Adaptive Abnormal Oil Temperature Diagnosis Method of Transformer Based on Concept Drift

: The diagnosis of abnormal transformer oil temperature is of great signiﬁcance to guarantee the normal operation of the transformer. Due to concept drift, the oil temperature abnormal diagnosis of the oil-immersed main power transformer is usually unstable via the classic data mining method. Thus, this paper proposes an adaptive abnormal oil temperature diagnosis method (AAOTD) of the transformer based on concept drift. First, the bagging ensemble learning method was used to predict the oil temperature. Then, abnormal diagnosis was performed based on the difference between the predicted oil temperature and the actual measured oil temperature. At the same time, based on the concept drift detection strategy and Adaboost ensemble learning methods, adaptive update of the base classiﬁer in the abnormal diagnosis model was realized. Experiments validated that the algorithm proposed in this paper can signiﬁcantly reduce the inﬂuence of concept drift and has higher oil temperature prediction accuracy. Furthermore, since this method only utilizes the existing power grid data resources to realize abnormal oil temperature diagnosis without extra monitoring equipment, it is an economic and efﬁcient solution for practical scenarios in the electric power industry.


Introduction
The transformer is a core piece of equipment in the power system [1]. If the transformer is overloaded for a long time, then the oil temperature of the transformer will be conspicuously higher than the normal standard, the components of the transformer will experience accelerated aging, and the working condition of the transformer will be unstable [2]. Therefore, the abnormal diagnosis of transformer's oil temperature is a significant issue to maintain the stable and safe operation of the transformer.
In recent decades, there has been important progress in the field of transformer oil temperature abnormal diagnosis. However, traditional transformer oil temperature abnormal diagnosis is generally based on the thermal circuit model and oil chromatographic analysis [3]. Based on the monitoring and analysis of related parameters from the chromatographic method, it can be judged whether the top-level oil temperature of the transformer is abnormal or not. Although the accuracy of the chromatographic method is high, it still has many problems, such as complicated parameter adjustment, the expensive cost of deployment, equipment maintenance, etc. Those problems make it difficult to widely use this method in most practical scenarios.
With the development of artificial intelligence research, scholars have attempted to use machine learning technology to analyze historical working condition data of the transformer to diagnose the abnormal oil temperature of the transformer. He et al. [4] proposed a method based on the artificial neural network to predict the top-level oil temperature of the transformer. Pradhan et al. [5] proposed a method based on the ANN algorithm to predict the internal oil temperature of the transformer. Du et al. [6] applied 1.
The diagnosis method of transformer abnormality is proposed. First, a series of base classifiers are generated in parallel using datasets randomly selected from a dataset of transformer historical operating conditions. Then an integrated decision is made with the help of a voting weighting mechanism to predict the oil temperature of the transformer. Finally, the abnormal diagnosis of the transformer is performed based on the relationship between the predicted oil temperature, the measured oil temperature and the time of the three judgment thresholds.

2.
A concept drift detection method based on three-branch decision and an adaptive update algorithm of classifier based on ensemble learning are proposed to judge which decision should be made through the test accuracy of the model. If the decision model is no longer applicable to the data at this stage, the base learners and weights are adjusted according to the learning effect of each base learner on the previous data. In this way, the poorly performing base learners in the model are continuously replaced to ensure that each base classifier in the model is optimized. The model converge quickly and achieves stable learning results, and the historical importance of the base classifier is not ignored. The model can be adapted to the concept drift data stream.
This paper is organized as follows. After the introduction in Section 1, Section 2 illustrates the dataset in this paper and explains the methodology of adaptive abnormal oil temperature diagnosis method (AAOTD). Section 3 analyzes and discusses the experimental results to validate the efficiency of AAOTD method. Section 4 summarizes the work of this paper and represents our perspective.

