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

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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)

- The 25% of nation's 601,411 bridges are either as structurally deficient or functionally obsolete. Lots of monitoring and maintenance are required.

- 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

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

- 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

Sense

Reduce data

Transmit

- 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

Examples

- General wavelet-based threshold
- Lada’s RRE

- We usually approximate the given signal with a finite number of basis functions minimizing the MSE.

p

- 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

- 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

- 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)

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

USE QUADRATURE for Integration

DP

USE L0 norm = p

PN

- 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

- 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

Cumulative amount of information,

covariance (A|B) covariance (A, B)

1-

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

- 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

Thank you for attention.