## 1 Introduction  
Railway systems have become one of the main modes of transportation in the world. Therefore, the stability, reliability, and safety of railway systems are particularly important. At present, the service state monitoring of railway systems mainly relies on the combination of manual inspection, train inspection, and on-board inspection equipment. Due to the need for offline processing and analysis of monitoring data, there is a serious delay in the monitoring of sudden faults. In order to improve the real-time and reliability of railway system service status monitoring, a cable-based status monitoring and transmission system can be constructed in critical monitoring areas. Video, fiber Bragg grating, and stress-strain monitoring and transmission technologies can be used to realize on-line monitoring of railway system infrastructure. However, due to some drawbacks of cable-based communication itself, it is difficult for on-line monitoring systems based on wired communication to achieve full coverage of railway infrastructure. Wireless sensor network (WSN) [1] has the ability to accurately perceive monitoring objects and transmit information steadily. WSN has the characteristics of easy maintenance, easy expansion, and high reliability. It can make up for the defects of railway status monitoring systems based on wired communication, and improve the efficiency of monitoring. However, the transmission bandwidthof WSN is small, so it is not suitable for application in monitoring areas with large transmission volume [2; 3; 4; 5]. The main factors restricting the large-scale application of WSN in railway system status monitoring are as follows: Firstly, the energy storage capacity of wireless sensor node is low, and it is not easy to replace power supply. Its energy utilization efficiency will determine the life cycle of nodes and even the whole network, and then it will affect the sustainability and stability of railway infrastructure and its status monitoring. Secondly, the mutual relay and forwarding of data between wireless sensor nodes will increase the transmission delay of monitoring data and affect real-time monitoring. Thirdly, WSN has low communication bandwidth, and there are many kinds and large amounts of data for the objects in railway monitoring systems. The efficiency of bandwidth resources will affect the efficiency and reliability of monitoring data transmission. In recent years, railway status monitoring systems based on wireless sensor networks have been widely used, including intelligent monitoring system for high speed railway [6], wireless automatic monitoring and early warning system for subgrade settlement of high speed railway [7], bearing temperature monitoring system for railway freight cars based on ZigBee and GPRS (General Packet Radio Service) [8]. However, in these railway systems, the location of monitoring objects is usually fixed, and the location of sensor nodes is relatively fixed; they have not fundamentally solved the application of wireless sensor network in the railway service status monitoring system. It is necessary to optimize the allocation of limited energy and bandwidth resources in the sensor network from the routing protocol layer and data processing layer, so as to enhance the efficiency and capability of the wireless sensor network of the railway status monitoring system. Because the battery capacity of sensor nodes is very limited, a large number of nodes will be distributed in the monitoring area to rotate for prolonging the network life cycle. Therefore, how to select the optimal nodes and effectively cover the monitoring area with the least working nodes under the condition of ensuring a certain coverage rate has become an important research field in wireless sensor network of the railway status monitoring system. [PERSON] et al. [9] proposed the optimal full coverage algorithm under the condition that the locations of sensors are known--it is used to realize the optimal configuration of network nodes under full coverage.