Dataset of the Transformer's Working Condition and Oil Temperature
The oil temperature working condition dataset of the oil-immersed transformer recorded the parameters related to the operation of the oil-immersed transformer. These parameters included the timestamp of working condition data (OCCUR_TIME); active power of the high-voltage side, medium-voltage side, and low-voltage side (YG_YC_G/Z/D); reactive power of the high-voltage, medium-voltage, and low-voltage side (WG_YC_G/Z/D); power factor of the high-voltage, medium-voltage, and low-voltage side (COS_G/Z/D); AC current RMS value of the high-voltage, medium-voltage, and low-voltage side (I_YC_G); winding temperature of the A/B/C phase (RZWDA/B/C_YC); and the oil temperature of the A/B/C phase (YWA/B/C_YC). The sample period was 5 min. The specific explanation of the above parameters related to the transformer is shown in Table 1: The external environment of the transformer can conspicuously influence the heat radiation of the transformer, such as the rise of the transform's restraining tempera-ture due to cold and windy weather. Therefore, in this paper, the weather data at the location of the transformer were also taken into consideration as important parameters, including the timestamp of weather data (OCCUR_TIME), local temperature (TEM-PERATURE), highest temperature of the day (HIGH_TEMPERATURE), lowest temperature of the day (LOW_TEMPERATURETEM), rainfall capacity (RAIN), wind direction (WIND_DIRECTION), wind velocity (WIND_VELOCITY), pressure (PRESSURE), and humidity (HUMIDITY). The sample period was 5 min. The specific explanation of the above parameters related to the weather data is shown in Table 2: The formal expression of the dataset for the abnormal oil temperature abnormal diagnosis of transformer in information system is IS = {(X, Y)}, where X are the attributes of working conditions with weather data and Y are the decision attributes, which are oil temperature from the sensors measurement at 1 phase of the transformer.

Abnormal Detection of Oil Temperature Based on Bagging Ensemble Learning
Based on background knowledge about the strong correlation between transformer working conditions and oil temperature, this paper proposes an abnormal detection approach of the transformer oil temperature based on bagging ensemble learning. According to bagging ensemble learning, the oil temperature prediction model is organized with a set of base classifiers and their power weights, which are trained in parallel by random sampling from historical working condition datasets and oil temperature datasets with replacements.
The steps of Algorithm 1 are described as follows: Oil Temperature Prediction Based on Bagging Ensemble Learning.
Output: Trained base classifiers C and their power weights w = {w 1 , w 2 , . . . , w k }. The Steps of Algorithm 1: Step 1. Sample k training datasets {IS 1 , IS 2 , . . . , IS k } from IS independently from X with corresponding Y, where X j ⊆ X and Y j ⊆ Y.
Step 2. Train base classifier C j from training set IS j . Therefore, k training datasets from IS j ∈ IS can independently construct k base classifiers C j ∈ C.
Step 3. The expected value of predicted oil temperature TY can be calculated as TY = ∑ k i=1 w i Y i from k prediction results Y i of C i , according to C i ∈ C, and w i ∈ w, where w i = 1/k and ∑ k i=1 w i = 1. According to trained base classifiers C and their power weights w from Algorithm 1, the present oil temperature can be predicted from the present working condition data. Furthermore, through 2 preset thresholds {α, β}, (0 < α < β < 1), the deviation rates between the predicted oil temperature and actual oil temperature can be used to judge the present working state of the transformer using the 3-way decision-making rule. The flowchart of the 3-way decision-making rule is shown in Figure 1.
IS j ∈ IS can independently construct k base classifiers C j ∈ C.
Step 3. The expected value of predicted oil temperature TY ′ can be calculated as from k prediction results Y i ′ of C i , according to C i ∈ C, and w i ∈ w, where w i = 1 k ⁄ and ∑ w i k i=1 = 1.
According to trained base classifiers C and their power weights w from Algorithm 1, the present oil temperature can be predicted from the present working condition data.
Furthermore, through 2 preset thresholds {α, β}, (0 < α < β < 1), the deviation rates between the predicted oil temperature and actual oil temperature can be used to judge the present working state of the transformer using the 3-way decision-making rule. The flowchart of the 3-way decision-making rule is shown in Figure 1.  Input: Present working condition data TS, present actual oil temperature Y, k base classifiers C = {C 1 , C 2 , . . . , C k } and their power weights w = {w 1 , w 2 , . . . , w k }, and 2 preset thresholds α and β.
Output: k base classifiers C and their power weights w, working state of transformer S. The Steps of Algorithm 2: Step 1. Input the present transformer's working condition data TS into k trained base classifiers C, respectively, and obtain k values of prediction Y 1 , Y 2 , . . . , Y k .
Step 2. Calculate the expected value of k prediction results TY = ∑ k i=1 w i Y i as the present predicted oil temperature.
The steps of Algorithm 2 are described as follows: Step 2.1. If TY − Y /Y ≤ α, then the working state of transformer S = FINE , and the algorithm ends. Otherwise, it goes to the next step.
Step 2.2. If α < TY − Y /Y < β, then the working state of transformer S = WARNING , which means the transformer has potential problems but can still work, and the algorithm ends. Otherwise, go to the next step.
Step 2.3. If TY − Y /Y ≥ β, then the working state of transformer S = ERROR , which means the transformer has serious problems and should stop to overhaul. Step 3. Algorithm ends and outputs C, w, and S.
The above oil temperature prediction and abnormal detection model based on bagging ensemble learning is the foundation of the oil temperature abnormal diagnosis method in this paper. However, if concept drift occurs in the working condition dataset of the transformer, then the prediction and abnormal detection model will have obvious bias and inevitably lead to the incorrect diagnosis result.

