where xi ,yi are coordinates of sensor node Si and x,y are coordinates of grid point P.
Taking into account the binary detection model (Franklin & Urick, 2005), which expresses the coverage Cxy (Si) of a grid point P by sensor node Si thereby expressed as in Equation (2).
where r and dip represents sensing radius of node and Euclidean distance between grid point and sensor node. The shrewd objective of coverage optimization issue is to provide sufficient coverage rate (CR) by using less number of sensor nodes. The CR is used to estimate the performance of sensor network. Generally, coverage rate (CR) can be computed by Equation (3).
The 2D area is partitioned into M*N grid points. It is assumed that grid point can be covered by any sensor node only once. The summation of grid points which are covered by sensor nodes are represented as Neffect.
2. Bodacious-Instance Mechanism
Bodacious-instance mechanism (BiM) is an investigative search technique. BiM is encouraged by attractive capabilities, for instance discovering their target and identifying various kinds of insect species even in the complete dark environment. The enhanced echolocation proficiency of instances draws the attention of the researchers to investigate BiM. The instance uses sonar system (NOAA, n.d.), also also known as echolocation mainly used to identify the food and escaping hurdles. Instances have ability to locate the sites of the items by scattering loud and small acoustic signals and by clashing and sending back these spread signals (Ashraf & Ahmed, 2020). For BiM, the echolocation features are perfect within the context of the below mentioned rules by advancing such characteristics of instances.
- Entire group of instances make benefit of echolocation to measure distance and they are also capable of distinguishing between the target and background obstacles.
- Instances fly arbitrarily with velocity Vi frequency Fmin at location Xi, fluctuating wavelength and some loudness value ( A0 ) to find the target. Instances have an ability to modify the frequency of the released signals automatically and also they can change the extent of signal emission ri [0,1] according to the closeness of the object.
- However, the loudness can fluctuate in several ways, it is supposed that the loudness is changing from positive value A0 to a lowest value Amin.
Initially, instances are generated with some random velocities and locations in the exploration area. The positions (Xti ) and velocities ( Vti ) of instances are modified at some time t according to the given Equations (4-6)
where β is an arbitrary vector whose value is lies between 0 and 1, Fmax represents maximum frequency and X* is a current overall best solution which is selected after equating all the results among all the instances at every iteration. Primarily, all instances are arbitrarily assigned a wavelength which is selected consistently from [ Fmin, Fmax ].
3. BiM Based Node Deployment
Node deployment is a critical issue in sensor system. Therefore, BiM is applied to the sensor node deployment problem for improving the coverage rate ( Ashraf et al., 2014). Initially, instances are generated with some random positions and velocities for finding the target in the monitoring area ( Aoudia et al., 2016). Then Euclidean distance between sensor node positions and coordinates of grid points is calculated. The minimum distance value and its coordinates are stored and checked to achieve best minimum distance value after every iteration (Ashraf et al., 2020). If best distance value is achieved, then its position is updated otherwise process will be repeated. The various deployment steps explained through flow chart illustrated in Figure 1.
Figure 1. Flow Chart of Proposed BiM Based Sensor Nodes Deployment
Step 1: Initialize all the parameters including the group size (n), the maximum number of iterations and the initial positions of instance (sensor node) group (Xinitial,Yinitial), step length, number of grid points, loudness and pulse rate, minimum and maximum frequency, upper and lower bounds thereby expressed in Equations (7) and (8).
where i vary from 1 to n , LB and UB is lower and upper bounds, and n is the size of instance group.
Step 2: The positions, velocities and frequencies of sensor b nodes (instances) at time t are updated by using Equations (4), (5) and (6).
Step 3: The distance of all the sensor nodes (instances) from the grid points (Distm ) are computed by using below Equation (9).
where Xm and Ym are initial positions of m sensor nodes (instance), xj and yj are coordinates of j grid points.
Step 4: The instance (node) which has minimum distance value between grid point and nodes as compared to all other instances (sensors) is selected. Then the position index of that sensor node is found.
