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Improving the quality of monitoring and guaranteeing target coverage and connectivity in energy harvesting wireless sensor networks (EH-WSNs) are important issues in near-perpetual environmental monitoring. Existing solutions only focus on the utility of coverage or energy efficient coverage by considering target connectivity for battery-powered WSNs. This paper focuses on optimizing the maximum monitoring frequency with guaranteed target coverage and connectivity in EH-WSNs. We first analyzed the factors affecting monitoring quality and the energy harvesting model. Thereafter, we presented the problem formulation and proposed the algorithm for maximizing monitoring frequency and guaranteeing target coverage and connectivity (MFTCC) that is based on graph theory. Furthermore, we presented the corresponding distributed implementation approach. On the basis of the existing energy harvesting prediction model, expensive simulations show that the proposed MFTCC algorithm achieves high average maximum monitoring frequency and energy usage ratio. Moreover, it obtains a higher throughput than existing target monitoring methods.

Wireless sensor network (WSN) is a multihop wireless network consisting of many sensor devices and is widely applied in environmental monitoring, precision agriculture, and natural disaster relief [

These studies mainly focused on three coverage types: area, point (target coverage), and barrier coverages. For the area coverage, the sensor nodes in a WSN must be deployed optimally to cover each point in a given area. In the point coverage, a set of point targets must be covered by sensor nodes in a given region. The barrier coverage mainly focuses on intruder detection in a given belt region and does not cover every point of a region. In the existing studies on the three coverage types above, most of the proposed coverage algorithms mainly focus on battery-powered WSNs. Battery-powered WSNs are failure-prone due to their limited power supply. Therefore, the existing studies mainly concentrated on extending the network lifetime to address the coverage problem. Moreover, some studies did not consider the connectivity between the targets and the sink station and only aimed to maximize the coverage of targets.

The advent of energy harvesting technologies (such as solar, wind, and vibration) can be utilized to solve the power supply limitation in WSNs. A sensor node in an energy harvesting WSN (EH-WSN) can be powered perpetually. Therefore, the coverage problems in EH-WSNs tend to concentrate on quality-aware target coverage, but not the extension of network lifetime for the coverage problem [

However, few algorithms consider the problem of target monitoring quality for guaranteeing target coverage and connectivity in EH-WSNs. In this work, we are interested in developing an efficient algorithm for improving the quality of monitoring while ensuring the target coverage and connectivity of EH-WSNs. The proposed algorithm aims to maximize the monitoring frequency of all targets covered by the sensor nodes and the requirement of connectivity between the target and the sink node. Maximum monitoring frequency is defined as the maximum number of monitoring each target receives in a monitoring cycle of an EH-WSN. The two corresponding constraint conditions are as follows. The first constraint is the monitoring of each target by at least one sensor node for a given period. The second constraint is the need to construct a connected path between each target and sink node. To solve the optimization problem, we first divide the monitoring period into

The main contributions of this paper are as follows:

We first integrated the monitoring frequency of a target with coverage and connectivity and presented the solution of maximizing monitoring frequency under guaranteed target coverage and connectivity in an EH-WSN.

We proposed an efficient maximizing monitoring frequency algorithm with a guaranteed coverage and connectivity optimization algorithm (MFTCC) based on graph theory. The proposed algorithm not only achieves the maximum monitoring frequency with guaranteed target coverage and connectivity but also embodies the fairness of target monitoring. Moreover, we provided the distributed implementation and analysis of MFTCC.

The rest of this paper is organized as follows. Section

The coverage problem in traditional WSNs is one of the fundamental problems for which many coverage algorithms have been proposed. These algorithms can be categorized as area, target (discrete point), and barrier coverages [

However, these existing target coverage and connectivity algorithms mainly focus on the maximum network lifetime of battery-powered WSNs or the coverage utility in EH-WSNs. Few studies have considered the maximum monitoring frequency of targets with guaranteed target coverage and connectivity.

In this section, we first present the network model of target coverage in an EH-WSN and the definition of energy consumption for monitoring, forwarding, and receiving information. Subsequently, the energy harvesting model based on the weighted moving-average (EWMA) algorithm is introduced.

