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Abstract

3D coverage is not only closer to the actual application environment, but also a research hotspot of sensor networks in recent years. For this reason, a node optimization coverage method under link model in passive monitoring system of three-dimensional wireless sensor network is proposed in this article. According to wireless link-aware area, the link coverage model in three-dimensional wireless sensor network is constructed, and the cube-based network coverage is used to represent the quality of service of the network. This model takes advantage of the principle that the presence of human beings can change the transmission channel of the link. On this basis, the intruder is detected by the data packets transmitted between the wireless links, and then the coverage area is monitored by monitoring the received signal strength of the wireless signal. Based on this new link awareness model, the problem of optimal coverage deployment of the receiving node is solved, that is, how to deploy the receiving node to achieve the optimal coverage of the monitoring area when the location of the sending node is given. In the process of optimal coverage, the traditional genetic algorithm and particle swarm optimization algorithm are introduced and improved. Based on the genetic algorithm, the particle swarm optimization algorithm which integrates the idea of simulated annealing is regarded as an important operator of the genetic algorithm, which can converge to the optimal solution quickly. The simulation results show that the proposed method can improve the network coverage, converge quickly, and reduce the network energy consumption. In addition, we set up a real experimental environment for coverage verification, and the experimental results verify the feasibility of the proposed method.

Keywords

Wireless sensor network three-dimensional coverage link model received signal strength indicator coverage verification

Introduction

Wireless sensor network (WSN) is a self-organizing network composed of a large number of microsensor nodes deployed in the monitoring area. It can be widely used in national defense and military, agriculture and forestry monitoring, rescue and disaster relief, and many other fields.¹ Because the nodes have certain physical perception and communication computing ability, they can be deployed in some harsh environments that cannot be reached by human beings and sparsely populated complex environments, in order to replace human beings for perceptual monitoring. Usually, the range within the sensing radius of the sensor can be effectively covered by the monitoring system, which is the traditional disk sensing model.

Recently, the research in the field of passive location provides a new perceptual coverage model for the research of coverage control in sensor networks.^2–4 Passive location system can detect and locate the existence of people around us through the wireless signal propagation of multiple wireless links. This new sensing model uses the packet transmission between wireless links to monitor whether there is a target intrusion. The principle is that the existence of human beings will change the transmission channel of the link; monitoring the received signal strength indication (RSSI) of the wireless signal can sense whether people appear around the link. Previous experiments have verified that the sensing region of the wireless link can be approximated to an ellipse whose focus is located at the location of the transmitting node and the receiving node. This new perception model provides a new idea for the design of a new monitoring system. At the same time, we observe that wireless nodes are basically pre-installed in the interior of the building, which can be used as sending nodes. In this case, we only need to deploy some receiving nodes to cover important monitoring locations within the area. In order to save deployment costs, we need to consider how to use a minimum number of destination receiving nodes to cover areas that need to be monitored.

Although coverage and optimal deployment have been deeply studied, it is not easy to solve the new three-dimensional (3D) coverage problem. The main challenge is that the shape of the monitoring area of the receiving node is irregular, and the deployment of a receiving node can form a monitoring unit with multiple sending nodes around it. For three-dimensional space, the monitoring area of the link model can be approximated to an ellipse. When multiple links formed by the same receiving node are combined, the monitoring area is shaped like a sunflower. This irregular coverage area makes some assumptions in the existing work untenable, and they assume that the coverage area of the node is a regular disk. In this article, we study the optimal link coverage problem. The goal is to deploy the least number of destination receiving nodes to co-cover the areas that need to be monitored. The main contributions of this article are as follows:

We construct the link coverage model in three-dimensional wireless sensor network (3D-WSN), extend the traditional plane coverage to spatial coverage, and extend the traditional disk awareness model to a more practical link model.

Based on this new link awareness model, we combine and improve the traditional genetic algorithm (GA) and particle swarm optimization (PSO) algorithm to explore the optimal coverage problem of receiving nodes. Based on the basic GA, the PSO algorithm which integrates the idea of simulated annealing is regarded as an important operator of the GA. The improved algorithm can converge to the optimal solution quickly and get the deployment location of the receiving node to cover the monitoring area.

Through the simulation experiment, the change curve of coverage rate under different parameters is given, and compared with other literature algorithms, the effectiveness of the proposed algorithm is verified.

Set up a real experimental environment for coverage verification, by comparing the RSSI fluctuation range and standard deviation to monitor the coverage area, the experimental results verify the feasibility of the method.

The rest of this article is organized as follows: we briefly review the related works in section “Related work.” In section “Problem modeling,” we describe the network model and related definitions of the method. We present the method design and the design details of the GA/self-adaptive particle swarm optimization (SAPSO) in section “GA/SAPSO algorithm design.” Experimental setups, evaluations, comparisons, results, and discussions are reported in section “Experimental results and discussion.” Finally, we conclude the work in section “Conclusion.”

Related work

The main goal of optimization in coverage problem is to reduce the number of deployed nodes and optimize the scheduling of working sensor set in order to prolong the survival time of WSNs. We introduce the existing research work according to the different coverage models.

