electrotechnical Commission) 60076-2 [30] which set the HST of transformer at 78 K and was then corrected using K a -10.Ea is the activation energy, which is uncertain depending on the presence of oxygen and water.Based on [31], which models the remaining lifetime of the power transformer derived from the result of previous research [28,29], the energy activation used for expected life estimation is 111 kJ/mol.

Transformer Dielectric Characteristics and Dissolved Gases Data
The predicted DP from the ANFIS model can be used as an alternative expected life estimation calculation for the transformer paper insulation if the current furfural level is unknown.Tables 1-4 show the dielectric characteristics and dissolved gases data from the three transformers to be assessed in this paper.

Results and Discussion
From transformed DP based on furfural data collected, a correlation analysis was performed on each of the dielectric characteristics, as shown in the Table 1. Figure 4 shows the scatterplots of acidity, interfacial tension, and color.Those three parameters have higher correlation with the DP value than do water content and voltage breakdown, which is proven by r (correlation coefficient).

Correlation Analysis
Correlation analysis is a highly general and therefore very flexible data analytic system.Basic linear regression may be used whenever a quantitative variable, the dependent variable is to be studied as a function of, or in relationship to, any factors of interest, the independent variables [32].
Linear regression is used in this study to find the highly-correlated parameters of dielectric characteristics and DGA to make a transformer paper condition assessment model.A correlation coefficient is a number that quantifies a type of correlation and dependence, meaning statistical relationships between two or more values in fundamental statistics.The correlation coefficient r is in the value range of −1 and +1.The closer 'r' is to −1 or +1, the more significant the correlation.If the value of 'r' is closer to +1, this means that the correlation between two variables is positive.Otherwise, if the value of 'r' is closer to −1, this means that the correlation between two variables is negative.
In this study, the correlation is verified by a t-test with α = 0.05.If the value of 'P' < α, this means that the result of linear regression is significant.
Table 5 shows that acidity, interfacial tension, and color are correlated with DP and are potential as transformer paper condition predictors.According to [19], acidity has a relationship with DP value through the oxidation of the insulation oil that degrades the insulation paper through a hydrolysis process.Interfacial tension is sensitive to the presence of soluble polar contaminants from solid insulating material [3].As the time elapsed, the degradation of the oil as well as the paper was indicated by the darker color of the aged oils [20].
Table 6 shows the correlation analysis of the DGA values, which resulted in TDCG, CO, and CO2 having relatively high correlation with the DP value.TDCG (Total Dissolved Combustible Gasses) is not used as a potential predictor because it is originally the sum of H2, CH4, CO, C2H2, C2H4, and C2H6.The highest concentration of TDCG comes from CO, which makes a high multicollinearity of CO and TDCG.