We consider an EH-WSN as an undirected topology graph _{1}, _{2}, …, _{i}, _{i+1}, …, _{n}} is the set of _{1}, _{2}, …, _{i}, _{i+1}, …, _{m}} is the set of _{ij}} is the set of all links. Each sensor node _{i}∈_{1}, _{2}, _{3}, …, _{i}, _{i+1}, …, _{L}}.

Let EZ_{j}(_{i}) be the energy consumption of monitoring a target (_{j}) once by sensor node _{i}, ER(_{i}) be the energy consumption of receiving monitoring data once on sensor node _{i}, and EF(_{i}) be the energy consumption of forwarding monitoring data once on sensor node _{i}. BE(_{i}) denotes the battery capacity of sensor node _{i}.

In this work, we mainly consider the environmental monitoring for an EH-WSN. We take solar power as the energy supply and use a widely adopted environmental energy harvesting assumption, that is, the harvesting energy of each sensor node in a future period is uncontrollable but predictable through its historic energy harvesting profile. Moreover, the consumption energy of each sensor node is less than the harvesting energy. For a long-period monitoring task, the monitoring frequency for each target is determined by the usable energy of the sensor node. Furthermore, we assume that a monitoring period is divided into _{h}(_{i}) denotes the prediction value of the amount of harvested energy at monitoring cycle _{i}. _{h}(_{i} − _{i}, _{i}), for sensor node _{i} ∈ _{i}, _{i}) is the battery capacity and RE(_{i}, _{i}) is the residual energy of sensor node _{i} at current monitoring cycle _{i}.

In this section, we first describe the requirement of monitoring quality, coverage, and connectivity in EH-WSNs. Thereafter, we present the problem formulation of maximizing the monitoring frequency with guaranteed target coverage and connectivity in an EH-WSN.

Section

For the target coverage and monitoring for the EH-WSN, the following factors must be considered into monitoring quality, such as the monitoring frequency and fairness of monitoring frequency for targets. Furthermore, target coverage and connectivity should also be fundamental requirements for target monitoring in an EH-WSN. To understand the monitoring quality, we explain the influencing monitoring quality and present some fundamental requirements, which are shown in Figure

Factors of influencing monitoring quality and fundamental requirements.

Figure

Therefore, we aim to maximize the monitoring frequency based on fairness under guaranteed target coverage and connectivity in EH-WSNs. Specifically, we consider the maximizing monitoring frequency as the quality of monitoring and take it as the optimization objective. The constraints mainly include the monitoring fairness, target coverage, and connectivity. The problem is defined as follows:

In the above formulation, FM_{t}(_{i}) denotes the monitoring frequency for the target (_{i}) covered by a sensor node at monitoring cycle _{t}(_{i}) denotes the number of sensor nodes covering target _{i} at monitoring cycle _{i}) denotes the set of sensor nodes covering target _{i}. _{i}), _{i}. If target _{i} is connected to the sink node, then _{i}), _{i}), _{i}. In (

In literature [

In this section, we present a heuristic algorithm for solving the proposed optimization problem, that is, the optimization algorithm for maximizing monitoring frequency with guaranteed target coverage and connectivity (MFTCC). First, the idea of the proposed MFTCC algorithm is introduced. Thereafter, a detailed description of the MFTCC algorithm is presented.

The proposed MFTCC algorithm guarantees that each target is covered by a sensor node and the connectivity between the target and sink nodes. Moreover, it reflects the fairness of the monitoring frequency of sensor nodes covered targets. Before presenting the MFTCC algorithm, we present the idea of achieving the MFTCC. The MFTCC algorithm utilizes graph theory to solve the problem presented in Section

Establishment of link weight.

Energy consumption of each sensor node on path.

Figure _{1} is equal to EZ_{1}(_{1}) + EZ(_{1}) and that relay node _{i} is equal to ER(_{i}) + EF(_{i}). Section

Virtual connection between targets and sensor nodes.

In Figure _{i}. Figure

Network based on virtual source node Sr.

