Towards Efficient Sensor Placement for Industrial Wireless Sensor Network

Received 22 December 2020, Revised 26 December 2020, Accepted 27 December 2020. Industrial Wireless Sensor Network (IWSN) is the recent emergence in wireless technologies that facilitate industrial applications. IWSN constructs a reliable and self-responding industrial system using interconnected intelligent sensors. These sensors continuously monitor and analyze the industrial process to evoke its best performance. Since the sensors are resource-constrained and communicate wirelessly, the excess sensor placement utilizes more energy and also affects the environment. Thus, sensors need to use efficiently to minimize their network traffic and energy utilization. In this paper, we proposed a vertex coloring based optimal sensor placement to determine the minimal sensor requirement for an efficient network.

Placement (VC-OSP) the algorithm proposed to determine them for efficient target coverage for the green network in IWSN.
The rest of the paper organized as follows: Section 2 deals with the target coverage problem, the quality of coverage, and the implementation of the proposed algorithm for determining the sensor requirement and its optimal position. Section 3 describes the efficiency of the proposed algorithm with a series of simulation results. Section 4 provides the conclusion.

PROBLEM FORMULATION
Consider a set of targets in a fixed region , as = { 1 , 2 , … , }. Let = { 1 , 2 , … , } be the set of sensors ( need to be determined), where < and be each sensor sensing range. Let ( , ) and ( , ) be the position of the sensor and target respectively. A target is said to be monitored by the sensor if and only if its distance between them is less than its sensing range and represented as where 1 ≤ ≤ , 1 ≤ ≤ . The coverage of the targets is represented as where , = { 1, 0, ℎ ; 1 ≤ ≤ , 1 ≤ ≤ The quality of target coverage in the network is obtained as follows This paper focuses on maximizing the quality of target coverage in the network by deploying a minimum number of sensors in the predetermined spots. Even though various algorithms have proposed to enhance the quality of coverage, the problem still needs better solutions since the existing algorithms focus on the effective utilization of a fixed number of sensors to monitor the considered targets in the network. This method fails to monitor the entire targets in every scenario because of the variation in sensor requirement due to the target's spatial coordinates, as shown in Figure 1. Four targets considered in Figure 1 and its positions are varied and described in Figure 1 (a), (b) and (c) respectively. As in every optimal sensor placement algorithm, the number of sensors is assumed as two to monitor the four targets. By optimally deploying two sensors, four targets monitored of Figure 1. (a). Whereas the same two sensors are not sufficient to provide full coverage in Figure  1 (b) and Figure 1. (c) due to the target's spatial coordinates. Thus, finding optimal spatial coordinates for a considered set of sensors provides either excess coverage or insufficient coverage depending on the target's positioning. Hence, there is a need for a generalized algorithm, which not only optimizes the sensor utilization but also determines the sensor required for the target coverage in the network. Thus, the main objective of this paper is to determine, in other words, the number of sensors required and its optimal spot such that it monitor targets. Hence, Vertex Coloring based Optimal Sensor Placement (VC-OSP) the algorithm proposed to determine them for efficient target coverage in the network.

. The ideology of VC-OSP algorithm
The VC-OSP algorithm proposed to determine the sensor requirement and its optimal spot to monitor all the targets in the network. As shown in Figure 1, the main reasons for the variation in the sensor requirement are the target's spatial coordinates and the sensor's sensing range. The proposed VC-OSP algorithm partitions the target set into the independent subsets in which each subgroup consists of a set of targets whose pairwise distance is less than the sensing range. In other words, the VC-OSP algorithm partitions the target set into sets, each group consists of a set of targets that are close to each other such that a common sensor is enough to monitor those targets. Then, the cardinality of such minimum independent subsets corresponds to the minimum number of sensors required to monitor the entire targets. Hence, to partition the targets, the VC-OSP algorithm utilizes the vertex coloring with the help of the graph, . The Vertex Coloring Problem (VCP) assigns a minimum number of colors to the vertices of the graph, such that no two adjacent vertices receive the same color. From the mathematical perspective, vertex colouring partitions the vertex-set of the graph into an independent subset comprising all the vertices of the same colour. Thus, vertex coloring is simply an intuitive way to represent the target set partition.
Let us consider a sample network to analyse the process of the proposed algorithm. Considered sample network in IWSN is of size × units where and in the real-time application be 1000 × 1000 square meters, 2000 × 2000 square meters or maybe 100 × 100 Acers. But, to consider a simple dimension sample network for easy explanation, the size of the region × units projected to 10 × 10 units by considering the region as 10 × 10 units. Let us consider a sample network of size 10 × 10 consist of ten targets whose coordinate points are (3,5), (1,5), (2,4), (9, 1), (4,5), (6,4), (2,10), (6,5), (10,5), and (10, 4). The sensing range of each sensor considered as three units. The objective is to determine the number of sensors required and its optimal spots to monitor these ten targets.

