Data Collection Optimization Method for Wireless Sensor Networks Based on Linear Regression

Abstract

In the event monitoring applications of wireless sensor networks, the sensing data collected by sensor nodes near the same monitoring area has a great spatial-temporal correlation. In order to reduce the amount of data transmission in the network and the energy consumption of communication among nodes, an energy-efficient distributed data collection optimization strategy based on linear regression for wireless sensor networks is proposed. linear regression model of local sensing data is constructed to represent and predict the actual sensing data monitoring values of sensor nodes. Within the allowable range of errors, the node does not need to transmit the actual monitoring sensing data to the sink node, but only transmits the parameter information of the regression model basis function. Without losing the basic structural characteristics of data, the communication overhead caused by frequent data transmission between sensor nodes is effectively reduced, and the linear regression model of sensing data adopts the incremental update method with low computational complexity. he simulation results show that the data collection optimization strategy based on linear regression can effectively predict and estimate perceptual data with less network energy consumption, and achieve the goal of reducing network energy consumption.

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Data Collection Optimization Method for Wireless Sensor Networks
Based on Linear Regression
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AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
1
Data Collection Optimization Method for Wireless Sensor
Networks Based on Linear Regression
Meng Zhang*, Xiaomei Zhang and Yinghui Huang
School of Information Science and Technology, Nantong University, Nantong,
Jiangsu, 226019, China
*18036160804@163.com
Abstract. In the event monitoring applications of wireless sensor networks, the sensing data
collected by sensor nodes near the same monitoring area has a great spatial-temporal
correlation. In order to reduce the amount of data transmission in the network and the energy
consumption of communication among nodes, an energy-efficient distributed data collection
optimization strategy based on linear regression for wireless sensor networks is proposed.
linear regression model of local sensing data is constructed to represent and predict the actual
sensing data monitoring values of sensor nodes. Within the allowable range of errors, the node
does not need to transmit the actual monitoring sensing data to the sink node, but only
transmits the parameter information of the regression model basis function. Without losing the
basic structural characteristics of data, the communication overhead caused by frequent data
transmission between sensor nodes is effectively reduced, and the linear regression model of
sensing data adopts the incremental update method with low computational complexity. he
simulation results show that the data collection optimization strategy based on linear regression
can effectively predict and estimate perceptual data with less network energy consumption, and
achieve the goal of reducing network energy consumption.
1. Introduction
Data collection is the basic function of wireless sensor networks and the basis of most monitoring
applications. The main research goal of data collection technology in wireless sensor networks is to
reduce the energy consumption of the network, prolong the life cycle of the network, and avoid the
huge overhead of redeploying the wireless sensor network monitoring system in the process of data
collection.
At the Moboicom 2002 meeting, Deborah Estrin pointed out in an invitation report that the energy
required for a sensor node to transmit 1 bit of information 100 m away is equivalent to the energy
consumed to execute 3,000 computational instructions. Sahingoz compared the power consumption of
Mica2dot nodes in communication and computation modes, and found that transmitting 1 bit data is
equivalent to running 2090 clock cycles of node microcontrollers. It proves that the energy
consumption of nodes is much less than that of communication. That is to say, the main factor
affecting the total energy consumption of wireless sensor networks is the communication energy
consumption in networks [1].On the basis of node clustering, Slepian-Wolf bound coding and other
distributed source coding techniques are used to compress the sensing data information and optimize
the information rate allocation in the cluster, so as to minimize the communication energy
consumption [2] [3].Zhang J, Tang J, Chen F synthesize the advantages of prediction model and
clustering technology, and propose a hierarchical data collection framework for wireless sensor

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
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networks based on integrated adaptive prediction model. In this framework, cluster head implements
data collection and effective prediction analysis of cluster nodes. According to the analysis results of
network state and performance, the energy consumption of communication and prediction calculation
is balanced, and the prediction model is adaptively selected to achieve energy-efficient data
aggregation processing in wireless sensor networks[4]. If considering from the aspect of node
scheduling, it is also an effective way to save energy consumption by allocating and optimizing the
active slots of nodes, using stochastic Petri net model and designing reasonable scheduling strategy to
find a more suitable sleep wake-up mechanism for nodes[5][6][7].
Regression analysis is a statistical analysis method to determine the quantitative relationship
between two or more variables. In the application of event monitoring sensor networks, sensing data
has temporal and spatial correlation to a certain extent, which reduces the network energy
consumption caused by a large amount of data transmission. In this paper, a linear regression model is
established based on historical data measured by regression analysis method. By solving the
parameters of the corresponding base function of the model, the nodes only transmit the relevant
parameter vectors, which reduces the amount of redundant data transmission. Moreover, the model can
receive new actual measurements by simple incremental updating method, and the parameters of the
basis function can also be solved by the linear regression model constructed at any time.
2. Distributed linear regression model for sensor networks
According to the specific application environment of the network and the performance indicators of
storage space and processing capacity of sensor nodes, the nearest sensing datas of sensor nodes in a
certain time interval are selected. Assuming that where and represent sampling time points, can be
affected by measurement errors. Using perceptual datas to construct functions. The approximation
error is very small (within the confidence interval of the data collected by the monitoring system). The
form of function depends on the specific problem. Here can be expressed in the form of equation (1):
)()( tAtp j
n
jj

