1 Introduction

An individual node in the network has constrained capacity in recognizing the environment and what’s more, is not sufficient for get together the helpful data from a precise domain. This information gathering process can be expert by the total work of different nodes. In numerous applications, the number of sensor nodes could be very huge. These co-operatively functioning sensor nodes shape a network named it as wireless sensor network (WSN).

There are extensive range of potential applications for WSN [1], for ex area monitoring, health care monitoring, military operations, surveillance system, and earthquake detection, etc. These networks consist of small, economical, low power sensor nodes capable of monitoring a desired occasion locally and forwarding it to the sink. The location of sink depends on the application type either far away or near the observing region. Each sensor node has sensing unit, embedded processors, communication unit and power unit. Sensor node closer to the sink will drain their restricted energy more quickly, since they should forward huge information to the sink. In this way, network lifetime will be decreased in view of energy hole issue [2]. Consequently, clustering techniques [3, 4] have been adapted generally for better execution. Yet, unreasonable cluster head selection may lead to coverage issue [5,6,7] which reflects how well a region is observed by sensors.

In this paper, Voronoi diagram [8] is used for dividing the observing area to provide evidence for the coverage problem [9] and to improve the lifetime of nodes [10]. The name Voronoi was originates from Gregory Voronoi he was the mathematician in German. Enhanced dynamic cluster head selection method (EDCHSM) is proposed for selecting reasonable cluster leader in a two level heterogeneous networks in two stages. In this proposed method, the nodes are deployed randomly in each coverage area and then the first stage of cluster head is a redundant node that can be completely covered by other nodes. After the death of all redundant node, second stage of cluster head is selected based on survival time estimation algorithm.

This paper composes of some related works based on coverage problem and a few cluster leader determination method based on energy is presented in Sect. 2. The existing system DCHSM is outlined in Sect. 3. Our proposed method EDCHSM is briefly explained in Sect. 4. In Sect. 5, Experimental outcomes are compared with existing protocols like SEP, DEEC, DCHSM and analyzed. Section 6 conclude the proposed work and demonstrate about the future work.

2 Related works

These days researchers deals about the network coverage, energy efficiency of the node (i.e. network lifetime), however the network lifetime are yet not be satisfied. To accomplish energy efficient sensor networks, clustering has to be done properly. To overcome these problems, a variety of clustering algorithms were proposed. In clustering based approach, the entire observing area is isolated into clusters, then non cluster node will send their sensed information to the CH, this will communicate the data aggregation information to the end user. Sometimes unreasonable cluster head will also cause a coverage problem in the network. Some of the clustering methods are discussed below.

Heinzelman et al. [11] and Handy et al. [12] explains that LEACH is a clustering technique in which nearly all nodes in the network will transmit the sensed information to the CH, and the cluster head compress all the information from remaining node in the network and forward it to the sink. CH need to do significantly work more than the normal sensor nodes, thus they disseminate significantly more liveliness and may die quickly. In order to maintain a stable network, some of the node will act as a cluster head in each round. So, the performance of the entire network will be affected because cluster head keep on rotating in every round.

Smaragdakis et al. [13] clarify that SEP was a change over LEACH in the way that it considers the heterogeneity of networks. In SEP, nodes with high energy is assumed as advanced nodes and the probability of advanced nodes to become a cluster head. Network lifetime is lengthen by SEP protocol. The main drawback in this method is that the advanced and normal nodes are not dynamic.

Younis et al. [14] make clear that HEED is a distributive clustering method which uses residual energy as essential constraint and distance to neighbors is considered as auxiliary constraint for choosing the cluster head. In this method, initial energy is same for all sensor nodes. The node with most prominent remaining energy and need the minimum distance for communication is elected as CH. This method has a very low processing time complexity per node and furthermore ends after a steady number of rounds.

Ye et al. [15] clearly explains that EECS is a LEACH like Clustering protocol in that a constant amount of sensor nodes are selected and among that selected node, cluster leader is selected based on node residual energy. But this protocol does not take care about data transmission.

Qing et al. [16] explain that DEEC is a heterogeneous routing algorithm where nodes are randomly dispersed in the observing area. The nodes which has more initial and remaining energy will become a cluster head compared with nodes with low energy. If the residual energy for the advanced node getting reduced, then they come in the range of the normal nodes. In such a situation, the advanced nodes die quickly than the other node.

He et al. [17] describes about EBCA in which entire observing area is divided in to rectangular grids. Here cluster leader is preferred based on a node with residual energy greater than the threshold value.

Kumar et al. [18] clearly explains that EEHC is a heterogeneous protocol in which node with high residual energy is selected as CH.

