1. Advanced Metrology Lab., Texas A&M University Goal-oriented wavelet data reduction and the application to smart infrastructure Jun. 1, 2009 by Chiwoo Park

2. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 2 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. * the number of deficient bridges in the U.S as of December 2008 (US Department of Transportation)

3. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 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. * Courtesy of BusinessWeek Example: Strain Gauges St. Anthony Falls Bridge in the Mississippi river

4. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 4 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? SensorProcessorRadio Battery vs. 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 Processor Power Consumption 20μW1.1nJ/instrPXA255(Stargate) 30μW4nJ/instrATMega 128 (MicaZ) Sleep modeActive modeProcessor  Reduce data transmission  Use energy harvesting Solutions  Digesting all the data streaming  Providing power to operate wireless sensors Issues Radio Power Consumption 90nJ/bit802.11 Radio (Stargate) 430nJ/bitCC2420 Zigbee Radio (MicaZ) TransmissionRadio module

5. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 5 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. Vibration sensor OBJECTIVE: ① Minimize the size of data transmitted to the central control systems ② Minimize the computation burden on sensors ③ Maximize the damage detection capability Vibration on bridges Features only relevant to structural weakness Sense Re du ce da ta Transmit

6. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 6 Data reduction: General function approximation view We usually approximate the given signal with a finite number of basis functions minimizing the MSE. Examples  General wavelet-based threshold  Lada’s RRE p

7. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 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. Fitting errors = residual energy Penalty on model complexity Avoid keeping too many basis p

8. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 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. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 9 Experiment: hardware We tried to have experimental verification of the new formulation Experimental setup I: normal beam (300 signals sampled) Experimental setup II and III: abnormal beam (462 signals sampled) Actuator  AGILENT 33220A waveform generator  Generate 50MSa/s (mega sample / s) Sensor  INSTEK GDS-820S digital storage oscilloscope  Sample 100MSa/s (mega sample / s)

10. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 10 Experiment: procedure 300 samples (Experimental setup I) 150 samples (Experimental setup II) 312 samples (Experimental setup III) 200 samples 100 samples Random samplin g 200 Reduced dataset Training data Data reduction ratio (R) α errorβ errors Damage detector (T 2 < UCL) Data Reduction (β 1..p ) Data Reduction (β 1..p )

11. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 11 Experiment: procedure Data Reduction (β 1..p ) Data Reduction (β 1..p ) One signal discretely sampled to 50k points Wavelet transform (Function approximation by wavelet basis) β1β1 β2β3β4 β5β6β7β8β9….. βn scales time Goal-oriented data reduction (subset selection) Minimize L’(p) = - Detection Power (DP) + Penalty on complexity (PN) DPPN We implemented the goal-oriented approach in a very simple form. DP PN USE L 0 norm = p USE QUADRATURE for Integration

12. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 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. Wavelet thresholding Summary statistics for damage severity Goal-oriented data reduction

13. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 13 Experiment: numerical results KEY OBSERVATION Redundancy still exists. But, much less redundant are the wavelet coefficients selected by the goal-oriented approach 90% Goal-oriented method chose RRE s chose BA Cumulative amount of information, covariance (A|B) covariance (A, B) 1-

14. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 14 Experiment: numerical results We can see significant different in the wavelet coefficients from a normal beam and a damaged one. Regions explained by the selected wavelet coefficients Wavelet map for the normal beamWavelet map for the damaged beam

15. Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009 15 Thank you for attention.