Maximize Lifetime of Wireless Rechargeable Sensor Networks with Mobile Energy-Limited Charging Device

Mobile charging devices (MCDs) have been regarded as a promising way to solve the energy shortage of wireless sensor networks. Due to ignoring some important factors, such as redundant sensor nodes, there is still room to improve network lifetimes. We propose a charging strategy for wireless sensor networks with one energy-limited MCD. To give the best support for sensor nodes which need charging the most, an algorithm is proposed to find the minimum sensor nodes which keep the coverage and connectivity of the network and have the least energy requirements. Then, the goal of maximizing network lifetime is changed into how to utilize the limited energy of the MCD to guarantee the minimum sensor nodes work as long as possible. If the MCD has enough energy for all sensor nodes, the charging algorithm is designed to minimize the outage time of the network and maximize charging efficiency. Otherwise, if the energy capacity is larger than the least energy requirement, the charging target minimizes the outage time of the minimum sensor node; otherwise the charging problem becomes maximizing the lifetime of minimum sensor nodes, which has lower complexity. The results of simulation experiments confirm that our scheme prolongs network lifetime and improves charging efficiency.

Deep Reinforcement Learning-Based Online One-to-Multiple Charging Scheme in Wireless Rechargeable Sensor Network

Wireless rechargeable sensor networks (WRSN) have been emerging as an effective solution to the energy constraint problem of wireless sensor networks (WSN). However, most of the existing charging schemes use Mobile Charging (MC) to charge nodes one-to-one and do not optimize MC scheduling from a more comprehensive perspective, leading to difficulties in meeting the huge energy demand of large-scale WSNs; therefore, one-to-multiple charging which can charge multiple nodes simultaneously may be a more reasonable choice. To achieve timely and efficient energy replenishment for large-scale WSN, we propose an online one-to-multiple charging scheme based on Deep Reinforcement Learning, which utilizes Double Dueling DQN (3DQN) to jointly optimize the scheduling of both the charging sequence of MC and the charging amount of nodes. The scheme cellularizes the whole network based on the effective charging distance of MC and uses 3DQN to determine the optimal charging cell sequence with the objective of minimizing dead nodes and adjusting the charging amount of each cell being recharged according to the nodes' energy demand in the cell, the network survival time, and MC's residual energy. To obtain better performance and timeliness to adapt to the varying environments, our scheme further utilizes Dueling DQN to improve the stability of training and uses Double DQN to reduce overestimation. Extensive simulation experiments show that our proposed scheme achieves better charging performance compared with several existing typical works, and it has significant advantages in terms of reducing node dead ratio and charging latency.

Trajectory Optimization of Laser-Charged UAVs for Charging Wireless Rechargeable Sensor Networks

This paper considers a laser-powered unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) system. In the system, a UAV is dispatched as an energy transmitter to replenish energy for battery-limited sensors in a wireless rechargeable sensor network (WRSN) by transferring radio frequency (RF) signals, and a mobile unmanned vehicle (MUV)-loaded laser transmitter travels on a fixed path to charge the on-board energy-limited UAV when it arrives just below the UAV. Based on the system, we investigate the trajectory optimization of laser-charged UAVs for charging WRSNs (TOLC problem), which aims to optimize the flight trajectories of a UAV and the travel plans of an MUV cooperatively to minimize the total working time of the UAV so that the energy of every sensor is greater than or equal to the threshold. Then, we prove that the problem is NP-hard. To solve the TOLC problem, we first propose the weighted centered minimum coverage (WCMC) algorithm to cluster the sensors and compute the weighted center of each cluster. Based on the WCMC algorithm, we propose the TOLC algorithm (TOLCA) to design the detailed flight trajectory of a UAV and the travel plans of an MUV, which consists of the flight trajectory of a UAV, the hovering points of a UAV with the corresponding hovering times used for the charging sensors, the hovering points of a UAV with the corresponding hovering times used for replenishing energy itself, and the hovering times of a UAV waiting for an MUV. Numerical results are provided to verify that the suggested strategy provides an effective method for supplying wireless rechargeable sensor networks with sustainable energy.