The first research on the optimization problem in coverage is based on the disk perception model. In order to solve the problem of coverage redundancy caused by the random deployment of large-scale sensor networks, Miao et al.⁵ proposed a 3D self-deployment algorithm, which uses negotiation strategy to ensure the effective connectivity of the network, and introduces density control strategy to make the nodes distribute evenly. The algorithm can realize the uniform and autonomous deployment of nodes in three-dimensional space with obstacles. Zhang et al.⁶ proposed an efficient mobility scheme energy-efficient motion strategy (EEMS), triangulates the monitoring area, and judges the coverage hole by monitoring whether the key point is within the perceptual range of the network node. And the greedy algorithm is used to match the mobile nodes with the key points to get the optimal scheduling scheme. Saha and Das⁷ divide the network deployment area into equilateral hexagons, with each vertex and center of the hexagonal as the target coverage location. The algorithm ensures coverage by selecting the most appropriate node near each target location to move to the corresponding location. Li et al.⁸ proposed a randomized robot-assisted relocation of static sensors (R3S2) that uses robots to assist node relocation to detect and repair holes. The holes and redundant nodes in the network are determined by the random movement of the robot in the monitoring area, and then the redundant nodes are moved to the holes to repair the holes. Ammari and Das⁹ proposed a centralized cluster K coverage configuration protocol, using the constructed network model to analyze the coverage protocol, and given the comparative relationship between communication radius and perception radius when K coverage is completed. T Razafindralambo and D Simplot-Ryl¹⁰ proposed a connectivity-preserving coverage algorithm, which uses the relative neighbor graph and the characteristics of node deployment to maintain network connectivity and coverage in the mobile deployment of sensor nodes. In order to solve the problem of network connectivity, Liao et al.¹¹ proposed a Steiner tree scheme with limited edge length to solve the problem of mobile sensor node deployment.

The research work based on disk model provides some ideas for solving the actual coverage problem, but because the attenuation of actual signal propagation and the influence of measurement error are not taken into account, the scale disease model is often too simple and impractical. Subsequent researchers^12,13 began to consider the coverage problem based on the probabilistic coverage model, which is closer to the perceptual behavior of the actual sensor than the disk model. In order to reduce the false alarm rate of the sensor and improve the recognition rate, the data fusion technology is introduced into the coverage research. For the monitoring of the target position, the data fusion processes the sensor monitoring data around the target position to determine whether the target appears or not. Data fusion effectively reduces the impact of measurement errors on sensor coverage. Researchers began to introduce data fusion into target classification, target recognition, and target tracking to improve the monitoring performance of the system. Tan et al.¹⁴ pointed out that the probabilistic perception model can improve network coverage performance more effectively than the 0/1 model. The 0/1 model is only suitable for the case of high signal-to-noise ratio (SNR), and the probabilistic perception model is based on data fusion. It can be applied to the case of low SNR ratio. Xing et al.¹⁵ gave the relationship between coverage, network density, and SNR ratio of received signals from the point of view of theoretical analysis and proved that compared with disk coverage, data fusion can effectively reduce the number of deployed nodes through cooperation between sensor nodes. Under the probability perception model, Zorbas and Razafindralambo¹⁶ increase the lifetime of the network by constructing the primary connected dominated set (CDS) of the network to select the coverage set of the target. Cao et al.¹⁷ considered the problem of maximizing network lifetime based on the value fusion model in data fusion. Lu and Guo¹⁸ studied the fence coverage under the probability perception model and proposed an optimal deployment strategy which can monitor the moving target less than the critical speed using the data fusion technology of adjacent nodes.

In recent years, the research in the field of passive location^19–22 provides a new sensing model to monitor the presence of intruders. The new sensing model uses packet transmission between wireless links to monitor the presence of intruders. Previous experiments²³ have verified that the sensing area of the wireless link can be approximated to an ellipse focusing on the location of the transmitting node and the receiving node. Different from the traditional sensor node–centric sensing model, the new sensing model is a wireless link–centric coverage model.²⁴ The optimization problem under the link coverage model has not been studied by researchers. Therefore, we study the area coverage problem of the minimum receiving node based on this new link awareness model.

Problem modeling

In this section, we will describe the problem based on the link coverage model and give the relevant definitions.

Link coverage model

The link coverage model originates from the research of passive location. The location system realizes the location of the target through the influence of the existence of human on the wireless transmission channel, that is, the change of wireless signal RSSI. This provides a new coverage model for us to study the coverage problem. We call it the link coverage model by checking the RSSI of the signal on the wireless link to detect the existence of human beings.

The implementation of link coverage requires the sending node to periodically send packets to the surrounding receiving nodes. For a stable environment, the RSSI value received by the receiving node is stable, that is, the standard deviation of the RSSI value is very small. When a person appears around the link, the RSSI value received by the receiving node of the link has a large standard deviation relative to the stable environment. The main reason is that the existence of human beings will affect the wireless transmission channel, resulting in the change of RSSI value. We can set a threshold to sense whether the people around us exist or not. Early studies have shown that the sensing area of a wireless link can be approximated by an ellipse at the location of the receiving node and the transmitting node. Therefore, in our three-dimensional space, the perceptual region of the link coverage model can be approximated to an ellipse, as shown in Figure 1.

Figure 1.

Link coverage model.

Human appearance in the region of ellipsoid perception can be sensed, and appearance in the outside of the ellipsoid cannot be detected. For a link-aware area consisting of a sending node s and a receiving node r, according to the property that the sum of the two focus distances from the point on the ellipse to the ellipse is equal to the long axis of the ellipse, a condition for a target t to be covered by the link is

$d (s, t) + d (r, t) \leq 2 λ$ (1)

where $d (\cdot)$ is the Euclidean distance and $2 λ$ is the long axis of the ellipse. In general, $2 λ$ is less than the communication radius of the wireless sensor node. In addition, a receiving node may form a link monitoring unit with a plurality of surrounding transmitting nodes. The sending node may produce packet conflicts when broadcasting packets. Conflicts are generally handled by the medium access control (MAC) layer in the existing passive location research, such as token ring protocol and time-division multiple access (TDMA) protocol. Each node is given a unique way for ID, to broadcast packets sequentially using token rings to avoid conflicts.

