advanced metrology lab., texas a&m university goal-oriented wavelet data reduction and the...

Advanced Metrology Lab., Texas A&M University

Goal-oriented wavelet data reduction and the application

to smart infrastructureJun. 1, 2009 by Chiwoo Park

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Advanced Metrology Lab., Texas A&M UniversityPresented by Chiwoo Park on Jun 1, 2009

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)

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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

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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?

Sensor Processor Radio

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

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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 Reduce data Transmit

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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

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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

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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

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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)

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Experiment: procedure

300 samples(Experimental

setup I)


setup II)


setup III)

200 samples

100 samples

Random samplingRandom sampling

200 Reduced dataset

Training data

Data reduction ratio (R)

α error β errors

Damage detector (T2 < UCL)Damage detector (T2 < UCL)

Data Reduction(β1..p)


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Experiment: procedure



One signal discretely sampled to 50k points

Wavelet transform

(Function approximation by wavelet basis)

β1 β2 β3 β4

β5 β6 β7 β8 β9 … .. ..

.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. βn

scal

es

time

Goal-oriented data reduction

(subset selection)

Minimize L’(p) = - Detection Power (DP) + Penalty on complexity (PN)DP PN

We implemented the goal-oriented approach in a very simple form.

DP

PN USE L0 norm = p

USE QUADRATURE for Integration

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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

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KEY OBSERVATION

• Redundancy still exists.

• But, much less redundant are the wavelet coefficients selected by the goal-oriented approach

90%

Goal-oriented method chose

RREs chose

B A

Cumulative amount of

information,

covariance (A|B) covariance (A, B)1-

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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 beam Wavelet map for the damaged beam

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Thank you for attention.

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