Abstract: Aiming at the problem that the peak density was usually chosen as the cluster head in the wireless sensor networks, and these nodes might not have the optimal energy state or network location, and might fail prematurely due to energy depletion, forming energy holes that affected the stability of network operation, we proposed  an optimization algorithm for multi-level circular clustering in wireless sensor networks. Firstly, we divided the network area equally based on the distance from the boundary of the wireless sensor network area to the base station to obtain multiple circular areas. Secondly, within each circular region, the clustering by fast search and find of density peaks （CFSFDP） algorithm was used to cluster nodes based on their density and distance to balance the distribution of nodes within the cluster and optimize communication load. Thirdly, after determining the optimal number of clusters within each layer of the circular region, we calculated the weight values of each node and selected the node with the higher weight value as the clustering center to complete node clustering. Finally, we considered the remaining energy and relative density of nodes,  dynamically selected cluster heads, and established a multi-level clustering structure.  At the same time, we sorted data transmission according to the remaining energy ratio of cluster heads to balance the energy consumption of each node, avoid premature failure of some nodes, ensure connectivity and transmission efficiency, and achieve multi-level circular clustering optimization in wireless sensor networks. The experimental results show that the number of surviving nodes of the proposed method remains above 280, and the maximum and minimum remaining energy of the nodes are both above 3.5 J.  The load balancing value is the highest, which can be maintained above 0.8. This can avoid the energy hole caused by energy depletion and ensure the stable operation of the wireless sensor networks.

Key words: wireless sensor network, multi-level circular clustering, CFSFDP algorithm, remaining energy, relative density