Problem description

Assuming that some of the sending nodes have been pre-deployed to the monitoring area, selecting the least number of locations to deploy the receiving nodes to cover the monitoring area as much as possible is called the optimal link coverage problem. Considering the deployment of sensor nodes, an important indicator is how to continuously supply power to sensor nodes. For short-term experiments, three No. 5 batteries per node are sufficient. However, for the long-term deployment of monitoring systems, the power supply of sensor nodes is generally supplied by direct current. In indoor and outdoor application environments, the location of AC sockets is usually limited, which correspondingly limits the location where the receiving node can be deployed.

Figure 2 shows a simple example of an optimal link coverage problem in which there are four monitoring targets (M1, M2, M3, and M4) and four sending nodes (S1, S2, S3, and S4). Here are two kinds of covering sets. In this case, an overlay set refers to a collection of node deployment locations where the deployment node can cover all monitoring targets. The overlay set in Figure 2(a) is {L2}, while the overlay set in Figure 2(b) is {L2}. It is clear that Figure 2(b) is better deployed, requiring only the deployment of nodes at candidate location L2 to form a wireless link with the four sending nodes to cover all monitoring targets.

Figure 2.

3D link coverage set: (a) two receiving nodes are deployed in L1, L3 and (b) a receiving node is deployed in L2.

Related definition

Definition 1 (valid coverage area):²⁵ When an intruder is located at any point in a specified area and can be perceived by node $i$ , the specified area is called the coverage area $ψ (i)$ of node $i$ . The effective coverage area $ξ (i)$ of node $i$ is defined as the intersection of coverage area $ψ (i)$ and monitoring area $Ω$

$ξ (i) = ψ (i) \cap Ω$ (2)

Definition 2 (coverage):²⁵ The coverage of node $i$ is defined as the ratio of the effective coverage area $ξ (i)$ of node $i$ to the volume of the monitoring area $Ω$ . The coverage rate of the network is defined as the ratio of the union of the effective coverage area of all nodes in the monitoring area to the volume of the monitoring area

$ζ = \frac{V (\underset{i}{\cup} ξ (i))}{V (Ω)}$ (3)

Definition 3 (connectivity):²⁵ If the total number of nodes in the monitoring area is $n$ , the number of nodes $φ (i)$ connected to node $i$ satisfies $0 \leq φ (i) \leq n - 1$ . When all nodes can communicate in pairs, the network communication path is the largest, and the total number is $n (n - 1) / 2$ . Network connectivity is defined as the ratio of the total number of current communication paths to the total number of maximum communication paths

$ε = \frac{\frac{1}{2} \cdot \sum_{i} φ (i)}{n (n - 1) / 2} = \frac{\sum_{i} φ (i)}{n (n - 1)}$ (4)

Network coverage under link model

Ideally, if a part of the monitoring area is within the perceptual range of any node, the area is said to be fully covered and the network coverage is 1. In practical application, due to the particularity of the shape of the link model, it is difficult to calculate the union of the node coverage area, resulting in the solution of network coverage is more difficult. Therefore, this article proposes a cube-based network coverage solution in three-dimensional environment, which converts the situation of the monitoring area perceived by the node into the situation that the cube is perceived by the node.

The method of approximate calculation of network coverage is to divide the monitoring area into cubes with equal volume. If the cube is divided small enough, the degree to which the cube is covered by nodes can be approximated to the degree to which the center point of the cube is covered by nodes. In this way, the coverage of the network can be approximated to the case where all the center points of the cube are covered by nodes. Assuming that the number of cubes in the monitoring area is $A_{c}$ , the number of sending nodes is $A_{s}$ , and the number of receiving nodes is $A_{r}$ , the probability that the center point of cube $C_{i}$ is perceived by the three-dimensional link model formed by the sending node $S_{m}$ and the receiving node $R_{n}$ is

$P_{c, s, r} (C_{i}, S_{m}, R_{n}) = {\begin{matrix} 1, d (C_{i}, S_{m}) + d (C_{i}, R_{n}) \leq 2 λ \\ 0, d (C_{i}, S_{m}) + d (C_{i}, R_{n}) > 2 λ \end{matrix}}$ (5)

In the formula, $d (C_{i}, S_{m})$ represents the distance between the center point of cube $C_{i}$ and the sending node $S_{m}$ , $d (C_{i}, S_{r})$ represents the distance between the center point of cube $C_{i}$ and the receiving node $R_{n}$ , and $λ$ represents half of the long axis of the link model.

Because the center point of cube $C_{i}$ can be perceived by each node as an independent event, from the knowledge of probability theory, the probability that cube $C_{i}$ is perceived by at least one node is as follows

$P_{c} (C_{i}) = 1 - Π_{m = 1}^{A_{s}} Π_{n = 1}^{A_{r}} (1 - P_{c, s, r} (C_{i}, S_{m}, R_{n}))$ (6)

In this article, the probability that the center point of all cubes in the monitoring area is perceived by at least one node is approximated to network coverage $η$

$η = \frac{\sum_{i = 1}^{A_{c}} P_{c} (C_{i})}{A_{c}}$ (7)

GA/SAPSO algorithm design

In this section, we will introduce the implementation of GA/SAPSO in the GA part and the PSO algorithm part and then introduce the fusion of these two parts.

GA part

The GA takes all the individuals in a population as the object and uses the random optimization technique to search the encoded parameter space efficiently. In the search process, the information of the search space is automatically obtained and accumulated, and then the search process is controlled adaptively to obtain the optimal solution. In each generation of GA, individuals are selected according to the adaptability of individuals in the problem domain and the reconstruction methods in natural genetics, and genetic mechanisms such as crossover and mutation are used to recombine individuals. Finally, according to the principle of survival of the fittest, an approximate optimal solution is generated one after another among all the potential solutions. Among them, selection, crossing, and mutation are the basic operations of GA. Parameter coding, initial population setting, fitness function design, genetic operation design, and control parameter setting are the core contents of GA.