=

(1)
The number of neutral terms is
n
and the specific basis function
j
A
depend on the actual problem.
In general, the selected basis function can be
1
)( −
=j
jttA
. Then the equation (1) can be expressed as
the t-th polynomial of
1−n
, that is:
12
321 ...)( −
++++= n
nttttp

(2)
Choosing
mn =
can calculate the corresponding value exactly, but it is easy to interfere with the
data when calculating higher-order functions. When predicting the corresponding
p
value of
unforeseen
t
, its accuracy will be affected. It is better to choose a value far less than
m
, that is
mn 
.By choosing the values of coefficients, the estimated values of the functions corresponding to
the measured values are obtained. In wireless sensor network applications, a third-order polynomial
function model is constructed based on the assumption that 50 temperature measurements recently
collected by nodes are selected:
3
4
2
321
)( ttttp

+++=
; the estimated measurement value
)50,...,3,2,1( =ipi
is enough. And the nodes do not need to transmit 50 actual measurements. After
constructing the function model, only four parameter values, namely
4321 ,,,

, need to be
transmitted in the network as the compressed representation of measurement values, so the amount of
information transmission in the network is reduced. If the coefficients are obtained by linear
regression model, the polynomial representation model needs to be transformed into matrix
representation. In this way, the node does not need to solve the higher order polynomial solution, but
only needs to maintain the correlation matrix. Let the coefficient
n
dimension vector be

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
3
T
n),...,,( 21

=
.The m-dimension vector of the actual measured value is
T
m
pppp ),...,,( 21
=
.The basis function matrix of the corresponding time sampling point
i
t
is:












=
)(...)()(
............
)(...)()(
)(...)()(
21
22121
11211
mnmm
n
n
tAtAtA
tAtAtA
tAtAtA
U
For matrix element
()
ij j i
m A t=
)( ijij tAm =
, the predictive function m-Dimension vector
T
m
tptptpp ))(),...,(),(( 21
=
of equation (1) at
i
t
sampling time point is expressed as equation (3):
























=












mmnmm
n
n
mtAtAtA
tAtAtA
tAtAtA
U
tP
tP
tP
P




...
)(...)()(
............
)(...)()(
)(...)()(
)(
...
)(
)(
2
1
21
22121
11211
2
1
(3)
Then the approximation error vector

can be expressed as an equation, i.e.
Up

 = −
(4)
In order to minimize the approximation error

of the estimated value, the optimal objective is to
minimize the norm of the approximation error vector:
2 1/2
1
( ( ) )
m
i
i
Min
=
 = 

(5)
Combining equation (4) and (5) to optimize the objective, we can get:
22 2
11
( ( ) )
mm
ij j i
ii
Min U p u p

==
 = − = −

(6)
By calculating the differential of
2

for each
( 1,2,..., )
kkn

=
and making the result 0, the
minimum value of

can be obtained:
2
11
2( ) 0, [1, ]
mm
ij j i ik
ii
k
du p u k n
d


==
= − = =

(7)
According to equation (4), the following matrix equation equivalent to equation (7) can be deduced,
namely:
( ) 0
T
U y U

−=
(8)
( ) 0
T
U U y

−=
(9)
TT
U U U y

=
(10)
Because the defined base function is
1
() j
j
A t t −
=
, the base function matrix
U
is column full rank
matrix. For any column full rank matrix
U
, we can get that
T
UU
is positive definite, so
T
UU
exists.
According to equation (10), we can get the D solution of coefficient vector as follows:

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
4
1
()
TT
U U U y

−
=
(11)
Set















==
nnnn
n
n
T
AAAAAA
AAAAAA
AAAAAA
UUO
...
............
...
...
21
22212
12111
(12)















==
yA
yA
yA
pUk
n
T...
2
1
(13)
According to equation (12), (13), equation (11) can be written as:
kO 1−
=

