# The Augmented Approach towards Equilibrated Nexus Era into the Wireless Rechargeable Sensor Network

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## Abstract

**:**

## 1. Introduction

#### 1.1. Milieu and Impetus

#### 1.2. Functions

- The mobile data compilation and charging path optimization problem formulation for determining an efficient charging schedule for the wireless charging device.
- The concepts of connectivity matrix, shortest hop matrix, and sensor node aptness are commenced to achieve the connection and distance relationship flanked by sensor nodes to augment the idle time of the wireless charging vehicle.
- Development of a PSO-based virtual clustering technique is presented during the routing process to replenishing the energy of the sensor nodes.
- A mobile data compilation and charging path optimization strategy dependent on the wireless charging device is proposed. The approach classified into three parts: the selection of cluster head nodes using the PSO-based virtual clustering approach, the establishment of data collection clusters and the shortest path planning. First, the cluster head node set determines according to the residual energy of the SNs and the connection relationship between the sensor nodes. Secondly, the data collection cluster has established. Finally, the wireless charging vehicle collects data and charges according to the path determined by the shortest path optimization strategy.

#### 1.3. The Architecture of the Manuscript

## 2. Akin Literature

#### 2.1. Wireless Power Transfer

#### 2.2. Analogous Study

## 3. The Framework of the Present Study

#### 3.1. Problem Sketch

**Definition**

**1.**

**Sensor Network (SN):**The SNs and the base station form a sensor network, which is chiefly accountable for data collection, forwarding, and storage and processing.

**Definition**

**2.**

**Wireless Charging Device (WCD):**The wireless charging device periodically replenishes the sensor nodes in the sensor network deployment area. Wireless charging device uses wireless power transfer (WPT) technology to recharge the sensor nodes.

**Definition**

**3.**

**Wireless rechargeable nodes (WRN):**Wireless rechargeable sensor nodes are competent of computing, sensing, and energy harvesting amid a wireless charging device.

**Definition**

**4.**

**Maintenance Station (MS):**When the charging task has accomplished, the mobile charger proceeds towards to the maintenance station to replenish energy to prepare for the next charging cycle.

**Definition**

**5.**

**Charging System (CS):**The maintenance station and the wireless charging device form a charging system and chiefly accountable for providing energy supply of the sensor network via wireless power transfer technology to recharge the sensor nodes.

**Definition**

**6.**

**Charging Path (CP):**WCD initiated its operation from the maintenance station and traveled to the deployment area of the sensor network at a steady speed. Furthermore, it moves in the deployment area, according to a particular route and charges a specific range of sensor nodes during the movement.

**Definition**

**7.**

**Network Charging Model (NCM):**In the current work, PSO-based virtual clustering approach is accountable for recharging the sensor nodes. Therefore, this paper considers using the sensor nodes that are being replenished energy as the cluster head node of the sub-network. It obtains information from nearby sensor nodes and transmits it directly to a wireless charging device to diminish the energy consumption and stable the network lifetime of the network.

#### 3.2. Sculpt of Network

- The WCD initiates its operation from the maintenance station and traverses the battery of the sensor node $i$ on the specified path in a specific order.
- During this time, the WCD moves to the node $i$ and recharges its battery wirelessly using wireless power transfer. When the battery of the node $i$ is charged to ${E}_{max}$, the wireless charging device leaves the SN $i$ and moves to the next SN to charge it. Also, ${\tau}_{i}$ represents the charging duration of the wireless charging device spends in each charging cycle.
- Once the wireless charging device traverses all the nodes in the WRSN, the WCD proceeds towards to the maintenance station for maintenance (e.g., replenishing the battery or replacing the battery). The maintenance time of the WCD at the maintenance station is the idle time, indicate as ${\tau}_{vac}$. After replenishing itself, the wireless charging device initiates to move for the next charging cycle. $\tau $ represents the duration of each charging cycle. Furthermore, Notations used in this paper presented in Table 1.

