## 5 Energy Balanced Routing Protocol Based on Thick Lwsn (ebrp-tl)  
After each round of self-organization, ordinary nodes distributed across the monitoring area perceive the surrounding environment and transmit data to the base station for analysis, enabling real-time security monitoring of the entire monitoring area. During the intracluster routing phase, each node sends the data gathered to its respective cluster head via single-hop communication, and the cluster heads perform data fusion. We assume the packet size remains unchanged before and after data fusion is \(k-bit\). Due to the linear structure of the monitoring target, using a single-hop transmission approach for intercluster routing would result in significant energy consumption for cluster heads located far from the sink, demanding higher node power. Therefore, we employ a hybrid approach combining single-hop and multihop transmission methods. If the sink is within the communication radius of the cluster head, it directly transmits data to the sink  
Figure 7: The connectivity of node \(N_{0}\). via single-hop. Otherwise, the cluster head extends its communication radius three times to discover candidate cluster heads for the next hop. To ensure data forward transmission, the distance from candidate cluster heads to the sink must be less than that from the current cluster head node to the sink, as follows:  
\[NextCH(N_{i})=\left\{N_{j}|d_{sink}(N_{j})<d_{sink}(N_{i})\right\} \tag{13}\]  
All nodes have the same initial energy, but their energy consumption differs due to their varying positions and surrounding connectivity. When selecting the next-hop cluster head node, priority should be given to those with higher remaining energy to protect nodes with lower energy from premature depletion and failure and help balance the network's energy consumption. Therefore, the remaining energy of the nodes is a crucial factor in selecting the next-hop node, and the energy factor is defined as follows:  
\[EF(N_{i})=\frac{E_{R}(N_{i})}{\overline{E}} \tag{14}\]  
The transmission distance is an essential factor affecting node energy consumption. Under the same conditions, the farther the transmission distance, the more energy nodes consume. However, when monitoring linear infrastructure such as tunnels and bridges, where the length of the monitoring area is much greater than its width, as shown in Figure 8, nodes \(N_{1}\) and \(N_{2}\) are candidate cluster heads for node \(N_{0}\). In this case, the transmission distances from \(N_{0}\) through \(N_{1}\) and node \(N_{2}\) are almost equal. Therefore, \(N_{0}\) prefers to select node \(N_{2}\) as the next cluster head because this path involves fewer hops. Thus, those closer to the sink nodes are more likely to be chosen when selecting the next hop cluster head. The distance factor is defined as  
\[DF(N_{i})=\frac{W-d_{sink}(N_{i})}{d_{sink}(N_{i})} \tag{15}\]  
In intercluster routing, some cluster heads may be selected as next-hop nodes by multiple other cluster heads. This can lead to these nodes handling excessive data forwarding tasks in the current round, consuming too much energy and causing uneven energy distribution in the network. To prevent multiple nodes from choosing the same cluster head as the next hop, we define the load cluster heads in Formula (16). \[PreCH(N_{i})=\left\{N_{j}|d_{sink}(N_{j})>d_{sink}(N_{i})\right\} \tag{16}\]  
Figure 8: The connectivity of node \(N_{i}\). So, we choose cluster heads with fewer load cluster heads as the next hop nodes during the election process. The node's load factor is as follows:  
\[LF(N_{i},N_{j})=\frac{Pre_{max}(N_{i})-PreCH(N_{j})}{CH-Pre_{max}(N_{i})} \tag{17}\]  
Here, \(Pre_{max}(N_{i})\) represents the maximum number of the load cluster heads among candidate cluster heads of \(N_{i}\). \(CH\) is the total number of cluster heads in the current round, calculated and communicated to all nodes by anchor nodes after clustering is completed.