Wireless sensor nodes widely exist in the Internet of things, these nodes are typically battery-powered and the amount of power they can use is relatively limited. Generally, most of the wireless sensor nodes are deployed outdoors, i.e., trees by the river, the roof of buildings and objects in the water. In these conditions, the battery cannot be replaced easily by us because of sensor nodes housed in a sealed waterproof case. As the development of the Internet of things, there are a trillion wireless sensor nodes all around the world while a million nodes need daily battery replacements. It is difficult and unrealistic to change batteries one by one in practical appliance. Therefore, how to prolong the network survival time has become an urgent problem and also a research hot area [1
The current research mainly focuses on the following two aspects: (1) Energy saving. For example, nodes working in a low duty cycle mode maximize energy savings and prolongs the lifetime of the network by reducing the power consumption of sensor node [2
]. In addition, some methods are scheduled according to the length of the data packet, so as to obtain a reasonable and effective energy management strategy [3
]. However, the sensor data can not be uploaded to the sink node or the cloud server of the Internet of things in real-time. (2) Energy harvesting. Another way to solve the energy problem is powered from multiple low-level energy harvesting sources, including solar energy, wind energy, vibration energy, RF energy and more [4
], especially in the usage of wireless power technology [5
] in recent years. Currently, the emphasis has been placed on energy harvesting as the most important means of maintaining the wireless sensor network [1
]. The Wireless Rechargeable Sensor Network (WRSN) has become a newly emerging research area of sensor network that utilizes RF charging as a convenient and efficient charging method [6
] for sensor nodes or devices.
There is a great number of research works dedicated to wireless rechargeable sensor networks. Currently, the research directions of wireless rechargeable sensor networks are mainly divided into two aspects: on one hand, it is hardware which many researchers are trying to improve the efficiency of charging by the internal design of the sensor node and energy harvesting or wireless charging technology for improving the performance of the wireless rechargeable sensor networks; on the other hand, the researches focus on software improvement [7
]. Some algorithms pay attention to optimizing the number of chargers, aiming to find the minimum number of charging nodes that satisfy the regional charging task, such as the algorithm in static scene [10
] and the algorithm in dynamic scene [11
], in order to improve the utilization of chargers. The other charging algorithms consider that the energy value of the sensor nodes needs to remain above a threshold to stabilize the operation. In order to reduce the charging delay, some algorithms for minimizing the charging delay are proposed, such as [12
When most research resources were placed on the charging efficiency, there is a potential problem with the electromagnetic radiation exposure problem. In some literature, high electromagnetic radiation exposure has been recognized as a potential hazard to humans, including mental illness [16
], tissue damage [17
] and brain tumors [18
]. There is also some tangible evidence that pregnant women and children are more vulnerable to high electromagnetic radiation [19
]. For example, children’s heads absorb electromagnetic waves twice that of adults [20
] under the same condition. In recent research, the radiation safety problem of wireless charging has begun to attract attention. Radiation safety charging algorithms in static scenes have been proposed, such as the Safe Charging for Wireless Power Transfer algorithm (SCWPT) [12
], the Safe Charging with Adjustable PowEr algorithm (SCAPE) [21
] and so on. The research scenario of these literature is that the chargers and sensor nodes are all stationary, and the radiation exceeding the standard value is avoided by controlling the switching sequence and time of each charger. The main difference is that SCWPT is based on the case where the charging voltage is variable, while SCAPE is based on the case where the voltage is not variable. Unfortunately, to the best of our knowledge, in the current algorithms, the safe charging algorithm is relatively few. The safe charging algorithm in the scene of static chargers is mainly studied. In this scenario, the charging node only responsible for charging some fixed number of sensor nodes has low usage efficiency and charging efficiency.
As the size of wireless sensor networks expands, multiple mobile chargers should be added and moved in the sensor networks [23
]. However, safety problems have been taken into concern. In order to balance the relationship between charging efficiency and radiation safety in mobile conditions, this paper proposes a safe charging algorithm based on multiple mobile chargers.
The main contributions of this paper are as follows:
The mobile chargers can find and charge the wireless sensor nodes quickly by using the charging time and antenna waveform.
The non-partition charging algorithm is designed based on the solution of Multiple Traveling salesman Problem with a fixed depot, which is better than the performance of the partition one. In this algorithm, the performance of the chargers is fully utilized relative to partition charging one.
This paper proposes a safe charging algorithm based on multiple mobile chargers, which can minimize total charge time and improve some performance, ensuring electromagnetic radiation below the safe threshold.
The remainder of the paper is organized as follows. In the Section 2
, we express the basic model, node position correction method, and propose a safe charging algorithm based on multiple mobile chargers. Section 3
describes the details about the algorithm. Simulates and analyzes results are presented in the Section 4
. Section 5
summarizes and discusses the future work.
4. Simulation Test and Performance Analysis
In order to verify our algorithm, we test our framework by coding in python 3.7 importing the matplotlib, numpy and pandas packages. Gurobi [28
] is used for solving the multiple travelling salesman problem. All tests are run on a desktop with a 1.8 GHz Intel i5-8250U processor and 8 GB of memory. Unless otherwise specified, the following default parameters setup is used in the simulation. It is supposed that there are 16 wireless rechargeable sensor nodes and 4 robots with chargers distributed in a 100 m × 100 m area. Regarding the charging model and EMR model, the EMR threshold is set to Rt = 125
. To simplify the experiment, the size of the waiting time slot and charging time slot are both set as 5 s.
