Journal of Sensors

Volume 2018, Article ID 2343891, 14 pages

https://doi.org/10.1155/2018/2343891

## A Deterministic Sensor Deployment Method for Target Coverage

^{1}Hefei University of Technology, Hefei 230009, China^{2}Jiangsu University of Technology, Changzhou 213125, China

Correspondence should be addressed to Zhaoneng Jiang; nc.ude.tufh@gnenoahzgnaij

Received 17 October 2017; Revised 25 January 2018; Accepted 19 February 2018; Published 26 April 2018

Academic Editor: Fanli Meng

Copyright © 2018 Ye Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to monitor the gas leakage, the gas sensors are deployed conventionally in chemical industry park, with little considerations given to the gas characteristics and weather conditions, which give rise to the problems of coverage hole and coverage repetition. To solve the problems, this paper proposes a deterministic sensor deployment method with the gas diffusion models which takes into account wind speed and direction and then studies the influence of wind speed and direction on the monitoring error of gas sensors. Then, we research the deterministic deployment method of gas sensors in condition of the main wind speed and direction somewhere. Firstly, we use the CFD theory to simulate the gas diffusion situation so as to obtain the concentration value of the relevant points. Secondly, we put forward a new optimization criterion, namely, the more alarm concentration points covered by gas sensors, the coverage performance is better, and the deployment method is better. Accordingly, a new objection function is built. Thirdly, we obtain the weight values of the function using entropy estimation method. Finally, we deploy the gas sensors determinately using particle swarm optimization (PSO) algorithm. The simulation results show that the proposed method can improve the monitoring efficiency and the coverage performance of gas sensor network.

#### 1. Introduction

In order to monitor the gas leakage, the gas sensors will be installed in the chemical industrial park according to some conventional industry standards, and the gas sensors act as alarm to provide some guidance for the supervisors when the leakage accidents happened. However, the health and safety executive (HSE) pointed out in 1993 and 2003 [1] that more than half gas leakage accidents happened in the chemical industrial parks cannot be detected on the grounds that the current deployment methods do not take the factors affecting gas diffusion into account, and the factors include the following: leakage source locations, the number of leakage sources, gas composition, weather conditions, design of pipeline, process conditions, building structure, isolation system, vacuum system, and monitoring frequency. Due to the influence of the factors on the monitoring efficiency, the deterministic deployment method should be considered.

The deployment of wireless sensor networks (WSN) can be mainly divided into two types according to the type of sensors, the application background, and the environment condition: deterministic deployment method and stochastic deployment method. We mainly adopt the deterministic deployment method in the cases where locations of sensors have a great impact on the operation of the WSN, such as deployment of sensor nodes on the pipe [2, 3], deployment of image/video sensors indoors [4–6], deployment of underwater sensors [7], and deployment of seismic sensors for volcano monitoring [8]. However, we adopt the stochastic deployment method in some special occasions [9, 10], especially when the gas leakage happened in the chemical industrial parks. When the wind speed and direction influence the gas diffusion model, the sensor nodes deployed may be invalid, and the research of the deterministic deployment method is very important.

Aimed at the problem of hazard gas diffusion in the chemical industrial park, there are also many methods that study the deployment of gas sensors considering the gas diffusion model [11], including the heuristic analysis method [12], which is only designed for the serious leakage scenario, without considering the uncertainty of the leakage scenario. Besides, there is a method based on the theory of risk analysis that is proposed by the US International Standard Committee, wherein risk is the objective function to be minimized, and the disadvantage thereof is that the method can only get local optimal solution. And there is also a mixed integer linear programming by Legg and others according to the sensor deployment scheme of water pollution, which considers the impact of node failure on the network, but cannot consider the time series and is not in conformity with the actual situation, just like the assumption of node failure probability. The methods above are based on the simple diffusion model and with no consideration of environmental features such as wind speed and direction, so the node deployment is not accurate.

The main purpose of the WSN is to meet such demand of network performance as assuring integrity of the transmission data, reducing the delay time, reducing power consumption, prolonging the network lifetime, and increasing the coverage. Usually, we adopt the deterministic deployment method to meet these demands, and the optimization targets of the deterministic deployment mainly are coverage, connectivity, lifetime, and so on. All the deployment methods are desired to satisfy the demands with high efficiency, and the deployment methods designed by scholars can improve such performance of the WSN as better connectivity and longer lifetime [13–16]. Besides, there are some studies mainly about the load balance and fault tolerance [17, 18].

The coverage of WSN directly influences the possibility to monitor the target accurately and provide the high-quality perceived service and also directly reflects the working performance of the WSN. Usually, the coverage ratio represents the performance of the coverage, and to maximize the coverage of monitoring targets is a main goal of the deployment of WSN. To solve the problem, there are many researches at home and abroad, which are mainly based on such perception model of the sensors such as Boolean disc model [19], directed model [20], and three dimensional sphere model [21], and there are also many researches based on such characteristics of monitoring targets as fixed monitoring points, mobile monitoring points, and monitoring areas that correspond to target coverage problems [22–26], barrier coverage problems [9, 27, 28], and area coverage problems [29, 30].

