際際滷

際際滷Share a Scribd company logo

Energy Efficient Compression of Shock Data using Compressed Sensing

Jerrin Panachakel
Jerrin Panachakel

The document discusses using compressed sensing to efficiently compress shock data from avionics components. It describes how shock data is sparse in multiple domains and compressed sensing offers lower computational complexity than other compression methods while achieving similar compression efficiency. The document outlines the mathematics behind compressed sensing and recovery algorithms, and evaluates the performance of compressed sensing on shock data compared to discrete cosine transform and wavelet thresholding in terms of percentage root mean square difference, compression ratio, and execution time. Compressed sensing was able to compress shock data almost 1000 times faster than discrete wavelet transform while satisfying the constraints of low computational complexity and minimum error.

1 of 25
Energy Ef鍖cient Compression of Shock Data using Compressed Sensing Jerrin Thomas Panachakel, Finitha K.C., September 2, 2016
Overview Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 2
Introduction Avionics components encounter shock from several sources Components should be tested for reliability Shock data: acceleration v/s time plot Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 3
Problem Compression of Shock Data Constraints Computational complexity should be low Error should be minimum Why CS? Shock data is sparse in multiple domains Has lower computational complexity Has almost equal compression ef鍖ciency Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 4
Shock Data (1/2) Plot of magnitude of shock pulses v/s time Causes1: Rocket motor ignition Staging events Deployment events Measured using accelerometers 1Tom Irvine. An Introduction to the Vibration Response Spectrum. In: Rev C, Vibrationdata (2000). Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 5
Shock Data (2/2) source: https://www.youtube.com/watch?v=KZVgKu6v808 Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 6
Shock Respose Spectra Calculated from acceleration time history For estimating damage potential For estimating integrity of shock data Figure: SRS Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 7
Shock Respose Spectra- Calculation (1/2) Figure: SRS Model ni = Ki Mi (1) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 8
Shock Respose Spectra- Calculation (2/2) (a) Shock data and response to SDOF systems (b) Shock data and Shock Response Spectra data Figure: Shock data and SRS Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 9
Integrity from SRS (a) SRS of a saturated shock data (b) SRS of a good shock dataJerrin Thomas Panachakel jp@ee.iisc.ernet.in 10
Compressed Sensing (CS)-Motivation Why go to so much effort to acquire all the data when most of what we get will be thrown away ?2 N samples acquired but only K are required Basic requirement, sparsity Figure: Comparison between sparse signal and compressible signal 2Jon Dattorro. Convex optimization and Euclidean distance geometry. Meboo Publishing USA, 2005. Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 11
Mathematics behind CS (1/3) x = N i=1 sii (2) weighing coef鍖cients, si =< x, 率 >, x RN or equivalently, x = 率s (3) y = 陸x (4) using (3), y = 陸率s = s (5) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 12
Mathematics behind CS (2/3) Recoverable if the four columns are LI For M measurements, all M K sub-matrices are ideally close to orthonormal basis RIP: 1 ||陸v||2 ||v||2 1 + Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 13
Mathematics behind CS (3/3) Design of RIP matrix is almost impossible RIP matrices are around us!3 iid Gaussian iid Bernoulli M cKlog(N K ) Figure: Gerhard Richer- 4096 Farben 3Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 14
Recovery (1/3) Solution to 陸s = y lies in the translated null space of 2 recovery: S = argmin||s ||2, such that S = y Figure: 2 minimization Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 15
Recovery (2/3) 0 recovery: S = argmin||s ||0, such that S = y Computationally complex 1 recovery: S = argmin||s ||1, such that S = y Figure: 1 minimization Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 16
Recovery (3/3) Figure: Sparse signal and its reconstruction Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 17
Sparsity Analysis (a) Time (b) DCT (c) Haar (d) Daubechies Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 18
Performance Metrics Percentage Root Mean Square Difference: [1] PRD = N n=1 (x[n] x[n])2 N n=1 (x[n] 俗x[n])2 100% (6) Compression Ratio: [1] CR = Norg Ncomp Norg 100 (7) Execution time Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 19
Time Domain (a) (b) (c) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 20
Shock Respnse Spectra (a) (b) (c) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 21
PRD v/s CR Figure: PRD v/s CR Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 22
Time v/s CR Figure: Execution Time v/s CR Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 23
Conclusion Shock data compression performed using CS CS inferior in terms of PRD for higher CR CS is almost 1000 times faster than thresholding based DWT compression Implemented technique satis鍖es the requirements Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 24
Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 25

