## 3 Model for Predicting the Health of an Unmanned Aerial Vehicle Data-Link System
### Constructing a Bayesian Network Root Node Prediction Model  
By analyzing the path of information transmission in the UAV data-link system and the connection relationship between devices, we can use the radio frequency receiver, radio frequency transmitter and modern as the root nodes of the Bayesian network. For ground data terminals and for the UAV and repeater satellites, the radio frequency receiver, radio frequency transmitter and modern can be described with tandem logic as terminals that perform communication functions. Considering that the radio frequency receiver, radio frequency transmitter and modern have no influence on the quality of information transmission, this paper combines these three nodes into communication terminal module nodes for modeling. Under this approach, the sensors are set in each communication terminal module to collect corresponding data and a prediction model of the BN root node is established. Considering that the most important characteristic of the link terminal equipment is the transmission  
Figure 3: Schematic diagram of unmanned aerial vehicle (UAV) data-link communication mode. power, the radio frequency device is the key component after the failure mode and mechanism analysis. The power-MOSFET has been adopted for all the airborne terminal equipment in this paper [31]. To establish a predictive model, we combined the degradation model for power-law [32] (considering time), Arrhenius model [33] (considering temperature) and Eyring model [34] (considering electrical stress) with [PERSON]'s stochastic degradation process [35]. Taking the equipment whose performance degrades from the Wiener process as an example, we introduce the prediction model. Assuming the performance parameter P is a key indicator of product health status and is sensitive to stress \(S\), the parameter then follows the [PERSON] degradation process as follows [36]:  
\[P(t)=d(s)\cdot t+\sigma\cdot B(t)+P_{0}, \tag{3}\]  
where \(P_{(t)}\) is the product performance at time \(t\) and \(d(s)\) is the drifting reflecting the performance degradation rate, which is a function of stress and time. In an accelerated model \(d(s)=\exp[\beta_{0}+\beta\phi(s)]\), where \(\phi(s)\) is a function of stress \(S\); Constant \(\sigma\) is the diffusion coefficient that is irrelevant with respect to environment and time, \(B(t)\sim N(0,t)\) is the standard Brownian motion and \(P_{0}\) is the initial value of the parameter. The degradation amount within the time \(\Delta t\) from the properties of the Wiener process is \(\Delta p\sim N(d(s)\Delta t,\sigma^{2}\Delta t)\). \(L\) is defined as the failure threshold of performance \(p\) and then the time \(t\) that performance parameter value first passed through \(L\) satisfies the inverse Gaussian distribution. The distribution function is the unhealthy state function of the product and the corresponding probability density function is given by:  
\[f(t;P_{0},L)=\frac{L-P_{0}}{\sqrt{2\pi\sigma^{2}t^{3}}}\exp\Bigg{\{}-\frac{[( L-P_{0})-d(s)t]^{2}}{2\sigma^{2}t}\Bigg{\}}. \tag{4}\]  
The corresponding health state function is the prediction model of equipment, as follows:  
\[R(t)=\Phi\frac{(L-P_{0})-d(s)t}{\sigma\sqrt{t}}-\exp\Bigg{\{}\frac{2d(s)L}{2 \sigma^{2}}\Bigg{\}}\Phi\frac{(L-P_{0})+d(s)t}{\sigma\sqrt{t}}, \tag{5}\]  
where \(\Phi(*)\) is the cumulative distribution function of the standard normal distribution. A Bayesian Network Model of an Unmanned Aerial Vehicle Data-Link System Considering the Networking Mode  
After constructing the BN root node prediction model, we can create the UAV repeater satellite communication (UAV-RS communication) and the ground data terminal repeater satellite communication (G-RS communication) according to the information transfer path and the logical link relationship between the components. Next, we provide a line-of-sight wireless communication link and a non-line-of-sight communication link for the UAV data-link.