HQCA-WSN: High-quality clustering algorithm and optimal cluster head selection using fuzzy logic in wireless sensor networks

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Fuzzy Sets and Systems ••• (••••) •••–•••

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www.elsevier.com/locate/fss

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HQCA-WSN: High-quality clustering algorithm and optimal cluster head selection using fuzzy logic in wireless sensor networks

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Amir Abbas Baradaran

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a,∗

, Keivan Navi

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a Department of Computer Science and Engineering, Shahid Beheshti University, Tehran, Iran b Faculty of Computer Science and Engineering, Shahid Beheshti University G.C., Tehran, Iran

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Received 14 May 2018; received in revised form 26 February 2019; accepted 29 November 2019

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Abstract Reducing the consumption of energy and the network lifetime are the main challenges that affect wireless sensor networks (WSNs). High-quality clustering is one of the most important approaches for reducing the energy consumption in WSNs. Various criteria can be used to assess the quality of the clusters and considering all of these criteria can lead to high-quality clustering. In this study, we propose a method called the high-quality clustering algorithm (HQCA) for generating high-quality clusters. The HQCA method uses a criterion for measuring the cluster quality, which can improve the inter-cluster and intra-cluster distances as well as reducing the error rate during clustering. The optimal cluster head (CH) is selected based on fuzzy logic and according to various criteria such as the residual energy, the minimum and maximum energy in each cluster, and the minimum and maximum distances between the nodes in each cluster and the base station. The main advantages of this method are its high reliability, low error rate during the clustering process, the independence of key CHs, better scalability, and good performance in large-scale networks with a high number of nodes. The validity of the clustering quality is also measured based on external and internal criteria. Simulation results demonstrated that the HQCA-WSN method can significantly improve the energy consumption and network lifetime. The proposed method also significantly enhances the first node dies and last node dies metrics compared with similar methods. © 2019 Elsevier B.V. All rights reserved.

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Keywords: Clustering; Energy consumption; Fuzzy logic; Quality; Wireless sensor network

1. Introduction

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Wireless sensor networks (WSNs) comprise a set of nodes for monitoring and recording environmental data [1]. The node distributions in WSNs are random or deterministic [2]. In places that are difficult for humans to access, the nodes are randomly distributed (e.g., by throwing them onto the site). The number of nodes is high and little initial energy is used to charge them. Therefore, energy consumption and the network lifetime are the main challenges that affect these networks [3–5]. The data collected by the nodes are transmitted to a base station (BS) for processing

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* Corresponding author.

E-mail addresses: [email protected] (A.A. Baradaran), [email protected] (K. Navi). https://doi.org/10.1016/j.fss.2019.11.015 0165-0114/© 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Single-hop and multi-hop data transfer in WSNs.

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Fig. 2. Clustering in a WSN.

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[6]. Data transfer can be conducted in a single-hop or multi-hop manner [7,8]. Fig. 1 illustrates the single-hop and multi-hop methods. Some major applications of WSNs include monitoring forest fires, controlling the status of sensitive patients, and controlling military areas and traffic [9–12]. In general, the key factors that affect the design of WSNs are fault tolerance, scalability, costs, hardware limitations, reliability, the WSN topology, the transmission environment, and energy consumption [13–15]. The two approaches used to increase the lifetime of WSN are clustering and routing [16–20]. During clustering, a group of sensors is placed in a category called a cluster according to a set of common attributes. A highly qualified node in each cluster is selected as the cluster head (CH). The role of the CH is to collect the data received from cluster members and to transfer it to a BS or higher level CH depending on the type of transmission (single-hop or multi-hop). CHs transfer the received data directly to the BS during single-hop transmission, whereas the CHs transfer the received data to higher-level CHs during multi-hop transmission and the higher-level CHs then transfer the data to the BS. Multi-hop transmission is always used in large-scale networks. The cluster members are generally divided into two groups comprising common nodes and CHs. Fig. 2 illustrates the clustering process in a WSN. One of the key challenges in clustering is ensuring the quality of the clusters [21]. Many criteria can be used to assess the quality of clusters, where density and separation (inter-cluster and intra-cluster distances) are among the basic indices utilized for measuring the quality of clusters [22,23]. The data belonging to each cluster should be sufficiently close and the clusters formed should be sufficiently separate to minimize their overlapping. Separation is defined according to the following three parameters: the distance between the nearest data in two clusters, the distance between the farthest data in two clusters, and the distance between the centers of two clusters. The other criteria used for measuring the quality of clusters can be divided into three categories: external criteria, internal criteria, and relative criteria. External criteria such as the normalized mutual information (NMI) and entropy are dependent on predefined structures. Thus, these criteria can be used when we have correct clustering results to compare with our own results [24,25]. Lower entropy values and higher NMI values result in better quality clustering. Unlike the external criteria,

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Table 1 Features of clustering methods.

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Clustering method

Advantages

Disadvantages

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Partition-based clustering

• Simplicity and scalability (fairly good) • Suitable for relatively low node numbers and spherical clusters • High performance with split clusters

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Hierarchical clustering

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• Access all data and obtain the best solution • High flexibility • Suitable for point-to-point communications (e.g., tree structures)

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Density-based clustering

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Spectral clustering

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Grid-based clustering

Low performance in large-scale networks Number of clusters determined by the user High dependence on the initial phase (setup) Sensitive to noise Inefficient in harsh environments Unsuitable for convex clusters with different sizes Inefficient with crowded and non-uniform clusters

• Unsuitable (high complexity) for the integration and separation of data • Lack of proper solutions to prove the quality of the clusters • Uncertainty regarding the criteria for terminating clustering • High costs when applied to large-scale and high-density networks

• Dynamic clustering (number of clusters not fixed) • Suitable for clusters with different shapes, sizes, and properties • Robust to noise and good performance in harsh environments

• High dependence on input parameter settings • Fails to provide a proper solution to confirm or reject the quality of the cluster • Inefficient in dense networks

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Suitable for image processing Low processing time Uses a similarity matrix for clustering Simple implementation Suitable for low number of nodes

• High complexity when generating the similarity matrix • Sensitive to input parameters selected for clustering • High complexity during large-scale data clustering

