bouabdellah kechar [email protected] oran university
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Bouabdellah KECHAR [email protected] Oran University Faculty of science – Department of Computer Science Algeria. Using Polynomial Approximation as Compression and Aggregation Technique in Wireless Sensor Networks. June 4, 2007 Workshop on Wireless Sensor Networks Marrakech - Morocco. - PowerPoint PPT PresentationTRANSCRIPT
Using Polynomial Approximation as Compression and Aggregation Technique
in Wireless Sensor Networks
Bouabdellah KECHAR
Oran University
Faculty of science – Department of Computer Science
Algeria
June 4, 2007Workshop on Wireless Sensor Networks
Marrakech - Morocco
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Outlines
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Introduction (1)
Characteristics of WSN
Important density
Limited processing speed
Limited storage capabilities
Limited power supply (energy)
And limited bandwidth
Need design and development of new protocols and algorithms at each level of WSN-layers stack (independently or using Cross layer approach) in order to minimize the dissipated power and consequently extend network lifetime
Values referenced here are resources available in MICA2mote
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Introduction (2)
The reduction of the volume of data to be transmitted in WSN constitutes the most convenient method to reduce energy consumption in a WSN.
This is motivated usually by the fact that processing data consumes much less power than transmitting data.
One way to achieve this goal is :
Data Compression and Aggregation
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Objective (1)
Sensor stack
Sensor Layer
Physical Layer
Sensor Channel
Network stack
Compression & aggregation
Transport Layer
Multihop Routing Protocol
WSN-MAC Layer
Transceiver Unit
Wireless Channel
Temperature, relative humidity, wind speed, … (Environmental readings)
Collected data
Polynomial approximation algorithms and
Local aggregation
Polynomial packet
(fixed or variable window)
IN OUT
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Objective (2)
Applications concerned ?Environmental monitoring
Temporal constraint is not required
Nature of analysis is qualitative
Resolution method ?Approach based on the theorem of Stone-Weierstrass(theory of approximation of functions) Compression
Protocol based on calculation of correlation coefficients between polynomials Local aggregation
Validation method ?Simulation using Matlab tool
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Related works
LTC (Lightweight Temporal Compression) [Schoellhammer & al 2004]
PREMON (PREdiction-based MONitoring) [Goel & al 2001]
TiNA (Temporal in-Network Aggregation) [Sharaf & al 2003]
CAG (Clustered AGgregation) [SunHee & al 2005]
TREG (TREe based data aGgregation) [Torsha & al 2005]
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Requirements and Constraints
Temporal coherency in physical phenomenon Environmental data as temperature, humidity and others, have a common property : continuous variation in time for relatively small temporal windows. The evolution of these properties is roughly linear
this characteristic of natural phenomena allows designers of applications to adapt the model of data collection.
Interpolation and approximationStone-Weierstrass theorem
Application scenario and suppositionsEvery sensor have: CPU, RAM, RADIO, protocols
Variation of error tolerated by application
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Algorithms of compression : Fixed WindowDim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
Sensed and collected data at time tj
Dim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
m: Polynomial degree
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Algorithms of compression : Fixed WindowDim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
Variation of error
Dim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
m: Polynomial degree
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Algorithms of compression : Fixed WindowDim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
m: Polynomial degree
Find a new polynomial while condition is true, otherwise save polynomial and transmit it
)1(
)()(
22
nn
EEnEVarErr
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Algorithms of compression : Fixed WindowDim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
Start Approximation using Least-Squares method
Dim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
m: Polynomial degree
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Algorithms of compression : Variable Window
Dim: number of readings by sequence
Tab: collected readings
Poly: polynomial coefficients
ni: sensor node object
VarErr: evaluation of polynomial and calculation of variation
WindowMin: minimal size of time window
WindowMax: maximal size of time window
OldDegree: Degree of last approximation
m: Polynomial degree
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Algorithms of compression : Variable Window
Sensed and collected data of initial window
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Algorithms of compression : Variable Window
Initialization
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Algorithms of compression : Variable Window
Check if the old polynomial is extensible
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Algorithms of compression : Variable Window
A new collected value is added and the old degree is saved
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Algorithms of compression : Variable Window
To limit the algorithm by a number of readings (WindowMax)
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Local Aggregation
Coefficient of correlation
YXYX
YXCov
*
),(,
11 , YX
n
iyixi yx
nYXCov
1
))((1
),( With
IDS tn V1 ….. Vn
Packet structureWithout compression
IDS tn P(ti)
Packet structureWith compression
Correlated polynomial Transmit juste
IDS tn
Packet structureWith compression
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Experiments and Simulation (1)
Compression ratio during one period
100Re
xradingNumbe
tsNumberCoefficiennRateCompressio
Algorithm with Fixed Window
Compression Quality vs Window SizeWith Tolerable error variation =0.1
Experiment: samples of 1000 readings (experimental, Temperature, Humidity and Wind speed) Environmental Real values
If we increase the number of readings, that do not imply automatically a corresponding better rate. Contrary, when the window sizes are reduced, the correlation is very expressive and then the approximation process is better.
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Experiments and Simulation (2)
Algorithm with Variable Window
Compression Quality vs Tolerable variation of error
Compression ratio fully depends on the tolerable variation of error, which implies the strong connection between the quality of data and the desirable compression ratio.
Temperature Humidity Wind Speed
Tolerable Error Variation
0.1 0.1 0.1
Compression Rate 15.09% 75.92% 64.21%
Restitution Rate 99.98% 100% 99.80%
Restitution Rate
This table shows that the majority of the values reconstituted by the evaluation of the polynomials will be in the specified margin
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Experiments and Simulation (3)
Comparison of compression rate
If we fix the variation of error at 0.1 and we consider an optimal size of the fixed window (80 readings) for the algorithm with fixed window, the algorithm with variable window is more powerful.
Experimental Data Temperature Humidity Wind Speed
ASFW Algorithm 78 % 27.55 % 83.37 % 80.83 %
ASVW Algorithm 15.14 % 15.09 % 75.92 % 64.21 %
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Contents
Introduction
Objective
Related works
Requirements and constraints
Algorithms of compression
Fixed window based
Variable window based
Local aggregation
Experiments and simulation
Conclusion and future works
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Conclusion
Data compression is an important technique to reduce communications and hence save energy in WSN.
Our proposed approach (New data compression and aggregation technique for WSN) is a simple idea but it is quite novel and interesting.
The results obtained are encouraged to follow this research direction.
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Perspectives
What are the computation cost and memory requirement at each sensor node ?
A comparison with other compression techniques in terms of accuracy and cost (like TiNA and LTC).
Additional experimental effort to prove the effectiveness of the approach (Energy calculation).
Extend the approach to Multi-objective WSN (several data types in the same network with cooperation capabilities)
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Questions & remarks
Thanks for your attention.
Using Polynomial Approximation as Compression and Aggregation Technique in Wireless Sensor Networks