- Based on wireless charging device, the charging energy is inadequate, along with the energy utilization of the sensor nodes disseminated in the wireless rechargeable sensor network is not equilibrated. Subsequently, the energy of the sensor nodes near the center of the base station is generally higher. The node replenishment energy and charging time need to be considered comprehensively.
- Considering that the charging plan is to ensure that the WRSNs work persistently and effectively. Consequently, the charging plan deliberated in this paper is dependent on periodicity. Additionally, the charging cycle $\mathsf{\tau}$ of the wireless charging device for the energy utilization of a sensor node $i$ in the network should assure the following points.

**Definition**

**8.**

**General charging cycle:**The sensor node has the same energy level both at the commencement and the completion of the charging cycle. The battery capacity of each rechargeable sensor node is${E}_{max}$and fully charged initially. The energy of each rechargeable sensor node is not lesser than the known threshold${E}_{min}$at the time$t$. The minimum energy required for the sensor node to work normally is${E}_{min}$.

**Definition**

**9.**

**Charging schedule:**The WCD initiates its operation from the maintenance station at the commencement of the charging cycle. Once the charging task is finished, the WCD proceed towards to the maintenance station for its replenishment. The residual driving energy and enduring charging energy of the wireless charging device should not less than a known threshold. Therefore, the same sensor node is not recharging repetitively, and the traversal path used for charging schedule is the shortest path. The period of this time is called a round of charging plan.

**Definition**

**10.**

**Scheduling interval:**The interval amid the completion of one round of charging scheduling and the initiation of the next series of charging schedule is referring to the scheduling interval. The time at which the wireless charging device stays at the maintenance station.

#### 3.3. Problem Framework

## 4. Charging Path for Wireless Charging Device

#### 4.1. Dijkstra Algorithm and Shortest Hop Number Solution

#### 4.2. Dijkstra Algorithm

#### 4.3. Solution Steps

**Step (1)**At the beginning of the network, the sensor node set ${S}_{e}$ contains only ${S}_{1}$, which represents, ${S}_{e}=\left\{{S}_{1}\right\}$, and the distance of ${s}_{1}$ is 0. Further, ${S}_{h}$ includes all sensor nodes except ${S}_{1}$, which refers to ${S}_{h}=S\backslash \left\{{S}_{1}\right\}$. Subsequently, if the sensor nodes in ${S}_{h}$ connected to ${S}_{1}$, the distance between these sensor nodes is recorded as the actual distance between the two sensor nodes. Finally, if the sensor nodes in ${S}_{h}$ are not connected to ${S}_{1}$, the distance between these sensor nodes is marked as $\infty $.

**Step (2)**Select the sensor node ${s}_{i}$ from $S$ which has the smallest distance from ${s}_{1}$ and put ${s}_{i}$ into ${S}_{e}$, which is the shortest path length of ${s}_{1}$ to ${s}_{i}$;

**Step (3)**Use ${s}_{i}$ as a new intermediate sensor node to update the distance of each sensor node in ${S}_{h}$. If the distance from ${s}_{1}$ through ${s}_{i}$ to ${s}_{j}\in {S}_{h}$ is shorter than the distance without ${s}_{i}$. Consequently, update the distance of the sensor node ${s}_{j}$, which represents the sum of the shortest path length of ${s}_{1}$ to ${s}_{i}$ and the path length of ${s}_{i}$ to ${s}_{j}$.

**Step (4)**Repeat steps 2 and 3 until ${S}_{e}$ includes all sensor nodes.

#### 4.4. Network Parameters

**Connected matrix:**A matrix that characterizes the connectivity flanked by two points, which based on the location information about recognized sensor nodes and obstacles, is called a connected matrix. In this paper, the two points are blocked by an obstacle. To get the connection between the nodes, we introduce the concept of the connected matrix, whether the obstacle prevents the two points. Consequently, according to the known obstacle information, if the connectivity matrix is $M$, the set of the connection relationship flanked by the two points is as shown in Equation (4).