• Dependent on the number of input data • Low processing time • High performance with irregular data distributions • Low computational complexity

• Probability of some grids being empty in random distributions • Imbalanced cluster formation • Low scalability to large-scale networks

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internal criteria such as the sum of squared errors or mean squared error are not dependent on previous knowledge and they can directly measure the quality of clusters based on the original data [26]. Relative criteria involve comparisons between different clusters, e.g., a clustering method may be applied to different data and the results are then compared. Clustering can be conducted with several methods such as hierarchical clustering [27], partition-based clustering [28], spectral clustering [29], grid-based clustering [30], and density-based clustering [31,32]. A tree structure is often used in hierarchical clustering, where greedy algorithms and stepwise optimization are employed. Two approaches are used in hierarchical clustering, which comprise top-down or bottom-up methods. In partition-based clustering, the data are divided into several partitions and each partition represents a cluster. In spectral clustering, a similarity matrix is used for clustering. In grid-based clustering, the grid is divided into multiple regions and nodes are added to these areas based on certain features. In density-based clustering, the clusters are areas with higher density separated from regions with lower density. Fig. 3 shows simple graphical examples of the different types of clustering methods. Table 1 provides general comparison of the different clustering methods. The aim of routing is to find the optimal route from the clusters to the BS in order to transfer the collected data. The most important parameters that affect routing are the network dynamics, energy constraints, data aggregation, and data transfer. The network dynamics depend on the type of application, which can generally be divided into fixed sensors and motion sensors. In applications such as traffic control or fire control, the sensors are usually fixed and motionless. In applications such as tracking targets, the sensors are mobile.

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Fig. 3. Simple graphical example of clustering methods: a, partition-based clustering; b, hierarchical clustering; c, spectral clustering; d, grid-based clustering; and e, density-based clustering.

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Table 2 Features of clustering methods.

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Protocol name

Features

Protocol type

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Flooding Directed Diffusion SPIN EAR

Request from BS

Data-centric

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LEACH TEEN APTEEN PEGASIS

Setup and steady phase. The clusters are formed in the first phase and the CHs are then selected. Information is transmitted in the second phase.

Hierarchical

GEAR PGR GAF

Global positioning system needed to determine the positions of the nodes

Based on geographic locations

SAR

Based on tree structure. BS is usually rooted. Edges shaped according to quality of service, energy, and prioritization.

Quality of service-Based

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Energy constraints affect multi-hop and single-hop transmission approaches. In the multi-hop approach, the power consumption and transmission range are lower. In general, many factors can determine energy losses but the most important are collisions, overheating, and idle listening. The data transfer model is also divided into three categories: time-driven [33], event-driven [34], and query-driven [35]. In the time-driven model, data are collected periodically and sent by each node. In the event-driven model, nodes report when an event occurs. In the query-driven model, a request is sent by the BS and the nodes then respond to this request. The routing protocols are divided into four general categories and Table 2 shows these general categories of routing protocols together with the protocol names and types. The remainder of this article is organized as follows. In Section 2, we summarize previous research into clustering as well as discussing the strengths and weaknesses of various methods. In Section 3, we explain the details of the proposed algorithm, network model, radio model, and energy model. In Section 4, we present the clustering process as well as the criteria comprising α, , and μ for measuring the cluster quality. These criteria ensure the quality of clustering. In Section 5, we explain how to select the CH using a fuzzy logic method. Finally, the simulation results are presented in Section 6.

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2. Related work

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One of the main methods for WSN clustering is the LEACH protocol [36]. LEACH is a hierarchical, probabilistic, distributed, and single-hop protocol, which improves the network lifetime by distributing the power consumption across the nodes. In this method, data aggregation is conducted on the nodes, which reduces the number of messages sent, and thus the energy consumption. In LEACH, the nodes are organized in local clusters and a node in each cluster is selected as a CH. The cluster is selected randomly using a probability function called T (n). Equation (1) shows the threshold used in this protocol. ⎧ p ⎨ T (n) = if n ∈ G 1 − p(r mod p1 ) (1) ⎩ 0 otherwise

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According to equation (1), a node decides to be a CH with probability p and broadcasts this decision. After the CHs are specified, they send acknowledgment messages to the other nodes and each node that is not a CH will select a cluster to join. This selection is based on two criteria: the minimum energy required for connection and the received signal strength indicator (RSSI). An important advantage of LEACH is that the CH role alternates among all of the nodes to achieve load balancing. This alternation is achieved by selecting a random number between zero and one for a sensor. A node in the current round is CH if its random number is less than T (n). LEACH also provides fully integrated load distribution. By randomly changing CH, LEACH can balance the energy consumption. The local synchronization scheme in LEACH provides better scalability during cluster formation. Despite its benefits, LEACH has three major

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Fig. 4. PEGASIS protocol.