In Figure _{i} ∈ _{j} once by sensor node _{i} is EZ_{j}(_{i}). Thus, these link weights between the virtual source and sensor nodes are defined as follows:_{i}) indicates that the value of the link weight is equal to the energy of monitoring target _{j} once by sensor node _{i}. It is the minimum consumption energy of monitoring a target once for each sensor node on the path between the target and sink nodes.

According to the definition of link weight, we can transform the optimization problem in Section

Input: Topology of energy harvesting WSN _{i}, _{t}) for sensor node _{i} ∈ _{t} monitoring cycle,

Output: The set of active sensors in each monitoring cycle MZ(_{t}), _{i})

Calculate link weights _{i}) and _{i}, _{j}) according to equation (

Initialize _{i}) = 0, MZ(_{t}) =

Build directed graph _{d} (

For each link (_{i}, _{j}), node _{i} is replaced by _{j} is replaced by

Establish the new connection relationship and increase the direct links, which include (

Set the link weight: _{i}, _{t}); _{j}, _{t}); _{i}, _{t}), SE(_{j}, _{t})).

Select virtual source node Sr and set

Find a feasible path (_{d} (

Goto exit

_{i}, _{j}) ∈ _{d} (

_{i}, _{j}) ∈ _{i} ∈ {_{i}} and _{j} ∈ {

SE(_{j}, _{t}) = SE(_{j}, _{t}) − (EZ_{i}(_{j}) + EF(_{j}))

_{i}, _{j}) = _{i}, _{j}) − EZ_{i}(_{j})

_{j}, _{i}) = _{j}, _{i}) + EZ_{i}(_{j})

_{i}, _{j}) ∈ _{i} ∈ {_{j} ∈ {

SE(_{j}, _{t}) = SE(_{j}, _{t}) − (ER_{i}(_{j}) + EF(_{j}))

_{i}, _{j}) = _{i}, _{j}) − (ER_{i}(_{j}) + EF(_{j}))

_{j}, _{i}) = _{j}, _{i}) + (ER_{i}(_{j}) + EF(_{j}))

_{i}, _{j}) ∈ _{i} ∈ Sr and _{j} ∈ {_{j}}

_{j}, _{t}) = SE(_{j}, _{t}) − (EZ_{i}(_{j}))

_{i}, _{j}) = _{i}, _{j}) − EZ_{i}(_{j})

_{j}, _{i}) = _{j}, _{i}) + EZ_{i}(_{j})

_{i} and _{i} ∈

FM(_{i}) = FM(_{i}) + 1

MZ(_{t}) = MZ(_{t}) ∪

_{i}, _{j}) ∈ _{d} (

_{i} ∈ Sr and _{j} ∈ {_{j}}) or (_{i} ∈ {_{i}}and _{j} ∈ {

_{i}, _{j}) = EZ_{j}(_{i})

_{i}, _{j}) = min{SE(_{i}, _{t}), SE(_{j}, _{t})}

In Algorithm _{i}) = _{i}, _{i}) = EZ_{j}(_{i}), _{i}, _{j}) = min(SE(_{i}, _{t}), SE(_{j}, _{t})) in line 1, and some variables are initialized (line 2). Node decomposition is implemented in line 3 (as shown in Figure

Operation of node decomposition.

In lines 4–29 (as shown in Figure _{i}, exists, the target node can be monitored once, and one is added to the number of monitoring (line 27). When _{d} (

Calculation of feasible paths.

In this section, we propose and explain the distributed implement scheme of the proposed MFTCC algorithm.

The proposed distributed algorithm is more suitable for the practical deployment in WSNs. In this section, the distributed implementation of the proposed MFTCC is presented, and the distributed implementation is performed using the neighbor nodes’ information of each node. The central MFTCC algorithm in Section

To solve the abovementioned problem, we first present the design idea of the distributed implementation of the MFTCC algorithm. The implementation procedure is mainly composed of the following three parts. In the first part, each sensor node exchanges residual energy with neighbor sensor nodes. Thereafter, each sensor establishes a connection relationship based on the node decomposition. In the second part, all sensor nodes covering the targets monitor a time in the beginning of a monitoring cycle and send the energy information of all nodes in the transmission path to the sink node. Subsequently, the frequency of monitoring in the next monitoring cycle is calculated on the basis of the collected energy information of the sink node. In the final part, the sink node sends feedback to all sensor nodes to update the target monitoring frequency of the next monitoring cycle.