Construction of undirected graph for implementation of VC-OSP algorithm
The VC-OSP algorithm constructs an undirected graph = ( ( ), ( )) by considering targets as its vertex set and the adjacency made between the vertices (target and target ) whose distance is greater than the sensing range. The reason for this adjacency is, for any graph, in vertex coloring, the adjacent vertices receive different colors. Whereas in IWSN, the targets which are far away in other words that couldn't be monitored by the same sensor require additional sensors to monitor them. Hence, the edge set consists of the pair of targets whose distance is greater than the sensing range. Thus, each target receives different colors (sensors) using the vertex coloring technique.
The matrix representation of the adjacency of the targets is as follows where , = { 1, √ ( − ) 2 + ( − ) 2 > 0, ℎ , 1 ≤ ≤ , 1 ≤ ≤ and ( , ) denotes the position of the target The VCP is NP-Complete because of determining the minimum number of colours required to colour all the vertices, which termed as the chromatic number, of a graph, . But, this complex nature of VCP does not affect VC-OSP algorithm, since we aim to determine the minimum number of partitions whose cardinality, should be less than and not necessarily equal to . To achieve < , we assume that the constructed undirected graph should not to be complete. In other words, for any considered network, we assume that there exists at least one target , for any other target , whose distance is less than the sensor's sensing range. Mathematically, ∃ , for any ∋ ( , ) = 0.
For the considered sample network, the adjacency matrix is obtained using equation (3) as

Assigning colors for the constructed undirected graph using VC-OSP algorithm
The proposed VC-OSP utilizes a sequential coloring algorithm [13] to provide vertex coloring for the constructed graph, to partition the target set. Initially, the vertex set reordered concerning its neighbour vertices, and each vertex color assigned as zero. From the reordered vertex set, the algorithm considers each vertex to determine its neighbouring vertices and colors assigned to it and represent it as ℎ and ℎ respectively. This process helps to find the maximum number of colors, utilized till previous iterations. Now, to assign color for the considered vertex, the algorithms check to reuse the colors assigned termed as availability of the colors, using (1: , ℎ). If is zero, then algorithm assigns + 1 color for the considered vertex otherwise assigns minimum numbered color from the . This process iterated until colors assigned for each vertex. Each color assigned for each vertex partitions the vertex set into independent subsets. The cardinality of those independent subsets is the number of sensors required to monitor the entire targets.

Determining the optimal spots for the sensors
As each independent subset requires one sensor to monitor them, the positioning of the sensor again depends on the position of the targets of each subset. The VC-OSP algorithm identifies the position of each target from each subset and determines its mean position for the optimal positioning of each sensor. In other words, the x-coordinate and y-coordinate of the sensor say is the sum of the x-coordinates and y-coordinates of each target of an independent subset divided by the cardinality of the independent set respectively, and represented as follows where 1 ≤ ≤ , 1 ≤ ≤ ; ( , ) and ( ̅ , ̅) denotes the position of the target and sensor respectively.