Saini et al. [19] make clear that TDEEC will increase the lifetime of the network when compared to DEEC. Here, CH is selected with respect to the probability ratio of residual energy of a network and average energy of the entire network, but the threshold value for selecting the node to become a CH is adjusted.

Zhang et al. [20] describes about EEDCP in which the entire network is first separated into virtual grid. A node with minimum weight is elected as cluster leader. Weight of all active nodes is calculated based on the ratio of total remaining energy of all active nodes in the cluster divided by the residual energy of each active node.

Han et al. [21] clearly shows that AEOC in which cluster leader is elected based on a node with higher residual energy and minimum distance to reach the sink node.

Jia et al. [22] make clear that in DCHSM two stages of cluster heads are selected for extending the network lifetime. At first, Voronoi diagram is used for achieving clustering in the observing region and then first class of cluster head is selected among the redundant nodes which has minimum value of network perception contribution. If all the redundant nodes under same coverage area died, then the second class of cluster head is selected based on survival time estimation algorithm. In this method, dead nodes are not taken care, this will loss the sensing information.

Fig. 1
figure 1

Blanket coverage

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Fig. 2
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Barrier coverage

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3 Existing system

Network topology means which node is in touch with remaining nodes in the network. The quality of topology control influences directly on the network lifetime. The following three variables are be considered for assessing the wireless sensor networks topology control.

  1. (I)

    Coverage It implies that the measure of to what extent the sensors can watch the physical condition.

    Based on different applications, different degrees of coverage in the observing region are required. Some of the types of coverage are discussed below.

    1. (i)

      Blanket coverage/area coverage In this coverage, each node is to be monitored in the observing area, otherwise this will lead to coverage hole problem. Therefore, probability of detection rate of point in the observing region is maximized (Fig. 1).

    2. (ii)

      Barrier coverage Is a coverage refers to the detection of movement across a barrier of sensors. In this coverage, probability of undetected penetration through the barrier is minimized (Fig. 2).

    3. (iii)

      Sweep coverage Is a coverage that addresses a explicit balance between maximizing the detection rate of point and limiting the quantity of missed detection.

    4. (iv)

      Point coverage Is a coverage in which object with well-known location is to be analyzed (Fig. 3).

  2. (II)

    Connectivity It is a measure of the degree to which a specific node in the network are associated with all other node.

  3. (III)

    Network lifetime Is a time until the sensor nodes run out of energy.

Fig. 3
figure 3

Point coverage

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Fig. 4
figure 4

Indiscriminate organization of nodes

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Assume that the sensor network consist of \(M \times M\) observing area which is a two dimensional planar rectangular region as shown in Fig. 4.

N static nodes are randomly dispersed and sink is positioned in the midpoint of the observing area which may lead to existing the overlapping sensing field. So coverage model is proposed based on Voronoi diagram. The observing area can be divided into a set of clusters and cluster leader is elected from each cluster as shown in Fig. 5.

Fig. 5
figure 5

Voronoi clustering

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The cluster head selection process is shown in Fig. 6.

Fig. 6
figure 6

Cluster head selection process

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The first stage of cluster head selection process are shown below.

  1. (i)

    A node \(\hbox {S}_i\) is located at (\(\hbox {X}_{i}, \hbox {Y}_{i}\)), then the probability of each node \(\hbox {S}_i\) detects an object in w(X,Y), then the euclidean distance between \(\hbox {S}_{i}\) and \(\hbox {w}\) is computed as follows (1).

    $$\begin{aligned} d(S_i,w) = \sqrt{(X_i -X)^{2}+(Y_i -Y)^{2}} \end{aligned}$$
    (1)

    The mathematical model for the coverage probability from \(\hbox {S}_i\) to w is expressed as (2)

    $$\begin{aligned} P(S_i ,w)= & {} 1\; {\textit{for}}\;d(S_i ,w)<R_s +u\nonumber \\&e^{-\alpha d_i }\;\textit{for}\; R_s -u \le d(S_i ,w)<R_s +u\nonumber \\&0\;{\textit{for}}\;d (S_i ,w) \ge R_s +u \end{aligned}$$
    (2)

    where \(d_i =d(S_i ,w)-(R_s -u)\), u is a measure of uncertainty of the sensor detection, \(\alpha \) is the parameter related to physical device monitoring, \(\hbox {R}_s\) represent perceived radius.

  2. (ii)

    Node public perception (NPP) of all sensor node is calculated as follows (3).

    $$\begin{aligned} \textit{NPP}(i) = \sum _{i=1}^N P(S_i,w) \end{aligned}$$
    (3)

    If a sensing node within the network satisfy \(\hbox {NPP}(\hbox {i})\ge \text {threshold}\) of the perceived probability (\(\hbox {M}_{\min }\)), set the redundant flag as 1 for a particular node.

