# 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  
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. Figure 1: The flowchart of 3-way decision-making rule in Algorithm 2. According to the difference between the predicted oil temperature and actual oil temperature, the 3 transformer states FINE, ERROR, and WARNING were obtained. Suppose that, during timeseries \(t=\{t_{1},t_{2},\ldots,t_{n}\}\), there is transformer's working condition data series \(V_{x}=\{X_{t_{1}},X_{t_{2}},\ldots,X_{t_{n}}\}\) and the actual oil temperature data series \(V_{y}=\{Y_{t_{1}},Y_{t_{2}},\ldots,Y_{t_{n}}\}\), where \(X_{t_{i}}\in V_{x}\) represents the working condition data at \(t_{i}\) time, and \(Y_{t_{i}}\in V_{y}\) 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 \(V^{\prime}_{y}=\{Y^{\prime}_{t_{i}},Y^{\prime}_{t_{2}},\ldots,Y^{\prime}_{t_{n }}\}\) 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 \(\delta_{t_{i}}\) at time \(t_{i}\) is as follows:  
\[\delta_{t_{i}}=\frac{\left|Y^{\prime}_{t_{i}}-Y_{t_{i}}\right|}{Y_{t_{i}}} \times 100\% \tag{1}\]  
Hence, the set of relative error rate during all time is \(\delta=\{\delta_{t_{1}},\delta_{t_{2}},\ldots,\delta_{t_{n}}\}\). The preset threshold \(\gamma\) of relative error rate is defined as the warning trigger. If the relative error rate \(\delta_{t_{i}}\) is greater than threshold \(\gamma\), 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 \(\mu\) and \(\
u\). Suppose that the set of relative error rate \(\delta=\{\delta_{t_{1}},\delta_{t_{2}},\ldots,\delta_{t_{n}}\}\) exists k elements \(\delta_{t}\), which are less than the warning threshold \(\gamma\) defined in definition 1. If k is greater than or equal to the threshold \(\
u\), 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 \(\mu\), 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 \(\
u\) but greater than the threshold \(\mu\), 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:  
\[\left\{ \begin{array}{ll}&k\geq\
u,&L=\text{With Influence of Concept Drift}\\ &k\leq\mu,&L=\text{Without Influence of Concept Drift}\\ &\mu<k<\
u,&L=\text{Delay to Make Decision}\end{array} \right. \tag{2}\]  
Note: k is the number of \(\delta_{t}<\gamma\). 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.