Research on the deployment scheme of electric power IoT sensor nodes based on multi-objective planning

In recent years, with the continuous development of science and technology in China, it has promoted the extensive use of power Internet of Things sensing technology. In the monitoring process of electric power equipment, the use of sensor technology can carry out real-time monitoring, and continuously improve the quality of monitoring as well as detection efficiency [1-3]. For China’s power grid companies, scientific methods need to be used in the process of managing power equipment, so that they can provide strong data support for the huge operating system. The use of power IoT sensor technology can effectively realize online monitoring of power equipment [4-6]. At the same time, the use of sensor technology is also able to carry out online monitoring of the status of power transmission and transformation equipment, which can enable the relevant personnel to timely determine whether there is a failure in the operation of each piece of equipment, effectively improve the reliability of the equipment operation, and continuously optimize the system of electric power equipment, so that the value of the application of the power system can be effectively improved [7-9].

Sensor technology combined with the Internet of Things can form a huge system. Through the sensor technology can help the relevant personnel to realize the transformation of analog signals to digital signals, which can enable the computer to complete the processing of information. At present, in the electric power Internet of things, the sensor technology mainly includes six types, liquid level sensor, speed sensor, humidity sensor, gas-sensitive sensor, infrared sensor and visual sensor [10-12]. Through different sensor technologies can meet the different needs of the power Internet of Things, so that it can effectively guarantee the steady application of power equipment. In order to be able to promote the online real-time application of electric power Internet of Things sensor technology in the monitoring of electric equipment, the relevant personnel should carry out comprehensive laying work, effectively improve the monitoring efficiency, and combine the electric power Internet of Things sensor technology with Internet technology to build a mature network platform, arrange for the relevant personnel to carry out timely maintenance of the sensors to protect the quality of the sensors, so that they can successfully use the sensor technology to Implementation of online monitoring of electrical equipment [13-16].

The application of power Internet of Things sensor technology in the online monitoring of electrical equipment mainly contains two aspects, on the one hand, online monitoring of transmission equipment, on the other hand, online monitoring of substation equipment. In the use of electric power Internet of Things sensor technology to realize the online monitoring process of power transmission equipment, it can monitor the operating conditions of power transmission equipment and the operating environment in real time, which can effectively improve the power transmission equipment [17-19]. In the operation process may appear tower tilt and other situations, the use of sensor technology can be in advance of these risks, so as to be able to guarantee the stability of the operation status of power transmission equipment. Through real-time monitoring of the online operating status of power transmission equipment, it helps to maintain the stability of the power system and guarantee the normal use of electricity in the whole society [20-21]. Through the use of electric power IoT sensor technology, on the one hand, it can effectively collect the operating information of electrical equipment, on the other hand, it can realize online management of power substation equipment, so that it can effectively assess the operating status of electrical equipment, promote the development of power substation equipment in the direction of intelligence, effectively improve the monitoring efforts, and guarantee the smooth operation of power substation equipment [22-23].

The Internet of Things (IoT) technology is rapidly upgrading, and the national power grid is comprehensively applying IoT technology, aiming to achieve full coverage. In the network environment, it is important to have an understanding of the operating conditions of power equipment, and online monitoring can be implemented, in which the power IoT sensor technology plays an important role [24]. In order to improve the applicability of this technology, it is necessary to analyze the application of this technology to the online monitoring of electric power equipment based on the definition of electric power Internet of Things sensor technology, and to clarify the key problems that exist in order to improve the value of the application of the technology [25].

In this paper, we use hybrid algorithms to study how to optimize the sensor node deployment scheme. The monitoring methods of three common sensor sensing models, namely, 0-1 sensing model, probabilistic sensing model, and directed sensing model, are described, and the monitoring advantages and disadvantages of different sensing models are clarified. The improved firefly algorithm is applied to WSN coverage optimization, and the particle swarm algorithm is further combined with the improved firefly algorithm to obtain a hybrid algorithm with better performance. The effectiveness of the convergence performance of the hybrid algorithm is tested and analyzed through controlled experiments with several different algorithms. Several different algorithms are applied to WSN sensor node deployment simulation experiments to verify whether the hybrid algorithm can synergistically optimize coverage and average distance traveled in node deployment.