Concept Drift Solution of Oil Temperature Prediction and Abnormal Detection Model
Given that the specified factors, such as the aging of the transformer's components, cause the fluctuation of the transformer's working condition feature, concept drift always influences the result of oil temperature prediction. Therefore, in this paper, a concept drift solution based on performance testing is proposed to reduce the influence of concept drift.
Suppose that, during timeseries t = {t 1 , t 2 , . . . , t n }, there is transformer's working condition data series V x = {X t 1 , X t 2 , . . . , X t n } and the actual oil temperature data series V y = {Y t 1 , Y t 2 , . . . , Y t n }, where X t i ∈ V x represents the working condition data at t i time, and Y t i ∈ V y represents the oil temperature data at t i time. According to the transformer's working condition data series V x , the predicted oil temperature results V y = Y t 1 , Y t 2 , . . . , Y t n can be obtained from the oil temperature prediction model.

Definition 1. Relative Error Rate of Oil Temperature Prediction.
The relative error rate is the quotient of the absolute difference between the predicted oil temperature and actual oil temperature divided by actual oil temperature. The formal equation of relative error rate δ t i at time t i is as follows: Hence, the set of relative error rate during all time is δ = {δ t 1 , δ t 2 , . . . , δ t n }. The preset threshold γ of relative error rate is defined as the warning trigger. If the relative error rate δ t i is greater than threshold γ, then the prediction result considers that concept drift occurred. Otherwise, the prediction is considered without influence from concept drift.