A Novel Epidemic Model Base on Pulse Charging in Wireless Rechargeable Sensor Networks

As wireless rechargeable sensor networks (WRSNs) are gradually being widely accepted and recognized, the security issues of WRSNs have also become the focus of research discussion. In the existing WRSNs research, few people introduced the idea of pulse charging. Taking into account the utilization rate of nodes’ energy, this paper proposes a novel pulse infectious disease model (SIALS-P), which is composed of susceptible, infected, anti-malware and low-energy susceptible states under pulse charging, to deal with the security issues of WRSNs. In each periodic pulse point, some parts of low energy states (LS nodes, LI nodes) will be converted into the normal energy states (S nodes, I nodes) to control the number of susceptible nodes and infected nodes. This paper first analyzes the local stability of the SIALS-P model by Floquet theory. Then, a suitable comparison system is given by comparing theorem to analyze the stability of malware-free T-period solution and the persistence of malware transmission. Additionally, the optimal control of the proposed model is analyzed. Finally, the comparative simulation analysis regarding the proposed model, the non-charging model and the continuous charging model is given, and the effects of parameters on the basic reproduction number of the three models are shown. Meanwhile, the sensitivity of each parameter and the optimal control theory is further verified.

A Joint Energy Replenishment and Data Collection Strategy in Heterogeneous Wireless Rechargeable Sensor Networks

In wireless rechargeable sensor networks, mobile vehicles (MVs) combining energy replenishment and data collection are studied extensively. To reduce data overflow, most recent work has utilized more vehicles to assist the MV to collect buffered data. However, the practical network environment and the limitations of the vehicle in the data collection are not considered. UAV-enabled data collection is immune to complex road environments in remote areas and has higher speed and less traveling cost, which can overcome the lack of the vehicle in data collection. In this paper, a novel framework joining the MV and UAV is proposed to prolong the network lifetime and reduce data overflow. The network lifetime is correlated with the charging order; therefore, we first propose a charging algorithm to find the optimal charging order. During the charging period of the MV, the charging time may be longer than the collecting time. An optimal selection strategy of neighboring clusters, which could send data to the MV, was found to reduce data overflow. Then, to further reduce data overflow, an algorithm is also proposed to schedule the UAV to assist the MV to collect buffered data. Finally, simulation results verified that the proposed algorithms can maximize network lifetime and minimize the data loss simultaneously.

Epidemic Analysis of Wireless Rechargeable Sensor Networks Based on an Attack-Defense Game Model

Energy constraint hinders the popularization and development of wireless sensor networks (WSNs). As an emerging technology equipped with rechargeable batteries, wireless rechargeable sensor networks (WRSNs) are being widely accepted and recognized. In this paper, we research the security issues in WRSNs which need to be addressed urgently. After considering the charging process, the activating anti-malware program process, and the launching malicious attack process in the modeling, the susceptible–infected–anti-malware–low-energy–susceptible (SIALS) model is proposed. Through the method of epidemic dynamics, this paper analyzes the local and global stabilities of the SIALS model. Besides, this paper introduces a five-tuple attack–defense game model to further study the dynamic relationship between malware and WRSNs. By introducing a cost function and constructing a Hamiltonian function, the optimal strategies for malware and WRSNs are obtained based on the Pontryagin Maximum Principle. Furthermore, the simulation results show the validation of the proposed theories and reveal the influence of parameters on the infection. In detail, the Forward–Backward Sweep method is applied to solve the issues of convergence of co-state variables at terminal moment.

Hybrid Cyber Petri net Modelling, Simulation and Analysis of Master-Slave Charging for Wireless Rechargeable Sensor Networks

Wireless charging provides continuous energy for wireless sensor networks. However, it is difficult to replenish enough energy for all sensor nodes with fixed charging alone, and even more unrealistic to charge a large number of nodes within a short time via mobile charging. In order to overcome the above weaknesses, this paper firstly puts forward a Master-Slave Charging mode for the WRSN (Wireless Rechargeable Sensor Network), where fixed charging is the master mode and mobile charging is the slave mode, respectively. However, Master-Slave Charging is a typical hybrid system involving discrete event decision and continuous energy transfer. Therefore, the Hybrid Cyber Petri net system is proposed to build a visual specification with mathematical expression of Master-Slave Charging. Moreover, wireless charging in the WRSN is modeled and evaluated from the perspective of a hybrid system for the first time. Furthermore, a greedy-genetic algorithm is proposed to obtain the deployment of fixed chargers and the path planning of a mobile charger, by maximizing the actual electric quantity of the master charging problem and minimizing the mobile charger's travelling path of the slave charging problem. Finally, the simulation results confirm and verify the Hybrid Cyber Petri net model for Master-Slave Charging. It is worth noting that the proposed model in this paper is highly adaptable to various charging modes in the WRSN.