2

Network perception model and algorithm optimization

In Wireless Sensor Networks (WSNs), the perception model of a node is determined by the hardware characteristics of the node, which is one of the important properties of a sensor node that determines its monitoring capability. This section will focus on the commonly used sensing models in coverage problems and the optimal design of the algorithms used for them.

2.1

Sensor Node Sensing Model

2.1.1

0-1 perception model

The 0-1 sensing model is the most basic sensing model in the sensing network, which is also generally called the Boolean sensing model. In the coverage analysis, the area to be monitored is defined as a two-dimensional plane or a three-dimensional space, and at the same time, the sensing node is defined as a circle with the node as the center and the sensing range as a circle with a radius of R_s. Usually, assuming that there is a target node C and a sensor node S_i on the two-dimensional plane, and that $d (S_{i}, C)$ denotes the Euclidean distance between the target node C and the sensor S_i, the probability of a target point in the monitoring area being monitored by the sensor can be expressed as: (1) $p (S_{i}, C_{j}) = {\begin{array}{l} 1 & d (S_{i}, C_{j}) \leq R_{s} \\ 0 & O t h e r \end{array}$

When $d (S_{i}, C)$ is less than or equal to the sensing radius R_s, it means that the target node can be monitored by the sensor and the monitoring probability of the target node is recorded as 1, otherwise it is 0. $p (S_{i}, C)$ is the probability that the target point is covered by the sensor. When in three-dimensional space, the sensing range of node S is a sphere with radius R_s.

2.1.2

Probabilistic Perception Model

Uncertainty in target detection occurs due to terrain or environmental disturbances that block the node’s detection signal. In order to make the study closer to the actual situation, a study introduces a probability-based perception model, which mainly relies on the perceived intensity reflected by the distance between the sensor node R_s and the target point C, and then converts this intensity into the corresponding perception probability, which is shown in the following equation by the above definition, and the probability that the target point C is perceived by the perception node S_i: (2) $p (S_{i} C_{j}) = {\begin{array}{l} 0 & d (S_{i}, C_{j}) \geq R_{s} + r \\ e^{- γ a^{β}} & R_{s} - r < d (S_{i}, C_{j}) \leq R_{s} + r \\ 1 & d (S_{i}, C_{j}) \leq R_{s} - r \end{array}$

where γ, β are adjustable sensing parameters indicating the extent to which the sensing ability of the sensor S_i to the target node C decays with increasing distance and is related to the physical properties of the node, r is the sensor node monitoring threshold under ideal conditions, and $a = d (S_{i}, C) - (R_{s} - r)$ .

2.1.3

Directed perception models

The directed sensing model is a mathematical model used to describe the information transfer and dependency relationships between nodes in a sensing network. It is based on the concept of directed graphs, which are used to represent the nodes in a sensing network and the information flow relationships between them. In a directed graph, nodes represent sensing nodes and directed edges represent the direction of information transfer. In the directed sensing model graph of Fig. 1, information flows from one node to another node following the direction of the directed edges, which indicates that there is an information dependency between the nodes, where the output of one node can be the input of another node. The directed sensing model is widely used in a variety of sensor network applications, including wireless sensor networks, Internet of Things, social network analysis, and communication networks. It plays an important role in analyzing network topology, information transfer efficiency, and signal processing flow.

The expression for the directed perception model in Figure 1 is: (3) $f (d (s, z), a_{s} (s, z)) = {\begin{array}{l} 1 & d (s, z) \leq R_{s}, α - β \leq a_{s} (s, z) \leq α + β \\ 0 & Other \end{array}$

where d(s, z) is denoted as the Euclidean distance between any point z and node s, and a_s(s, z) denotes the angle between the two.

