Keywords

127.1 Introduction

It is the hot research direction in wireless sensor network (WSN) that is how to utilize the energy of every sensor point effectively to prolong the life cycle of WSN as well as equilibrium of all energy in WSN. LEACH [1] is a typical hierarchical routing protocol. Later the scholarship of MIT Hein Zelman proposes the algorithm of LEACH-C [2] that is based on LEACH algorithm. It solves the problem that hasn’t considered the reminder energy in a cluster head election to improve the quality of generated clusters. HEED [3] algorithm through a calculation to broadcast AMRP and to become temporary cluster head with the probability of initialization \( CH_{p} = \hbox{max} (C_{p} \times \frac{Er}{Em},p_{\hbox{min} } ) \), which select the head of a cluster in terms of reminder energy as first factor and communication in the network as a second factor. The algorithm of HEED is different to the algorithm of LEACH in criteria of cluster head selection and the mechanism of competition, it had improved in speed of clustering and pick more reasonable cluster head to transmit data by considering of inner cluster communication and reminder energy in order to make whole WSN more equilibrium. On the base of above mentioned viewpoints, there are someone propose a method to guarantee the optimized strategy of minimum energy cluster head selection [4, 5], which is based on twice the selection of cluster head and this method makes full consideration of energy parameter and hot zone of WSN. What’s more, there are someone use K-MEANS [6, 7] to select a cluster head. These methods, however, are only considered the problem of energy and cost of routing without considering the similarity of sensing in some areas. This paper uses fuzzy cluster method to partition similar area of sensing and use HEED algorithm to select a cluster head to transmit sampling data to SINK point. Therefore, under the condition of request of accuracy and real-time is not high, we can partition similar area to reduce transmission quantity effectively, to reduce the computation of data fusion [8, 9], to cut down the total energy consumption and finally to prolong the life cycle of the whole network.

127.2 Concerned Question Description and Definition

For the area of sensing, the sensing data may have similar change regulation. We can use the similarity of change regulation of sampling data to utilize fuzzy clustering to partition the whole area into several similar areas. In every similar area, we can use HEED algorithm to select a cluster head and utilize it as representation to monitor neighbourhood variation. When inner similar area’s real sensing data deviate from the data sampled by cluster head, which exceed threshold \( MaxError \). The system should reparation and select the head of clusters to collect the district sensing data. In there, sensing vector is \( X = \{ p^{(1)} , \ldots ,p^{(i)} , \ldots ,p^{(n)} \} \) which denote the n sensing data with m sensing results from time \( t_{x} \) to \( t_{y} \). For example, vector with order number is \( p_{i} = \{ p_{1}^{(i)} , \ldots ,p_{m}^{(i)} \} \), the raw sensing data can be expressed by matrix \( \mathop {SensoringMatrix}\limits_{{T \in [t_{x} ,t_{y} ]}} [n][m] \).

Definition1

sensing similarity is \( \mathop {SimSensoring}\limits_{{p_{i} ,p_{j} \in X}} (p_{i} ,p_{j} ) \): suppose there are two sensor points \( p_{i} \) and \( p_{j} \) in some area \( SimArea \) and for the given sensor point set \( X = \{ p^{(1)} , \ldots ,p^{(n)} \} \) has no objects with m dimensions, we define similarity of sensing as follows:

$$ SimSensoring(p_{i} ,p_{j} ) = \sigma d_{s} (p_{i} ,p_{j} ) + (1 - \sigma )\left| {\cos (p_{i} ,p_{j} )} \right| $$
(127.1)

Definition 2

max error of sensing \( MaxError \): as a classified similar area \( SimArea \), we can find two sensor points \( p_{i} \) and \( p_{j} \) they have max dissimilarity, so the\( MaxError \) in this area satisfy that it \( \mathop {Min}\limits_{{p_{i} ,p_{j} \in SimArea}} \{ SimSensoring(p_{i} ,p_{j} )\} \) is true it implicates value \( \frac{{\sqrt {\frac{1}{m}\sum\limits_{k = 1}^{m} {(p_{i} - p_{j} )^{2} } } }}{{Max\{ p\} - Min\{ p\} }} \) is close to\( \alpha \), \( \alpha \) is max tolerance of real measurement error and range of \( MaxError \)is (0,1).

Definiton 3

similar sensing area (SSA): SSA is a set of sensing points that satisfy the condition \( A_{j} (P_{i} ) = \{ P_{i} \left| {Min\{ SimSensoring(P_{i} ,C_{j} )\} > \delta } \right.\} \), \( C_{j} \) is a regional centre of \( A_{j} (P_{i} ) \), so the whole sensing area can be expressed by \( sensorArea = \bigcup\limits_{j = 1}^{N} {A_{j} (P)} \) and for \( \forall A_{i} (P),\forall A_{j} (P) \in sensorArea \) there is the expression \( A_{i} (P) \cap A_{j} (P) = \phi \) is correct.