**Shortest hop matrix:**Based on identified sensor node information and obstacle information, the matrix of the minimum number of hops that can communicate amid two points is called the shortest hop matrix. Let, set the matrix of the shortest hop count as $H$. If ${M}_{ij=1}$, the Dijkstra algorithm is used to calculate the minimum hop count in the communication range between sensor node $i$ and sensor node $j$. If ${M}_{ij=1}$, sensor node $i$ needs to find neighbors to reach the sensor node $j$. Furthermore, if there is no neighboring sensor nodes can reach the sensor node, it indicates that the sensor node $i$ and sensor node $j$ cannot communicate. Herein, applying the concept of the connected matrix and the shortest hop matrix. Conversely, the sensor node fitness F(i,j) is defined to characterize the appropriate degree amid the sensor node to sensor node. The sensor node aptness is used to measure the connectivity amid sensor nodes and is also an imperative source for sensor node selection. The calculation method is as follows:

## 5. Particle Swarm Optimization (PSO) Routing Algorithm.

#### 5.1. Particle Swarm Optimization

#### 5.2. Clustering with Particle Swarm Optimization

**Step (1)**SNs in the WRSN sends the information of the location and enduring energy of the SNs to the BS. The sensor node will divide the entire network area by PSO and initialize the K particles based on the information received by the sensor node.

**Step (2)**$\left(x,y,{\theta}_{x},{\theta}_{y}\right)$, represents the parameters of particles which are randomly assigned to determine the network area division line. The network area dividing line can be calculated based on Formula (6). Further, the entire network is partitioned into $K\times 2$ sub-areas. Finally, the fitness value $F$ of each sensor node is calculated according to Formula (7).

**Step (3)**Calculate $K$ different fitness values of each sensor node and compare them with the global minimum fitness values obtained from the last search. If its value is better than the pair, update it to the current fitness value. Further, compare the fitness value of the individual particle and take the minimum value to update it to the current fitness value. Finally, update the $L=\left(x,y,{\theta}_{x},{\theta}_{y}\right)$, according to the following equations.

**Step (4)**Where ${c}_{1}$ and ${c}_{2}$ both represent the learning factors, $\omega $ denoted as weight factor and $t$ defines the number of current iterations.

**Step (5)**After the particle gets a new dividing line, $L=(x,y,{\theta}_{x},{\theta}_{y})$, then go to step 3 to continue the search. When the optimal global solution is searched, or the maximum number of iterations is reached, the algorithm terminates.

**Step (6)**After the area is first divided, the sub-areas continue to be classified according to the above method until the final $M$ clusters are formed in the network. The process of the clustering with particle swarm optimization to split a network area is provided in Algorithm 1.

Algorithm 1: Proposed PSO-based Clustering Algorithm |

1. Initialize the swarm size (N), dimension (D) of the particle position X 2.//Initialize the particle position 3. for i = 1 to N4. for j = 1 to D5. X(i,j) = Xmin + (Xmax − Xmin) × rand(i,j); 6. end for7. fit(i) = F(X(i))//calculate the objective function value 8. end for9. //Initialize the velocity of particles V 10. for i = 1 to N11. for j = 1 to D12. V(i,j) = Vmin + (Vmax − Vmin) × rand(i,j); 13. end for14. end for15. Xpbest = X; pbest = fit; gbest = Inf; 16. // update the velocity and particle position 17. while (termination criteria)18. for i = 1 to N19. for j = 1 to D20. V(i,j) = w*V(i,j) + C1*rand()*(Xpbest(i,j) − X(i,j)) + C2*rand()*(Xgbest(j) − X(i,j)); 21. X(i,j) = X(i,j) + V(i,j); 22. end for23. fit(i) = F(X(i)) //calculate the objective function value 24. if fit(i) < pbest(i) then //update the pbest25. pbest(i) = fit(i); 26. end if27. if fit(i) < gbest then //update the gbest28. gbest = fit(i); 29. end if30. end for31. end while |

#### 5.3. Selection of Cluster Head

## 6. Simulation and Experiment Analysis

#### 6.1. Simulation

#### 6.2. Experiment Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A wireless rechargeable sensor network (WRSN) structural model based on clustering via single-hop & multiple-hop.

