## 4 Results and Analysis
### Satellite Spread-Spectrum Transponder Fault Case
#### 4.2.2 Results and Comparison of Detecting the Fault  
We used a total of 5,215,000 samples of real telemetry data obtained from satellite measurements and control systems from 0:0:0 on 1 July 2018 to 8:05:49 on 3 October  
Figure 10: The phenomena of the spread-spectrum transponder fault: (**a**) the spread spectrum transponder telemetry performance before failure; (**b**) the relationship of the 5 V voltage and the temperature.  
2018. Each sample included three telemetry parameters: the spread-spectrum transponder temperature; the 5 V voltage of the spread-spectrum transponder; and the 12 V voltage of the spread-spectrum transponder, as shown in Figure 11. Due to the influence of the variation of satellite-Z's angle to the sun, the temperature of the spread spectrum transponder drifts slowly with time. Consequently, in the experiment the temperature telemetry data were de-drifted. The sampling rate of all data was 1 Hz, and the satellite orbital period was 46,468 s. However, the data were discontinuous in time, which is due to the influence of the visible arc segment of the satellite and the ground station measurement and control resources. This resulted in telemetry data not being transmitted downward during part of the time.  
In this article, the satellite orbital period was used as the length of the sliding window. The sliding window interval was 10,000 s, and a total of 539 sliding windows were retained with more than 20,000 samples within each sliding window. The first 380 sliding windows were selected as normal windows, and the last 159 sliding windows were used as on-line test windows. The first 64 windows in the on-line test windows were the normal windows, and the windows after that were the fault windows. The significance level of the PCA + KLD1 method and PCA + KLD2 method participating in the comparison were set to 0.05, 0.025 and 0.01, respectively, and significance level of the proposed method was set to 0.01.  
Figure 12a-c shows the results of the spread spectrum transponder fault detection on the three PVs obtained from the PCA method. It can be seen from Figure 12 that only the second PV was sensitive to the fault. With a significance level of 0.01, there were still 23% of the fault windows located below the detection threshold. With a significance level of 0.025, 15% of the fault windows were still located below the detection threshold and a normal window was considered to be a fault window.  
In comparison, Figure 13 shows the results of the proposed method for the spread-spectrum transponder fault. It is evident that the detection results on the local optimum PVs were better than those on the fixed PVs. Most of the fault windows were located above the detection threshold, with a high fault detection rate of 92.63% and a false alarm rate of 0%. With the significance level of 0.01, the PCA + KLD2 method can also obtain a 92.63% fault detection rate. However, 23.44% of the normal windows were considered to be fault windows. The fault detection results were calculated and are summarized in Table 2. This  
Figure 11: Raw telemetry data of the spread spectrum transponder.  
real case of detecting the fault in a satellite's spread spectrum transponder further verifies the effectiveness and superiority of the method proposed in this paper.  
Figure 12: The results of detecting the spread-spectrum transponder fault by using the PCA + KLD1 method and the PCA + KLD2 method at different significance levels: (**a**) the result of first PV for the fault; (**b**) the result of second PV for the fault; (**c**) the result of third PV for the fault.  
Figure 13: The detection result of the proposed method for the spread-spectrum transponder fault.