## 6 Test and Analysis of Results
The impact of node degree is minimal, just in the clustering process, cluster heads with higher degrees can prevent the number of clusters in the network from becoming too large. Therefore, in the experiments, the values of \(\alpha\) and \(\gamma\) are relatively large. The cluster distribution in Figure 10 illustrates a round of network clustering. We unevenly distribute clusters by Formula (10), resulting in nodes farther from the sink having larger communication radii and thus forming larger clusters. For instance, node \(CH_{131}\) is farther from the sink than \(CH_{193}\), and its cluster covers a larger area. However, network clusters use the timing mechanism where cluster head election considers factors such as remaining node energy, node degree, and distance to the sink. Node \(CH_{24}\) might have a shorter timer duration and become a cluster head earlier than node \(CH_{96}\), resulting in surrounding nodes joining its cluster first. So it forms a smaller cluster despite node \(CH_{96}\) being farther from the sink than node \(CH_{24}\). This clustering approach reduces energy consumption within clusters closer to the sink, preserving energy for intercluster forwarding and balancing the network energy consumption. After clustering is complete, the surviving nodes will begin monitoring. In each round of network operation, each node will send a monitoring data packet to its cluster head only once. In intracluster routing, nodes send data to the cluster head using a single-hop method, and the cluster head fuses the data. In intercluster routing, the cluster head decides on the transmission method based on the distance to the sink. The operational details of the cluster head in intercluster routing are provided in Algorithm 1. During intercluster routing, the communication radius of the cluster head is expanded to three times its original size. If the sink is within this communication radius, single-hop transmission occurs. Otherwise, the cluster head will collect information about its candidate cluster heads. The candidate cluster heads are closer to the sink, and the cluster head will select the best candidate cluster head as the next hop for multihop transmission based on Formula (18). Figure 10: The clusters of network. ```
1\(R_{C}(CH_{i})=3R_{C}(CH_{i})\)
2 Broadcast
3 ifReceived the broadcast from \(CH_{j}\)then
4 if\(d_{sink}(CH_{i})>d_{sink}(CH_{j})\) and \(CH_{j}\) is a neighbor nodethen
5 Add \(CH_{j}\) to \(NextCH(CH_{i})\)
6 end if
7
8 end for
9 forCH\({}_{j}\) in \(NextCH(CH_{i})\)do
10 Calculate \(select(CH_{i},CH_{j})\)
11 end if
12 if\(select(CH_{i},CH_{j})\) is the largestthen
13\(Nexthop(CH_{i})=CH_{j}\)
14 end if
15 if\(R_{C}(CH_{i})>d_{sink}(CH_{i})\)then
16 Send data to the sink
17
18 end if
19 else
20 Send data to the \(Nexthop(CH_{i})\)
21 end
```  
**Algorithm 1**Intercluster Routing Algorithm  
When the energy consumption in a network becomes unbalanced, some nodes may prematurely exhaust their energy and fail. Therefore, to assess whether a network's energy is balanced, one can evaluate the time the first node fails, reflecting the advantage of a routing protocol in balancing energy. The method proposed in this paper is suitable for the thick LWSNs in monitoring infrastructures such as railway tunnels and bridges. Hence, the number of failed nodes in the network had better be at most 10% of the total number of nodes for ensuring safety. Figure 11 compares the changes in total surviving nodes across different rounds for the LEACH, E-LEACH, EEUC, and EBRP-TL. With the LEACH protocol, the network experiences the first node failure early, and the death of the network is faster, primarily due to the randomness in cluster head election and the energy consumption from single-hop transmissions. E-LEACH improves upon LEACH by considering the node's energy during cluster head election and reduces energy consumption during intercluster data transmission by introducing a root cluster head. As a result, it offers improvements compared with LEACH. The EEUC protocol conducts unequal clustering.