In the link of GA, GA/SAPSO algorithm adopts real number coding. Assuming that there are $M$ receiving nodes and mapping the three-dimensional coordinate $(x_{i}, y_{i}, z_{i})$ of the receiving node to a chromosome, the individual in the population can be composed of a one-dimensional array $P$ of length $M$ , where each receiving node $P [i]$ is a triple $(x_{i}, y_{i}, z_{i})$ . Assuming that the long axis of the link coverage model is $2 λ$ , given a different number of receiving nodes $M$ , the GA/SAPSO algorithm initializes the population by random distribution, that is, the coordinate information of each receiving node is given. On this basis, the fitness function of GA/SAPSO algorithm is as follows^26,27

$f (R_{n}) = \frac{\sum_{i = 1}^{A_{c}} {1 - Π_{m = 1}^{A_{s}} Π_{n = R_{n}}^{R_{n}} (1 - P_{c, s, r} (C_{i}, S_{m}, R_{n}))}}{A_{c}}$ (8)

After that, the core links of GA, such as selection, crossing, and mutation, are performed. The probability that each receiving node is selected is proportional to its fitness. Assuming that the population size, that is, the number of receiving nodes is $A_{r}$ , and the fitness function of the receiving node $R_{n}$ is $f (R_{n})$ , then the probability of the receiving node being selected is²⁸

$P_{R_{n}} = \frac{f (R_{n})}{\sum_{n = 1}^{A_{r}} f (R_{n})}, (n = 1, 2, \dots, A_{r})$ (9)

Among them, the crossing rate is $P_{c}$ and the variation rate is $P_{m}$ .

PSO algorithm part

PSO algorithm is to simulate the flight foraging behavior of birds, through the collective cooperation between birds to achieve the best. When using PSO algorithm to solve practical problems, the feasible solution of the problem is equivalent to the position of birds in search space; these birds are particles. Particles have position and velocity information that determines the direction of the search and the distance they move. Particles have a fitness value, which is calculated by the fitness function and is used to determine the performance of the particle searchable solution. The PSO algorithm initializes the particle swarm into a set of random solutions, and all the particles search for the optimal solution in the solution space according to the current optimal particles. In the iterative process, the particle determines the next search direction and distance according to the two extremes, that is, to calculate the updated position and velocity information, which are the individual extremum and the global extremum, respectively. Among them, the individual extreme value is the optimal solution found by the particle itself, and the global extreme value is the optimal solution found by the whole particle swarm.

GA/SAPSO algorithm extends the particle swarm into three-dimensional space; a sensor node is a particle. In the population $X = (x_{1}, x_{2}, \dots, x_{N})$ composed of $N$ particles, the position coordinates of particle $i$ can be expressed as $X_{i} = (x_{i}, y_{i}, z_{i})$ , the flight speed can be expressed as $V_{i} = (v_{ix}, v_{iy}, v_{iz})$ , and the fitness function is the same as the previous link.²⁹ The flight speed and position update formula of the particle, that is, the receiving node, is as follows^30,31

$v_{i} (t + 1) = w \cdot v_{i} (t) + c_{1} \cdot r_{1} \cdot (P_{i} - X_{i} (t)) + c_{2} \cdot r_{2} \cdot (P_{g} - X_{i} (t))$ (10)

$x_{i} (t + 1) = x_{i} (t) + v_{i} (t + 1)$ (11)

where $t$ is the number of iterations; $w$ is the inertia weight; the main function is to produce disturbance to prevent the premature convergence of the algorithm. $c_{1}$ and $c_{2}$ are acceleration coefficients, which adjust the maximum step length for particles to fly to the individual best particles and the global best particles, respectively. $r_{1}$ and $r_{2}$ are random numbers in the range of $[0, 1]$ , $P_{i}$ is the optimal coordinate of the current receiving node $i$ , and $P_{g}$ is the current optimal coordinate of all $N$ receiving nodes.

In 1983, Kirkpatrick et al. compared the solid annealing process with the optimization problem and proposed a simulated annealing algorithm for the global optimal solution of the combinatorial optimization problem. Compared with some previous algorithms, this method has the advantages of simple description, flexible operation and low initial conditions, and is especially suitable for parallel computing, which has attracted extensive attention. The simulated annealing algorithm has the ability of probability mutation in the search process and can effectively prevent the algorithm from falling into local optimization in the iterative process. PSO algorithm is easy to fall into local optimization in the process of search, which leads to premature convergence. Therefore, in the part of PSO algorithm, we combine the global search ability of PSO algorithm with the local detection ability of simulated annealing algorithm to improve the performance of PSO algorithm.³² We set the initial temperature to

$T_{0} = \frac{f (P_{g})}{\ln 5}$ (12)

According to the adaptation value $f (i)$ and the global optimal value $f (P_{g})$ of each particle $i$ , the formula for calculating the adaptation value of each particle when the temperature is $t$ is as follows

$TF (i) = \frac{\exp (- (f (i) - f (P_{g})) / (f (i) - f (P_{g})) t t)}{\sum_{i = 1}^{pop} \exp (- (f (i) - f (P_{g})) / (f (i) - f (P_{g})) t t)}$ (13)

The cooling operation is as follows

$T_{k + 1} = λ \cdot T_{k}$ (14)

where $λ$ is the annealing constant and $k$ is the number of iterations.

Algorithm implementation

GA/SAPSO algorithm is based on the basic GA; at the same time, the PSO algorithm which integrates the idea of simulated annealing is regarded as an important operator of the GA, which can converge to the optimal solution quickly and improve the running efficiency of the algorithm. First of all, the GA/SAPSO algorithm is selected according to the fitness function, and the selected receiving nodes directly enter the next-generation population. Second, the unselected receiving nodes are optimized by the improved SAPSO algorithm, and the optimized nodes also enter the next-generation population. The fitness function of the next-generation population was recalculated after crossing and variation operation, so that the adaptation function could be iterated.