4.1. Simulation Experiment Data Analysis
These main parameters are as follows:
Charging delay time: The time from charging request sending to being charged by the charger.
Charger moving distance: The distance traveled by the charger to charge sensor nodes during the movement in the network.
Total number of messages: The total number of information related to charging between the charger and the sensor node during the entire network operation.
4.1.1. Performance Comparison with Sensor Node Number Change
Among these experiments, the sensor nodes number gradually increases from 60 to 150. As shown in the Figure 16
, non-partition algorithm can handle it due to the uneven energy consumption in different regions, so its charging delay is lower than the one of the partition algorithm. As shown in the Figure 17
, the partition algorithm prefers the charger in this area to the non-partition algorithm, which tends to choose the nearest charging node, so The non-partitioned algorithm moves at a lower distance than the partition algorithm. As shown in the Figure 18
, the node with non-partition algorithm needs to communicate with all chargers every charge, while the partition node only needs to communicate with the chargers it is responsible for in its area. The partition algorithm is better than the non-partition algorithm.
4.1.2. Performance Comparison with Chargers Number Change
In these experiments, the chargers number increased from 2 to 7. As shown in the Figure 19
, the number of chargers is negatively correlated with total delay time. The charging delay of the non-partition algorithm is lower than that of the partition algorithm. As shown in the Figure 20
, since the partition algorithm will select the charger as much as possible rather than the non-partition algorithm, it will tend to choose the nearest charger, so the moving distance of non-partition algorithm is lower than the partition algorithm. As shown in the Figure 21
, since the non-partition algorithm needs to communicate with all chargers for each charging, the partition algorithm is superior to the non-partition algorithm.
4.2. Comparison between SCBMC, SCWPT and SCAPE
The main difference between SCBMC, SCWPT and SCAPE algorithm in the scene include charging methods, mobility and distribution density. The different charging methods make the energy utilization different, calculated according to the Equation (2
). Since the SCBMC algorithm selects the sensor node near the charger for charging, charging efficiency is relatively stable. While the SCWPT algorithm has lower charging efficiency when there are fewer nodes in the area. As node number increases, the charging efficiency increases gradually. When there are 10 sensor nodes, the charging efficiency is higher than the SCBMC algorithm. It can be seen that SCWPT is suitable in high density sensor networks. When the density is low, the SCBMC algorithm is more efficient. With the decreasing of the density of sensor nodes, the SCWPT algorithm will face unusable conditions, while the SCBMC algorithm can be used at any node density. From the Figure 22
and Figure 23
, as the sensor network area expands, chargers number increases in these algorithms. The growth rate of the SCWPT and SCAPE algorithm is faster than that of the SCBMC algorithm and the number of chargers required in a large-scale network is more. The SCBMC algorithm can cover a larger area because the charger can move, so when the network area increases, the number of required chargers grows slowly.
depicts the radiation metric for each algorithm. As we see, the radiation safety level of the SCBMC algorithm outperforms that of the SCWPT algorithm and the SCAPE algorithm. The waiting time slot and charging time are both the same, therefore the average radiation value of the SCBMC algorithm usually equal to half of the EMR threshold. According to the literature of SCWPT and SCAPE, the radiation values of them are just a little bit below the threshold. In details, the radiation value of the SCBMC is 65
, however, the radiation value of the SCWPT is 110
and the radiation value of the SCAPE is 105
. At the same time, ensuring the safety threshold value, the total moving distance of chargers can be kept to a minimum.
In this subsection, the robustness against the different number of the chargers and sensors about the proposed methods is tested on simulation programming implemented in python. The gurobi solver can solve the unique solution in a relatively short period of time. At the same time, for simplification in computation, the waiting time and charging time have been set to slot t. Therefore, the unique solution for the minimum total distance also ensures the robustness of the algorithm.
The background of wireless charging technologies has been reviewed extensively first, and then with the boom of the wireless network, the safety problem about charging has been taken into consideration. The classical models of energy transmission have been modeled by us. Use the charging time and the antenna waveform to further segment and narrow the possible location of the node to improve the charging effectiveness. This paper proposes a safe charging algorithm for wireless rechargeable sensor networks under multiple mobile chargers. This type of charging problem is converted into a MTSP-fixed problem and the subroute of every charger can be solved robustly. After the confirmation of the subroute, every charger move, wait and charge the rechargeable sensors along the way of subroutes which ensure that the EMR value is not greater than the healthy level. The simulation results show that the SCBMC algorithm has better charging effectiveness than others below the safe threshold.
However, there are some limitations to our proposed SCBMC algorithm. The first limitation of SCBMC is that most of it is performed in only simulations. In the future, we will establish a test-bed to verify all the simulations. The second main limitation of SCBMC is that we suppose the charging area discretization. In the future, we will explore a more fine-grained discretization method for EMR. The third limitation of SCBMC is that we do not consider a longest delay minimization problem for sensor charging under multiple chargers because this is another NP-hard problem. In the future, we will investigate a novel safety algorithm that meets this condition.