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Goal-oriented wavelet data reduction and the application to smart infrastructure

Goal-oriented wavelet data reduction and the application to smart infrastructure. Jun. 1, 2009 by Chiwoo Park. * the number of deficient bridges in the U.S as of December 2008 (US Department of Transportation). Motivating problem : Smart infrastructure.

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Goal-oriented wavelet data reduction and the application to smart infrastructure

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  1. Goal-oriented wavelet data reduction and the application to smart infrastructure Jun. 1, 2009 by Chiwoo Park

  2. * the number of deficient bridges in the U.S as of December 2008 (US Department of Transportation) Motivating problem : Smart infrastructure • The 25% of nation's 601,411 bridges are either as structurally deficient or functionally obsolete. Lots of monitoring and maintenance are required.

  3. Motivating problem : Smart infrastructure • Sensor networks emerge as one of the key technologies for efficient maintenance. In the current smartest bridge, only 323 sensors monitor the span for structural weakness and they all are wired by cables. St. Anthony Falls Bridge in the Mississippi river Example: Strain Gauges * Courtesy of BusinessWeek

  4. Sensor Processor Radio Processor Power Consumption Radio Power Consumption Processor Active mode Sleep mode Radio module Transmission ATMega 128 (MicaZ) 4nJ/instr 30μW CC2420 ZigbeeRadio (MicaZ) 430nJ/bit PXA255(Stargate) 1.1nJ/instr 20μW 802.11 Radio (Stargate) 90nJ/bit Battery Motivating problem : Smart infrastructure • The next generation will be wireless because that’s much cheaper, enabling thousands of sensors to be installed. However, how will thousands or millions of sensors be powered? vs. Issues • Digesting all the data streaming • Providing power to operate wireless sensors • Energy harvesting technology • Harvest the vibrations of the bridges • by an aircore tubular linear generator which responds to one of the natural vibration frequencies of the bridge Solutions • Reduce data transmission • Use energy harvesting

  5. Sense Reduce data Transmit Problem: data reduction on sensors • Want to formulate a data reduction method so that it reduces as much data as possible if we do not lose the capability to detect structural weakness. Features only relevant to structural weakness Vibration sensor • OBJECTIVE: • Minimize the size of data transmitted to the central control systems • Minimize the computation burden on sensors • Maximize the damage detection capability Vibration on bridges

  6. Examples • General wavelet-based threshold • Lada’s RRE Data reduction: General function approximation view • We usually approximate the given signal with a finite number of basis functions minimizing the MSE. p

  7. Data reduction: General function approximation view • Basically, such a general approach is to try to fit in the original data. Getting the approximate of small p basis is one of the goals of our formulation, but not include the maximization of damage detection capabilities. p Fitting errors = residual energy Penalty on model complexity Avoid keeping too many basis

  8. Goal-oriented formulation • We propose a single formulation incorporating all of our goals. This term just explains the type-II error. x: the shift on beta caused by structural damages

  9. Experiment: hardware • We tried to have experimental verification of the new formulation Actuator • AGILENT 33220A waveform generator • Generate 50MSa/s (mega sample / s) Sensor • INSTEK GDS-820S digital storage oscilloscope • Sample 100MSa/s (mega sample / s) Experimental setup I: normal beam (300 signals sampled) Experimental setup II and III: abnormal beam (462 signals sampled)

  10. Experiment: procedure 300 samples (Experimental setup I) 100 samples 150 samples (Experimental setup II) 312 samples (Experimental setup III) Random sampling Damage detector (T2 < UCL) 200 samples Training data Data Reduction (β1..p) 200 Reduced dataset Data reduction ratio (R) α error β errors

  11. USE QUADRATURE for Integration DP USE L0 norm = p PN Experiment: procedure • We implemented the goal-oriented approach in a very simple form. Data Reduction (β1..p) One signal discretely sampled to 50k points Wavelet transform (Function approximation by wavelet basis) β1 β2 β3 β4 scales β5 β6 β7 β8 β9 … .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. βn time Goal-oriented data reduction (subset selection) Minimize L’(p) = - Detection Power (DP) + Penalty on complexity (PN) DP PN

  12. Experiment: numerical results • The following numerical results show that general wavelet thresholding methods keep too many coefficients. The goal-oriented formulation is one of the top performers in the list. Goal-oriented data reduction Summary statistics for damage severity Wavelet thresholding

  13. Cumulative amount of information, covariance (A|B) covariance (A, B) 1- Experiment: numerical results KEY OBSERVATION 90% • Redundancy still exists. • But, much less redundant are the wavelet coefficients selected by the goal-oriented approach B A Goal-oriented method chose RREs chose

  14. Experiment: numerical results • We can see significant different in the wavelet coefficients from a normal beam and a damaged one. Wavelet map for the normal beam Wavelet map for the damaged beam Regions explained by the selected wavelet coefficients

  15. Thank you for attention.

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