2.2

Objective function

WSN coverage optimization is a multi-objective optimization problem, and the objective function can be established based on the coverage quality evaluation metrics, which include coverage rate, coverage redundancy, node mobility distance, and deployment cost for WSN. 1)

Coverage C_r. Define the total number of grids effectively covered as P_cov, and any target point C_j that meets the requirements as $P_{cov} = P_{cov} + 1$ . Therefore, the coverage C_r is the ratio of the total number of grids effectively covered to the total number of grids in the monitoring area, and the specific expression is as follows: (4) $C_{r} = \frac{P_{cov}}{l \times m}$

2)

Coverage redundancy C_e. C_e can characterize the uniformity of the distribution of nodes, and its value is equal to the ratio of the effective coverage area to the maximum coverage area, and the larger the value, the more uniform the distribution of nodes and the smaller the redundancy, the specific expression is as follows: (5) $C_{e} = \frac{C_{r} l m}{n π R^{2}}$

3)

Average node mobility distance d_av. Reducing the energy consumption of nodes is beneficial to extend the working time of the network to perform monitoring tasks, the energy of nodes is mainly consumed in sensing, mobility and communication processes. For mobile nodes, the energy consumption of node movement is much larger than the energy loss in the sensing and communication process, and the energy consumption of movement is mainly determined by the node’s movement distance. The specific expression is as follows: (6) $d_{a v} = \frac{1}{n} \sum_{i = 1}^{n} d_{i}$

4)

Deployment cost. Due to the limited resources of the sensing nodes, increasing the number of nodes to achieve high coverage of the monitoring area may lead to ineffective duplicate coverage and waste of resources. Therefore, the aim of multi-objective optimization is to minimize the mobile energy consumption of the nodes while appropriately reducing the node deployment cost, and maximize the effective coverage of the network.

The objective function adopts the idea of weights, and the specific expression is: (7) $f (x) = ω_{1} C_{r} + ω_{2} C_{e} + ω_{3} \frac{1}{d_{a v}}$

where ω₁, ω₂, and ω₃ are the weighting factors and satisfy Equation ω₁ + ω₂ + ω₃ = 1.

Based on the above analysis, the constraints of WSN multi-objective optimization coverage are: (8) ${\begin{array}{l} \min f (x) = ω_{1} C_{r} + ω_{2} C_{e} + ω_{3} / d_{a v} \\ 0 \leq x_{i} \leq l, 0 \leq y_{i} \leq m \\ i \in {1, 2, \dots, n}, j \in {1, 2, \dots, l \times m} \\ ω_{1} + ω_{2} + ω_{3} = 1 \\ P_{cov} \geq l \times m, C_{r} l m \geq n π R^{2} \end{array}$

2.3

Particle swarm algorithm applied to WSN coverage optimization

Currently PSO becomes one of the most widely and successful intelligent algorithms applied to WSN coverage optimization. In this case, each particle represents a deployment scheme of sensor nodes, and since the coordinates of the nodes are two-dimensional, denoted as $(x_{i}, y_{i})$ , the dimensionality of the particles at this time is twice the number of nodes. Particle swarm algorithm in WSN coverage optimization application, its fitness function is the coverage of the network. Different coordinate information of nodes is stored in different particles and different node locations correspond to different network coverage.

2.3.1

Improved Firefly Algorithm Applied to WSN Coverage Optimization

When applied to WSN coverage optimization, each firefly is considered as a sensor node. Each iteration still consists of a fluorescein update phase, a movement probability update phase, a position update phase, and a domain range update phase, which are formulated as shown in the previous section and will not be described here. Unlike the above, the fluorescein that a sensor node has is the one that represents the denseness of the nodes around him, where the size of the fluorescein depends not only on the number of nodes within the decision radius, but also takes into account the distance between the nodes. Therefore, $J (x_{i} (t))$ is calculated using the following equation: (9) $J (x_{i} (t + 1)) = \sum_{j = 1}^{k} \frac{l_{j} (t + 1)}{d_{i j} (t + 1)}$

where $j \in N_{i} (t + 1) = {j : d_{i j} (t + 1) < r_{d}^{j} (t + 1), ‖ x_{j} (t) - x_{i} (t + 1) ‖ > 0}$ , denotes the set of neighboring nodes of node i, d_ij denotes the Euclidean distance between node i and node j, and $r_{d}^{j} (t)$ is the decision radius of node j under the tth iteration of the algorithm.

