## 1 Introduction  
Wireless sensor network (WSN) has been a hot research topic in the recent decades, as it provides a fundamental communication tunnel and information collection from different environments [1]. WSNs have been widely used in daily life or industry area, such as the detection of temperature, pressure, traffic, power grid, and a patient's physical signs. Many WSN application scenarios have entered the mature stage and various application modes have been emerging, one after another [2; 3; 4]. For example, the information in a smart grid can be provided to power companies through a wireless sensor system and achieve high system efficiency and a feasible scheme for state monitoring [5; 6]. [PERSON] et al. tried to reduce the cost of intelligent transportation system and enhance its intelligence by using WSNs [7]. [PERSON] et al. discussed a series of WSN applications in urban areas [8]. [PERSON] et al. created and applied one scenario of WSN in the field of agriculture [9]. Obviously, the rapid development of unmanned applications make the WSN become an indispensable issue in the near future. Usually, engineers have to design the best scenario for the sensor locations. The most essential aspect in designs and applications of the WSNs is the large scale node deployment. Virtual force algorithm (VFA) is a novel algorithm strategy for sensor deployment using virtual force, which is pursued by many scientists. [PERSON] et al. proposed a dynamic deployment strategy, which can take both the historical local information and virtual forces for sensor into consideration [10]. In order to increase the converge speed, [PERSON] et al. added an expression of exponential function for the relationship of virtual force [11]. [PERSON] et al. introduced a strategy that, only if two nodes in the Delaunay graph are connected, the neighboring relationship of WSN nodes can be well defined and the virtual force can only be applied from neighboring nodes within the communication range [12]. By introducing the force model of centripetal force and grid theory, [PERSON] et al. proposed a coverage enhancement algorithm based on a virtual centripetal force, which can effectively turn off the redundant sensors and improves the coverage effect [13]. However, most of the recent WSN node deployment strategies are mainly for a two dimensional plane. In real applications, an effective three dimensional algorithm for large scale network deployment still requires further attention. Recently, [PERSON] et al. introduced a 3D spatial self-deployment algorithm which uses a weighted Voronoi diagram (3 dv-hdda) to move the sensor nodes and introduces a virtual boundary torque to rotate sensor nodes to reach the best positions [14]. [PERSON] et al. proposed a heuristic algorithm suitable for limited communication environment [15]. The selected redundant sensor nodes can move to their selected areas to improve the efficiency of WSN coverage and connectivity. For different \(k\) coverage requirements to achieve uneven regional coverage optimization, [PERSON] et al. proposed a \(k\)-equivalent radius enhanced virtual force algorithm (called k-ervfa) [16]. [PERSON] et al. introduced a negotiation strategy to ensure the network connectivity and also used a density control strategy to balance all the distributed sensor nodes [17]. Referring to an artificial potential-field theory, [PERSON] et al. proposed a three-dimensional dynamic path planning algorithm for mobile anchor nodes based on virtual force [18]. This algorithm indicates that the movements of anchor nodes by calculating the virtual force can be exerted by unknown anchor nodes in different regions. Interestingly, based on the phenomenon that dust particles can automatically form Yukawa crystal structure, [PERSON] et al. presented an adaptive deployment algorithm for large-scale WSN node deployment and discussed in detail the effects of calculation scale and shielding length on the algorithm [19; 20].