# Non-Uniform Clustering Algorithm for UWSNs Based on Energy Equalization
## 1 Introduction  
With the invention of wearable devices and some of their hardware devices, and the continuous research on efficient communication protocols, underwater wireless sensor networks (UWSNs) have attracted more attention from researchers and made great progress in recent years [1]. Research on UWSNs is divided into many directions, such as node deployment, node localization, and routing protocols, among which the most complex and important is the study of routing protocols [2]. This is because UWSNs are subject to a variety of challenges and limitations: limited battery energy of sensor nodes, dynamic network topology, narrow bandwidth, high propagation delay, high noise, and high ocean interference. The design of routing protocols is one of the solutions to these problems, which can efficiently transmit data from source nodes to destination nodes in the network [3]. Usually, hardware devices such as underwater wearable devices, drifters, hydroacoustic motors [4], and senor nodes are low-power devices. Moreover, UWSNs, unlike terrestrial sensor nodes, are powered by batteries and cannot collect solar energy. Due to the harsh underwater environment, it is very burdensome to recover the batteries [5]. Therefore, to make the sensor network work longer, balancing the network energy consumption and extending the network lifetime are the key goals of routing protocols. In addition, the influence of dead nodes on the monitoring area should be also considered in the routing process to ensure the reliability of the network. Extensive work has shown that cluster routing protocols and multi-hop routing are effective in finding the optimal routing path for data transmission, saving energy, and extending the network lifetime [6]. However, multi-hop routing suffers from the hot zone problem because sensor nodes near the receiver can quickly exhaust their energy and these nodes can die earlier, thus leading to the inability to observe the area of interest [7]. At the initial stage of node deployment for the underwater sensor network, the sensor nodes are often randomly distributed on the water surface by aircraft or ship [8]. The presence of underwater current motion can lead to the uneven distribution of underwater sensor nodes [9], and thus the selection of cluster heads for the clustering algorithm and cluster size is key to avoiding excessive load differences between clusters in sparse and dense areas of nodes. At the same time, in UWSNs based on cluster architecture, when cluster heads transmit data to sink nodes with single-hop or multi-hop communication, they run out of energy and die prematurely due to large amounts of data overload, leading to early blindness in coverage of the monitored area [10]. In addition, due to ocean current activities and other natural factors, underwater nodes are prone to drift, causing the dynamic topological evolution of the network [11]. Therefore, the underwater routing protocol should be scalable to accommodate the dynamic topological change and stability in the network for different emergencies [3]. To address the above problems, an energy-balanced non-uniform clustering (NUC-EB) algorithm is proposed for the underwater sensor network in this paper. The clustering-based multi-hop transmission mechanism is used to balance the network energy consumption and extend the network lifetime. The algorithm first considers the number of neighbor nodes and the distance to each neighbor node and constructs a node density weight function to make cluster heads more evenly distributed in the network. Then, the coverage redundancy index is introduced by cluster heads to improve the fault tolerance of the detection area for cluster heads. Finally, the cluster maintenance mechanism is designed by considering the water flow and the residual energy of cluster heads.