Correlation Analysis of Temperature Measurements from Wireless Sensor Nodes

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Correlation Analysis of Temperature Measurements from Wireless Sensor Nodes

  1. 1. Distributed  Measurement  Systems   Nestor  Michael  C.  Tiglao   IST/UTL     INESC-­‐ID  Lisboa    N  etworks  and  Mobility  Group  
  2. 2. !  Task  Description   !  Experimental  setup   !  Methodology   !  Discussion  of  the  results   !  Conclusion   2  
  3. 3. !  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   3  
  4. 4. !  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   4  
  5. 5. !  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     5  
  6. 6. !  Actual  Measurements   !  Considered  different  sampling  rates  and   observation  periods   !  Varied  the  location  of  the  WSN  nodes   !  Spatio-­‐Temporal  Correlation  Analysis   6  
  7. 7. !  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   7  
  8. 8. 8   0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 900 1000 Single-Sided Amplitude Spectrum of y(t) Frequency (Hz) |Y(f)| data1 data2
  9. 9. !  Euclidean  distance  metric     !  Longest  Common  Subsequence  (LCSS)   provides  more  flexibility  and  robustness  to   noise   9   2 1 ( , ) ( [ ] [ ]) N t D x y x t y t = = −∑ Euclidean  Distance   LCSS  
  10. 10. 0 100 200 300 400 500 600 700 800 900 1000 -3 -2 -1 0 1 2 3 Minimum 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 10   Original   sensor   readings   Similarity  =   0.53582  
  11. 11. 11   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 3 Minimum 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
  12. 12. 0 100 200 300 400 500 600 700 800 900 1000 -3 -2 -1 0 1 2 3 Minimum 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 12   Signal  2   shifted  23   times  units   Similarity  =   0.93189  
  13. 13. 0 100 200 300 400 500 600 700 800 900 1000 -3 -2 -1 0 1 2 3 4 Minimum 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 13   Similarity  =   0.92879   Signal  2   shifted  24   times  units  
  14. 14. 14   0 500 1000 1500 2000 2500 3000 -2 -1 0 1 2 3 Minimum 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  
  15. 15. !  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   15  
  16. 16. FOURIER  TRANSFORM-­‐BASED     !  R(f)  is  the  real  component     !  I(f)  is  the  imaginary   component   WAVELET-­‐BASED   !  CWT  is  the  continuous   wavelet  transform   16   ( ) ( ) 1,21 1,2 * 1,2 1 2 1,2 cos CWT where tan CWT CWT CWT CWT CWT S A θ θ − = ℑ = ℜ = × = 1 2 1 2 2 2 2 2 1 1 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 perfect correlation 0 no correlation 1 anticorrelation R f R f I f I f S f R f I R f I + = + + +⎧ ⎪ = ⎨ ⎪−⎩
  17. 17. 17   0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 x 10 7 23.2 23.4 23.6 23.8 Data 1 CWT Wavelength 100 200 300 400 500 600 700 800 900 200 400 600 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 x 10 7 23.5 24 Data 2 CWT Wavelength 100 200 300 400 500 600 700 800 900 200 400 600 Semblance Wavelength 100 200 300 400 500 600 700 800 900 200 400 600 Both  sensors   located  near   the  window   Observation   period  is  ~15   hours  
  18. 18. 18   Sensor  1:   window   Sensor  2:   cabinet  top   Observation   period  is  ~2   days   2 4 6 8 10 12 14 16 x 10 7 22 23 24 Data 1 CWT Wavelength 500 1000 1500 2000 2500 1000 2000 2 4 6 8 10 12 14 16 x 10 7 23.5 24 24.5 Data 2 CWT Wavelength 500 1000 1500 2000 2500 1000 2000 Semblance Wavelength 500 1000 1500 2000 2500 1000 2000
  19. 19. !  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   19  
  20. 20. !  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   20  
  21. 21. Distributed  Measurement  Systems  

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