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problems. First, the selection of a CH and its alternation are probabilistic, so there is still a likelihood of selecting low-energy nodes as a CH. Thus, the selected CHs may be concentrated in a specific area of the network. Therefore, a suitable distribution of CHs is not guaranteed by this protocol and there may be no CH in some node areas. Second, this protocol assumes that a CH has a wide range of communication and that the data can be sent directly to the BS. These are not realistic assumptions because a CH is a common node and the BS is not directly available to all nodes in most cases. Third, LEACH uses intra-cluster and inter-cluster communication with single-hop transmission, which is not sufficiently effective in large-scale networks. Due to the major problems with LEACH, a centralized approach was developed called the LEACH-C protocol [37]. The LEACH-C protocol is based on LEACH but each node sends information to the BS concerning its current position and energy level. In this protocol, the clusters are formed centrally by the BS. Thus, in each round and after determining the CH, the BS sends a message containing the CH identifier to all of the nodes. If the CH identifier for each node matches the desired identifier, then it is a CH; otherwise, it is considered a common node and it stays in the sleep mode provided that it does not have a transition. Selecting an optimal CH is an NP-hard problem in this protocol. Simulation results have shown that this method transmits more than 40% of the data per unit of energy relative to LEACH. The PEGASIS protocol [38] is the advanced mode of LEACH, which creates a connection chain between all of the sensors in the network instead of forming different clusters. In this protocol, each sensor is associated with its neighbor and only one sensor in the entire network is selected to send the data to the BS, which is referred to as the vital sensor (leader). Fig. 4 shows the PEGASIS protocol. The major benefits of PEGASIS included an extended network lifetime, improved first node dies (FND) and last node dies (LND) metrics, and lower overheads during the clustering process. However, the existence of a vital sensor in this protocol is a fundamental challenge because all of the network information will be lost after the destruction of this node, and thus this method has low reliability. TEEN is a hierarchical clustering protocol and it is also considered an energy-efficient clustering protocol [39]. The TEEN protocol uses multi-hop transmission and it can improve the network lifetime. This method lacks an appropriate distribution for the energy consumption by the clusters. In addition to the protocols introduced above, other protocols such as EECF [40], LLACA [41], CACH [42], BARC [43], LEACH-SWDN [44], O-LEACH [45], PSO-C [46], CBL [47], SONS [48], PECRP [49], and HUCL [50] can reduce the power consumption and increase the network lifetime. Table 3 compares many of the previously proposed protocols. Tarachand et al. proposed an algorithm called ERA [51], which forms clusters based on the remaining energy of the node and the inter-cluster distance. In this method, each sensor node performs self-organized and independent CH selection, so no messages are exchanged. In ERA, two parameters are employed comprising the remaining energy and distance, where each node directly decides to be a CH. Bhatia et al. proposed a method called GADA-LEACH where CH selection is performed by a genetic algorithm [52]. This protocol uses a relay node that serves as an interface between a CH and the BS. The main task of the relay node is to facilitate communication between a CH and the BS. Despite the benefits of GADA-LEACH, low-density regions cannot be differentiated from high-density regions in this method. In addition, due to the genetic algorithm used in this method and the random selection of CHs, the number

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Table 3 Comparison of previously proposed protocols for WSN clustering.

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Features

Protocol type

CH selection

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EECF

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Distributed

• Based on a three-step message, remaining energy, and degree of each node

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Hierarchical

• Based on two phases (setup and steady) • Efficient load balancing • Introduces a new energy model for the steady phase • Uses Z-MAC and CSMA/CA protocols for intracluster communication

Hierarchical

LEACH-SWDN

• Uses a sliding window • FND and LND improvements

Hierarchical

• Based on threshold, probability, and residual energy

PSO-C

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For homogeneous and heterogeneous networks High scalability Based on particle swarm optimization (PSO) Uses three phases: cluster formation, choosing the optimal CH, and data transfer • Intra-cluster communication organization

Hierarchical

• Based on fitness function, PSO, quality of clusters, energy, and network coverage

• Combination of LEACH and PEGASIS protocols • For large-scale networks • Uses TDMA

Hierarchical

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BARC

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CBL

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SONS

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PECRP

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HUCL

• Based on local information about neighbors

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• Based on the highest data received at the start

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• Based on the proposed energy model, residual energy, and adjacency

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• Based on threshold, probabilities, and rotational

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Multi-hop protocol For large-scale networks Routing by spanning tree Based on three phases: pre-setup, process, and startup

Hierarchical

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Combination of LEACH and HEED protocols Multi-hop protocol Good aggregation High scalability

Distributed

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Static clustering and dynamic routing Multi-hop protocol Low overheads during clustering High overheads during routing

Centralized

• Based on the spanning tree and the remaining energy level of the node

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• Based on residual energy and distance to the neighboring node

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• Based on residual energy, distance to the BS, and number of neighbors

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• Based on two phases (setup and steady) • Uses TDMA scheduling in the transmission phase • Selects CHs rotationally • Single-hop transmission

CACH

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Centralized

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• Clustering algorithm based on machine learning • Cluster formation based on two phases (initial clustering and Re-clustering)

LLCA

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Uses the SAB message Partition-based clustering CH selection using RCRA messages Best complexity: O(1) Worst complexity: O(n)

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of CHs may be higher in some parts of the network and load balancing can be inadequate. Thus, low-density areas may have more CHs than high-density areas. The CBCCP [53] method employs a new hierarchical clustering protocol that focuses on reducing the data transmission time and energy consumption by using a multi-hop data aggregation approach, where routing is performed via a predetermined path called the new transmission algorithm. Clustering is an efficient approach for network organization by increasing the network lifetime, error tolerance, scalability, data aggregation, and load balancing, and obtaining a better topology. One problem that affects high-quality

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clustering is how to consider all of the useful parameters in the clustering process. Fuzzy logic is one of the most effective approaches for addressing this type of problem. In the FUZZY-TOPSIS protocol [54], a multi-criteria fuzzy decision-making technique is used to select CHs. This method selects CHs based on the remaining energy, energy consumption of the nodes, number of neighboring nodes, mean distance between neighboring nodes, and the distance from the BS. After applying these five criteria in FUZZY-TOPSIS, an index is created for each node, which allows the common nodes to decide whether to be a CH or not. After determining a CH, a message is sent to its neighbors. Common nodes join the corresponding CHs according to the maximum RSSI value and the smallest distance. In this method, CH selection is performed in six phases based on a random distribution of nodes, detection of neighboring nodes, CH selection, CH arrangement, a mechanism for organizing intra-cluster communication and inter-cluster multi-hop communication, and node mobility using a predictable weighted decision matrix and random paths. Another method based on fuzzy logic was proposed by Azad et al. where this protocol is a centralized clustering approach with a CH selection criterion based on multiple attribute fuzzy decision making (MADM). ECPF [55] is a protocol that uses three techniques comprising selecting tentative CHs based on the remaining energy, using fuzzy logic to select the final CHs, and demand-based clustering. The OCM-FCM [56] method uses a C-means-based fuzzy clustering algorithm, where the optimal CHs are selected based on the node density in the network. Clustering is conducted using the C-means algorithm in this method where CHs are selected based on the distance and degree of membership for each node. However, selecting the C parameter (number of clusters) is a fundamental challenge for the C-means algorithm. Baranidharan et al. proposed a method called DUCF [57] where the CHs are selected using fuzzy logic with an unequal clustering approach based on three criteria: remaining energy of the node, distance to the BS, and degree of each node. The final CHs are selected using the fuzzy inference system. Many fuzzy logic methods have been proposed, including CHEF [58] and EAUCF [59]. These methods obtain remarkable improvements compared with other previously developed methods, but an algorithm has not yet been proposed that considers the cluster density and the inter-cluster and intra-cluster distances simultaneously in addition to the criteria defined above. Thus, the routing process can only begin after ensuring the accuracy and quality of the clusters. Therefore, in order to optimize the energy consumption, increase the network lifetime, and improve the cluster quality, we propose a high-quality clustering algorithm based on a multi-dimensional fuzzy approach for selecting the optimal CHs. In general, the advantages of the proposed method are as follows.