PERFOMANCE EVALUATION
The performs of the proposed VC-OSP algorithm is evaluated by a series of simulations in 1000 × 1000 region using MATLAB. The main idea of VC-OSP is to identify the sensor requirement and its optimal position to monitor the targets such that (indicates the number of targets covered by the sensors) attains maximum. But, the VC-OSP algorithm determines the optimal spots for sensors depending on the target's positions this sometimes leads to the deployment of sensors over the targets (Like the positions of sensor 1 and 2 in Figure 4. Deploying the sensors over the targets in industrial applications may increase the probability of affecting the sensors due to its pressure, vibration, temperature, etc. in the system. Hence, to provide better optimal spots for the obtained set of sensors using the VC-OSP algorithm, the algorithm utilizes the existing algorithms such as random deployment, discrete Haar Wavelet transforms algorithm [6], and cuckoo search algorithm [4]. The results obtained are tabled. Fig. 4. The coverage of sensors using VC-OSP algorithm Table 3 represents the estimated set of sensor requirements using VC-OSP with the variation in both targets and sensing range. The first column in Table 3 represents the variation in the targets from 100 to 250 with an increment of 25. The first row in Table 3 illustrates the variation in the sensing range from 55 to 85, with an increment of 5. The first entry of Table 3 means that the network requires 66 sensors to monitor 100 targets using the proposed algorithm with the sensing range of 55 units. Similarly, to survey 100 targets, the system requires 60, 57, 56, 54, 51, and 48 sensors with the sensing range of 60, 65, 70, 75, 80, and 85, respectively. Hence followed for other rows. Thus, Table 3 provides the sensors requirement using the VC-OSP algorithm for the considered set of targets in 1000 × 1000 region for the varied set of targets and sensing range. Targets  Sensing range  55  60  65  70  75  80  85  100  66  60  57  56  54  51  48  125  74  70  68  63  62  57  54  150  85  83  81  77  73  65  61  175  94  89  81  79  76  70  68  200  105  100  91  86  80  73  69  225  116  107  101  95  87  83  79  250  118  112  107  99  94  87  84 With the help of the obtained set of sensor requirements using the VC-OSP algorithm, the optimal spots determined using evolutionary algorithms and its corresponding quality of coverage ( ) in the system also determined. Table 4, Table 5, Table 6 and Table 7 provides the estimated quality of coverage obtained under different conditions such as varying the targets set, sensing range, area, and sensor requirement respectively to evaluate the in the system. Table 4 represents the by varying the targets from 100 to 250 targets in 1000 × 1000 region with the fixed sensing range of 50 units. To compare the results of random deployment, DHWT algorithm, and cuckoo search algorithm, the target positions and the number of sensors utilized should be the same. But these algorithms do not determine the sensor requirement and randomly fix the value of for target coverage. Thus, the VC-OSP algorithm utilized to determine the sensor requirement of sensors to monitor targets, and column 2 of Table 3 represents the obtained set of sensor requirements using VC-OSP. Column 3 to 5 of Table 3 shows the results of random deployment. Column 6 to 8 presents the results of DHWT columns 9 to 11 provide the results of the cuckoo search algorithm, and columns 12 to 14 describe the work of the VC-OSP algorithm. The minimum (Min.), average (Avg.) and maximum (Max.) in Table 3 are obtained by executing the algorithm fifty times. Here, the average of fifty experimental results is represented in percentage for easy understanding.