Step 5: Keep the best distance value within lowest distance value and store its coordinates, then instance cluster fly towards that best place by using their exploratory conception.
Step 6: The best distance value is then compared with lowest distance value at every iteration. If best distance value is less than lowest distance value then lowest distance value and its coordinates are updated otherwise repeat steps from 2 to 5.
Step 7: Calculate the coverage of each sensor node by using Equation (2). The final coverage rate of all the sensor nodes is computed by using Equation (3).
4. Simulation Results and Discussion
In order to validate the efficiency of node deployment based on BiM the simulation trials are conducted using MATALAB R2016a ( Ashraf et al., 2020). The performance among BiM, tuned BiM and FOA is carried out using simulation setup parameters given in Table 1.
Table 1. Simulation Parameters for BiM
To observe the performance of aforementioned algorithms, nearbout 60 sensor nodes were deployed randomly in the monitoring area of size 60 × 60 m2 . To demonstrate the performances of FOA, BiM and tuned BiM, the initial and final node deployment is being presented in Figure 2 and 3.
Figure 2. Deployment of Sensor Nodes by BiM (a) & (b) Initial (c) & (d) Final
Figure 3. (a) Initial Deployment of Sensor Nodes for Tuned BiM (b) Final Deployment of Sensor Nodes by Tuned BiM
These figures 2 and 3, signifies the initial and final node deployment after executing FOA and BiM algorithms. Thereupon, it can be clearly understood that node deployment based on (BiM) has minimum redundancy and is utmost uniform as compared to node deployment by the FOA mechanism.
Figure 2. a and b shows the initial and final FOA sensor node deployment.
Table 2 signifies the influence of pulse emission rate (r) on coverage of sensor nodes. The value of r changes from 0.1 to 1 whereas value of other instance mechanism parameters such as loudness, maximum frequency and sensing radius is kept constant to 0.5, 2 and 5 respectively. To beat the effect of arbitrariness, instance mechanism is simulated 50 times and the greatest value of coverage is picked every time. The maximum value of coverage after performing BiM is attained as 93.54% at pulse emission rate of 0.9. As instances move towards respective target (grid points) they emit a greater number of pulses, therefore, the pulse emission rate will be high when sensor nodes move close to the grid points (Ashraf et al., 2020). Thereupon, value of pulse emission rate is kept to 0.9.
Table 2. Influence of Pulse Emission Rate on Coverage Rate
Further to see the effect of loudness parameter for instance mechanism on the coverage rate of sensor nodes, the value of loudness (Ao ) is varied from 0.1 to 1 while pulse emission rate (r) is set to 0.9 and value of other parameters is 0.5, sensing radius (rs ) is fixed to 5 meters.
Table 3, shows the variations of loudness, initial and final coverage rate of nodes after implementing BiM. The BiM is run 50 times and the best value of initial and final coverage rate is selected. The coverage rate after executing BiM is obtained maximum of highest about 93.1% at 0.2 value of loudness. When sensor nodes (instance) is near to the grid point the intensity of emitted pulses is low, therefore loudness parameter should be kept low. Thereupon, the value of loudness parameter is fixed to 0.2.
Table 3. Effect of Loudness on Coverage Rate
In addition to this Table 4, demonstrates the effect of maximum frequency (fmax) on coverage; its value has been changed from 0.1 to 2. The constraints of instance mechanism for instance pulse emission rate, loudness and sensing radius are kept constant to 0.9, 0.2 and 5 respectively. For each variation of maximum frequency the instance mechanism has been executed 50 times and supreme values of coverage before and after execution of instance mechanism has been chosen. The best value of coverage after implementing BiM is 93.31% when fmax is 1.3. Thus the value of fmax is set to 1.3.
