## 2 Materials and Methods
### Realization of Sensor Fault Location  
According to the national standard of China JB/T 7631-2005 [18], the displayed temperature difference between the sensors shall not exceed 0.5 \({}^{\circ}\)C. Exceeding this temperature range can be regarded as the occurrence of failure. To locate the faulty sensor. The maximum value of the selected three-channel sensor data after diagnosis is defined as the reference value X, and the remaining two sensor data are defined as Y and Z, respectively. We combined the five typical fault types of impact fault, drift fault, brownout fault, constant value output, and deviation fault [21], and then summarized them into seven scenarios [22]. The fault location decision tree was constructed as shown in Figure 2.  
Scenario 1: The temperature difference between the temperature values of the three sensors is less than 0.5 \({}^{\circ}\)C, indicating that there is no sensor fault. This scenario is to prevent misdiagnosis by the PCA troubleshooting model. The secondary diagnosis of the sensor data is performed here to improve the accuracy of the data diagnosis.  
Scenario 2: The maximum temperature difference between X and Y and between Y and Z is less than 0.5 \({}^{\circ}\)C, but that between X and Z is more than 0.5 \({}^{\circ}\)C. It is considered that the three-channel temperature value is X \(>\) Y \(>\) Z. Then, the LSTM predictor is started at this point. If the temperature difference between the predicted result P and X is less than 0.5 \({}^{\circ}\)C, sensor Z is faulty. If the temperature difference between the predicted results of P and Y is less than 0.5 \({}^{\circ}\)C, sensor X is faulty. Such failures are often deviation failures.  
Scenario 3: The temperature difference between the maximum value X and Y is less than 0.5 \({}^{\circ}\)C, however, between X and Z, Y and Z are all more than 0.5 \({}^{\circ}\)C. Then, start the LSTM predictor at this point. If the temperature difference between the predicted results P and \(Z\) is less than 0.5 \({}^{\circ}\)C, it is considered that the sensors X and Y are faulty. Otherwise, sensor Z is faulty. Such faults are often impulse faults or open circuit faults.  
Scenario 4: The temperature difference between the maximum value X and Y is more than 0.5 \({}^{\circ}\)C, however, between X and Z, Y and Z are all less than 0.5 \({}^{\circ}\)C, the same as Scenario 2.  
Scenario 5: The temperature difference between the maximum value X and Z is less than 0.5 \({}^{\circ}\)C, but between X and Y, Y and Z are all more than 0.5 \({}^{\circ}\)C, the same as Scenario 3.  
Scenario 6: The temperature difference between the maximum X and Y, X and Z are all more than 0.5 \({}^{\circ}\)C, but between Y and Z it is less than 0.5 \({}^{\circ}\)C. Then, start the LSTM predictor. If the temperature difference between the predicted results P and X is less than 0.5 \({}^{\circ}\)C, the sensors Y and Z are faulty. Otherwise, sensor X is faulty.  
Scenario 7: The difference between the temperature values of the three sensors is greater than 0.5 \({}^{\circ}\)C. All three sensors are faulty.  
Therefore, to meet the positioning requirements, the prediction accuracy of the predictor needs to be high enough, and the difference between the predicted value P and the actual value should not exceed 0.5 \({}^{\circ}\)C to ensure the accuracy of the fault location. Otherwise, there will be no way to isolate the faulty data.