  3. (iii)

    Network perception contribution (NPC) between sensor node \(\hbox {S}_i\) (Xi, Yi) to all nodes in the whole observing area is defined as (4)

    $$\begin{aligned} \textit{NPC}(i)= \frac{P(S_i ,w)}{\sum _ {P(S_i ,w)} } \end{aligned}$$
    (4)

    The redundant node which has minimum NPC value is elected as first stage of cluster head.

If all the redundant nodes under the same coverage area died, then second stage of cluster head is chosen based on survival time estimation algorithm.

Table 1 Simulation parameters
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The selection steps to find the second stage of cluster head.

  1. (i)

    Calculate the remaining nodes which is alive in the observing area.

  2. (ii)

    Assign normal nodes with energy of \(\hbox {E}_o \) and advanced nodes with energy of \(\hbox {E}_o\) (\(1+\hbox {a}\)).

  3. (iii)

    Probability for cluster head selection is shown in formula (5)

$$\begin{aligned} p=\left\{ \begin{array}{ll} \frac{p_{\textit{opt}} E_{\mathrm{int}} (r)}{(1+\textit{an}) \cdot E_{\textit{avg}} (r)}&{} \quad \hbox {for normal nodes}\\ \frac{P_{\textit{opt}} (1+a)E_{\mathrm{int}} (r)}{(1+\textit{an})E_{\textit{avg}} (r)}&{} \quad \hbox {for advanced nodes}\\ \end{array}\right. \end{aligned}$$
(5)

where \(p_{\textit{opt}} \) is the reference value, \(\hbox {E}_{\mathrm{int}} \) represents sensor node initial energy during round r, \(\hbox {E}_{\textit{avg}} \) is the network average energy which is estimated as (6)

$$\begin{aligned} \hbox {E}_{\textit{avg}} =\frac{1}{N}*{E}_{\textit{tot}}^{*}\, \left( 1-\frac{r}{\textit{NL}}\right) \end{aligned}$$
(6)

where \(\hbox {E}_{\textit{tot}}\) represents total initial network energy, NL represents network lifetime and found as (7)

$$\begin{aligned} \hbox {Network lifetime (NL)}=\frac{E_{\textit{tot}} }{E_{\textit{rou}} } \end{aligned}$$
(7)

where \(\hbox {E}_{\textit{rou}}\) represents energy exhausted by the network and is equal to (8)

$$\begin{aligned} \hbox {E}_{\textit{rou}}= & {} \hbox {h}(2\,^{*}\,\hbox {N}\,^{*}\, \hbox {E}_{\textit{elec}} +\hbox {N}\,^{*}\,\hbox {E}_{\textit{DA}} +\upbeta \hbox {E}_{\textit{mp}} \,^{*}\, \hbox {dis}^{4}_{\textit{CHtoBS}} \nonumber \\&+\, \hbox {N}\,^{*}\,\upbeta \,^{*}\, \hbox {E}_{\textit{fs}} \,^{*}\, \hbox {dis}^{2}_{\textit{CMtoCH}}) \end{aligned}$$
(8)

where \(\hbox {h}\) represents data packet size, \(\hbox {E}_{\textit{elec}} \) represents energy consumed per bit to run the transceiver circuitry, \(\hbox {E}_{\textit{DA}} \) is the data aggregation energy dissipation, \(\hbox {E}_{\textit{mp}}\) is the multipath model, \(\hbox {E}_{\textit{fs}} \) is the free space model, \(\hbox {dis}_{\textit{CHtoBS}}\) means average distance between cluster leader and base station and is calculated using the formula \(0.765\,^{*}\,\frac{M}{2}\), where M is the location of sensor node in X axis, \(\hbox {dis}_{\textit{CMtoCH}} \) is the average distance from a non cluster member node to a cluster leader and is calculated using the formula \(\frac{M}{\sqrt{2\,^{*}\,\Pi *\beta }}\), \(\upbeta \) represents ideal number of cluster heads and is derived by taking partial derivative of \(\hbox {E}_{\textit{rou}}\) with respect to \(\upbeta \), we get (9)

$$\begin{aligned} \sqrt{\frac{0.5\,^{*}\,N \,^{*}\, {E}_{\textit{fs}} }{\Pi *{E}_{\textit{mp}} }} *\frac{M}{\textit{dis}_{\textit{CMtoCH}}} \end{aligned}$$
(9)
  1. (iv)

    In DEEC protocol, the probability threshold is set as

    $$\begin{aligned} \hbox {Threshold}= \left\{ \begin{array}{ll} \frac{p}{1-p\left( { ran}\, ^*\, \hbox {mod} \left( \frac{1}{p}\right) \right) } &{}\quad \hbox {if}\;\hbox {N}\, \varepsilon \, M\\ 0 &{}\quad \hbox {Otherwise}\\ \end{array}\right. \end{aligned}$$
    (10)

where M is the number of nodes qualified as a cluster leader in a specific round r. ran is a irregular integer. If an integer is less than threshold as defined in Eq. (10), then that particular node is qualified to become head of the cluster for a particular round r.