Notation | Definition |
---|---|

WCD | Wireless charging device |

N | Sensor nodes (SNs) |

BS | Base Station node |

MS | Maintenance Station |

${E}_{max}$ | The maximum battery capacity of sensor nodes |

${E}_{min}$ | The minimum energy required to SNs work properly |

$V$ | Traveling speed of the wireless charging device |

$U$ | The full charging power |

${R}_{i}$ | The data rate generates in the network at SN $i$ |

${R}_{c}$ | Communication radius |

${g}_{ij}\left(t\right)or{g}_{iB}\left(t\right)$ | The data flow rate in the network from SN $i$ to SN $j$ at the time $t$ |

$\rho $ | The energy consumption coefficient for receiving the data |

${C}_{ij}or{C}_{iB}$ | The energy consumption for forwarding the data from SN $i$ to SN $j$ |

${p}_{i}\left(t\right)$ | The rate of energy consumption from SN $i$ to SN $j$ at the time $t$ |

$\tau $ | The time an SN in the network performs a charging task |

${\tau}_{i}$ | WCD spends the time to charge sensor node $i$ |

${\tau}_{vac}$ | The wireless charging device at the service station for vacation |

${X}_{c},{Y}_{c},$ | The centroid |

x_{i}, y_{i} | The coordinates of SN $i$ |

$\mathrm{D}$ | The time interval between centroid and sensor node |

$\mathrm{T}$ | Indicates the completion of one round of transmission cycle in WRSN |

Parameters | Values |
---|---|

Network Size | 1000 m × 1000 m |

Number of Nodes ($N$) | 25 |

Initial energy $({E}_{max}$) | 10,800 J |

Minimal energy $({E}_{min}$) | 540 J |

Moving Speed $\left(V\right)$ | 5 m/S |

Charging Power $\left(U\right)$ | 5 W |

Communication radius (Rc) | 100 m |

Path Loss | Log-Normal Shadowing |

Antenna | Omni Directional |

Charging Scheme | Grid Clustering, particle swarm optimization algorithm (PSO) |

Simulation Period | 1 h |

Properties Values | |||||||||
---|---|---|---|---|---|---|---|---|---|

Total Distance (m) | Traveling Time (s) | Charging Time (s) | |||||||

Algorithms | 10 | 25 | 50 | 10 | 25 | 50 | 10 | 25 | 50 |

Grid Clustering | 1884 | 4089 | 6763 | 376 | 817 | 1353 | 386 | 842 | 1395 |

Proposed | 1245 | 2968 | 6142 | 249 | 593 | 1228 | 259 | 618 | 1277 |

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## Share and Cite

**MDPI and ACS Style**

Ali, A.; Ming, Y.; Chakraborty, S.; Iram, S.; Si, T.
The Augmented Approach towards Equilibrated Nexus Era into the Wireless Rechargeable Sensor Network. *Symmetry* **2018**, *10*, 639.
https://doi.org/10.3390/sym10110639

**AMA Style**

Ali A, Ming Y, Chakraborty S, Iram S, Si T.
The Augmented Approach towards Equilibrated Nexus Era into the Wireless Rechargeable Sensor Network. *Symmetry*. 2018; 10(11):639.
https://doi.org/10.3390/sym10110639

**Chicago/Turabian Style**

Ali, Ahmad, Yu Ming, Sagnik Chakraborty, Saima Iram, and Tapas Si.
2018. "The Augmented Approach towards Equilibrated Nexus Era into the Wireless Rechargeable Sensor Network" *Symmetry* 10, no. 11: 639.
https://doi.org/10.3390/sym10110639