Definition 2. Three-Way Decision-Making Rule of Conceptual Drift Whether Influences Oil
Temperature Prediction or not.
The thresholds of the 3-way decision-making rule were preset as µ and ν. Suppose that the set of relative error rate δ = {δ t 1 , δ t 2 , . . . , δ t n } exists k elements δ t , which are less than the warning threshold γ defined in definition 1. If k is greater than or equal to the threshold ν, then concept drift influences prediction model, and the detection result will be L = 'With Influence of Concept Drift'. If k is less than or equal to the threshold µ, then there is no influence of concept drift on prediction model, and detection result will be L = 'Without Influence of Concept Drift'. If k is less than the threshold ν but greater than the threshold µ, then the decision will be delayed, and detection result will be L = 'Delay to Make Decision'.
According to Definition 2, the formal expression of 3-way decision-making rule is: Note: k is the number of δ t < γ. Based on definition 2, a concept drift detection algorithm is proposed in this paper. When the relative error rates of a specified number of base classifiers are higher than the preset thresholds, the decision can be made that concept drift has occurred and has obviously influenced the result of the prediction model.
Moreover, to reduce the influence of concept drift on the prediction model, we designed a concept drift detection algorithm. The flowchart of concept drift adaptation is shown in Figure 2.
First, use the concept drift detection algorithm (see Algorithm 3 for details) to detect whether the current concept drift occurs. The process is to calculates the relative error rate on the prediction data using the oil temperature prediction algorithm, and then obtain the detection result through Definition 2. If the result is that the concept drift did not happen, the algorithm ends. If the result requires a delayed decision, then update the prediction data and redetect the concept drift. If the result is that the concept drift happens, the oil temperature prediction model must be adjusted (see Algorithm 4 below for details). The following is a detailed description of Algorithm 3, the detection algorithm of concept drift.
{ k ≤ μ, μ < k < ν, L = Without Influence of Concept Drift L = Delay to Make Decision Note: k is the number of δ t < γ. Based on definition 2, a concept drift detection algorithm is proposed in this paper. When the relative error rates of a specified number of base classifiers are higher than the preset thresholds, the decision can be made that concept drift has occurred and has obviously influenced the result of the prediction model.
Moreover, to reduce the influence of concept drift on the prediction model, we designed a concept drift detection algorithm. The flowchart of concept drift adaptation is shown in Figure 2. First, use the concept drift detection algorithm (see Algorithm 3 for details) to detect whether the current concept drift occurs. The process is to calculates the relative error rate on the prediction data using the oil temperature prediction algorithm, and then obtain the detection result through Definition 2. If the result is that the concept drift did not happen, the algorithm ends. If the result requires a delayed decision, then update the prediction data and redetect the concept drift. If the result is that the concept drift happens, the oil
Output: The prediction result matrix M of all base classifiers and the decision of concept drift detection result L.
The Steps of Algorithm 3: Step 1. Initialize the delay decision threshold λ = 0 and the count number of delay decision a = 0.
Step 2. Input the transformer's working condition data series V x into k base classifiers C, and, respectively, obtain the prediction results: Note: Y C j t i ∈ M, i ∈ [1, n] and j ∈ [1, k] Step 3. Calculate the expected value of prediction TY = TY t 1 , TY t 2 , . . . , TY tn based on M, where Step 4. According to Definition 1, calculate relative error rate δ t i = TY t i − Y t i /Y t i × 100% and δ = δ t 1 , δ t 2 , . . . , δ tn .
Step 5. According to the 3-way decision-making rule in Definition 2, the decision L, whether to use the concept drift influence prediction model or not, will be made by the count number m of relative error rate set δ, which are less than the warning threshold γ.
Step 5.1. If the decision L = 'With Influence of Concept Drift', then go to Step 6 and output the decision L and the prediction result matrix M.
Step 5.2. If the decision L = 'Without Influence of Concept Drift', then go to Step 6 and output the decision L.
Step 5.3. If the decision L = 'Delay to Make Decision', then update the count number of delay decision a to a = a + 1 and compare a with the delayed decision threshold λ as following: Step 5.3.1. If a ≥ λ, then return to Step 5.1.
Step 5.3.2. if a < λ, then update the transformer working condition data series V x and oil temperature data series V y and return to Step 2. Step 6. Algorithm ends.
According to the decision from Algorithm 3, the update of prediction model will be executed only when the decision L is 'With Influence of Concept Drift'.
Based on the decision L of the concept drift detection result and the prediction result matrix M of all base classifiers, the adaptive update algorithm of base classifiers tends to update each base classifier C i ∈ C and their power weight w to reduce the influence of concept drift the following Adaboost ensemble learning approach if the decision of concept drift L = 'With Influence of Concept Drift'.
Step 2. Update the base classifiers C and their power weights w. Step Train base classifier C updated j based on IS j , and calculate total error rate Step 2.3. Update the power weight w j of base classifier C j .
Step 2.5. Normalize the sample weights η Step 2.6. Set j = j + 1 , and return to Step 2.1 until j = k.
Step 2.7. Normalize the power weights w Step 4. Algorithm ends.
In summary, Algorithm 1 (Oil Temperature Prediction Based on Bagging Ensemble Learning) was first utilized to construct k base classifiers and their power weights. Then, Algorithm 2 (Abnormal detection of the transformer's working state) was utilized for the transformer's abnormal oil temperature diagnosis. After a period of time, Algorithm 3 (Concept Drift Detection Algorithm) was used to evaluate the influence of concept drift. If the concept drift did not influence the prediction result of model such that L = 'Without Influence of Concept Drift', then the working state S of the transformer from Algorithm 2 was the final decision of diagnosis. If the concept drift happened and influenced the prediction of model such that L = 'With Influence of Concept Drift', then Algorithm 4 (Adaptive Update Algorithm of Base classifiers Based on Adaboost ensemble learning) was used to update the base classifiers and their power weight. Then, we returned to Algorithm 2 again to obtain the final working state S of the transformer.