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• • • • • •

Reduced energy consumption, increased network lifetime, and improved FND and LND parameters. A standard is created to ensure the accuracy and quality of the clusters. Relationships are established between the number of nodes, number of clusters, and quality of the clusters. Improved inter-cluster and intra-cluster distances. Improved C-means clustering and selection of better cluster centers. A new criterion is established for differentiating clusters in high-density areas and clusters in low-density areas. This criterion can be used to determine whether the node distribution in a cluster is balanced or uniform, and whether the energy consumption is less in a cluster where the node distribution is balanced. • CH selection is conducted according to the remaining energy on the node, cluster quality criterion, node distribution in the cluster, distance of the node to the BS, mean nodes in the cluster, and cluster density. • The protocol can be applied to large-scale networks with many nodes (better scalability). • The proposed protocol is independent of the vital nodes. 3. Details of the proposed algorithm Before explaining the details of the proposed algorithm, we define the assumptions considered in our method. 3.1. Network model

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The high-quality clustering algorithm (HQCA)-WSN has N sensor nodes and all of the sensors are distributed randomly in a square area measuring n ∗ n. The sensors have different initial energies and they cannot be added or removed after deployment. Sensors cannot be recharged after their energy has drained. Sensors know their positions and their positions are also known to the BS. It is also assumed that a media access control (MAC) layer prevents scheduling interruptions during the transmission of messages. Furthermore, the following assumptions are considered.

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– – – –

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BS is located outside the area of the nodes and its location is variable in different scenarios. Wireless communication between nodes is symmetrical. The energy, memory, and power of the BS are infinite. The positions of the nodes are determined by positioning algorithms or a global positioning system.

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3.2. Radio model

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The proposed method uses a radio model based on the distance between the transmitter and receiver, where the shortest distance is considered the crossover distance. The transmission power is defined as follows:

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Pt Gt Gr λ2 , (2) (4πλ)2 where Pt , Gt , and λ are the transmission power, transmission antenna gain, and wavelength of the signal, respectively. When the distance of the receiver is greater than the crossover distance, the transmission power is equal to:

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ptr =

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Ptr =

Pt Gt Gr h2t h2r , d4

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3.3. Energy model

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The Heinzelman energy model is used where the energy consumption required to receive an m-bit message at a distance of d meters is defined as follows:    Ec (m, d) = m Eelect + εfs d 2 d < dc   , (4) 4 d ≥ dc Ec (m, d) = m Eelect + εmp d

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where εfs and εmp depend on the sender’s sensitivity and the shape of the noise, Eelect is the electrical energy required to setup the electronic equipment, which depends on digital encoding, modulation, and filtering, and dc is the crossover distance between the transmitter and receiver. The radio energy required to receive an m-bit message is defined as follows. Ec = mEelect

(5)

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3.4. Proposed method

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where ht and hr represent the transmitter and receiver antenna heights, respectively.

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One of the most important factors that affect high-quality clustering is simultaneously considering the two criteria comprising the intra-cluster and inter-cluster distances. In most of the previously proposed methods, only one of these two criteria is considered or neither. In methods where these criteria are considered, the accuracy and quality of the clusters are not measured at the end of the clustering process. The error rate during cluster formation is one of the most important issues that affect the formation of high-quality clusters. Most clustering methods use a fixed number of clusters at the beginning of the clustering process. For example, the C-means and K-means methods use a fixed number of clusters at the beginning of the process. Methods based on these algorithms are also problematic because the cluster quality depends on the number of clusters and the points considered as cluster centers. Clusters may also be formed with no members (empty clusters). In the following, we propose several criteria for measuring the cluster quality. The first criterion is based on the inter-cluster and intra-cluster densities. We show that if this criterion is low, then the quality of the cluster is better. Thus, if this criterion is low, the inter-cluster and intra-cluster distances will both be better. We also introduce another criterion that indicates whether an error has occurred in the clustering process. One of our high-quality clustering criteria is the arrangement of the nodes in a cluster. If more uniform nodes cover the cluster surface, then the clusters will be more balanced and the energy consumption by the nodes will be decreased. Finally, another criterion represents the balance of the nodes in the clusters. The accuracy of this criterion is proved based on statistical assumptions and the measurement error. Before introducing these criteria, we explain the clustering process in the following. In the proposed method, CH selection is performed by fuzzy logic and the formed clusters obtained are the highest quality.

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In the proposed method, the region where the sensors are distributed is divided into grids with the same size. The centers of gravity are then calculated for the grid and sensors. Two types of clustering are performed based on the centers of gravity for the grids and the sensors in each grid, where the centers of gravity for the grid and the sensors in each grid are considered the primary centers of the cluster. This process is repeated until the new cluster centers do not differ from that the previous cluster centers. If a grid is initially formed with no sensors or the number of its sensors is less than three, then its sensors are added to the nearest adjacent grid. This method avoids empty clusters or those with a low number of sensors, and the clusters have will have the lowest intra-cluster distance. The distance between the centers of gravity for the grid and the sensors in each grid is called the confidence interval and it is represented by μ0 . After conducting the two clustering methods, the quality of the clusters is measured using the three criteria and the highest quality cluster is selected. Measuring the cluster quality is more important than the clustering process. These criteria can also be used to measure the quality of clusters in previously proposed methods or future methods.