The specific implementation process of GA/SAPSO algorithm is as follows:

Each possible point of the search space is encoded, that is, the coordinates of the receiving node and its definition domain.

To determine the number of initial receiving nodes $A_{r}$ , fitness function $f (R_{n})$ , crossing rate $P_{c}$ , and variation rate $P_{m}$ .

An initial population $P (0)$ with size $A_{r}$ is generated randomly in the domain. The evolutionary algebra is $G = 0$ .

The fitness function value of the receiving node in $p (G)$ is calculated and sorted.

Calculate whether the current population is full of nodes with fitness requirements at the end of the algorithm, if so, go to step 17, otherwise go to step 6.

According to the value of node fitness function, a part of the nodes is selected to enter the $G + 1$ generation population directly.

The remaining nodes in step 6 are used as the initial particle swarm to initialize the basic parameters such as the maximum number of iterations, inertia weight, learning factor, and annealing constant. The position of each particle in the initialization population is the coordinate of the remaining receiving node in step 6, and the velocity of each particle is randomly initialized.

After calculating the adaptation value $f (i)$ of each particle $i$ , the current position and adaptation value of each particle are regarded as the historical optimal position $P_{i}$ and the optimal adaptation value $pbest$ of the particle, respectively. And the position of the particle with the best adaptation value and the corresponding adaptation value are regarded as the historical optimal position $P_{g}$ and the optimal adaptation value $gbest$ of the population, respectively.

Determining the initial temperature according to formula (12).

Combining the fitness value $f (i)$ and the global optimal value $f (P_{g})$ of each particle $i$ , the adaptation value of each particle fitness value under the current temperature $t$ is calculated according to formula (13).

The substitute value ${P_{g}}^{'}$ of the global optimal particle $P_{g}$ is determined from all the particles according to the adaptation value of the fitness value of each particle in combination with the roulette strategy. Substituting the motion update equation of the particle for the next iteration to calculate the new velocity and new position of the particle.

Calculate the fitness value of each particle to update the $pbest$ of each particle and the $gbest$ of the population.

Perform a cooling operation according to equation (14).

If the particle swarm reaches the preset precision value or the maximum number of iterations, the particle position is selected as the $G + 1$ generation population, otherwise go to step 10.

Perform crossover and mutation operators on the $G + 1$ generation population to generate the next-generation population $p (G + 1)$ . At this time, $G = G + 1$ .

If $G$ reaches the prescribed maximum evolutionary algebra, go to step 17, otherwise go to step 4.

Selecting the position information of the individual with higher fitness value in the current population as the result output.

The algorithm ends.

Experimental results and discussion

In this section, we explain the analysis of experimental setups and results. Experimental simulation and experimental verification of the proposed method were carried out. In the experimental simulation part, we simulated the performance of the algorithm in MATLAB programming and compared it with other algorithms. In the experimental verification part, the real indoor and outdoor experimental scenes were built for coverage verification, and the coverage area was monitored by comparing the fluctuation range of the RSSI value and the standard deviation.

Experimental simulation

In order to verify the performance of the algorithm, we use MATLAB 2014 to carry out simulation experiments. In the simulation experiment, we can adjust the parameters as follows: the size of the ellipsoid semi-long axis $λ$ in the link model, the number of sending nodes, the number of receiving nodes, namely the number of populations, and the maximum number of iterations. For each parameter adjustment, we verify the effect of the algorithm in five stochastic networks. The long axis $2 λ$ in the link model is usually related to the communication radius of the sensor node. According to the manual of the STM32W108 wireless transceiver module, the communication radius is usually 20–50 m. Therefore, we set the long axis $2 λ$ of the link model to be 20, 30, 40, and 50 m, respectively. Other simulation parameters are shown in Table 1.

Table 1.

Simulation parameters.

Name	Description
Simulation area	100 m × 100 m × 50 m
Crossing rate, $P_{c}$	0.85
Variation rate, $P_{m}$	0.005
Inertia weight, $w$	0.9
Acceleration coefficient, $c_{1}$	0.55
Acceleration coefficient, $c_{2}$	0.45
Annealing constant, $λ$	0.75
Number of cubes, $A_{c}$	50 × 50 × 25
Link model long axis, $2 λ$	[20 m, 50 m]
Number of sending nodes, $A_{s}$	[25, 40]
Number of receiving nodes, $A_{r}$	[3, 15]
Maximum number of iterations	[40, 200]

Effect of tunable parameters on algorithm performance

In order to verify the performance of the algorithm and the effects of the tunable parameters $2 λ$ and the number of transmitting nodes, we performed the following experiments separately, and adjusted one parameter at a time and kept other parameters fixed. In the first set of experiments, we randomly deployed 32 transmit nodes in the monitoring area. In the ellipsoid model, the parameter $2 λ$ is set to 20, 30, 40, and 50 m, respectively. We increase the number of steps from 2 receiving nodes to 15 receiving nodes in two steps and compare the performance of the four cases. In the second set of experiments, the parameter $2 λ$ in the ellipsoid model was set to 35 m, and the number of transmitting nodes randomly distributed in the monitoring area was 25, 30, 35, and 40, respectively. We also increased the number of steps from 2 to 15 receiving nodes in two steps and compared the performance of the four cases. The effect of two adjustable parameters on coverage is shown in Figure 3(a) and (b).

Figure 3.

(a) The performance of the algorithm with the change of parameter $2 λ$ and (b) performance of the algorithm when the number of sending nodes changes.