The aim of target coverage is to cover some discrete points whose locations are known, the classical Art Gallery Guard Problem [24] is aimed at solving the problem above, and in order to achieve the max coverage ratio, the paper [31] proposed the minimum cost based on integer linear programming, and the paper [22] provided a randomized algorithm to solve the coverage problem. And the coverage problem in the chemical industrial park is a critical problem we need to consider. The deterministic deployment has been little pursued in conventional deployment methods, and the coverage ratio is quite low. Aimed at this problem, we see the deployment problem as the Art Gallery Guard Problem; the location of the alarm gas concentration points in the chemical industrial park acts as the pictures in the art gallery, the sensors deployed act as the video cameras, and the locations of the cameras maximize the coverage ratio and achieve the balanced coverage.

The innovative points of this paper are listed as follows: (1)We obtain the deterministic deployment method based on the gas diffusion model and research the influence of the wind speed and direction on the monitoring performance of the deployment method.(2)We get the locations of the alarm gas concentration points simulated through the simulation of gas diffusion using the CFD theory.(3)In order to solve the coverage hole problem, we propose a new optimization criterion, namely, the more alarm concentration points are covered by gas sensors and the more balanced the coverage is, the more optimal the deployment scheme is.(4)We put forward a new objective function based on the new optimization criterion; meanwhile, we get the weight values of the function using the entropy estimation method.(5)We provide a new deterministic deployment method based on the PSO algorithm and compare the new deterministic deployment method with the conventional deployment method and find that the performance of the method we proposed is better.

The next section of this paper is to first introduce the particle swarm optimization algorithm in Section 2. And we introduce the gas diffusion model considering the wind speed and direction in Section 3. In Section 4, we first put forward a new deterministic deployment method based on the gas diffusion model, then we research the influence of the wind speed and direction on the monitoring performance of the method proposed and conduct the simulated experiments and analysis. Aimed at the special wind speed and direction somewhere, we propose a deterministic deployment method to solve the coverage hole and unbalanced coverage in Section 5. In Section 6, we also compare the method we proposed and the conventional deployment methods to see the differences there between in terms of the performance of the coverage ratio and coverage balance. At last, we conclude the paper in Section 7.

#### 2. Particle Swarm Optimization Algorithm

Particle swarm optimization algorithm (PSO) is developed by an American social psychologist James Kennedy and an electrical engineer Russell Beernaert [32, 33] in 1995; the basic idea is inspired by the results of the simulation of their early study and modeling of group behavior of many birds. PSO algorithm is a new evolutionary computation technique based on swarm intelligence, the optimization research is instructed by swarm intelligence produced by cooperation and competition among swarms in colony, and it has some features such as fast convergence speed, implementation simplicity, less parameter, and strong commonality. And now the PSO algorithm has attracted more attention and made great progress so as to be widely applicable in recent years.

The basic ideas of PSO are that each particle represents a feasible solution of the objective function, each particle has a fitness value determined by the objective function, and each particle has a speed within the scope of the solution. By changing speed constantly to traverse the feasible region, all the particles can search the best value in the current fitness value. In each iteration, every particle corresponds to a fitness value, also there is a global optimal fitness value, and the corresponding solutions of the global optimal fitness value are the global optimal positions of the sensors. Every iteration updates constantly based on their locations and global optimal location until finding the required optimal solution, then we can end the iteration.

We assume that the particles search optimal solution in a *D* dimensional space, and the specific process of PSO algorithm is as follows:
(1)Determine the objective function (2)Initialize the positions of particles (3)Initialize each dimension velocity of every particle (4)Calculate the fitness value of each particle (5)Compare each particle’s own fitness and get the global optimal value .(6)Update the speed according to the velocity update formula (7)Update the particle’s position according to the location updating formula

As for steps 6 and 7, we illustrate as follows:
(1) means the *i*th particle, means the *d*th element of the particle, and means the *k*th iteration.(2) means the cognition of the particle itself, which is generally set to be 2.(3) means the overall recognition of the particle swarm, which is usually set to be 2.(4) and are random numbers in the range [0,1].(5) means a coefficient added in front of the speed when updating the position, namely, a constraint factor, which is generally set to be 1.(6) is the particle’s velocity, in the range , when , , and when , .(7)As for the velocity update formula we usually use the improved formula which is and is inertia weighting factor [34]. At the beginning of the iteration, the inertia weighting factor is large, which has a good convergence speed for global search. With the increase of the number of iterations, the inertia weighting factor decreases, which has a good convergence speed for local search. The paper [35] proposed a PSO algorithm with linear decreasing inertia weight.

where is the number of max iterations.