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4.1. First criterion: intra-cluster and inter-cluster densities

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¯˛ = {∂ n | n = 1, 2, . . . , k}, where k and ∂ n are the numbers of clusters The set of cluster centers is denoted by O and cluster centers, respectively. The set of sensors that are not cluster centers is denoted by O ˛ = {∂i | i = 1, 2, . . . , ¯˛ }, where is the total number of clustered sensors and  − O  −O ˛¯  represents the total number of nodes except ¯˛ for the cluster centers. For example, if we have 100 sensors and five clusters, then k = 5 and = 100. In addition, O and O ˛ are defined as follows.

  ¯˛ = ∂ n n = 1, 2, 3, 4, 5 = ∂ 1 , ∂ 2 , ∂ 3 , ∂ 4 , ∂ 5 O O ˛ = {∂i | i = 1, 2, . . . , 95} = {∂1 , ∂2 , . . . , ∂95 }

indicates the average similarity between the cluster center ∂ n

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The cluster quality is defined as follows:

k 1 m + n (k) = ( min , 1≤m≤k k mn

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where n and all members of the cluster O ˛ , m indicates ˛ m , mn is also the similarity the average similarity between the cluster center ∂ m and all members of the cluster O between the ∂ n and ∂ m clusters, and n , m , and mn are defined as follows:  1  ∂i , ∂ n (7) n = n O ˛  n ∂i ∈O ˛    1 m = ∂j , ∂ m (8) m O ˛  ∂j ∈O ˛m   (9) ∂ n, ∂ m , mn =

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where O ˛  and O ˛   are the number of nth cluster members and the number of mth cluster members, respectively,  n m ∂i ∈O ˛ n (∂i , ∂ ) and  ∂j ∈O ˛ m (∂j , ∂ ) are the total Euclidean distances of the nth and mth cluster sensors from their n m own cluster centers, (∂ , ∂ ) is the total Euclidean distance of the cluster centers from each other, and mn is the similarity between m and n clusters. The similarity is based on the proximity in terms of the Euclidean distance to the cluster centers. For example, we consider the distribution of sensors and clusters shown in Fig. 5. In this example, the sensors with coordinates (1, 24), (2, 20), (2, 22), and (4, 15) are the members of cluster 1 and the sensors with coordinates (3, 13), (1, 5), (5, 3), (3, 3), and (4, 8) are the members of cluster 2. In addition, the sensors with coordinates (1, 24), (2, 20), (2, 22), and (4, 15) are the members of cluster 3. Thus, K = 3 and = 100. According to the definitions given above, we have the following.



 ¯˛ = ∂ n n = 1, 2, 3 = (3, 20.25), (3.2, 6.4), (14.8333, 10) O

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O ˛ = {∂i | i = 1, 2, . . . , 97} = {∂1 , ∂2 , . . . , ∂97 }  1  ∂i , ∂ n 1 = n O ˛  ∂i ∈O ˛n    1 (1 − 3)2 + (24 − 20.25)2 + (2 − 3)2 + (20 − 20.25)2 + (5 − 3)2 + (22 − 20.25)2 = 4 

+ (4 − 3)2 + (15 − 20.25)2 = 3.3207  1  ∂i , ∂ n 2 = n O ˛  ∂i ∈O ˛n   1  (3 − 3.2)2 + (13 − 6.4)2 + (1 − 3.2)2 + (5 − 6.4)2 + (5 − 3.2)2 + (3 − 6.4)2 = 5  

+ (3 − 3.2)2 + (3 − 6.4)2 + (4 − 3.2)2 + (8 − 6.4)2 = 3.6505  1  ∂i , ∂ n 3 = n O ˛  ∂i ∈O ˛n  1  (16 − 14.8333)2 + (11 − 10)2 + (20 − 14.8333)2 + (10 − 10)2 = 6    + (17 − 14.8333)2 + (19 − 10)2 + (15 − 14.8333)2 + (5 − 10)2 + (9 − 14.8333)2 + (5 − 10)2 

+ (12 − 14.8333)2 + (10 − 10)2 = 5.2466   ∂ n, ∂ m mn =  = (3 − 3.2)2 + (20.25 − 6.4)2 + (3 − 14.8333)2 + (20.25 − 10)2 + (3.2 − 14.8333)2 + (6.4 − 10)2 = 24.1919

k 1 1 + 2 1 + 3 2 + 3 m + n 1 (k) = ( min , , = min 1≤m≤k k mn 3 mn mn mn n=1

n=m

1 min{0.2882, 0.3541, 0.3678} = 0.0961 3 Next, we assume that the clusters are formed as shown in Fig. 6. By repeating the calculation given above, the following parameters are obtained. =

1 = 4.1273 2 = 3.0826 3 = 4.4782

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mn = 24.5112 (k) = 0.0980 By comparing the two criteria for the first and second cases, we conclude that the first clustering results are better quality because the value of is lower. Thus, the intra-cluster and inter-cluster distances are better in the first case than the second case. In the next example, we assume that the distribution of the sensors is as shown in Fig. 7. Then, we have the following. ∂1 = (2.875, 4.625)

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3 = 1.4281 mn = 12.8517 = 0.0807 Next, we assume that the clusters are formed as shown in Fig. 8. In this case, is equal to 0.07964, which indicates that the clusters are better in the first case. During clustering, entropy is considered as an external criterion and its value ranges between zero and one. The cluster quality is lower when the entropy value is closer to one.

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Table 4 Error table.

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Definition 1. If C and Pi are the number of clusters and the probability of data belonging to the ith cluster, respectively, then the entropy is equal to: Entropy = −

c 

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Lemma 1. Entropy is always between zero and one, and always positive. Proof. Suppose that 0 ≤ pi ≤ 1 and Log(pi ) < 0. Thus, pi ∗ log(pi ) is always negative. Therefore, the entropy value is always positive and its value ranges between 0 and 1. 2

The clustering entropy in Example 1 for the second mode (Fig. 6) is defined as follows.             5 5 5 5 5 5 Entropy = − log − log − log = 0.4771 10 10 10 10 10 10 Therefore, the clustering entropy is lower in the first case, and thus the quality is higher. After calculating the clustering entropy in Example 2, we also find that clustering quality is better in the first case than the second case. Thus, the low entropy and values indicate that the clustering quality is better. Therefore, we can demonstrate the accuracy of the criterion by calculating the entropy.

