## 3 Results and Discussion  
### Sensor Failure Simulation Experiment  
Since the internal temperature of dry-type transformers is mainly composed of the coil temperature rise, it is also influenced by the local air temperature [24]. The air temperature is characterized by seasonal changes, where the coil temperature will rise and fall with the increase or decrease in load and show daily periodicity. To better verify the algorithm's performance of each function, the verification set should contain the above two features. Therefore, the experiment selected the measured temperature of the whole-day on 10 April in spring and 10 December in winter as examples for verification. Since the sampling frequency of the monitor was once a second, there were 86,400 monitoring data of three-way sensors per day. The sensor fault diagnosis function of the algorithm needed to be verified with the fault data. The fault temperature data could be obtained by the method of laboratory fault simulation because the measured data came directly from the normal temperature monitored by the sensor. By superimposing the fault states based on normal data, it simulated the shock faults, drift faults, power failure faults, constant output, and deviation faults [25; 26]. The specific method was as follows:  
Impulse faults were caused by random disturbances, surges, and spark discharges in the power and ground wires. This caused a sharp jump in the data measured by the sensor in a short period. A linear function could be superimposed on this to make the temperature rapidly increase and fall back in a short time to simulate a shock failure. Drift faults were caused by the gradual shift in the sensor measurement values. Generally speaking, drift faults are linear drift faults. These can be fitted by a superimposed linear relationship, and a drift step size set to 0.01 \({}^{\circ}\)C. That is, if the drift is 0.01 \({}^{\circ}\)C per second, the drift is 0.6 \({}^{\circ}\)C per minute. The power failures were caused by broken signal lines, disconnected chip pins, or poor circuit contact. This kind of fault would cause the measured output value to be 0 \({}^{\circ}\)C. Therefore, the temperature value of this period can be directly set to 0 \({}^{\circ}\)C for the simulation. The constant value output belongs to the hard fault in the sensor type fault. When the fault occurs, the sensor loses its measurement ability and keeps a constant value. It is possible to represent a constant temperature value by setting a constant. The bias faults were caused by the bias current or bias voltage. This would make the data measured by the sensor deviate from the normal measurement value, which could be simulated by superimposing the deviation value.  
The above five fault simulation methods were added to the time series monitored by the three-way sensors A, B, and C. The whole-day temperature measured on 10 December 10 in winter was used as the test set. Shock faults were added to sensors A and B between 1000 and 2000 s. Open circuit faults were added to sensor B between 8000 and 13,000 s. Then, we made sensor C power down between 20,000 and 26,000. Next, sensor C had a drift fault in the interval of 31,000 to 35,000 s, drifting at 0.01 \({}^{\circ}\)C per second. For the deviation fault, three faults were designed: high, low, and multi-sensor deviation. From 40,000 to 44,000 s, sensor A was 10 \({}^{\circ}\)C higher, and from 50,000 to 54,000 s, sensor B was 10 \({}^{\circ}\)C lower, and between 64,000 and 74,000 s, sensor B and C had low faults, where B was 10 \({}^{\circ}\)C lower and C was 20 \({}^{\circ}\)C lower. The all-day fault temperature simulated by the above method is shown in Figure 5.