# Hybrid Trust Model for Node-Centric Misbehavior Detection in Dynamic Behavior-Homogeneous Clusters
## 6 Hybrid Trust Value Based on Weighted Vehicle Behavior
### Vehicle Node Layer Trust Value Computation
RSS is a part of the wireless transmission layer that can determine link quality and whether there is a need to increase the strength of broadcast transmissions. Therefore, using the RSS attenuation model, the distance between nodes can be calculated [32], which in turn helps further determine a node's direct trust value. The specific expression for this calculation is as follows: \[\begin{array}{l}T_{d}D(v_{i})=\left\{ \begin{array}{l}-1\quad D_{RSSI}>D_{ norm}Max\text{ or }D_{RSSI}<D_{norm}Min\\ 1\quad D_{norm}Min<D_{RSSI}<D_{norm}Max\\ \end{array} \right.\\ D_{RSSI}=10^{\frac{10}{10}{10}{10}}\frac{10}{10}\frac{10}{10}\frac{10}{10} \frac{10}{10}\frac{10}{10}\frac{10}{Here, \(RSSI_{reactive}(v_{i})\) represents the RSS strength for vehicle \(v_{i}\), \(D_{RSSI}\) is the distance between vehicle nodes, \(D_{norm}Min\) is the minimum threshold distance between nodes, and \(D_{norm}Max\) is the maximum threshold distance between nodes. Considering the previous analysis, the final direct trust value of a vehicle node is calculated based on three indicators from the interaction information: speed, transmission frequency, and node distance. The geometric mean can be used to consider different parameters [33]. Assuming \(T_{d}V(v_{i})=R_{1}\), \(T_{d}TF(v_{i})=R_{2}\) and \(T_{d}D(v_{i})=R_{3}\) are the trust values calculated from these respective indicators, the calculation process for the direct trust value of a vehicle \(v_{i}\) is as follows:  
\[T_{d}(v_{i})=\left[\prod_{j=1}^{k}\alpha_{j}R_{j}\right]^{1/k} \tag{10}\]  
where \(\alpha_{j}\) are weight coefficients, \(R_{j}\) is the trust assessed through different observation indicators, and \(k\) is a constant parameter. 2. **Indirect Trust Value** The indirect trust value of a vehicle is determined based on the information provided by neighboring vehicles. Therefore, the indirect trust \(T_{r}(v_{i})\) of vehicle \(v_{i}\) is evaluated based on the direct trust values about vehicle \(v\) received from its neighboring vehicles \(v_{j}\). Since the degree of association differs between nodes, the trustworthiness of the feedback from a node with a high degree of association is more reflective of the actual situation of vehicle \(v_{i}\) compared to a node with a low degree of association. Hence, the degree of association between nodes is used as a weight in the calculation of indirect trust values. The indirect trust value of vehicle \(v_{i}\) is calculated by taking a weighted average of the trust values about vehicle \(v_{i}\) provided by other vehicles, with each data point being independent and not influencing each other. Assume that the trust value about vehicle \(v_{i}\) provided by vehicle \(v_{j}\) is \(T_{r}^{i}(v_{i})\), and the association weight between vehicles \(v_{j}\) and \(v_{i}\) is \(\omega_{ij}=Re_{ij}(v_{i},v_{j})\), where \(i\
eq j,j=[1,n]\). The expression for the indirect trust value is as follows:  
\[T_{r}(v_{i})=\frac{1}{n}\sum_{j=1}^{n}\omega_{ij}T_{r}^{i}(v_{i}) \tag{11}\]  
3. **Total Trust Value** The total trust value is calculated using the direct and indirect trust values of a vehicle, as per the following formula:  
\[T_{tot}(v_{i})=\mu T_{d}(v_{i})+\gamma T_{r}(v_{i}) \tag{12}\]  
\(\mu\) and \(\gamma\) represent the weights for the direct and indirect trust values, respectively, where \(\gamma\) is defined as \(1-\mu\). When \(0.5<\mu<1\) is set, it implies that the direct trust value is reliable while not neglecting the indirect trust value. The update of the total trust value is a smooth iterative update based on the previous trust value, and the method is as follows:  
\[T_{tot}(v_{i})=\sigma{T_{tot}}^{t}(v_{i})+\rho{T_{tot}}^{t-1}(v_{i}) \tag{13}\]  
In this formula, \({T_{tot}}^{t}(v_{i})\) represents the total trust value at time \(t\), and \({T_{tot}}^{t-1}(v_{i})\) represents the total trust value at the previous time period \(t-1\). \(\sigma\) represent the proportions of the current \(t\). \(\rho\) represent the proportions of the previous time periods \(t-1\). And \(\varepsilon\) is a threshold.