The detailed steps of the distributed MFTCC algorithm are summarized in Algorithm

Each sensor node _{i} calculates energy value SE((_{i}, _{t})) based on formula (_{i}, _{t})) to neighbor sensor _{i}).

Each node calculates link weight _{i}, _{j}) = min(SE(_{i}, _{t}), SE(_{j}, _{t})), saves it on the basis of the message of energy value SE((_{i}, _{t})), and establishes a connection relationship on the basis of the node decomposition.

_{i} covering target node _{j} first sends a message of constructing transmission path _{i} to the sink node by the distributed shortest energy path algorithm based on link weight 1/_{i}, _{j}).

Each node _{i} sends an energy information message, min{_{i}, _{j})} _{i}, _{j} ∈

_{i}, _{j})} < ER_{i}(_{j}) + EF_{i}(_{j})}, in transmission path

The sink node sends a reverse message of including monitoring times to each sensor covering the target nodes.

The sensor nodes perform the frequency of monitoring based on the reverse message from the sink node.

In this section, we first present the analysis of the proposed MFTCC algorithm, which includes the lower and upper bounds of the maximum monitoring frequency calculated by the MFTCC algorithm, the coverage and connectivity of the target nodes, and the difference in monitoring frequency between any two target nodes. Subsequently, the complexity of the MFTCC algorithm is analyzed.

The proposed MFTCC algorithm focuses on solving the quality-aware target coverage problem while guaranteeing target coverage and connectivity in the EH-WSN. We define the maximum monitoring frequency as the optimization objective of coverage quality, and the fairness of monitoring for each node is considered. Thus, we analyze the performance of the maximum monitoring frequency and the fairness of monitoring for the proposed MFTCC algorithm, which are as follows.

Given the monitoring network

We know from Section _{i}, _{j})) in the monitoring network

Given the monitoring network

Theorem 1 and Section

Given monitoring network _{e} links, for the total monitoring period (_{T}. Assuming that the energy consumption of monitoring each target in the minimum cut edge set is ET, the loop count is _{c} = _{T}/ET in lines 4 to 32 of the proposed MFTCC algorithm. In MFTCC, the node decomposition in lines 1 to 3 makes two nodes to convert to four nodes and add four links. Thus, the computational complexity is _{e}). The computational complexity of finding feasible path ^{2}). In lines 11 to 30, due to the node decomposition operation, the longest path is less that 2_{c}(_{e} + 4^{2} + 3 (2

In this section, we evaluate the performance of the proposed MFTCC algorithm through the following experimental simulation. We first verify the performance of the proposed MFTCC algorithm in terms of the maximum monitoring frequency, energy usage ratio, and the fairness of targets monitoring for 50 sensor nodes and 10 target nodes. Thereafter, we also evaluate the above performance, the throughput, and the end-to-end delay performance of networks with 50 nodes to 100 nodes and 10 targets to 35 targets.

We establish an EH-WSN with 50 sensor and 10 target nodes, which are uniformly distributed in 1000 × 1000 m^{2} regions. The transmission and monitoring ranges of all sensor nodes are 250 m and 200 m, respectively. The distribution of the sensor and target nodes is shown in Figure

Monitoring network. (a) Node distribution of the monitoring network. (b) Connectivity topology of the monitoring network.

Comparison of the maximum monitoring frequencies.

Proposed MFTCC | Distributed MFTCC | TMR-CU | TMR-SHP | |
---|---|---|---|---|

Ave. max. freq. of monitoring | 123.5 | 112.2 | 102.7 | 47.6 |

Energy usage ratio (%) | 37.86 | 21.34 | 18.98 | 7.23 |

Comparison of the fairness of target monitoring.

Proposed MFTCC | Distributed MFTCC | TMR-CU | TMR-SHP | |
---|---|---|---|---|

Max. difference of the monitoring frequency between any two target nodes | 1 | 1 | 8 | 10 |

In Table

To further validate our proposed MFTCC algorithm in terms of maximum monitoring frequency and energy usage ratio, we consider networks with 50 to 100 nodes and 10 to 35 targets randomly placed in a 1000

Parameter setting.