Table 3. Number of Sensors Required for Varying Targets and Sensing Range Using VC-OSP
As depicted in Table 4, to monitor 100 targets, the sensor requirement obtained using VC-OSP is 74. By randomly deploying 74 sensors to monitor 100 targets for fifty times, the minimum of random deployment is obtained as 21, the average is 24.2% and the maximum is 28. In DHWT, the minimum is 31, the average is 37.14% and the maximum is 44. By using cuckoo search algorithm the minimum is 56, the average is 59.24% and maximum is 59.24. Using VC-OSP algorithm the minimum, average and maximum is 100%. Similarly, Table 4 provides the quality of coverage obtained for each varied set of targets with the determined sensor requirement using the VC-OSP algorithm. From Table 4, it is clear that the quality of coverage increases as the target set increases. The reason is, we have considered a large system (1000 × 1000 region) and less set of targets (eg. 100 targets) this leads to having scattered target position in the system. Hence providing the coverage for these targets with the determined bound for sensors is comparatively less when compared with a large set of targets (e.g. 250 targets). From the results, the is achieved 100% using VC-OSP algorithm.  Table 5 provides the estimated obtained by varying the sensing range, where the sensor requirement for each varied set of sensing ranges obtained using the VC-OSP algorithm to monitor 200 targets in 1000 × 1000 region. Here the sensing range is varied from 55 units to 85 units. Column 2 provides the obtained sensor requirement using the VC-OSP algorithm. The results of deploying sensors to monitor 200 targets executed fifty times, the minimum, average and maximum are tabled in Table 4. The average of random deployment, DHWT, cuckoo search, and VC-OSP algorithm are 24.25%, 48.87%, 75.91%, and 100% by deploying 110 sensors with the sensing range of 55 units in 1000 × 1000 region respectively. Similarly, the is obtained and tabulated by increasing the sensing range. Here the VC-OSP algorithm performs better when compared with the random, DHWT, and cuckoo search algorithms. From the table, it is clear that as the sensing range increases, the also increases. The reason is as the sensing range increases the number of targets monitored by a sensor increases thus it enhances the in the system.  Table 6 provides the estimated obtained by varying the considered area from 700 × 700 square units to 1500 × 1500 square units. Column 2 of Table 6 provides the set of sensors required to monitor 150 targets with the fixed sensing range of 60 units for the various area using the VC-OSP algorithm. The results obtained by deploying these sensors categorized as the minimum, average and maximum by executing random, DHWT, and cuckoo search algorithms fifty times tabulated in Table 6 deployment, DHWT, cuckoo search algorithm, and VC-OSP are 75.54%, 76.09%, 88.46%, and 100% by deploying 68 sensors to monitor 150 targets in 700 × 700 region respectively. Similarly, the is obtained and tabulated by increasing the considered region. From the table, it is clear that as the area increases the sensor requirement also increases while decreases, even though the proposed algorithm achieves 100% coverage. The reason is, monitoring the fixed targets (150 targets) in larger regions, as stated before, the position of the targets tends to scatter over the area. The spread of targets increases the sensor requirement and deploying those sensors over the broader region with the fixed sensing range leads to decrease its . For the above estimations, the sensor requirement ( ) for each experiment is determined using the VC-OSP algorithm. Thus, it is essential to check the by considering the set of sensors less than and more significant than the determined . This estimation could help us to realize the advantage of determining the sensor requirement using the VC-OSP algorithm before optimally deployed. Hence, each algorithm executed fifty times to calculate the minimum, average and maximum for the sensor set less than, equal to, and more significant than the determined value in 500 × 500 square units. Table 7, Figure 5 and Figure 6 provides the performance evaluation of random deployment, DHWT, and cuckoo search algorithm with the varied set of sensor requirement (< , , > ). Column 2 of Table 6 shows the sensor requirement to monitor the mixed collection of targets in 500 × 500 regions with a fixed sensing range of 50 units. Using the VC-OSP algorithm, the sensor requirement to monitor 100 targets in 500 × 500 area with the fixed sensing range of 50 units obtained as 44. The average to monitor 100 targets by randomly deploying sensors less than 44 sensors estimated as 48.38% whereas the average by deploying 44 sensors (estimated sensor requirement using VC-OSP algorithm) is 72.04%. The result clearly shows the massive increase in after determining the sensor requirement. Even though the average of deploying sensors more excellent than 44 sensors is 72.96% (which is greater than the estimated sensor set ), excess sensor deployment leads to network traffic, increases the cost, and provides redundant coverage in the system. Hence, the obtained by deploying the estimated set of sensors (minimum sensors) using random deployment provides better coverage than the varied collection of sensor requirements and thus for the other entities. From Table 7, it is clear that determining sensor requirements before deciding its optimal spot provides a better result by enhancing the with minimum sensors. Similarly, the is estimated by varying the sensor requirement for DHWT and Cuckoo Search algorithm, and represented in Figure 5 and Figure 6, respectively.

CONCLUSION
IWSNs play an enormous role in improving the productivity of industrial systems through controlling, monitoring, and maintaining the business processes. Even though IWSN is a rapidly developing area, few issues still annihilate its future exploration. The problems in IWSN are green computing, target coverage problems, network connectivity, optimal sensor placement, localization, security, and adaptability. This paper focuses on the target coverage problem by deploying the minimum number of sensors at the optimal spot for green IWSN. A simple Vertex Coloring based Optimal Sensor Placement (VC-OSP) algorithm proposed to address the above issue. The VC-OSP partitions the target set using a sequential vertex coloring algorithm to determine the sensor requirement and determines its optimal spot using the mean position of the targets in each subset. But, the VC-OSP algorithm determines the optimal spots for sensors depending on the target's parts. This method of finding positions sometimes leads to the deployment of sensors over the targets. Deploying the sensors over the targets in industrial applications may increase the probability of affecting the sensors due to its pressure, vibration, temperature, etc. in the system. Hence, to provide better optimal spots for the obtained set of sensors using the VC-OSP algorithm, the algorithm utilizes the existing evolutionary algorithms. The results obtained tabled. The simulation results clearly show that the better target coverage has achieved by each evolutionary algorithms since the sensor requirements predetermined before determining its optimal spots. Min. Avg.
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