Correlation Analysis
Correlation analysis is a highly general and therefore very flexible data analytic system.Basic linear regression may be used whenever a quantitative variable, the dependent variable is to be studied as a function of, or in relationship to, any factors of interest, the independent variables [32].
Linear regression is used in this study to find the highly-correlated parameters of dielectric characteristics and DGA to make a transformer paper condition assessment model.A correlation coefficient is a number that quantifies a type of correlation and dependence, meaning statistical relationships between two or more values in fundamental statistics.The correlation coefficient r is in the value range of −1 and +1.The closer 'r' is to −1 or +1, the more significant the correlation.If the value of 'r' is closer to +1, this means that the correlation between two variables is positive.Otherwise, if the value of 'r' is closer to −1, this means that the correlation between two variables is negative.
In this study, the correlation is verified by a t-test with α = 0.05.If the value of 'P' < α, this means that the result of linear regression is significant.
Table 5 shows that acidity, interfacial tension, and color are correlated with DP and are potential as transformer paper condition predictors.According to [19], acidity has a relationship with DP value through the oxidation of the insulation oil that degrades the insulation paper through a hydrolysis process.Interfacial tension is sensitive to the presence of soluble polar contaminants from solid insulating material [3].As the time elapsed, the degradation of the oil as well as the paper was indicated by the darker color of the aged oils [20].
Table 6 shows the correlation analysis of the DGA values, which resulted in TDCG, CO, and CO 2 having relatively high correlation with the DP value.TDCG (Total Dissolved Combustible Gasses) is not used as a potential predictor because it is originally the sum of H 2 , CH 4 , CO, C 2 H 2 , C 2 H 4 , and C 2 H 6 .The highest concentration of TDCG comes from CO, which makes a high multicollinearity of CO and TDCG.CO and CO 2 are a result of thermal aging of paper insulation through oxidation process [2,3,20].Figure 5 shows the scatterplot of CO + CO 2 as opposed to the DP value.The correlation coefficient (r) of CO + CO 2 is the highest for the DGA values, making it a better potential variable as a transformer paper condition predictor than other forms of DGA.CO and CO2 are a result of thermal aging of paper insulation through oxidation process [2,3,20].Figure 5 shows the scatterplot of CO + CO2 as opposed to the DP value.The correlation coefficient (r) of CO + CO2 is the highest for the DGA values, making it a better potential variable as a transformer paper condition predictor than other forms of DGA. Figure 4 shows the scatterplots of estimated DP versus potential independent variables.The correlation of DP and acidity was statistically obtained with a correlation coefficient r of −0.432 and a p-value less than 0.05.This means that acidity has negative correlation with DP when the transformer paper is getting worse, the DP value is going down, and the acidity of the oil insulation is increasing.
The correlation of DP and interfacial tension was statistically obtained with a correlation coefficient r of 0.732 and a p-value less than 0.05.This means that interfacial tension has positive Figure 4 shows the scatterplots of estimated DP versus potential independent variables.The correlation of DP and acidity was statistically obtained with a correlation coefficient r of −0.432 and a p-value less than 0.05.This means that acidity has negative correlation with DP when the transformer paper is getting worse, the DP value is going down, and the acidity of the oil insulation is increasing.
The correlation of DP and interfacial tension was statistically obtained with a correlation coefficient r of 0.732 and a p-value less than 0.05.This means that interfacial tension has positive correlation with DP; when the DP value decreased, the interfacial tension of the oil insulation decreased.
The correlation of DP and color was statistically obtained by a correlation coefficient r of −0.686 and a p-value less than 0.05.This means that color has a negative correlation with DP; as the DP value decreases, the color of the oil insulation is getting darker.
The correlation of DP and CO + CO 2 was statistically obtained by a correlation coefficient r of −0.578 and a p-value less than 0.05.This means that CO + CO 2 has a reversed correlation with DP; as the DP value decreases, the amount of + CO 2 dissolved in the transformer oil is increased.
From dielectric characteristics, after content and voltage breakdown have relatively low correlation with the estimated DP.In dissolved gases, H 2 , CH 4 , C 2 H 2 , C 2 H 4 , and C 2 H 6 have low correlation with the estimated DP [33].Therefore, these parameters are not included as further potential input variables.

Various Combination of Input Variables
From the correlation analysis, several independent variables were statistically obtained, including CO + CO 2 , acidity, interfacial tension, and color.The various combinations of these independent variables were then tested to get the best predictors.Parameters such as R-Sq, R-Sq (adj), R-Sq (pred), and Mallows Cp are the specifications used in choosing the best predictor model.From Table 7, the best combination of variables is number 13, which consists of CO + CO 2 , acidity, IFT (Interfacial Tension), and color with the highest R-Sq, while the R-Sq (pred) value is not far from R-Sq (adj), and the mallows Cp is close to the number of predictors plus one.

Membership Functions Selection
The MF number of each input into the ANFIS model influences the accuracy of DP prediction.To obtain the optimal ANFIS model, various combinations of membership functions have been tested.Table 8 shows various combinations of MF numbers used as considerations for selecting the MF number in creating the ANFIS model.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, wherein, when given a different transformer scenario, the tendency of error is very high.A combination of 15, the green line indicates a similarly low training error and testing error.This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good.