A Novel Epidemic Model for Wireless Rechargeable Sensor Network Security

With the development of wireless rechargeable sensor networks (WRSNs ), security issues of WRSNs have attracted more attention from scholars around the world. In this paper, a novel epidemic model, SILS(Susceptible, Infected, Low-energy, Susceptible), considering the removal, charging and reinfection process of WRSNs is proposed. Subsequently, the local and global stabilities of disease-free and epidemic equilibrium points are analyzed and simulated after obtaining the basic reproductive number R0. Detailedly, the simulations further reveal the unique characteristics of SILS when it tends to being stable, and the relationship between the charging rate and R0. Furthermore, the attack-defense game between malware and WRSNs is constructed and the optimal strategies of both players are obtained. Consequently, in the case of R0<1 and R0>1, the validity of the optimal strategies is verified by comparing with the non-optimal control group in the evolution of sensor nodes and accumulated cost.

An Online Charging Scheme for Wireless Rechargeable Sensor Networks Based on a Radical Basis Function

The node energy consumption rate is not dynamically estimated in the online charging schemes of most wireless rechargeable sensor networks, and the charging response of the charging-needed node is fairly poor, which results in nodes easily generating energy holes. Aiming at this problem, an energy hole avoidance online charging scheme (EHAOCS) based on a radical basis function (RBF) neural network, named RBF-EHAOCS, is proposed. The scheme uses the RBF neural network to predict the dynamic energy consumption rate during the charging process, estimates the optimal threshold value of the node charging request on this basis, and then determines the next charging node per the selected conditions: the minimum energy hole rate and the shortest charging latency time. The simulation results show that the proposed method has a lower node energy hole rate and smaller charging node charging latency than two other existing online charging schemes.

Wireless Charging Deployment in Sensor Networks

Charging schemes utilizing mobile wireless chargers can be applied to prolong the lifespan of a wireless sensor network. In considering charging schemes with mobile chargers, most current studies focus on charging each sensor from a single position, then optimizing the moving paths of the chargers. However, in reality, a wireless charger may charge the same sensor from several positions in its path. In this paper we consider this fact and seek to minimize both the number of charging locations and the total required charging time. Two charging plans are developed. The first plan considers the charging time required by each sensor and greedily selects the charging service positions. The second one is a two-phase plan, where the number of charging positions is first minimized, then minimum charging times are assigned to every position according to the charging requirements of the nearby sensors. This paper also corrects a problem neglected by some studies in minimizing the number of charging service positions and further provides a corresponding solution. Empirical studies show that compared with other minimal clique partition (MCP)-based methods, the proposed charging plan may save up to 60% in terms of both the number of charging positions and the total required charging time.

Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network

Wireless Power Transfer (WPT) technology is considered as a promising approach to make Wireless Rechargeable Sensor Network (WRSN) work perpetually. In WRSN, a vehicle exists, termed a mobile charger, which can move close to sensor nodes and charge them wirelessly. Due to the mobile charger’s limited traveling distance and speed, not every node that needs to be charged may be serviced in time. Thus, in such scenario, how to make a route plan for the mobile charger to determine which nodes should be charged first is a critical issue related to the network’s Quality of Service (QoS). In this paper, we propose a mobile charger’s scheduling algorithm to mitigate the data loss of network by considering the node’s criticality in connectivity and energy. First, we introduce a novel metric named criticality index to measure node’s connectivity contribution, which is computed as a summation of node’s neighbor dissimilarity. Furthermore, to reflect the node’s charging demand, an indicator called energy criticality is adopted to weight the criticality index, which is a normalized ratio of the node’s consumed energy to its total energy. Then, we formulate an optimization problem with the objective of maximizing total weighted criticality indexes of nodes to construct a charging tour, subject to the mobile charger’s traveling distance constraint. Due to the NP-hardness of the problem, a heuristic algorithm is proposed to solve it. The heuristic algorithm includes three steps, which is spanning tree growing, tour construction and tour improvement. Finally, we compare the proposed algorithm to the state-of-art scheduling algorithms. The obtained results demonstrate that the proposed algorithm is a promising one.