In the probability calculation stage, in order to prevent the fluorescein from crossing the boundary and also to avoid the generation of negative values in the probability calculation, the following formula is used in this chapter to calculate the movement probability: (10) $p = \frac{| l_{j} (t) - l_{i} (t) |}{| 2 \sum_{k \in N_{i} (t)} l_{k} (t) - l_{i} (t) |}$

In the phase of sensor node movement, some improvements have been made in this part as well. That is, nodes with low fluorescein are used to move away from nodes with maximum fluorescein within its decision radius. This will reduce the dense distribution of nodes near the node with larger fluorescein and thus evenly distribute the deployment of nodes in the local range. The formula for this is as follows: (11) $x_{i} (t + 1) = x_{i} (t) - s * (\frac{x_{j} (t) - x_{i} (t)}{‖ x_{j} (t) - x_{i} (t) ‖})$

Where, s is the mobile minister, it is more reasonable to take $s = \sqrt{3} r - d_{i j}$ . $d = \sqrt{3} r$ is the optimal inter-node distance between sensor nodes that can achieve seamless coverage, in this paper it is subtracted from the Euclidean distance between two nodes to get the step length and then after the calculation of Equation (11), the optimal node distance between nodes i and j can be obtained.

The firefly algorithm is applied to the node deployment of WSN, and each time in its decision radius it selects the direction of movement according to the strength of the fluorescein of the neighbor node, and makes full use of all the neighbor node information of the node to move and adjust, because the node with larger fluorescein has a large number of neighbor nodes in its decision radius and is relatively close to it, then node i can alleviate the dense distribution of nodes near node j by being far away from the node j with the largest fluorescein in the neighbor node. In addition, the distribution of nodes in the local range is evenly distributed, so the deployment scheme of the whole node can be optimized through the good local search ability of the GSO.

2.3.2

Hybrid algorithm based on particle swarm and improved firefly algorithm

Particle swarm algorithm is a parallel search algorithm compared to other evolutionary algorithms, it is not sensitive to the initial value and has memory, but it does not have a strong local search ability and is prone to premature maturity. Firefly algorithm is an algorithm with strong local search ability, but it is sensitive to initial values, fast convergence in the early iterations, slow convergence in the later ones, and no memory. Therefore, this chapter combines these two algorithms to complement their strengths and proposes a hybrid algorithm based on the particle swarm algorithm and the improved firefly algorithm.

The hybrid algorithm takes the process of the particle swarm algorithm as the main body, and carries out the firefly local search after each particle carries out the velocity position update, so that each particle makes full use of its own stored node position information to make appropriate adjustments, and then updates the individual and global extreme values. The hybrid algorithm not only makes use of the firefly algorithm to carry out an in-depth local search for each particle to move the adjustment, and makes full use of the dense information of the neighbor nodes of each node to carry out the adjustment, but also maintains the global parallel search ability of the particle swarm algorithm itself, which makes it easier to get the global extreme value. Figure 2 is the flow chart of the algorithm, and the specific algorithm steps are described as follows:

Step1. Initialize each parameter of the PSo and GSo algorithms, and each particle is given a random position and parameters;

Step2. compute the initial coverage of all particles, which is denoted as the individual optimum of each particle p_best, and find out the particle with the maximum coverage among the initial particles, which is denoted as the global extreme value g_best;

Step3. Update the weight coefficients;

Step4. Update the velocity and position of each particle;

Step5. Perform a firefly GSO local search for each particle, sequentially using the firefly Eq;

Step6. Calculate the coverage of each particle, and update the individual historical optimal value p_best and global historical optimal value g_best of the particle based on the value of each particle, if the new value is greater than p_best, then update p_best, and note down the value of this particle, and similarly for g_best;

Step7. Judge whether the condition of stopping iteration is satisfied, if so output P_g and fitness value, otherwise go to step 3 to continue execution.