MF Type MF Shape MF Type MF Shape
The type of MF varies by shape.After the combination of variations in the number of MFs with the highest accuracy, MF type selection was performed with respect to training and testing RMSE.Table 9 shows the different shapes and types of MF.
Table 10 shows the various combinations of MF type.A red row shows a high testing error even though the training error is very small.This shows the overfitting of the training model, where, when given a different transformer scenario, the tendency of error can be very high.From the selection of MF types, Table 10 shows that combination 15, with TrapMF (Trapezoid Membership Function), has the lowest RMSE training and testing values.Figure 6 shows the RMSE training and testing graph of various combinations of numbers and types of MF.The higher the graph, the greater the error that occurs.Combination 15 shows the lowest RMSE testing value, with a relatively low RMSE training value as well.

ANFIS Model Result and Evaluation
The various parameter inputs to the ANFIS model (CO + CO 2 , acidity, IFT, and color) has been developed based on the 76 transformers that were used as a training data set with the membership function selection shown in Table 11. Figure 6 shows the structure of the ANFIS model developed.The prediction result from the ANFIS model tested uses the testing data set that consists of 32 different transformers from the training data set.Figure 7 shows the DP value target and the prediction result made by the ANFIS model, following the error from training and testing dataset.
Figure 7a,b show the estimated DP from the ANFIS model tested using the training dataset and the testing dataset.Blue dots show the targets of DP, and the red dots show the prediction results of the ANFIS model.Figure 7c,d show the residual value of the target and prediction results.It can be seen that the ANFIS is model able to predict the DP value using CO + CO 2 , acidity, interfacial tension, and color as input variables.
The performance indicators in Table 12 suggest that the ability of the ANFIS model to predict DP from multiple parameters has an accuracy of 89.07%for the training dataset and 85.75% for the testing dataset.

Figure 2 .
Figure 2. Network structure of an Adaptive Neuro Fuzzy Inference System (ANFIS) model.The training obtains as many rule numbers as does the training data as shown below.Rule 1: IF x is A1 AND y is B1 THEN f1 = 1 Rule 2: IF x is A2 AND y is B1 THEN f2 = 2 Rule 3: IF x is A1 AND y is B2 THEN f3 = 3 Rule 4: IF x is A2 AND y is B2 THEN f4 = 4 …. and so on where x and y are the input of the fuzzy logic, and fi is the output of a constant.At the first layer, all nodes are adaptive or the parameters can be changed by Equation (3).

Figure 2 .
Figure 2. Network structure of an Adaptive Neuro Fuzzy Inference System (ANFIS) model.

Figure 7 .
Figure 7. Results of the ANFIS model.(a) Degree of Polymerization prediction results of 76 training transformers; (b) Residual value of DP target and prediction results of 32 testing transformers; (c) Residual value of DP target and prediction results of 76 training transformers; (d) Residual value of DP target and prediction results of 32 testing transformers.

Table 5 .
The correlation coefficients of DP against the dielectric characteristics for oil-filled transformers.

Table 6 .
The correlation coefficients of DP against the dissolved gasses for oil-filled transformers.

Table 5 .
The correlation coefficients of DP against the dielectric characteristics for oil-filled transformers.

Table 6 .
The correlation coefficients of DP against the dissolved gasses for oil-filled transformers.

Table 7 .
Various combinations of independent variables for DP prediction.

Table 8 .
Various combinations of membership function (MF) numbers.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 9 .
Different MF types and shapes.

Table 10 .
Various combinations of MF types.

Table 11 .
Membership function (MF) number and type of created ANFIS model.

Table 12 .
Evaluation criteria of the model.

Table 12 .
Evaluation criteria of the model.

Table 12 .
Evaluation criteria of the model.