4 Proposed method

Selection steps of the first stage of cluster leader is as follows.

  1. 1.

    Initialize the wireless sensor network.

  2. 2.

    NPP of each sensor node is calculated using the formula (3).

  3. 3.

    If the sensor node satisfy \(\hbox {NPP}(\hbox {i})\ge \hbox {M}_{\min }\), set the redundant flag for a particular node as 1.

  4. 4.

    Network perception contribution is calculated using the formula (4).

  5. 5.

    Select the redundant node which has minimum network perception contribution is elected as first stage of cluster head.

Following are the steps to find the second stage of cluster leader.

Each sensor node have heterogeneity i.e. all nodes have diverse initial energy. Two level heterogeneous networks comprise of two nodes, normal and advanced nodes. nN advanced nodes equipped with original energy of \(\hbox {E}_O\) (\(1 + \hbox {a}\)), and (\(1 - \hbox {n})\hbox {N}\) normal nodes set with original energy of \(\hbox {E}_{O}\). The probabilities of normal and advanced nodes are same as (5).

In EDCHSM protocol, cluster head for a particular round is chosen based on survival time estimation algorithm. Here the threshold is set as:

$$\begin{aligned} \hbox {Threshold}=\left\{ \begin{array}{ll} \frac{p}{1-p\left( \textit{ran}\,^*\, \hbox {mod} \left( \frac{1}{p}\right) \right) }\,^*\,\frac{E_{\textit{int}} (r)*\beta }{E_{\textit{avg}} (r)}&{}\quad \hbox {if}\;\hbox {N}\, \varepsilon \, \hbox {M}\\ 0 &{} \quad \hbox {otherwise}\\ \end{array}\right. \end{aligned}$$
(11)

5 Experimental outcomes

The performance of EDCHSM is evaluated using Matrix laboratory and some of the simulation parameters are listed (Table 1).

Fig. 7
figure 7

Coverage simulation

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Table 2 Coverage hole
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Fig. 8
figure 8

First node death (in Rounds)

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Fig. 9
figure 9

Tenth node death (in Rounds)

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In this section, experimental results of proposed method were analyzed and compared with existing protocols like SEP, DEEC and DCHSM.

The diagram of coverage simulation is shown in Fig. 7. SEP algorithm first appears the coverage holes at 1142th round and gradually decreases to 0 at the 4432th round. DEEC algorithm first appears the coverage hole at 1351th round and gradually decreases to 0 at the 8308th round, DCHSM algorithm appears the coverage hole at 1512th round and gradually decreases to 0 at the 8837th round. EDCHSM algorithm appears the coverage hole at 1612th round and gradually decreases to 0 at the 9944th round (Table 2) .

Fig. 10
figure 10

All dead nodes during rounds

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Table 3 First node death
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Table 4 Tenth node death
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Table 5 All node death
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The diagram of first node death, tenth node death and all death nodes during rounds is shown in Figs. 8, 9 and 10. SEP algorithm appears the first node dead at 1142th round, tenth node dead at 1375th round and all node dead at 3530th round. DEEC algorithm appears the first node dead at 1351th round, tenth node dead at 1623th round and all node dead at 5729th round. DCHSM algorithm appears first node dead at 1512th round, tenth node dead at 1709th round and all node dead at 8166th round. EDCHSM algorithm appears the first node dead at 1612th round, tenth node dead at 1807th round and all node dead at 8697th round (Tables 3, 4, 5).

Fig. 11
figure 11

Packets send to the sink

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SEP, DEEC, DCHSM, EDCHSM, data packets send to the sink are 134570, 309771, 389224, 575597 respectively as shown in Fig. 11. The simulation results shows that EDCHSM is better than DCHSM and this method achieve superior result than DEEC. SEP performs most awful (Table 6).

6 Conclusion and future work

A Enhanced dynamic cluster head selection for sensor networks is proposed and results are analyzed by evaluating the lifetime of the network, amount of alive, dead nodes and packet send to the sink. The proposed method overcomes the imbalance of energy consumption and also expands the lifetime of the network. The extension of this proposed method would be a further discussion of the redivision of the observing area after the death of all redundant nodes under the same coverage area.

Table 6 Packets send to the sink
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