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4.2. Second criterion: error resulting from clustering (α)

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The clustering entropy in Example 1 for the first mode (Fig. 5) is defined as follows.             4 4 5 5 6 6 Entropy = − log − log − log = 0.4713 10 10 10 10 10 10

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pi log(pi ).

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As mentioned previously, the HQCA-WSN performs two types of clustering, where one is based on the center of gravity for the sensors in each grid and the other is based on the center of gravity for the grid. After forming both types of clusters, we apply the and entropy criteria to select one of the two clustering processes. Clearly, the cluster is selected with the lowest values for both criteria. The clustering error is denoted by α, which is calculated using a table called the error table. Table 4 shows the error table for the two types of clusters. It should be noted that this table can be expanded to any number of clusters.

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In Table 4, parameter a is the number of sensors in cluster A and they are the proper members of A. Similarly, parameter d represents the sensors in cluster B and they are correctly grouped in cluster B. The parameter c represents the sensors in cluster B and they are mistakenly grouped in cluster A. Finally, parameter b represents the sensors in cluster A and they are mistakenly grouped in cluster B. According to the error table, the clustering error is defined as follows:

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is always equal to a constant number denoted by μ0 , as follows.

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According to the statistical hypothesis, the accuracy of Lemma 2 can be determined at the significance level α (or error). 2

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Based on the statistical hypothesis, we can define the following hypothesis. H0 : μ ≤ μ 0 H1 : μ > μ0

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(13)

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In equation (13), H0 is the null hypothesis and H1 is the alternative hypothesis. The sensor distributions follow either the Z-distribution or Student’s t-distribution. If the number of sensors is less than or equal to 30, the distribution of the sensors follows the Student’s t-distribution. If the number of sensors is greater than 30, then according to the central limit theorem, the distribution of the sensors follows the Z-distribution. Therefore, if the number of sensors is denoted by n, we have the following two cases.

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• If n ≤ 30, then the distribution of the sensors follows the Student’s t-distribution and test statistic is defined as follows. X − μ0 t= SX

(14)

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then the distribution of the sensors in a cluster is balanced or uniform.

 Proof. Suppose that the value of

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where T and X represent the standard deviation and the average number of sensors in each cluster, respectively. After specifying the values defined above, the critical values (the boundaries of H0 and H1 ) should be specified based on α, as shown in Appendixes A and B. For clarity, we show each of the above definitions in the curve in Fig. 9. If the test statistic is in the acceptance zone for H0 , then the assumption of H0 is accepted; otherwise, the assumption of H0 is rejected.

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Fig. 10. Fuzzy set of energy levels.

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In the proposed protocol, CHs are selected using fuzzy logic. Fuzzy logic involves a fuzzifier, inference system, rules base, and defuzzifier. The input of the fuzzy system is usually a crisp value, which is converted into a suitable fuzzy variable. The fuzzified values are sent to the fuzzy decision block (FDB), which comprises fuzzy rules and a fuzzy inference system. The FDB maps the fuzzy output based on the fuzzy rules. Finally, the fuzzy output is converted into a crisp output using defuzzification approaches. CHs are selected based on the remaining energy in the sensors, maximum and the minimum distances of the sensors to the BS, lowest and highest amount of energy per cluster of sensors, cluster quality criteria, distribution of sensors in the cluster, mean distance of sensors in the cluster, and the cluster density. We propose four total energy levels comprising low, medium, high, and very high. In fact, these variables are the fuzzy linguistic variables for the total energy. Fig. 10 shows the fuzzy set of energy levels. According to Fig. 10, the membership functions of the fuzzy set are defined as follows.  1 Energy ≤ 0.25 (17) Low 0.35−Energy 0.25 < Energy ≤ 0.35 0.1  Energy−0.25 0.25 < Energy ≤ 0.5 0.25 Medium (18) 0.6−Energy 0.5 < Energy ≤ 0.6 0.1  Energy−0.5 0.5 < Energy ≤ 0.8 0.3 (19) High 0.89−Energy 0.8 < Energy ≤ 0.89 0.09

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Fig. 11 shows the different fuzzy levels (or membership functions) for the distances of sensors to the BS in each cluster, i.e., near, average, and far. The membership functions for the distance parameter are defined as follows: 1 x ≤ c1 Near (21) L−x c1 < x ≤ L L−c1  x−c 1 c1 < x ≤ L L−c1 (22) Average c2 −x c2 −L L < x ≤ c2  x−L c2 −L L < x ≤ c2 (23) Far 1 x > c2 In the equations above, c1 and c2 are the minimum and maximum sensor distances to the BS, respectively, x is the sensor’s distance to the BS, and L is the average distance to the BS, which is calculated as follows. L = (c1 + c2 )/2

(24)

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Fig. 12 shows the parameters c1 and c2 . Fig. 13 shows the different fuzzy levels used for choosing the optimal CH. Clearly, the selected CHs are the sensors with the highest energy and the lowest distance to the BS. Thus, in each cluster, several sensors have the possibility of being a CH and the sensor that satisfies the conditions best is selected as the final CH. In Fig. 13, T1 is the multiple of the minimum energy in the maximum distance to the BS and T2 is the multiple of the maximum energy in the minimum distance to the BS. Thus, we have the following. T1 = Emin ∗ Dismax T2 = Emax ∗ Dismin

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Table 5 shows the fuzzy rules employed for selecting tentative CHs. These rules are written based on the Mamdani approach.

