## 3 Experiments
### Fault Detection and Anti-Noise Analysis
The \(F_{1}\)_score_ is the harmonic mean of the _precision_ and _recall_, with a maximum of 1 and a minimum of 0. The larger the \(F_{1}\)_score_ value of the classification model, the better the classification ability of the model. \[F_{1}\;score=\frac{2*precision*recall}{precision+recall} \tag{14}\]  
We selected 2400 sample points from the test set of Node 7 data, and injected different numbers of three fault data into these sample points respectively. We used these sample points with fault to test the fault detection ability of the model which trained by using the original data of Node 7. We used the reconstruction error to determine which class the sample points are divided into. We recorded the mean \(e_{mem}\) and standard deviation \(e_{std}\) of the model's reconstruction error for original data with no data failure. When using the data with data failure test, if the reconstruction error value of the sample point is at \([e_{mem}-3*e_{std},\;e_{mem}+3*e_{std}]\), we judge that the sample point is normal data, otherwise, we judge that the sample point is fault data. The experimental results of the fault detection ability of the model are shown in Figure 9. We record the corresponding fault data ratio of the model which has the maximum \(F_{1}\)_score_ for different data faults. Figure 10 shows the data reconstruction and the anti-noise ability of the model when the model has the maximum \(F_{1}\)_score_ for different data faults. Figure 9: The fault detection performance of the model under different fault data ratios for three different fault. (**a**) noise fault, (**b**) short-term fault, (**c**) fixed fault. The value of the \(x\)-axis is the ratio of the number of fault data we add to the original sample to the total number of original sample data. When we inject the noise fault into the original data, the \(F_{1}\)_score_ of the model increases as the ratio of fault data increases. This shows that the model's ability to detect noise faults is also increasing. For different numbers of noise fault data, the _recall_ of the model is always above 90%, which means that the model can always detect most of the sample points with data fault. However, the low _precision_ value of the model indicates that the model also classifies some normal sample points as fault data. The low _precision_ value and high _recall_ value indicate that the model classifies a lot of data as fault data, which contains most of the real faults and a large amount of normal sample points. As the ratio of fault data increases, the _precision_ value also increases slowly, indicating that the detection accuracy of the model for normal sample points is also improved, that is, the ratio of classifying normal sample points to fault data is reduced. The results analysis of short-term fault are the same as the noise fault, but the ability of the model to detect short-term faults is generally worse than that of noise faults. Figure 10b,c show the reconstruction results of the model for noise fault and short-term fault, respectively, with the ratio of fault data is 50%. We can see that after adding the noise fault with the ratio of fault data is 50%, most of the original information of the sample points is covered by noise. At this time, the reconstruction of the proposed model can only use the hidden features learned from the original data, and cannot use the data with noise fault. At the same time, due to the high amplitude of the noise data, the reconstructed data amplitude of the model is also changing. However, the amplitude change of the noise data is not a fixed value, and the reconstructed data of the model will only move closer to the value where the amplitude changes greatly. Unlike noise faults, short-term faults change the amplitude of sample points by adding a fixed value. Therefore, we see that after adding the short-term fault with the ratio of fault data is 50%, the trend of the original data is maintained, but the amplitude changes drastically.