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