127.3 Distributed Data Collection Strategy

Data collection in the similar sensing area in this paper we can concisely define as SSADC. Firstly, WSN becomes ad hoc network use hierarchical method to collect data from sensing area. Next, using fuzzy clustering to partition data area by using the changing of value of points. Finally, we can use HEED algorithm to select the head of cluster in certain partitioned area. It can represent changing of data by sampling the monitoring areas’ data. The criteria for electing of cluster head is to take reminder energy as main factor and to take the density of sensing points as the second factor. With the passage of time, similar area may be changed more or less. Therefore when the sensing error exceeds a certain value, which should do a new fuzzy clustering and reselecting the head of cluster to finish the job of data collection. The algorithm of data collection by using fuzzy clustering as follows:

Method:

Step 1:

During the period \( [t_{x} ,t_{y} ] \), through statistic we record the sensing data by \( X \), \( p_{i} \in SSA \) (similar sensing area);

Step 2:

As for vectors \( X = \{ p_{i}^{(j)} \} \left| {_{1 \le i \le m,1 \le j \le n} } \right. \) that with n elements and each has m dimensions, for standardized \( p_{i}^{(k)} \) that can be standardized by \( p_{i}^{(k)} = \frac{{p_{i}^{(k)} - \mathop {Min}\limits_{1 \le i \le m} \{ p_{i}^{(k)} \} }}{{\mathop {Max}\limits_{1 \le i \le m} \{ p_{i}^{(k)} \} - \mathop {Min}\limits_{1 \le i \le m} \{ p_{i}^{(k)} \} }},1 \le k \le n \), to compact data into (0,1) and store the result in \( M_{n \times m} \);

Step 3:

According to the sensing similarity \( SimSensoring(p_{i} ,p_{j} ) \), compute the fuzzy similar Matrix \( SimMatrix[n][n] \);

Step 4:

For the given level of similarity \( \lambda \), through the maximum tree algorithm of fuzzy clustering to get clustering result \( C = \{ c^{(1)} , \ldots ,c^{(k)} \} \);

Step 5:

If for every clustering result there exist two max dissimilar points that satisfy \( \frac{{\sqrt {\frac{1}{m}\sum\limits_{k = 1}^{m} {(p_{i} - p_{j} )^{2} } } }}{{Max\{ p\} - Min\{ p\} }} < \alpha \), then set \( \lambda = \lambda + h \) (\( h \) is step length) and go to step (4) to redo cluster analysis;

Step 6:

For every \( c_{i} \in C \) in clusters result \( C \), we use HEED method to elect the head of cluster in every \( c_{i} \) to sample data and transmit it;

Step 7:

At an interval of time β, the system will check periodically if there exist two max dissimilar points \( \mathop {Min}\limits_{{p_{i} ,p_{j} \in SimArea}} \{ SimSensoring(p_{i} ,p_{j} )\} \) it satisfies \( \frac{{\sqrt {\frac{1}{m}\sum\limits_{k = 1}^{m} {(p_{i} - p_{j} )^{2} } } }}{{Max\{ p\} - Min\{ p\} }} > \alpha \), then go to Step 1 to recompute similar area;

Step 8:

The end of this algorithm.

For the convenience of data querying, we build a hash table \( I(C) \) to index the final clustering result. In the similar sensing area to take HEED algorithm to select the head of clustering for balance the energy and represent a similar areas’ sensing data.

127.4 Experimental Results and its Analysis

We use MATLAB7.0 to analyse \( 100\times100\,{\text{m}} \) agriculture plant area sensing data. In the monitoring area we randomly and uniformly laid out 300 soil humidity sensors, the collecting point SINK locates in coordination (0,100). We deploy the WSN to compare the performance of our method for collecting data to LEACH, LEACH-C and HEED. Suppose the sensor’s initial energy is 0.5 J, \( E_{elec} \) = 50 \( \text{nJ/bit} \), \( \varepsilon_{s}=0.0013\,{\text{pJ}/(\text{bit}.\text{m}^{4} )}\), \( E_{com}=5\,{\text{nJ}/\text{bit}}\), the length of the message is 500 Bytes, the delay of sending and receiving is 25 \( {\mu \text{s}} \). The test length is 1200 s and the intervals to repartition the similar area is 120 s.

Through the experiment in Fig. 127.1 we can see HEED method forming speed of the cluster has certainly improved compared to LEACH and LEACH-C, which thought the cost of the inner cluster communication after forming a cluster and select a cluster head that is more suitable to do the task of data transmit. Because this paper also uses HEED to choose the head of cluster in similar area it will be optimized in each partitioned field. What’s more, we utilize cluster head to transmit sensing data to represent regional data it will save a lot of cost of energy in data transmission.

Fig. 127.1
figure 1

The comparison of 4 cluster head selection methods in total energy cost

Full size image

127.5 Conclusion

Through the fuzzy clustering method to split the whole monitoring area into many similar sensing areas. As for each similar sensing region we elect the head of cluster by using HEED algorithm to sampling data to represent the areas’ sensing data. By using a distributed data collection method to collect monitoring data with less quantity of communication, to decrease the cost of energy in the whole network, to decrease data fusion calculation to improve the reliability of data, finally we can prolong the life cycle of WSN.