, that is:
Ok

=
(14)
Among them,
O
is the quantity product matrix of the base function and
k
is the projection of the
base function of the measured value vector. So far, the optimal regression coefficients can be obtained
by solving the typical linear system of Equal Formula (14) with known measured values and basis
functions.
3. Model parameter optimization
In the application of event monitoring in wireless sensor networks, with the extension of monitoring
time, the amount of monitoring data collected by sensor nodes is also increasing. Due to the limitation
of energy, storage and processing capacity of sensor nodes, the nodes can only store sampled data for
a certain period of time. When the linear regression model is used to calculate the data representation
coefficients, the updating operation of the model can be calculated in the following incremental
way[8].
Assuming that the number product matrix
O
and the projection vector
k
of the basis function in
the sampling period from
1
t
to
1−m
t
have been calculated, the new measurements in
m
t
are as follows:















=
)()(...)()()()(
............
)()(...)()()()(
)()(...)()()()(
)(
21
22212
12111
mnmnmmnmmn
mnmmmmm
mnmmmmm
m
tAtAtAtAtAtA
tAtAtAtAtAtA
tAtAtAtAtAtA
tO















=
)()(
...
)()(
)()(
)( 2
1
mmn
mm
mm
m
tytA
tytA
tytA
tk
Then the number product matrix and projection vector of the basis function in the new sampling
period are as follows:
( ); ( )
mm
O O O t k k k t +  +
(15)

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
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The sliding window mechanism is used for matrix
O
and vector
k
scale control[9].The system
considers the calculation, storage capacity and application requirements of nodes to set the sliding
window size.With the increasing scale of matrix
O
and vector
k
, when the data of time t exceeds the
setting of sliding window, the updated matrix
O
and vector
k
can be calculated according to formula
(16).
( ); ( )
mm
O O O t k k k t −  −
(16)
To sum up, the node can take the regression coefficient
kO =

by calculating the linear system,
and the matrix and vector parameters of the linear regression system model can be updated
incrementally.
4. Experimental test and performance analysis
In order to test the performance of the proposed distributed data collection optimization algorithm,
simulation experiments are carried out for network energy consumption analysis. The test uses NS2
network simulation tools to build wireless sensor network scenarios. The algorithm was added to the
improved LEACH protocol, and the typical LEACH [10] and LEACH-C protocols [11] were
compared in data acquisition. At the same time, the optimization effect of network energy
consumption using the two protocols was analyzed.
In order to test the impact of clustering-based WSN data acquisition algorithm on the network life
cycle and overall energy consumption, the network simulation tool NS2 is selected as the simulation
platform[12].LEACH protocol is a typical distributed clustering routing protocol. Its hierarchical data
forwarding mechanism produces much less network energy consumption than planar routing protocol.
In the experiment, the linear regression optimization process is added to the LEACH improved
protocol. While the cluster head node receives the sensing information of the nodes in the cluster, it
also calculates the linear regression model, and replaces the original sensing data with the parameter
information of the transmission regression model. Cluster head implements the estimation, prediction
and fault-tolerant processing of sensing data. The protocol still retains the LEACH cluster head
selection method[13]. However, change the direct communication between cluster head node and Sink
node to multi-hop data transmission between cluster heads. In the experiment, 100 sensor nodes are
randomly deployed in the plane area of 100m*100m. The location coordinates of the base station are
set to (50,80). The initial energy of each node is 2J. The energy attenuation model is shown in Fig.1.
According to the principle of wireless communication, the transmission power decreases
exponentially with the increase of transmission distance. If the distance between the sending node and
the receiving node is
l
, when
l
is less than the constant threshold
Thres
l
, the transmission power
decreases as
2
l
, that is, the free space attenuation model. When
l
is greater than
Thres
l
, the
transmission power decreases as
4
l
, i.e. the multi-path attenuation model. The energy consumption
),( lkET
generated by transmitting
k
bits data is composed of two parts,
)(kE elecT −
energy
consumption of transmitting circuit and
),( lkE amT−
energy consumption of power amplifier, as
shown in equation (17). The energy consumption
)(kER
generated by receiving
k
bits of data is only
caused by the energy consumption of the circuit, as shown in equation (18).
Thresmelec
Thresselec
amTelecTT lllkEk
lllkEk
lkEkElkE +
+
=+= −− 2
2
{),()(),(


(17)
elecRR EkkEkE e lecT == −)()(
(18)