Figure 3(a) shows the relationship between coverage and population size, that is, the number of receiving nodes, when the number of sending nodes is fixed and the long axis $2 λ$ in the ellipsoid model changes. It can be seen that with the increase of population size, the coverage rate is increasing in all four cases. This is because no matter what value $2 λ$ is taken, the link composed of the receiving node and the sending node can cover more grid points with the increase of the population size. When the population size is less than 9, the effect of parameter $2 λ$ on coverage is more obvious under the same population size, and when the population size is larger than 9, the effect of parameter $2 λ$ on coverage becomes smaller. This is because when the population size is small, there are more cover holes; when $2 λ$ increases, it can cover more grid points, so it has a greater impact on the coverage. With the increase of population size and coverage rate, the ellipsoid coverage area will overlap, and the larger the value of $2 λ$ , the more overlapping areas, so the impact on coverage will gradually become smaller. For the same $2 λ$ , with the increase of population size, the coverage rate increases continuously, and the growth rate increases continuously in the initial stage, and the growth rate slows down when the population reaches a certain size. This is also due to the small size of the population; there are more cover holes, so the increase in coverage is more obvious; with the increase of population size, there will be a certain degree of coverage redundancy, and the rate of coverage growth slows down.

Figure 3(b) shows the relationship between coverage and population size, that is, the number of receiving nodes, when the long axis b is fixed and the number of sending nodes varies in the ellipsoid model. As shown in Figure 3(a), with the increase of population size, the coverage rate increases in all four cases, and the growth rate increases at first and then slows down. This is also due to the small size of the population, for the same number of sending nodes, there are more coverage holes, so that the coverage rate is more obvious. With the increase of population size and reaching a certain value, the coverage cavity becomes less and replaced by coverage redundancy, so the growth rate slows down gradually. Unlike Figure 3(a), the coverage of the four cases in Figure 3(b) is smaller than that in Figure 3(a) when the population size is 3. When the population size is 15, the coverage of the four cases in Figure 3(b) is larger than that in Figure 3(a). It can be seen that when the population size increases from 3 to 15, the coverage of the four cases in Figure 3(b) changes greatly. This shows that compared with the long axis b in the ellipsoid model, the number of sending nodes has a greater impact on the coverage. For the same coverage, for example, when the population size is 5 and the number of sending nodes is 35, the corresponding coverage is the same as when the population size is 7 and the number of sending nodes is 25. It can be concluded that as the number of sending nodes increases, the number of receiving nodes that need to be deployed is decreasing.

Comparison of algorithm performance

In order to verify the feasibility and convergence speed of the algorithm, we select the classical GA and PSO algorithm as a comparison of the following experiments. In the first group of experiments, 32 sending nodes are randomly deployed in the monitoring area, and the parameter c in the ellipsoid model is set to 35 m. We increase the number of receiving nodes from 3 to 15 with a step size of 1 to compare the feasibility of the three algorithms. In the second group of experiments, under the same conditions, the number of receiving nodes is 15, and we increase the convergence rate of the three algorithms from 40 iterations to 200 iterations in 20 steps. The feasibility and convergence rate of the three algorithms are compared as shown in Figure 4(a) and (b).

Figure 4.

(a) Performance comparison of different algorithms and (b) comparison of convergence rate of different algorithms.

Figure 4(a) shows the relationship between coverage and population size when running GA/SAPSO, PSO, and GA algorithms. With the increase of population size, the three intelligent algorithms will improve the coverage of the network. It can be seen that the GA/SAPSO algorithm proposed in this article is obviously better than the PSO algorithm and the GA algorithm. In terms of the maximum coverage that can be achieved under different population sizes, the GA/SAPSO algorithm has a great improvement compared with the GA algorithm, but the advantage of the PSO algorithm is not obvious at the initial stage with the increase of population size. When the population size is larger than 9, the coverage rate of GA/SAPSO algorithm is larger, which is gradually better than that of PSO algorithm. In terms of coverage growth, the coverage growth rate of GA/SAPSO algorithm and GA algorithm increases at first and then slows down. Among them, when the population size is 12, the coverage rate of GA/SAPSO algorithm reaches 80% and then slows down. When the population size is 14, the growth rate of GA algorithm slows down after 83%. Both algorithms grow rapidly in the early stage, and can reach the peak quickly. However, the coverage rate of GA algorithm is only 74.5% when the population size is 12, while the coverage rate of GA/SAPSO algorithm is 90% when the population size is 14. Therefore, with the increase of population size, the coverage rate of GA/SAPSO algorithm and GA algorithm is faster and can reach the peak value quickly, but the peak value of GA/SAPSO algorithm is much higher than that of GA algorithm under different population sizes. When the population size is less than 9, the coverage of PSO algorithm and GA/SAPSO algorithm go hand in hand, but because the coverage rate of PSO algorithm is slow, when the population size is larger than 9, the coverage rate of GA/SAPSO algorithm is obviously higher than that of PSO algorithm. Therefore, no matter in terms of the maximum coverage that can be achieved under different population sizes, or in terms of coverage growth, the GA/SAPSO algorithm is superior to the GA algorithm and the PSO algorithm.

Figure 4(b) shows the relationship between coverage and the number of iterations when running GA/SAPSO, PSO, and GA algorithms. In terms of the maximum coverage that can be achieved by the same number of iterations, the GA/SAPSO algorithm is obviously superior to the GA algorithm and the PSO algorithm. In terms of coverage growth, the GA/SAPSO algorithm approaches the peak and converges rapidly at 140 iterations, while the remaining two algorithms are still growing rapidly after 140 iterations. Therefore, the GA/SAPSO algorithm can reach the optimal value faster and the convergence speed is faster. In the aspect of algorithm convergence, the GA/SAPSO algorithm shows a better simulation effect. From the change curve of the GA/SAPSO algorithm, it can be seen that the algorithm can continuously jump out of the local optimal solution and converge to the global optimal solution more quickly. Compared with Figure 4(a), the initial coverage in Figure 4(b) is relatively large and the later coverage is similar, indicating that the number of receiving nodes has a greater impact on the coverage than the number of iterations. To sum up, the feasibility and convergence speed of GA/SAPSO algorithm are better than the other two algorithms.

