## 4 Case Study  
To test and verify our model, we applied our model to a type of solar-powered UAV data-link system. The solar-powered UAV data-link system consists of two non-line-of-sight links and three line-of-sight links. The B-line-of-sight link (HF band) cannot transmit the task load information of large data such as pictures and images due to the bandwidth and cannot transmit the telemetry information. Therefore, only the telecontrol information can be uploaded in the simplex mode. A-Line-of-sight link (UHF band) and C-line-of-sight link (UHF band) are mutually redundant and the bandwidth of A-line-of-sight link (UHF band) and C-line-of-sight link (UHF band) is sufficient for simultaneous telecontrol and telemetry. Outside the line-of-sight range, the control command is received by the non-line-of-sight links and the long-distance data back-transmission is completed. \(\alpha\)-non-line-of-sight link (Ku band) and \(\beta\)-non-line-of-sight link (Ka band) form redundancy. The non-line-of-sight links are relayed by two satellites respectively but the airborne communication terminal can only point to one of them at a certain time and the two non-line-of-sight links share the airborne communication terminal. The normal operation of the UAV is inseparable from the real-time control of the data-link system. The data-link, a subsystem of the unmanned aircraft system that provides for information transmission, has high sensitivity. The airborne communication terminal, repeater satellite's communication terminal and ground data communication terminal of the unmanned aircraft system are in motion relative to each other at all times. The radio frequency transmitter, radio frequency output power, external interference and the type and gain of the transmitting/receiving antenna determine the maximum acceptable distance for the UAV data-link to establish wireless communication. Data transmission through the UAV data-link will experience channel fading as a result of an increase in the communication distance that goes beyond the range limit, which will have a negative impact on the continuity and stability of signal transmission. This unreliable condition is reflected in the communication quality as the error rate. Based on these considerations, we took the bit error rate and communication distance together as parameters affecting the quality of information transmission to establish the health state prediction model of the UAV data-link system. The factors influencing the quality of each channel of the link were composed of two parts: channel fading caused by increases in the communication distance and the bit error rate caused by random fluctuations. In our model, the communication interruption rate affected by the communication distance can be described by the Barnett-Vignant formula:  
\[FM=30\lg d+10\lg(6A\cdot B\cdot f)-10\lg(1-P)-70. \tag{9}\]  
The probability that the information will not be interrupted is:  
\[P=1-10^{3\lg d+\lg(6A\cdot B\cdot f)-7-FM/10}, \tag{10}\]  
where \(FM\) is the fading margin (dB); \(d\) is transmission distance (\(k\)); \(A\) is a factor of roughness; \(B\) is a factor of climate and environment; and \(f\) is the carrier frequency of the channel (GHz). Figure 6 shows the mode of the solar-powered UAV data -link system with three line-of-sight links and two non-line-of-sight links. The root node prediction model is shown in Table 1.  
We built a BN according to the networking mode of the solar-powered UAV data-link system and then we modified the BN by considering the impact of the communication interruption rate and bit error rate. We added 13 root nodes to indicate the factors affecting the health of each channel because of the communication distance and bit error rate. \(P_{Error_1}\sim P_{Error_13}\) are the BERs of the \(\alpha\)-chain