Introduction of Experiment
The experimental data were collected from 4,110 kv main oil-immersed main transformers in China from January 2018 to July 2018, as well as the local weather data during the same period. These data were equally divided into 18 sections in order of time sequence, and there are the data of 15 days in each section.
In order to validate the efficiency of our proposed adaptive abnormal oil temperature diagnosis method (AAOTD) of the transformer based on concept drift, we utilized five other methods for comparison, including classification and regression tree (CART) [25], random forest (RF) [26], support vector machine (SVM) [27], accuracy weighted ensemble (AWE) [18], and basic abnormal transformer oil temperature diagnosis of the transformer based on ensemble learning without concept drift (BAOTD).
In terms of the advice from experts in the relative domain, the critical parameters of the abnormal oil temperature diagnosis of he transformer were preset as the thresholds α = 0.2, β = 0.5, which are the deviation rate between predicted oil temperature and actual oil temperature from Algorithm 2; γ = 0.5, which is the warning threshold from Definition 1; µ = 3 and ν = 12, which are the decision-making thresholds from Definition 2; and λ = 6, which is the delay decision threshold from Algorithm 3.

Evaluation of Experiment
In this paper, two indicators were used to evaluate the efficiency of the algorithms: Oil temperature prediction accuracy rate P, and oil temperature abnormal warning rate R.
Oil temperature prediction accuracy rate P is illustrated as following: where N is the number of days in an evaluation period and M is the number of prediction procedure per day, so that N × M is the amount of all prediction procedure in one evaluation period. A represents the accuracy rate in one prediction procedure and is described as follows: where Y is the predicted oil temperature, Y is the actual oil temperature, and ε is the factor to magnify the relative difference between the predicted oil temperature and actual oil temperature. Oil temperature abnormal warning rate R is illustrated as following: where m is the number of days in which warning happened and N is the number of days per sections of dataset, such that N = 15. Figure 3 shows the broken line graph of the transformer oil temperature prediction accuracy rate of the six algorithms (CART, RF, SVM, AWE, BAOTD, and AAOTD) on the prediction set. The four subgraphs (a), (b), (c), and (d) of Figure 3 represent the experimental results on transformers at four different locations (Xinyu, Gulu, Xuzhou, and Yanghang). Since these six algorithms were trained using historical working condition data before the prediction timepoint, in the initial stage of prediction, all algorithms already had accurate values for the transformer oil temperature (Figure 3). However, as time passed, uninterrupted oxidation of the internal components of the transformer and irregular changes in the external load of the transformer were likely to cause unforeseen changes in the data of the transformer oil temperature. From the four subgraphs of Figure 3, after the algorithm predicted the transformers in Xinyu, Gulu, Xuzhou, and Yanghang through several prediction sets (after predicting the new data for about 2 months), the accuracy of the four algorithms (CART, RF, SVM, and BAOTD) in oil temperature prediction began to decline to varying degrees.