3

Simulation experiments and analysis of results

To verify the performance of hybrid algorithms based on particle swarm and improved firefly algorithms, three sets of experiments were performed using simulation software MATLAB R2016a. Firstly, the convergence performance of four algorithms such as particle swarm algorithm PSO, differential evolutionary algorithm DEA, improved firefly algorithm GSO, and hybrid algorithm based on particle swarm and improved firefly algorithm PGSO are tested by using the test function to analyze the performance of the algorithms. Then, the four algorithms are used to optimize the deployment of wireless sensor network nodes in the case of accessibility, respectively, and the experimental results are analyzed.

3.1

Algorithm convergence performance testing and analysis

In order to test the convergence performance of the five algorithms, six groups of different types of benchmark test functions were selected from the set of benchmark test functions to test the performance of the five algorithms. Among them, there are three sets of single-peak functions and three sets of multi-peak functions, and the theoretical optimal value is 0. Table 1 displays the characteristics of particular function names, expressions, and types. The population size of all algorithms was set to 35 with 400 iterations. For each test function, each algorithm was run independently 25 times with the dimension set to 35.

Table 1.

Benchmark functions

ID	Function name	Expression	Type
F1	Sphere	$f (x) = \sum_{i = 1}^{D} x_{i}^{2}$	Unimodal
F2	Schwefel2.22	$f (x) = \sum_{i = 1}^{D} \| x_{i} \| + \prod_{i = 1}^{D} \| x_{i} \|$	Unimodal
F3	Rosenbrock	$f (x) = \sum_{i = 1}^{n - 1} [\begin{matrix} 100 {(x_{i + 1} - x_{i}^{2})}^{2} \\ + {(x_{i} - 1)}^{2} \end{matrix}]$	Unimodal
F4	Rastrigin	$f (x) = \sum_{i = 1}^{D} [x_{i}^{2} - 10 \cos (2 π x_{i}) + 10]$	Multimodal
F5	Ackley	$\begin{array}{l} f (x) = - 20 \exp (- 0.2 \sqrt{\frac{1}{D} \sum_{i = 1}^{D} x_{i}^{2}}) \\ - \exp (\frac{1}{D} \sum_{i = 1}^{D} \cos (2 π x_{i})) + 20 + e \end{array}$	Multimodal
F6	Griewank	$f (x) = \frac{1}{4000} \sum_{i = 1}^{D} x_{i}^{2} - \prod_{i = 1}^{D} \cos (\frac{x_{i}}{\sqrt{i}}) + 1$	Multimodal

The single-peak function has only one extreme point, while the multi-peak function exists many local extreme points, which is a more difficult complex multimodal problem for optimization algorithms to deal with, and it is even less easy to find the global optimal solution. In order to more fully compare the advantages and disadvantages of the convergence performance of the five algorithms, such as particle swarm algorithm PSO, differential evolutionary algorithm DEA, improved firefly algorithm GSO, and hybrid algorithm PGSO, three sets of single-peak test functions and three sets of multi-peak test functions are selected in the benchmark test function set for full comparison. Their convergence curves are shown below, where Fig. 3(a)(b) shows the convergence curves of the four algorithms under F1 and F2 test functions, Fig. 3(c)(d) shows the convergence curves of the four algorithms under F3 and F4 test functions, and Fig. 3(e)(f) shows the convergence curves of the four algorithms under F5 and F6 test functions.

Figure 3 shows the convergence curves of the four algorithms under the six benchmark test functions, and it is clearly seen from the figure that the hybrid algorithm PGSO gives the optimal results among all the algorithms, whether it is a multi-peak or a single-peak function, and it has the highest convergence speed and convergence accuracy. This is because in PGSO, the move step size in the pre iteration is increased by the nonlinear convergence factor, so that the algorithm carries out a large number of global searches in the pre iteration, and approaches to the direction of the global optimum, which effectively balances the performance of the algorithm’s global exploration and local exploitation. The elite strategy can effectively accelerate the convergence speed of the algorithm, the dynamic weighting strategy further improves the algorithm’s optimization-seeking performance, and the adaptive mutation strategy enriches the diversity of the population, and these strategies improve the convergence performance of the hybrid algorithm PGSO.

