Correlation Analysis of Temperature Measurements from Wireless Sensor Nodes
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Transcript of Correlation Analysis of Temperature Measurements from Wireless Sensor Nodes
Distributed Measurement Systems
Nestor Michael C. Tiglao IST/UTL INESC-‐ID Lisboa N etworks and Mobility Group
! Task Description ! Experimental setup ! Methodology ! Discussion of the results ! Conclusion
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! Objective ! Implement a setup to analyze correlation of acquired data from two systems
! Outputs ! Temperature measurement ! Data transmission and logging ! Graphical representation of measured data ! Correlation of measurements
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! High sampling rates caused lost data and erroneous sensor readings
! WSN nodes do not have real-‐time clocks ! We stamped each sensor reading with the global time at the base station
! Clock skews are not too bad
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! Two Crossbow MicaZ motes ! Readings sent to a PC-‐based base station ! Base station logs the sensor readings ! Matlab used for offline time series analysis
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! Actual Measurements ! Considered different sampling rates and observation periods
! Varied the location of the WSN nodes ! Spatio-‐Temporal Correlation Analysis
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! Considerations ! Acquired measurements are time series data ! Temperature measurements are slow-‐varying, mostly flat, aperiodic
! Limited applicability of FFT-‐based analysis ! Correlation Analysis
! Longest Common Subsequence ! Wavelet-‐based Semblance Analysis
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0 5 10 15 20 250
100
200
300
400
500
600
700
800
900
1000Single-Sided Amplitude Spectrum of y(t)
Frequency (Hz)
|Y(f)
|
data1data2
! Euclidean distance metric
! Longest Common Subsequence (LCSS) provides more flexibility and robustness to noise
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2
1( , ) ( [ ] [ ])
N
tD x y x t y t
=
= −∑
Euclidean Distance LCSS
0 100 200 300 400 500 600 700 800 900 1000-3
-2
-1
0
1
2
3Minimum Bounding Envelope (MBE) for LCSS
0 100 200 300 400 500 600 700 800 900 1000
Point Correspondence, Similarity [δ=1,ε =0.3] = 0.53582
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Original sensor readings
Similarity = 0.53582
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Signal 2 shifted 10 times units
Similarity = 0.61405
0 100 200 300 400 500 600 700 800 900 1000-3
-2
-1
0
1
2
3Minimum Bounding Envelope (MBE) for LCSS
0 100 200 300 400 500 600 700 800 900 1000
Point Correspondence, Similarity [δ=1,ε =0.3] = 0.61405
0 100 200 300 400 500 600 700 800 900 1000-3
-2
-1
0
1
2
3Minimum Bounding Envelope (MBE) for LCSS
0 100 200 300 400 500 600 700 800 900 1000
Point Correspondence, Similarity [δ=1,ε =0.3] = 0.93189
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Signal 2 shifted 23 times units
Similarity = 0.93189
0 100 200 300 400 500 600 700 800 900 1000-3
-2
-1
0
1
2
3
4Minimum Bounding Envelope (MBE) for LCSS
0 100 200 300 400 500 600 700 800 900 1000
Point Correspondence, Similarity [δ=1,ε =0.3] = 0.92879
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Similarity = 0.92879
Signal 2 shifted 24 times units
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0 500 1000 1500 2000 2500 3000-2
-1
0
1
2
3Minimum Bounding Envelope (MBE) for LCSS
0 500 1000 1500 2000 2500 3000
Point Correspondence, Similarity [δ=1,ε =0.3] = 0.20939
Signal 1: window Sensor 2: cabinet top
Similarity = 0.20939
! Correlation between the phase angles ! Fourier transform-‐based analysis assumes frequency content is constant with time (or position)
! Wavelet-‐transform-‐based analysis allows changes in behavior to be analyzed ! Better temporal and spatial resolution ! One approach is cross-‐wavelet transform
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FOURIER TRANSFORM-‐BASED
! R(f) is the real component ! I(f) is the imaginary
component
WAVELET-‐BASED
! CWT is the continuous wavelet transform
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( )( )
1,21
1,2
*1,2 1 2
1,2
cos
CWTwhere tan
CWT
CWT CWT CWT
CWT
S
A
θ
θ −
=
ℑ=
ℜ
= ×
=
1 2 1 22 2 2 2
1 1 2 2
( ) ( ) ( ) ( )( )( ) ( )
1 perfect correlation0 no correlation1 anticorrelation
R f R f I f I fS fR f I R f I
+=+ +
+⎧⎪= ⎨⎪−⎩
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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
x 107
23.223.423.623.8Data 1
CWT
Wav
elen
gth
100 200 300 400 500 600 700 800 900200400600
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
x 107
23.524
Data 2
CWT
Wav
elen
gth
100 200 300 400 500 600 700 800 900200400600
Semblance
Wav
elen
gth
100 200 300 400 500 600 700 800 900200400600
Both sensors located near the window
Observation period is ~15 hours
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Sensor 1: window Sensor 2: cabinet top
Observation period is ~2 days
2 4 6 8 10 12 14 16
x 107
222324
Data 1
CWT
Wav
elen
gth
500 1000 1500 2000 2500
10002000
2 4 6 8 10 12 14 16
x 107
23.524
24.5Data 2
CWT
Wav
elen
gth
500 1000 1500 2000 2500
10002000
Semblance
Wav
elen
gth
500 1000 1500 2000 2500
10002000
! Correlation analysis tools allows us to effectively analyze the correlation of two or more independent sensor readings
! New tools, e.g. Wavelet-‐based methods, can be used to perform improved spatio-‐temporal correlation at different time scales
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! Crossbow MicaZ 2.4 GHz, http://www.xbow.com/Products/productdetails.aspx?sid=164
! Matlab, http://www.mathworks.com/ ! Cooper, G. R. and Cowan, D. R. 2008. Comparing time series
using wavelet-‐based semblance analysis. Comput. Geosci. 34, 2 (Feb. 2008), 95-‐102. DOI= http://dx.doi.org/10.1016/j.cageo.2007.03.009
! Tutorial: Hands-‐On Time-‐Series Analysis with Matlab, International Conference on Data Mining, Dec. 18-‐22, 2006
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Distributed Measurement Systems