Result Analysis
As the forecast continued, the model became increasingly inaccurate. After comparing with the original historical data, we found that the data distribution changed greatly when the prediction set was 3, 6, 8, 13, 16. data distribution, and the robustness of the model was poor. It can be seen from the red and brown lines in the four subgraphs (a), (b), (c), and (d) that the performance of algorithm AAOTD proposed in this paper and the commonly used concept drift adaptive algorithm AWE declined to a certain extent at the beginning. However, these two algorithms (AAOTD and AWE) can update themselves with the continuous arrival of new data, which is why the prediction accuracy of these two algorithms is better than the other four algorithms. Both the AAOTD and AWE algorithms use an ensemble framework to build the algorithm model and use the regression tree model as the base classifier in the ensemble algorithm. The relevant parameter settings of the base classifier are also the same. However, it can be seen from the comparison of the red and brown lines in Figure 3 that the AAOTD algorithm had a higher prediction accuracy than the AWE algorithm. This is because the AWE algorithm only replaces the base classifier by judging whether the performance of the base classifier is lower than the minimum threshold. This update method ignores the historical importance of the base classifier, and a small conceptual fluctuation Therefore, the model trained with historical data did not perform well on the new data distribution, and the robustness of the model was poor. It can be seen from the red and brown lines in the four subgraphs (a), (b), (c), and (d) that the performance of algorithm AAOTD proposed in this paper and the commonly used concept drift adaptive algorithm AWE declined to a certain extent at the beginning. However, these two algorithms (AAOTD and AWE) can update themselves with the continuous arrival of new data, which is why the prediction accuracy of these two algorithms is better than the other four algorithms.
Both the AAOTD and AWE algorithms use an ensemble framework to build the algorithm model and use the regression tree model as the base classifier in the ensemble algorithm. The relevant parameter settings of the base classifier are also the same. However, it can be seen from the comparison of the red and brown lines in Figure 3 that the AAOTD algorithm had a higher prediction accuracy than the AWE algorithm. This is because the AWE algorithm only replaces the base classifier by judging whether the performance of the base classifier is lower than the minimum threshold. This update method ignores the historical importance of the base classifier, and a small conceptual fluctuation may cause historically important base classifiers to be deleted by mistake. The method proposed in this paper to detect concept drift based on the three-way decision-making rule is a decision model based on human cognition, which can effectively avoid the influence of false concept fluctuations caused by misjudgment. Moreover, in updating the base classifier, the AAOTD algorithm adopts the update strategy of Adaboost, which makes it possible to avoid ensemble learning to overcome the problem of concept drift in the data.
Given working condition of transformer in Xinyu, Table 3 lists the detail of various methods' evaluations. Table 3. The results of the 6 algorithms on the transformer in the Xinyu area: The initial accuracy, the change of accuracy in the 3 conceptual drifts (a positive number represents an increase in accuracy, a negative number represents a decrease in accuracy), and the final accuracy.