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
6
Eelec is the energy consumption of transmitting (receiving) 1 bit data.
s

and
m

represent the
energy required to transmit 1 bit data power amplifier under free apace attenuation model and multi-
path attenuation model, respectively.
K-bits data
packet
Transmitter
Circuit Amplifier
Receiver
Circuit
K-bits data
packet
Figure 1. Energy attenuation model for wireless communication.
In addition, the energy consumption of the first regression model for cluster head nodes is:
re CH com
E n E=
, where
CH
n
denotes the number of cluster head nodes and
com
E
denotes the energy
consumption of the first regression model for cluster head nodes. The simulation assumes that
5
CH
n=
,
50 /
elec
E nJ bit=
,
2
10 / /
spJ bit m

=
,
2
0.0013 / /
mpJ bit m

=
,
5/
com
E nJ bit=
, bandwidth is 1Mbps,
message length is 500 bytes, sending and receiving delay is
25 s

, simulation time is 500 seconds, the
time interval for each round of cluster head election is 20 seconds, the number of linear regression
model data sampling is 20, and the update period of regression model is 60 seconds.
Figure 2. shows the total energy consumption of cluster head nodes with LEACH protocol and
linear regression strategy at simulation intervals of 20 seconds. From the experimental results, it can
be seen that the total energy consumption of each round of cluster head nodes in LEACH protocol is
between 4J and 5J, and the total energy consumption of each round of cluster head nodes in linear
regression strategy is between 1.5J and 2.5J, which is significantly lower than that of LEACH protocol.
Although the energy consumption of cluster head nodes in LEACH protocol decreases after the
simulation time reaches 380s, it does not actually reduce the total energy consumption. However, with
the increase of simulation time, the energy consumption of nodes in the network has approached the
initial energy of nodes. Some selected cluster head nodes consume 2J energy in their work and die in
the middle. The total energy consumption of cluster head nodes in normal work is calculated
experimentally. In addition, the experimental results in Figure 2. show that the total energy
consumption of cluster heads with 60 s interval of simulation time increases, because cluster heads
need to recalculate the parameters of regression model in each update cycle of regression model and
send the updated parameters to the base station. In this way, more computing and communication
energy consumption is generated than other simulation time.

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
7
Figure 2. The relation between cluster head energy consumption and time.
In order to simulate the effect of measured changes on the energy consumption of the algorithm in
the simulation environment, the updating cycle of the linear regression model is set to 10s, 30s and 60s
respectively, and the total energy consumption of each cluster head node is shown in Figure 3. As can
be seen from the experimental results, the shorter the regress renewal period is, the higher the mutation
frequency is. The more times cluster head nodes calculate and retransmit regression model parameters
is, the greater the total energy consumption is. In practical environmental monitoring applications, the
frequency of updating and retransmitting the regression model parameters will be very low when the
measured values are in linear change in most cases, and the total energy consumption of the network
will also be reduced.
Figure 3. Node energy consumption in
different regression periods
Figure 4. The relationship between total
network energy consumption and simulation
time
In the simulation time of 500 seconds, when the update period is 60 seconds, the total energy
consumption of nodes with linear regression strategy is shown in Figure 4.
As can be seen from Figure 4, compared with the typical LEACH protocol and LEACH-C protocol,
the addition of linear regression strategy reduces the overall energy consumption of the network under
the same amount of data to be transmitted. After adding the regression model, when the simulation
time reaches 500s, the energy consumption of the network is about 100J less than that of LEACH and

AMIMA 2019
IOP Conf. Series: Materials Science and Engineering 569 (2019) 032064
IOP Publishing
doi:10.1088/1757-899X/569/3/032064
8
LEACH-C protocols. Because the correlation of sampling data in time is considered in the regression
strategy when nodes transmit sampling data, a linear regression model is constructed based on their
own historical sampling data. Within the closed range of monitoring error, nodes can upload
regression model parameters to represent actual sensing data. Although the calculation energy
consumption of nodes is increased, the communication energy consumption between nodes is greatly
reduced.
5. Conclusion
In this paper, the basic idea and principle of distributed data collection optimization algorithm for
wireless sensor networks based on linear regression are described in detail. The incremental updating
method of regression model parameters is introduced and the complexity of the algorithm is analyzed.
The distributed data acquisition process of the algorithm is illustrated by an example. In the test and
analysis of network energy consumption performance, a node is randomly deployed in the monitoring
area, and a cluster tree-based wireless sensor network model is constructed. The changes of total
energy consumption of cluster-head nodes with simulation time are tested, and the changes of total
energy consumption of cluster-head nodes with different regression cycles are set. The experimental
results show that the proposed distributed data collection optimization strategy based on linear
regression has good performance in prolonging the network life cycle and reducing the total energy
consumption of the network, which reflects the feasibility and energy efficiency of the algorithm.
Acknowledgments
Thank you very much for the help and encouragement of my colleagues in this unit, which helped me
to complete my paper.
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