Field size | 1000 |

Maximum transmission range | 250 m |

Monitoring range | 200 m |

Number of sensor nodes | 50–100 |

Number of target nodes | 10–35 |

Harvesting energy range of sensor node | 20–30 (energy unit) |

Comparison of average maximum monitoring frequencies.

Comparison of energy usage ratios.

Comparison of the fairness of target monitoring.

Figures

To further verify the validation of the network performance of the MFTCC algorithm, we evaluate the performance of these different algorithms (including the proposed algorithm) by ns-2 simulations. We consider networks of 50 to 100 sensor nodes and 10 + (|

Throughput.

End-to-end delay.

Figure

The coverage problem is one of the most important research issues in WSNs. Related studies have mainly focused on area, target, and barrier coverages. Most of the works have concentrated on improving the coverage quality of battery-powered WSNs. Many energy efficient coverage algorithms have been proposed to extend the lifetime of WSNs. In recent years, energy harvesting technologies have been adopted to solve the problem of limited energy supply in WSNs. Given the continuous energy supply in EH-WSNs, the traditional coverage algorithms for battery-powered WSNs are unsuitable for the quality-aware target coverage problem in EH-WSNs. In this work, we investigated the problem of maximizing the monitoring frequency while guaranteeing target coverage and connectivity in EH-WSNs. Unlike previous works, we not only consider the monitoring quality but also guarantee the target coverage and connectivity. More importantly, we also consider the fairness of each target monitoring. First, the factors affecting the maximum monitoring frequency in the monitoring-cycle model of EH-WSN are analyzed, and the problem formulation is presented. To solve this problem, we define the link weight on the basis of the residual battery and the harvested energy of each sensor node and construct the virtual connection between targets and sensor nodes. We then devise a centralized MFTCC algorithm on the basis of graph theory and a distributed approach. We also analyze the lower and upper bounds of the maximum monitoring frequency calculated by the MFTCC algorithm. By experimental simulations, our proposed MFTCC algorithm achieves the highest monitoring frequency and energy usage ratio in a given monitoring cycle. Given that the proposed MFTCC algorithm can dynamically select the relay nodes based on the harvested energy of the sensor nodes in transmission progress, the simulation results affirm that the proposed MFTCC algorithm can achieve higher monitoring quality and energy usage ratio than the TMR-CU and TMR-SHP algorithms. This scenario also indicates that the proposed MFTCC utilizes the harvested energy and improves the monitoring coverage quality. Furthermore, the proposed MFTCC algorithm presents a better performance than other algorithms in terms of the fairness of target monitoring. The maximum difference in monitoring frequency between any two target nodes in the proposed MFTCC algorithm is only 1, whereas those in the TMR-CU, TMR-SHP algorithms exceed 8. In terms of network performance, the ns-2 simulations also demonstrated that although the proposed MFTCC algorithm has a high average end-to-end delay, it can effectively increase the throughput, also validating the maximum monitoring frequency. Thus, in data monitoring using EH-WSNs, the proposed MFTCC algorithm is more promising for quality-aware monitoring with guaranteed target coverage and connectivity than the traditional coverage algorithms.

In future work, we will continue to study the target coverage problem by considering the randomness of energy harvesting. Owing to the random dynamics of harvested energy, the long-term coverage performance must be considered to take full advantage of the harvested energy. Therefore, the target coverage problem, considering the long-term coverage quality, for EH-WSNs is the direction of future research. Moreover, the long-term performance of the video target coverage in EH-WSNs is also a future research plan.

The related simulation data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflicts of interest.

This research was supported by the Jiangxi Provincial Department of the Education Science and Technology Project (GJJ171013), the National Natural Science Foundation of China (grant no. 61401189), the Natural Science Foundation of Jiangxi Province, China (grant no. 20161BAB212036), and the Open Research Fund of the Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing (grant nos. 2016WICSIP023, 2016WICSIP028, and 2016WICSIP030).