Table 4. Effect of fmax on Coverage Rate
To observe the impact of grid points on coverage rate of nodes, value of grid point has varied from 0.1 m x 0.1 m to 1 m x 1 m. The various simulation factors such as pulse emission rate, maximum frequency, sensing radius and loudness are kept constant to 0.9, 1.3, 5 and 0.2 respectively. In Table 5 for every value of grid point BiM is run 50 times and uppermost values of coverage rate has been taken. The highest value of coverage rate of nodes is obtained after running BiM is 93.41% when grid points are set to 0.6 m x 0.6 m. Consequently, the grid points have been kept constant to 0.6 m x 0.6 m. Further, the sensing radius is varied from 1 m to 10 m.
The tuned values of various constraints of BiM such as loudness, maximum frequency, sensing radius, pulse emission rate and grid points are 0.2, 1.3, 6, 0.9 and 0.6 m x 0.6 m respectively. To validate the performance of node deployment based on BiM after setting above constraints values, the initial and final node deployment after executing tuned (BiM) are shown in Table 5.
Table 5. Influence of Grid Points on Coverage Rate
Thereupon, it can be obviously seen that node deployment based on tuned BiM has lowest redundancy than BiM and FOA. To further demonstrate the effectiveness of tuned BiM the coverage rate curve for tuned BiM, BiM and FOA for various iterations are shown in Figure 4. The iterations are varied from 0 to 500. The convergence speed of tuned BiM is more as compared to FOA. The tuned BiM converged around 150 iterations whereas FOA converges around 350 iterations due to exploitation characteristics of the instances.
Figure 4. (a) Coverage Rate for Various Iterations (b) Coverage Rate for Varying Number of Sensor Nodes
The tuned BiM has achieved more coverage rate about 99.46% as compared to 93.37%, 88.33% of BiM and FOA. In order to overwhelm the effect of randomnly tuned BiM, instance mechanism optimization and fruit fly algorithms are run 15 times respectively. The deployment results in terms of average coverage rate, standard deviation, best and worst coverage values for tuned BiM, FOA are represented in table 6. It can be obviously seen from table 6, that tuned BiM has achieved the average coverage rate about 98.29% as compared to 91.91%, 85.16% of BiM and fruit fly algorithm. Further the standard deviation for node deployment based on tuned BiM is less, so tuned BiM is more stable as compared to FOA and BiM. The best and worst coverage values for tuned BiM are 99.46% and 97.31% as compared to 94.30% and 90.02%, 87.49% and 78.20% for BiM and FOA based node deployment.
Table 6. Deployment Results for FOA, BiM and Tuned BiM
Further the comparison of tuned BiM, BiM and FOA in terms of computation time is represented in Table 7. The computation time for tuned BiM is less i.e. 0.016 seconds as compared to 0.019 seconds, 0.28 seconds for BiM and FOA. The tuned BiM and BiM converges at 25 iterations whereas FOA converged at 500 iterations, therefore the speed of tuned BiM and BiM is more and converges faster at earlier stage because of its exploitation feature as compared to fruit fly algorithm.
Table 7. Comparison of Computation Time of BiM, FOA and Tuned BiM
Conclusion
The significant improvement in wireless sensing coverage has been achieved by a bodacious instance mechanism BiM methdology. The analysis of various factors of BiM such as loudness, grid points, emission rate and radius of nodes, frequency has been identified and shrewd values of above parameters are discovered. Node deployment based on tuned BiM and BiM shows that both algorithms converge at earlier stage as compared to fruit fly algorithm. The simulation results demonstrate that tuned BiM has attained mean coverage rate about 98.29% which is higher as compared to FOA and BiM. Further various simulations have been done by varying number of sensor nodes, iterations and coverage rate curve is plotted for tuned BiM, BiM and FOA. The comparison of computation time is also represented in this paper. Tuned BiM has high coverage rate and less computation time as compared to FOA and BiM. In future the various evolutionary optimization algorithms can be applied to node deployment problem to increase the coverage rate of sensor nodes.
Funding Acknowledgment
This work is completely self-funded, thereby financial agency's role is not available.