Experimental verification

In order to verify the practical application of this method, we set up an experimental platform for practical verification. The equipment used in the experiment is the STM32W108 development board, and the node uses the STM32W108 radio frequency transceiver module which conforms to the IEEE802.15.4/ZigBee standard. The development board supports random selection of channels 11–26, and the radio frequency transceiver module sends broadcast packets on one of the channels randomly selected by the development board. Figure 5(a) and (b) shows the circuit boards of the STM32W108 development board and the radio frequency transceiver module, respectively, powered by a battery box with three No. 5 batteries. The online debugging circuit is a 20-pin Joint Test Action Group (JTAG) circuit, which can be connected to JLink to realize program burning and online debugging.

Figure 5.

(a) STM32W108 development board and (b) STM32W108 wireless RF transceiver module.

In the experiment, we select the indoor space of 5 m × 5 m × 3 m and the outdoor space of 10 m × 10 m × 3 m as the experimental scene. Among them, the indoor scene includes tables and chairs and other obstacles, as well as glass, display screen, and other special materials that can make the wireless signal multi-path propagation; the outdoor scene is flat and wide without any obstacles. The sensor node is deployed on a tripod with a maximum adjustable height of 2 m from the ground. In the center of the monitoring area, the development board connected to the PC through the serial port line is the receiving node, listens to all the data transmission in the network, and transmits the received data packets to the PC through the USB. Figure 6(a) and (b) shows the indoor and outdoor experimental scenarios we built, respectively.

Figure 6.

(a) Indoor experiment scene and (b) outdoor experimental scene.

Experimental design

In the experimental scenario of 5 m × 5 m × 3 m shown in Figure 6(a), we randomly select seven locations to deploy the sending node, and according to the coordinate operation algorithm of the seven randomly deployed sending nodes, we get the best deployment location of the receiving node. For the specific location of the sending node, see the yellow circle in Figure 6(a), and for the specific location of the receiving node, see the red circle in Figure 6(a). In the experiment, the long axis s of the link model is set to 2 m, the number of receiving nodes is 1, and the other parameters are the same as 5.1. To facilitate comparison, in the outdoor scene of 10 m × 10 m × 3 m shown in Figure 6(b), we deploy at 1:2 in the same location. When the receiving node is deployed to the iterative location of the algorithm, the network begins to run. At this time, the sending node sends a broadcast packet to the receiving node every 5 s, and the receiving node listens to all the data transmission in the network. The division of areas monitored by each sending node after the operation of the network is shown in Figure 7.

Figure 7.

Monitoring area division map.

In Figure 7, the red base station in the middle is the receiving node, and the seven wireless transceiver modules around are the transmitting nodes. We divide the monitoring area into seven subdomains, and the boundary of each subdomain is the angular bisector between the sending node and its adjacent nodes. After the operation of the network, taking into account the height of the sending node, the obstacles in the process of data transmission, and the multi-path effect of data transmission, we select four areas I, III, IV, and VI for coverage verification. In the process of coverage verification, we asked a tester with height of 173 cm to stand in each of the four selected areas. Since the presence of a person affects the channel of the wireless link, we can determine whether there is someone nearby based on the RSSI of the wireless signal to achieve coverage verification. The indoor scene test diagram is shown in Figure 8.

Figure 8.

Sub-domain coverage test chart in indoor scene: (a) tester appears in subdomain I, (b) tester appears in subdomain III, (c) tester appears in subdomain IV, and (d) tester appears in subdomain IV.

Figure 8 shows a test chart of an indoor scene with obstacles. In order to facilitate the comparison, we expand the indoor scene. First of all, the indoor space of 5 m × 5 m × 3 m is extended to the indoor space of 10 m × 10 m × 3 m, which becomes more empty in the experimental space. In addition, it eliminates the influence of obstacles and greatly reduces the interference of multi-path effect and becomes more accurate in data transmission. Other conditions remain the same, and the outdoor scene test effect is shown in Figure 9.

Figure 9.

Sub-domain coverage test chart in outdoor scene: (a) tester appears in subdomain I, (b) tester appears in subdomain III, (c) tester appears in subdomain IV, and (d) tester appears in subdomain IV.

Experimental analysis

Figures 10 and 11 show the coverage test results when the tester appears in four different subdomains in both indoor and outdoor cases, and the coverage effect is verified by the fluctuation of RSSI value. We compared the fluctuation curves of four groups of RSSI in the two cases. The black line in each set of curves represents the change of the RSSI value of the sending node in the subdomain of the tester. For a more intuitive representation, we give the standard deviation of each of the eight groups of curves, as shown in Table 2.

Figure 10.

Coverage test renderings of indoor scenes: (a) tester appears in subdomain I, (b) tester appears in subdomain III, (c) tester appears in subdomain IV, and (d) tester appears in subdomain IV.

Figure 11.

Coverage test renderings of outdoor scenes: (a) tester appears in subdomain I, (b) tester appears in subdomain III, (c) tester appears in subdomain IV, and (d) tester appears in subdomain IV.

Table 2.

RSSI fluctuation variance table.

Tester’s subdomain	Sending node RSSI fluctuation standard deviation in subdomains
Tester’s subdomain	I	II	III	IV	V	VI	VII
(Indoor) subdomain I	5.4540	0.5993	1.0286	0.8072	0.8944	0.5080	0.5059
(Indoor) subdomain III	1.5176	1.8275	4.9366	2.2500	2.0080	0.6816	1.3552
(Indoor) subdomain IV	1.3951	1.1482	2.2945	2.8296	0.4973	0.5467	1.3536
(Indoor) subdomain VI	0.6290	1.4241	0.9263	1.9045	1.0503	4.6973	2.0389
(Outdoor) subdomain I	4.7094	1.0462	0.7897	0.9146	1.3001	1.5394	2.0155
(Outdoor) subdomain III	2.1904	1.5788	2.8677	0.9783	1.3889	1.7271	1.2348
(Outdoor) subdomain IV	1.7007	0.9298	1.3263	3.7411	1.2487	1.2589	1.1932
(Outdoor) subdomain VI	1.1941	0.8289	1.0234	1.6323	1.2021	3.2439	0.8309

RSSI: received signal strength indicator.