3.2

Simulation experiments for WSN sensor node deployment

This chapter aims to validate the feasibility of the hybrid algorithm PGSO in the node deployment problem, for which 30 sensor nodes with heterogeneous characteristics of sensing radius are randomly arranged in a 60m × 60m area of interest, and subsequently different algorithms are used to synergistically optimize the two objectives of coverage and average distance traveled.

Fig. 4 represents one of the solutions in the respective Pareto solution set obtained after optimization of four multi-objective algorithms, DEA, PSO, GSO, and PGSO, to achieve replanning of the sensor nodes after the initial coverage under the condition that the initial coverage of the WSN is 63.37%. The coverage of the optimization strategy based on the DEA algorithm reaches 74.71%, which is 11.34% higher than the initial coverage, and the average movement distance of the sensor nodes is 5.68m. The coverage of the deployment scheme optimized by PSO and GSO algorithms is 80.54% and 82.62%, which is 17.17% and 19.25% higher than the initial coverage, respectively, and the average movement distance of the sensor nodes is 5.08m and 4.64m, respectively. The coverage of the deployment scheme based on the PGSO algorithm is 91.12%, which is 27.75% higher than the initial deployment coverage, and the average movement distance of the sensor nodes is 4.16 m. In summary, it can be concluded that, in this scheme, the coverage of the algorithm PGSO is increased by 16.41%, 10.58%, and 8.5% compared to the DEA, PSO, and GSO, respectively, and the average movement distance of the node is is reduced by 1.52m, 0.92m and 0.48m respectively. It can be seen that the proposed PGSO algorithm achieves an integrated approach to network coverage and average distance traveled, and its deployment effect is more significant.

4

Conclusion

In this paper, the hybrid algorithm is used to calculate the network coverage and average mobile distance of many sensor nodes, so as to plan the optimal deployment location of nodes and obtain the optimal deployment scheme. The convergence performance of the hybrid algorithm is tested through controlled experiments to study the optimization effect of the hybrid algorithm in node deployment. The hybrid algorithm effectively balances the global search and local exploration performance, which can effectively accelerate the convergence speed and improve the convergence effect. Under the condition that the initial coverage rate of WSN is 63.37%, the coverage rate of the deployment scheme based on hybrid algorithm is improved to 91.12%, which is more than 25%. The advantage of hybrid algorithms in improving network coverage has been verified. Comparing with the original position of the sensor nodes, the deployment scheme of hybrid algorithm makes the sensor nodes move 4.16m on average, and the moving distance is smaller than the other three tested algorithms, which are 5.68m, 5.08m, and 4.64m. It validates the advantage of hybrid algorithms in terms of the average moving distance.

Through this paper, it can be found that the hybrid algorithm effectively improves convergence performance and is able to quickly search for sensor nodes at both global and local locations. The deployment scheme for sensor nodes with higher network coverage and shorter average traveling distance is given. Optimizing the deployment scheme for electric power IoT sensor nodes using a hybrid algorithm can save deployment time and node cost while improving deployment efficiency.

Langue:: Anglais

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Research on the deployment scheme of electric power IoT sensor nodes based on multi-objective planning

Chen Yang

Xiaofeng Dong

Junhua Hao

Ren Gu

Publié en ligne: 26 mars 2025

Reçu: 30 oct. 2024

Accepté: 11 févr. 2025

DOI: https://doi.org/10.2478/amns-2025-0803

Mots clésMulti-objective planning, WSNs, Sensor nodes, Perception model, Hybrid algorithm, Convergence performance

© 2025 Chen Yang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Multi-objective planning, WSNs, Sensor nodes, Perception model, Hybrid algorithm, Convergence performance