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Table 5 Fuzzy rules for CH selection. Number

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If Energy is “Very High” ˆ distance to Bs is “Nearest,” then CH is “Candidate” If Energy is (“Very High” ∨ “high”) ˆ distance to Bs is “Nearest,” then CH is “Candidate” If Energy is (“Very High” ∨ “high”) ˆ distance to Bs is “Near,” then CH is “Candidate” If Energy is “Very High” ˆ distance to Bs is “Near,” then CH is “Candidate” If Energy is “Medium” ˆ distance to Bs is “Nearest,” then CH is “Candidate” If Energy is “Medium” ˆ distance to Bs is (“Near” ∨ “Average”), then CH is “Candidate” If Energy is “Very High” ˆ distance to Bs is “Average,” then CH is “Candidate” If Energy is “Medium” ˆ distance to Bs is “Nearest,” then CH is “Candidate” If Energy is (“Medium” ∨ “high”) ˆ distance to Bs is “Near,” then CH is “Candidate”

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We emphasize that in the proposed method, the quality of the clusters formed is more important than the clustering process. However, in the HQCA-WSN protocol, we provide three new criteria for measuring the cluster quality. Algorithm 1 presents the HQCA-WSN protocol. 6. Simulation results

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In this study, simulations were conducted with MATLAB. The energy of the sensors ranged between 0.2 and 0.9. The sensors were randomly distributed in a square measuring n ∗ n. The simulation parameters are shown in Table 6. The efficiency of the proposed algorithm was evaluated in term of the following parameters and the results were compared with those obtained in previous studies. • Network lifetime: One of the main goals of the proposed method to increase the network lifetime. The two main parameters that affect the lifetime of WSNs are FND and LND. Higher values for these two parameters indicate a longer network lifetime. • The number of CHs: The energy consumption is better during each round when more CHs are balanced in each round. • Improving the initial energy level for network setup: During the initial setup of the network, assigning low energy to each sensor is highly effective because it reduces the total amount of network energy in the initial setup. • Improving the energy consumption in each cluster: The energy consumption in each cluster should be improved in order to minimize the average energy in the entire network. • Evaluating the cluster quality using the confidence interval. • Determining the number of clusters using μ and α. • Evaluating the performance of large-scale networks with a large number of sensors. • Assessing the network performance with different BS situations. • Computational complexity of the proposed method.

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Algorithm 1 HQCA-WSN protocol. -

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Distribute nodes randomly and uniformly; Set up the environments for the nodes with equal size (grid); For (i = 1; i ≤ grid_number; i++) Counter = Number of grid_nodes[i]; If (Counter == “empty”) Delete the grid. End if; If (Counter < 3) The nodes in the grid are added to the nearest adjacent grid. End if; End for; Calculate the initial centers; Flag = true; While (Flag == true) Calculate the new centers using the distance between the nodes in each grid from the center of gravity for the grid and to the base station; Start clustering; New centers = Calculate the new centers using the distance between the nodes in each grid to the center of gravity for the grid and to the base station; Calculate the first cluster quality criterion ( ); Calculate the second cluster quality criterion (α); Calculate the entropy; Perform Lemma 1 and Lemma 2, and confirm one of the clustering processes in terms of the entropy, , and α criteria; If (New centers == Initial centers) Flag = false; End if; End while; Select the optimal CH using fuzzy logic and rules (Table 5); Start the transmission phase; End.

Table 6 Simulation parameters.

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50, 100, 200, 300, 500 100 ∗ 100, 200 ∗ 200, 300 ∗ 300, 500 ∗ 500 Rand [0.2–0.9] Variable Number of nodes < 5 50 nJ/bit 10 pj/bit/m2 0.0013 pj/bit/m4 5 nj/bit/signal 87 m

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Fig. 14 shows the energy consumption with the proposed method (HQCA-WSN). Figs. 15 and 16 show the energy consumption with the LEACH, LEACH-SWDN, LEACH-DCHS, ALEACH, HUCL, EAUCF, LEACH-C, CBL, PEGASIS, O-LEACH, GADA-LEACH, and MOFCA protocols. Clearly, the proposed method significantly improved the network lifetime as well as the FND and LND parameters. Fig. 17 shows that the HQCA-WSN method significantly improved the FND and LND metrics.

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Fig. 16. Network lifetime with HUCL, EAUCF, LEACH-C, CBL, PEGASIS, O-LEACH, GADA-LEACH, and MOFCA protocols. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

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will greatly increase the network lifetime and reduce energy the consumption because the presence of more CHs in the high-density area will reduce the total distances between the sensors and the CHs to enhance the network efficiency. Fig. 18 shows an example with a random distribution of nodes. The density of the nodes is higher in some areas of the network than other areas because of the random distribution. Thus, more CHs are selected in high-density areas

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and the performance of the algorithm will be better. Figs. 19, 20, and 21 show examples of CH selection, where more CHs are clearly selected in high-density areas. Fig. 19 shows the simulation results obtained in a square measuring 200 ∗ 200 m2 with nine clusters and 100 nodes. In Fig. 19, the white areas are regions where the densities of the nodes are higher than those in other areas, and thus the number of clusters selected (i.e., 9 clusters) is higher in these areas. Fig. 20 shows the simulation results obtained with 16 clusters and 100 nodes. According to Fig. 20, the HQCA-WSN protocol has high scalability with respect to the number of nodes, the network size, number of clusters, and density. Fig. 21 shows the simulation results obtained with 200 nodes where 16 CHs are selected (red areas). Thus, the proposed algorithm exhibits better scalability in large-scale networks than other methods. Therefore, if the number of nodes is high in high-density areas, more clusters are selected in these areas. Selecting appropriate cluster centers in each round is important for the formation of optimal clusters. In particular, a more balanced selection of cluster centers leads to the formation of better final clusters in terms of the inter-cluster and intra-cluster distances. Fig. 22 shows the selection of cluster centers in each round, where it is clear that the selection of cluster centers with the HQCA-WSN method can obtain an appropriate balance.

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Fig. 20. CH selection with 100 nodes and 16 clusters.

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6.3. Improved energy consumption in the overall network and each cluster

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The network setup will be more cost-effective if the initial amount of energy is lower for each node. Table 7 shows the initial amounts of energy during the formation of various networks. According to Table 7, the proposed method requires less energy compared with previously reported methods. Fig. 23 shows the energy consumption in each cluster. According to Fig. 23, the energy consumption in each cluster is balanced in an appropriate manner, where the highest energy consumption is between 0.4 J and 0.6 J. As shown in Table 7, the total amount of energy during the initial setup of the network is very low when using the HQCA-WSN protocol compared with other methods, which also explains why the proposed method works well in high-density areas. 6.4. Determination of the number of clusters and node balance in each cluster

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Table 7 Initial energy in HQCA-WSN and similar protocols.

