Increasing the lifespan of a group of distributed
wireless sensors is one of the major challenges in research. This is
especially important for distributed wireless sensor nodes used in harsh
environments since it is not feasible to replace or recharge their
batteries. Thus, the popular low-energy adaptive clustering hierarchy
(LEACH) algorithm uses the “computation and communication energy model” to
increase the lifespan of distributed wireless sensor nodes. As an improved
method, we present here that a combination of three clustering algorithms
performs better than the LEACH algorithm. The clustering algorithms included
in the combination are the

Wireless sensor networks are being used for many different applications, such as monitoring chemical spills, detecting and assessing the extent of environmental contamination, and monitoring the movement of soldiers and weapons on the battlefield. However, their limited lifespan is a great concern when they are used in remote locations or in harsh environments.

Radio energy model.

Many different techniques have been introduced in an effort to maximize
their lifespan, but these techniques have focused on having the nodes in a
cluster send their data to a selected cluster head node that, in turn,
reports the data to the base station. Therefore, the choice of the number of
clusters and the way the cluster head node is selected are the main focuses
of these techniques. Clustering and the use of cluster heads in wireless
sensor networks have the potential to enhance the lifespans of a group of
sensor nodes and to minimize the generation of noise in the signals
exchanged between the sensor nodes and the base station (sink) (Heinzelman
et al., 2000). In this approach, the cluster head organizes a reservation
scheme to improve communication with the sensor nodes in the cluster, and
the cluster head uses this scheme to aggregate, compress, and transmit the
cluster's sensing data to the base station. Several technologies have been
designed to improve the lifespan of the sensors. For example, algorithms were
developed for this purpose by the energy efficient heterogeneous clustered
scheme (EEHC) (Kumar et al., 2009) by the design of a distributed energy
efficient clustering (DEEC)(Qing et al., 2006), and by the low-energy
adaptive clustering hierarchy (LEACH) (Heinzelman et al., 2000). These goals
of these algorithms were to determine the optimal number of clusters in a
given number of sensor nodes and to selecting a head in a cluster of
sensors. The low energy consumption clustering routing protocol (Kumar et
al., 2009) improved the LEACH algorithm by utilizing the

In this paper, we have provided detailed discussions of clustering
algorithms; the combination of

The LEACH algorithm was developed to minimize the power consumption of
wireless sensor nodes by determining the optimal number of clusters,

Then, the total energy used to transmit a

The energy for

The receiver's energy for a

Let us now consider energy consumption by the sensor nodes in a cluster of a multi-cluster
sensor network. Assuming that there are

The energy consumption by a member node for transmitting a

Now, let us calculate the energy consumption in a cluster in the
aforementioned sensor network, i.e.,

Fourth, the total energy consumption for a cluster is the sum of that for the
cluster head and for the non-cluster head member nodes:

Finally, the optimal number of clusters,

Based on Eq. (12), let us assume that the number of sensor nodes (

The

For example, the first single initial center (

First, let us assume that the sensor nodes are represented by

Second, the algorithm generates a random number. Then, one of the values of

The distance of each sensor node and over the average distance of sensor
nodes is also calculated as

Again, the algorithm generates a random number to choose one of the values
of

Moreover, Arthur et al. (2007) chose the initialization center of a data set
one by one in a controlled fashion using the

The first step is to choose the first single initial center (

The algorithm generates a random number. Then, one of the values of

Calculate

The

Figure 2 illustrates how the

If we expand the illustrative example, the

The cluster center

“Gap statistics” is a standard technique for determining the optimal number of clusters for a data set (or a group of sensor nodes) by comparing the observed weight curve to the expectation of a referenced weight curve (Tibshirani et al., 2001).

The observed weight is the sum of the distance between all observed sensor nodes (actual data) and the center of the cluster; the referenced weight is the sum of the distance between all referenced sensor nodes (ideal) and the center of the cluster (Yan, 2005; Zhang, 2001). The observed weight and the expectation of the referenced weight can be derived mathematically as shown below.

First, let us assume that the sensor nodes are represented by

Sensor nodes in a cluster.