The paper [36] also proposed inertia weight nonlinear dynamic adjustment method based on fuzzy system.

#### 3. The Establishment of Gas Diffusion Model considering Meteorological Conditions

The gas diffusion model can be set up based on certain diffusion equations and some conditions, but due to such weather conditions having impact on the gas diffusion model as wind speed and direction, the previous diffusion model is not applicable, which may have the influence on the gas sensor deployment. The deployment of sensors cannot effectively monitor a gas leak.

The papers [37, 38] researched the gas diffusion mechanism sufficiently. The diffusion model without considering meteorological conditions is as follows:
is the concentration of gas source in space location of at *t* time, and are the positions of the gas source and their image positions relative to an interface, respectively, is the rate of diffusion of the gas source, the unit of the diffusion rate is m^{2}/s, the diffusion rate will vary with the change of environmental temperature, is the quality release rate of the gas source and the unit thereof is kg/s, and is the start time of gas source.

Taking wind speed and direction into consideration, wind speed vector is changed to be parallel to axis *x* by coordinate transformation, and denotes wind velocity; we assume that the gas source and the sensor nodes are in the same plane, namely, ; when the gas reached the steady state, concentration of gas diffusion can be simplified as follows:
is wind velocity paralleled to axis *x* after coordinate transformation, and are abscissas of the sensor and the leakage source after coordinate transformation, is the difference between the leakage source and sensor nodes after the coordinate transformation, is the distance between gas source and sensor nodes, and the coordinate transformations are as follows:
and are the position coordinates of the sensor nodes and the leakage source, respectively.

Prediction model is as follows:
is the wind velocity parallel to axis *x* after coordinate transformation.

Measurement model is as follows: is the wind direction which changes over time anticlockwise.

#### 4. The Simulation Experiments and Analysis of the Influence of the Meteorological Conditions on the Error Rate in the Deterministic Optimization Deployment Method of Gas Sensors

##### 4.1. The Simulation Scenario and Parameter Setting of the Deterministic Optimization Deployment Method

We simulate a propane gas leakage in a chemical industrial park, wherein the simulation area is 100 m × 100 m. There is only a leakage source, the number of sensors is changed according to the purpose of the experiment, which is in the range of [20, 39], diffusion time is set from 10 s to 50 s, and the number of particles is set from 20 to 50 according to the purpose of the experiment. The wind velocity in the prediction model is set to be 2 m/s, and the wind is blown to the negative axis. The wind velocity of the measurement model is set to be ; varies with the purpose of the experiment which is within the range of [0.2,1] m/s^{2}. The wind direction is set to be , the wind is blown to negative axis and varies anticlockwise, varies with the purpose of the experiment which is within the range of [18,90], and both of the two parameters above vary over time. Gas source diffusion rate is m^{2}/s, and the leaking source has an intensity of 20 kg/s, namely, kg/s; the value of inertia weight factor is 0.729, and the constant and are both set to be 1.496. And the number of iterations in every experiment is 500. All of the simulation experiments are completed by MATLAB software.
(1)Establish the objective function: Based on PSO optimization algorithm, the most important thing is to establish the objective function. This paper makes the average error of the prediction model and the measurement model as the objective function. There are sensor nodes, the deployed locations of the nodes are used as the solution vector, and the average concentration error rate of the sensors during the diffusion time is the objective function, which is made to be a minimum. The expression of prediction model is , and the expression of measurement model is . The objective function is as follows:
where is the number of gas sensors, is the number of the gas leakage sources, and time is denotes the gas diffusion time.(2) particles are initialized to -dimension matrixes randomly, which include the initial coordinates, the current coordinates, and the speed of each coordinate, as well as the individual fitness value and global best fitness value. The form is as follows:
where is the initial coordinates, is the current coordinates, is the speed of each coordinate, is an individual fitness value, and is the global best fitness value.(3)Calculate the fitness value of each particle (4)Compare each particle’s own fitness value and get the global best fitness value (5)Update the velocity according to the velocity update formula: (6)Update the particle’s position according to the location update formula: (7)Keep iterating until reaching the global optimal value and obtaining the corresponding coordinates.

##### 4.2. The Influence of the Wind Speed on Error Rate of Concentration in Deterministic Deployment Method

Under the condition that the number of the particles and the sensors are invariable and under different acceleration, first, we investigate the variation between the error rate of concentration in the deterministic deployment method and the time. The number of sensors is 20, the number of particles is 20, the diffusion time is in range of [10 s, 50 s], the wind direction is constant, the wind speed varies according to the equation , where is the acceleration in the range of [0 m/s^{2}, 1 m/^{2}], and the variation curve is shown in Figure 1.