Algorithm
Initial The AWE, AAOTD, and BAOTD algorithms had high accuracy in predicting oil temperature, reaching 98.98%, 99.42%, and 99.54% accuracy, respectively. This is because these three algorithms use an ensemble algorithm model. The final prediction result of the ensemble algorithm was obtained by the weighted average of the oil temperature prediction results of each base learner in the algorithm. Compared with a single complex classifier, this ensemble method has more stable accuracy, which also shows that using integrated algorithms is better in the context of transformer oil temperature prediction. Table 3 shows the three significant declines in the accuracy of oil temperature prediction. Among them, the accuracy of the BAOTD, CART, RF, and SVM algorithms decreased because these algorithms themselves do not have the ability to adapt to concept drift. When the concept drift occurred in the oil temperature working condition data, the abovementioned algorithms (BALOTD, CART, RF, and SVM) did not use the latest oil temperature working condition data to update the algorithm model, but still used the algorithm model trained with historical oil temperature operating condition data to predict the oil temperature. So, with the continuous change of the concept drift in the oil temperature working condition data, the accuracy of the algorithm model will continue to decline, while the accuracy of the algorithms with self-renewal (AWE and AAOTD) will experience a smaller decline.
For the AAOTD algorithm, when the accuracy of the algorithm changes, the concept drift detection will be performed according to the Concept Drift Detection Algorithm mentioned in Section 2. Then, different decisions will be made according to the Adaptive Update Algorithm of Base Classifiers Based on Adaboost Ensemble Learning algorithm to update the base classifiers, so that the updated base classifier can adapt to the conceptual drift in the oil temperature working condition data. From the data in the table, the final accuracy rate of the oil temperature prediction of the AAOTD algorithm proposed in this paper only slightly decreased, still reaching 95.55%. This shows that the performance of the AAOTD algorithm is stronger than other algorithms used in this experiment.
Next, we input the predicted oil temperature values of the above six algorithms into Algorithm 2 (Abnormal detection of transformer's working state) and calculated the changes in the warning rate of each algorithm in each prediction set according to Formula 8 to obtain Figure 4.
The four subgraphs (a), (b), (c), and (d) of Figure 4 plot the warning rate changes curves of the transformers in Xinyu, Gulu, Xuzhou, and Yanghang of the six algorithms. The yellow curve represents the abnormal rate of the transformer under real conditions. In real situations, there were fewer cases of warning and error in the transformer. The broken line of the AAOTD and AWE algorithm is more consistent with the broken line in the real situation, among which the AAOTD algorithm is the best.
It can be seen from Figure 4 that the other four algorithms also performed poorly in the early warning of the transformers. This is because they do not consider concept drift, so the accuracy of oil temperature prediction was not high, which led to poor diagnosis results of abnormal transformers. . 2021, 11, x FOR PEER REVIEW 13 of 15 The four subgraphs (a), (b), (c), and (d) of Figure 4 plot the warning rate changes curves of the transformers in Xinyu, Gulu, Xuzhou, and Yanghang of the six algorithms. The yellow curve represents the abnormal rate of the transformer under real conditions. In real situations, there were fewer cases of warning and error in the transformer. The broken line of the AAOTD and AWE algorithm is more consistent with the broken line in the real situation, among which the AAOTD algorithm is the best.
It can be seen from Figure 4 that the other four algorithms also performed poorly in the early warning of the transformers. This is because they do not consider concept drift, so the accuracy of oil temperature prediction was not high, which led to poor diagnosis results of abnormal transformers.
Overall, the AAOTD algorithm proposed in this paper had a higher oil temperature prediction accuracy and more correct oil temperature abnormal warning rate in the oilimmersed transformer-related dataset. Compared with classic concept drift adaptation algorithms and other machine learning algorithms that do not consider that the transformer oil temperature working condition data is prone to concept drift, this algorithm has concept drift adaptation capability, better transformer abnormal diagnosis results, and is more robust. Overall, the AAOTD algorithm proposed in this paper had a higher oil temperature prediction accuracy and more correct oil temperature abnormal warning rate in the oilimmersed transformer-related dataset. Compared with classic concept drift adaptation algorithms and other machine learning algorithms that do not consider that the transformer oil temperature working condition data is prone to concept drift, this algorithm has concept drift adaptation capability, better transformer abnormal diagnosis results, and is more robust.

Conclusions
In this study, an adaptive abnormal oil temperature diagnosis (AAOTD) method based on the concept drift was proposed. This method can significantly reduce the influence of concept drift from performance degradation of the transformer's components. The contributions of this paper are as follows. First, a new concept drift detection model was developed using three-way decision-making theories, which can infer the influence level of concept drift based on changes of model accuracy. Then, ensemble learning algorithm was employed to adaptively adjust the base learners and their weights to reduce the influence of concept drift. The efficiency of AAOTD methods was validated via the experiments. In the experiments, the average oil temperature prediction accuracy of AAOTD in four regions reached 95.03% (Xinyu: 94.27%, Gulu: 93.58%, Xuzhou: 95.82%, Yanghang: 94.46%), which is 1.52% higher than the AWE algorithm and 20-40% higher than other traditional machine learning algorithms. Furthermore, since this method only utilizes the existing power grid data resources to realize abnormal oil temperature diagnosis without extra monitoring equipment, it is an economic and efficient solution for practical scenarios in the electric power industry.
However, due to the ensemble learning steps, the computational complexity of the algorithm proposed in this paper is higher than the traditional methods. Therefore, in the future work of this research, we will focus on reducing the computational complexity of the algorithm.