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Protocol name

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Total energy

LEACH-SWDN CBL O-LEACH DCHS ALEACH HUCL PECRP ECPF PEGASIS CBCCP OCM-FCM FUZZY-TOPSIS ERA HQCA-WSN

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Fig. 24. Clustering based on the centers of gravity for the sensors and grid.

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sensors minus the center of gravity for the grid. The number of clusters can be determined based on this criterion and the number of sensors. Figs. 24 and 25 show the formation of clusters based on the center of gravity for the sensors in each grid and the center of gravity for the grid, respectively. Clearly, 200 sensors are organized in nine clusters. Table 8 shows the confidence intervals with both clustering methods, where it is clear that the clustering process in cluster 6 has an error, and this error is also clear in Figs. 24 and 25. Fig. 25 shows that a sensor in cluster 6 is incorrectly grouped in cluster 9 and a sensor in cluster 9 is incorrectly grouped in cluster 6. The errors are shown in Table 9. Based on the errors in Table 9 and the explanations given in the previous sections, we obtain the following.

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If we assume that the number of nodes is greater than 30, then according  to the central limit theorem, the distribution of the sensors follows the Z-distribution. The value of μ0 is equal to the hypotheses are defined as follows. H0 : μ ≤ 4.7140 H1 : μ > 4.7140

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Cluster number

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μ0 = 3.8276 μ0 = 6.1155 μ0 = 0.3205 μ0 = 6.4854 μ0 = 0.9014 μ0 = 1.8889 μ0 = 6.2791 μ0 = 1.4134 μ0 = 8.5576

μ0 = 3.8276 μ0 = 9.2190 μ0 = 4.2226 μ0 = 7.6785 μ0 = 0.9630 μ0 = 0.5884 μ0 = 8.4677 μ0 = 1.4134 μ0 = 10.1856

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The first mode in Fig. 9 is used to describe H0 and H1 . For example, we may calculate the values of T , X, Z, and SX for the first cluster with 29 nodes as follows. 200 = 6.8965 29 T = 99.8459 99.8459 T = 7.0602 SX = √ = √ n 200 X=

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Fig. 26. Decision diagram.

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Fig. 27. Quality of HQCA-WSN protocol (μ).

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According to Appendixes A and B, the statistical value for the error of 0.01 is 0.5040. Fig. 26 shows the graph obtained based on the findings described above. According to Fig. 26 and the values obtained, it is clear that the value obtained for α is above the value of Z. Thus, the value obtained for α is in the H1 area, so assumption H1 is verified. In addition, according to Lemma 2, if the distribution of the sensors is balanced, then μ must be greater than 4.7140. Therefore, we have the following.   Nodes Number 200 μ > 4.7140 ⇒ > 4.7140 ⇒ > 4.7140 Clusters Number Clusters Number 200 200 ⇒ > 22.221796 ⇒ Clusters Number < Clusters Number 22.221796 ⇒ Clusters Number < 9.000172 Thus, the number of clusters should be less than 9.000172, which indicates that selecting nine clusters at the beginning is a good choice because the first integer smaller than this value is 9. Fig. 27 show the clustering quality with both methods, where it is clear that the first method obtains better quality clusters (less μ) than the second method, although a violation occurs in cluster 6. Therefore, the two indexes μ and are the fundamental factors used for evaluating and verifying the quality of clusters. 6.5. Improvement of C-means clustering and selecting better clustering centers

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Number of clusters

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algorithms is the high scalability of the algorithms with the sensor network size. Thus, an algorithm performs well with small-scale networks containing a low number of sensors or large-scale networks containing a high number of sensors. Fig. 30 shows the lifetime for a large scale network containing a large number of sensors with the HQCAWSN method. Clearly, the HQCA-WSN method performs well with large-scale networks containing a large number of sensors. 6.6. Computational complexity of HQCA-WSN protocol

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An important characteristic of the HQCA-WSN algorithm is that its complexity is low. The most important advantage of using algorithms with low computational complexity is that they can be applied simply in high-density areas. Most hierarchical algorithms such as single-linkage, complete-linkage, and average linkage have a complexity of O(N 2 ) in both time and space. In addition, partitioning algorithms such as k-means have a complexity close to O(N) in both space and time. The proposed method has low computational complexity. To assess the computational complexity of HQCA-WSN, we assume that the number of nodes in the area is n. One CH is present in each cluster and the average number of common nodes per cluster is equal to n/k − 1, where k is the number of clusters. In the worst case, m comparisons are performed in k clusters and each cluster has n/k − 1 nodes, which equals m × k × (n/k − 1). Therefore, the time complexity of the HQCA-WSN algorithm is O(nm). Thus, the low computational complexity of HQCA-WSN facilitates its scalability to large-scale sensor networks. 7. Conclusion and future works

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Reducing the energy consumption and increasing the network lifetime are major challenges in WSNs. In this study, we proposed a method called HQCA-WSN for clustering based on the cluster quality. The nodes are classified using two methods based on several criteria and the highest quality cluster is selected. The cluster quality is evaluated based on the inter-cluster and intra-cluster intervals as well as the distribution of nodes in the network. We also proposed a measure of the error generated by clustering. In HQCA-WSN, we can determine the number of clusters according to a criterion called the confidence interval. The proposed protocol can select more clusters in dense areas and in areas where the distribution of nodes is high. In HQCA-WSN, CHs are selected based on the remaining energy, the energy consumption of the nodes, the number of neighboring nodes, the mean distance between the neighboring nodes, and the distance to the BS. Simulation results showed that HQCA-WSN could improve the network lifetime,

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FND, and LND compared with similar methods. HQCA-WSN reduced the average total energy in the network during the initial setup, as well as improving the average energy consumption in each cluster. The important advantages of the proposed method are that it can improve the clustering process and select better primary centers for clustering. In methods such as C-means, the cluster quality depends on the initial selection of the cluster centers. The HQCA-WSN method exhibits high scalability in large-scale networks. In the future, the performance of the HQCA-WSN method may be enhanced by including more parameters such as a new energy model, optimal cluster estimation based on the density, and the peripheral density of each node.

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Appendix B. Student’s t table

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