It can be seen that in the four cases shown in Figure 10, the fluctuation of the black line is more obvious, and the maximum fluctuation range is between 15 and 25. Compared with the black line, the fluctuation of the remaining six curves is relatively stable, and the maximum fluctuation range is between 1 and 10. By comparing the fluctuations of the seven curves in each case, the monitoring situation of each subdomain can be obtained. If the fluctuation value is less than 10, the fluctuation of the subdomain is more stable, and we regard it as normal fluctuation; if the fluctuation value is greater than 15, the fluctuation of the subdomain is more obvious, and we regard it as an intrusion. When the fluctuation value is between 10 and 15, we regard it as an error range, which may be a normal fluctuation or an invasion, which requires further analysis. In the indoor environment, combined with Table 2, we can see that when the tester appears in subdomains I, III, and VI, the standard deviation of the RSSI value corresponding to the sending node in all three cases is between 4.6 and 5.5. It is much larger than the standard deviation of 0.4–2.3 of the RSSI value of the remaining sending nodes. Therefore, the effect of coverage monitoring is better in these three cases. When the tester appears in subdomain IV, the standard deviation of the RSSI value of the sending node is only 2.83, and the maximum standard deviation of the RSSI value of the remaining sending nodes in the set of curves is 2.29. In this case, the two values are relatively close, so we need to combine the fluctuations of the two curves to analyze in detail. In Figure 10(c), the maximum fluctuation range of the RSSI value of the sending node corresponding to subdomain VI of the tester is 15, but when the tester does not appear, the RSSI value is more stable, so the standard deviation of the RSSI value is small. In this group of curves, the maximum fluctuation range of the RSSI value of the sending node corresponding to the standard deviation of 2.29 curve is 7, but under normal conditions, the RSSI value fluctuates greatly, so the standard deviation is larger.

As shown in Figure 10, the fluctuation range of the black line in the four cases shown in Figure 11 can still be significantly different from the remaining six curves. In the outdoor environment, the overall fluctuation range of the seven curves is small, and the RSSI values are all between −85 and −70. This shows that in the more open outdoor environment, after weakening the influence of obstacles and glass, display screen, and other factors, the fluctuation range of RSSI value is more stable. However, due to the expansion of the scope of the monitoring area, resulting in the overall reduction of RSSI, wireless signal reception intensity weakened. Similarly, combined with Table 2, we can see that when the tester appears in subdomains I, IV and VI, the standard deviation of the RSSI value of the corresponding sending node is much larger than that of the remaining sending node. When the tester appears in subdomain III, the standard deviation of the RSSI corresponding to the sending node and other sending nodes in the group is relatively close, which needs to be analyzed in detail according to the fluctuation of the two curves. Compared with indoor and outdoor conditions, although the fluctuation range of outdoor environment is small, but at the same time RSSI as a whole is also smaller. This shows that under the same conditions, the wireless signal reception intensity will be weakened when the monitoring range is expanded, but the effective coverage monitoring can still be achieved.

To sum up, whether in the indoor environment where there are obstacles and special materials that affect the multi-path propagation of wireless signals, or in the outdoor environment, which is relatively empty and greatly reduces the interference of multi-path effect, we can all monitor the coverage area through the fluctuation of RSSI.

Conclusion

The problem of coverage control in three-dimensional environment is a meaningful task. Similarly, the link-aware coverage model is more practical than the traditional disk model. In this article, a method of receiving node coverage deployment based on link model is proposed. We construct the link coverage model in 3D-WSN, extend the traditional plane coverage to spatial coverage, and extend the traditional disk awareness model to a more practical link model. Based on this new link awareness model, the area coverage problem of the minimum receiving node is explored. We combine and improve the traditional GA and PSO algorithm to quickly get the deployment location of the receiving node to cover the monitoring area. In addition, we set up a real experimental environment for coverage verification; by comparing the fluctuation range of RSSI value and standard deviation to monitor the coverage area, the experimental results verify the feasibility of the method. In the next step, we will expand the coverage verification area and further study the network energy consumption in the coverage verification process.

Footnotes

Handling Editor: Peio Lopez Iturri

Author contributions

Z.H. has contributed toward the algorithms and the analysis. N.Q. has proofread this article several times and provided guidance throughout the preparation of this article. N.Q. has contributed toward the algorithms,the analysis,and the experiments and wrote this article. X.D. and J.H. have revised the equations,helped in writing the introduction and the related works,and critically revised this article. All authors read and approved the final version of this article.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This research was funded by the National Natural Science Foundation of China under grant nos 61762079 and 61662070 and by the Key Science and Technology Support Program of Gansu Province under grant nos 1604FKCA097 and 17YF1GA015.

ORCID iD

Nanjiang Qu

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Node optimization coverage method under link model in passive monitoring system of three-dimensional wireless sensor network

Abstract

Keywords

Introduction

Related work

Problem modeling

Link coverage model

Problem description

Related definition

Network coverage under link model

GA/SAPSO algorithm design

GA part

PSO algorithm part

Algorithm implementation

Experimental results and discussion

Experimental simulation

Effect of tunable parameters on algorithm performance

Comparison of algorithm performance

Experimental verification

Experimental design

Experimental analysis

Conclusion

Footnotes

Author contributions

Declaration of conflicting interests

Funding

ORCID iD

References