More Related Content

Energy Efficient Compression of Shock Data using Compressed Sensing

  • 1. Energy Ef鍖cient Compression of Shock Data using Compressed Sensing Jerrin Thomas Panachakel, Finitha K.C., September 2, 2016
  • 2. Overview Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 2
  • 3. Introduction Avionics components encounter shock from several sources Components should be tested for reliability Shock data: acceleration v/s time plot Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 3
  • 4. Problem Compression of Shock Data Constraints Computational complexity should be low Error should be minimum Why CS? Shock data is sparse in multiple domains Has lower computational complexity Has almost equal compression ef鍖ciency Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 4
  • 5. Shock Data (1/2) Plot of magnitude of shock pulses v/s time Causes1: Rocket motor ignition Staging events Deployment events Measured using accelerometers 1Tom Irvine. An Introduction to the Vibration Response Spectrum. In: Rev C, Vibrationdata (2000). Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 5
  • 6. Shock Data (2/2) source: https://www.youtube.com/watch?v=KZVgKu6v808 Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 6
  • 7. Shock Respose Spectra Calculated from acceleration time history For estimating damage potential For estimating integrity of shock data Figure: SRS Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 7
  • 8. Shock Respose Spectra- Calculation (1/2) Figure: SRS Model ni = Ki Mi (1) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 8
  • 9. Shock Respose Spectra- Calculation (2/2) (a) Shock data and response to SDOF systems (b) Shock data and Shock Response Spectra data Figure: Shock data and SRS Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 9
  • 10. Integrity from SRS (a) SRS of a saturated shock data (b) SRS of a good shock dataJerrin Thomas Panachakel jp@ee.iisc.ernet.in 10
  • 11. Compressed Sensing (CS)-Motivation Why go to so much effort to acquire all the data when most of what we get will be thrown away ?2 N samples acquired but only K are required Basic requirement, sparsity Figure: Comparison between sparse signal and compressible signal 2Jon Dattorro. Convex optimization and Euclidean distance geometry. Meboo Publishing USA, 2005. Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 11
  • 12. Mathematics behind CS (1/3) x = N i=1 sii (2) weighing coef鍖cients, si =< x, 率 >, x RN or equivalently, x = 率s (3) y = 陸x (4) using (3), y = 陸率s = s (5) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 12
  • 13. Mathematics behind CS (2/3) Recoverable if the four columns are LI For M measurements, all M K sub-matrices are ideally close to orthonormal basis RIP: 1 ||陸v||2 ||v||2 1 + Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 13
  • 14. Mathematics behind CS (3/3) Design of RIP matrix is almost impossible RIP matrices are around us!3 iid Gaussian iid Bernoulli M cKlog(N K ) Figure: Gerhard Richer- 4096 Farben 3Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 14
  • 15. Recovery (1/3) Solution to 陸s = y lies in the translated null space of 2 recovery: S = argmin||s ||2, such that S = y Figure: 2 minimization Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 15
  • 16. Recovery (2/3) 0 recovery: S = argmin||s ||0, such that S = y Computationally complex 1 recovery: S = argmin||s ||1, such that S = y Figure: 1 minimization Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 16
  • 17. Recovery (3/3) Figure: Sparse signal and its reconstruction Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 17
  • 18. Sparsity Analysis (a) Time (b) DCT (c) Haar (d) Daubechies Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 18
  • 19. Performance Metrics Percentage Root Mean Square Difference: [1] PRD = N n=1 (x[n] x[n])2 N n=1 (x[n] 俗x[n])2 100% (6) Compression Ratio: [1] CR = Norg Ncomp Norg 100 (7) Execution time Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 19
  • 20. Time Domain (a) (b) (c) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 20
  • 21. Shock Respnse Spectra (a) (b) (c) Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 21
  • 22. PRD v/s CR Figure: PRD v/s CR Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 22
  • 23. Time v/s CR Figure: Execution Time v/s CR Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 23
  • 24. Conclusion Shock data compression performed using CS CS inferior in terms of PRD for higher CR CS is almost 1000 times faster than thresholding based DWT compression Implemented technique satis鍖es the requirements Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 24
  • 25. Jerrin Thomas Panachakel jp@ee.iisc.ernet.in 25