Figure 3 also illustrates the distance between each of the sensor nodes, the
number of clusters, and the number of sensor nodes in a cluster. For
example,

Second, the algorithm generates the referenced weight by adding a small
noise into the original sensor nodes or the observed sensor nodes. The
referenced weight is

Third, the algorithm calculates the expected value of the referenced weight,

As expressed above, the main goal of the gap statistics method is to compare
the curve of the observed weight (

Results of the example with three clusters:

However, when there is a small gap between the

For example, Fig. 4a shows a scatter graph in which the sensor nodes are
distributed across three clusters; one cluster is well separated from the
other two clusters, which are connected. Figure 4b shows that using the gap
statistics algorithm determines the optimal number of clusters in Fig. 4a.
As Fig. 4b shows, the increased number of clusters results in decreased
weight. The red line indicates the location of the original sensor nodes
within the cluster and has observed weight

Combination of the three clustering algorithms.

As summarized above, the LEACH (Heinzelman et al., 2000) algorithm uses a
computation and communication energy model to increase the lifespan of the
sensor nodes. But the method is still far from being a complete and optimal
solution to the problem. For example, the LEACH algorithm selects a fixed
number of clusters, but it ignores the fact that some of the sensor nodes in
a cluster can be reallocated to another cluster. It also ignores the fact
that the cluster head's energy will be depleted quickly when too many sensor
nodes remain in a single cluster, because more energy is required for
aggregating, compressing, and transmitting more information. With this
background of partial solutions to the problem, our intention was to attain
a complete solution by using other clustering algorithms that were developed
for other purposes. This section provides details concerning how they were
used. The operation of wireless sensor nodes is divided into three phases,
i.e., setup, advertisement, and steady state. In this research, we focused
only on the setup phase. During the setup phase, first, the sensor nodes
identify their locations and positions and then transmit the information to
a base station. At the base station, where this combined algorithm is
located and runs, the

Figure 5 shows the steps that are used to choose the optimal number of
clusters based on the three clustering algorithms (

In the first step, we represent the location of the sensor node. In the
second step, we initialize the cluster's center based on the

The first step starts with a number of sensor nodes represented by

Third, we calculate the optimal centers of the distributed sensor network
based on the

As expressed above, the main goal of the gap statistics method is to compare
the curve of the observed weight (

The test sensor network is of the sensor nodes randomly distributed between

For the simulation of the test sensor network, we used the LEACH algorithm's simulation parameters, as indicated in Table 1. For example, the initial energy for each of the sensor nodes was set to 0.5 J. Each of the data messages were 525 bytes long, and the broadcast packet size header was 25 bytes long.

100 wireless sensor nodes in the area of the sensing network.

Simulation parameters.

Sensor nodes grouped in seven clusters.

The radio electronics energy was 50 nJ bit

The simulation steps of the three combined algorithms are described in Table 2.
First, the

Combination of clustering algorithms.

The

After the optimal location of the center of the sensor nodes was calculated,
the gap statistics algorithm determined the optimal number of sensor nodes
by comparing the observed weight curve (

Figure 8 shows the observed and reference weight functions versus the number
of clusters. In addition, the red dots on the red curve are the
observed weight curve

log(mean) dispersion of reference and log dispersion original data sets.

We compare our approaches with the LEACH algorithm's approaches to determine which method provided a longer lifespan for the wireless sensor nodes.

As discussed in Sect. 2, the LEACH algorithm determines the optimal number
of clusters,

To assess the two methods, we used the LEACH algorithm to choose a cluster
head within sensor nodes in a cluster. For example, sensor nodes randomly
chosen from 0 to 1. When the randomly chosen value is less than the

The value of

The operation of the LEACH algorithm depends on the rounds. Each round has two phases, i.e., a setup phase and a steady-state phase. During the setup phase, the number of clusters and the cluster head are selected. In the steady-state phase, data are transferred from the sensor nodes to cluster head, which sends them to the base station.

Figure 9 shows the number of sensors still alive over time and shows the
advantage of using the combination of the clustering algorithms (blue curve)
over the LEACH algorithm (red curve). The energy of the sensor nodes begins
to diminish at

Lifespans of homogenous wireless sensor nodes: (red) LEACH algorithm; (blue) combination of clustering algorithms.

To improve the lifespan of sensor networks, we proposed using a combination
of clustering algorithms, i.e., the

Our simulation demonstrated the advantage of using the combination of clustering algorithms over using the LEACH algorithm in that the lifespan of the wireless sensor nodes was increased by 15 %.Edited by: R. Morello Reviewed by: two anonymous referees