# Adaptive Abnormal Oil Temperature Diagnosis Method of Transformer Based on Concept Drift
## 2 Materials and Methods
### Concept Drift Solution of Oil Temperature Prediction and Abnormal Detection Model
Expected value of predicted oil temperature \(TV^{\prime}\) can be calculated as: \[TV^{\prime}=\frac{k}{j-1}w_{j}^{\text{\emph{updated}}}\text{\emph{\emph{\emph{ \emph{\emph{\emph{\emph{\emph{\emph{\emph{\emph{\emph{\emph{\emph{\emph{\emph{\emphrandom 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 \(\alpha=0.2\), \(\beta=0.5\), which are the deviation rate between predicted oil temperature and actual oil temperature from Algorithm 2; \(\gamma=0.5\), which is the warning threshold from Definition 1; \(\mu=3\) and \(\
u=12\), which are the decision-making thresholds from Definition 2; and \(\lambda=6\), 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:

\[P=\sum_{i=1}^{N\times M}A_{i}/\left(N\times M\right) \tag{6}\]

where \(N\) is the number of days in an evaluation period and \(M\) is the number of prediction procedure per day, so that \(N\times M\) 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:

\[A=1-\frac{|Y^{\prime}-Y|}{\left(Y^{\prime}\times\varepsilon\right)}.\left( \varepsilon\geq 1\right) \tag{7}\]

where \(Y^{\prime}\) is the predicted oil temperature, \(Y\) is the actual oil temperature, and \(\varepsilon\) 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:

\[R=\frac{m}{N} \tag{8}\]

where \(m\) is the number of days in which warning happened and \(N\) is the number of days per sections of dataset, such that \(N=15\). ### Result Analysis

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. 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. 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.