Structural Health Monitoring in WSNs by the Embedded Goertzel Algorithm

Structural Health Monitoringin WSNs by the

Embedded Goertzel Algorithm

Maurizio Bocca, M.Sc.Department of Automation and Systems

TechnologyAalto University School of Electrical Engineering

www.wsn.tkk.fi

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What is Structural Health Monitoring?

Maurizio Bocca – ICCPS 2011, Chicago, IL, USA, 14.4.2011

Accurate diagnosis of the health of civil infrastructures from data collected by sensors

Brooklyn Bridge, NYCAfricanElephant

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How long can I keep it like this?

I suggest an immediate surgery to repair itIt’s a torn ligamentYou are sick!It’s in the kneeWhere?How bad is it?

A SHM system should be able to successfully carry out 4 tasks

Detect Localize Quantify Assess

COMPLEXITYMaurizio Bocca – ICCPS 2011, Chicago, IL, USA, 14.4.2011

Damage detectionDamage localizationDamage quantificationAssessment of the remaining lifetime of the structure

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Outline of the Talk


Goertzel algorithm (GA)

WSN architecture

Experimental evaluation

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Why the Goertzel Algorithm for SHM?

• Classic application: DTMF• Compared to the FFT, the GA:

allows to efficiently calculate the amplitude of the frequency spectrum at specific bins (frequencies of interests, fi)

works iteratively (no need to store the acceleration signals)

the number of samples (N) does not need to be a number power of 2


GA computationssample acquisition

samplingSTART

t

samplingEND

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Goertzel Algorithm Parameters

• 3 key parameters (set by the end-user): Sampling frequency (fs) Distance (db) between two consecutive bins on the

frequency axis (resolution r = 1/ db) Vector of frequencies of interest (fi)

• GA can be thought of as a 2nd-order IIR filter for each frequency of interest:


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1 2

1

1 2cos 2

i

s

i

fZ

f

fi

s

eH Zf Z Zf

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From the Goertzel Algorithm...

• Number of samples (N) to be collected to obtain the fixed resolution (r):

• Bins (k) corresponding to the selected frequencies of interest (fi):

• Coefficients (c) used in the iterations:

• Equations iteratively executed by the nodes during the sampling:

• Squared magnitude of the spectrum:


s

b

fNd

0.5 i

s

N fk

f

2cos 2 kcN

0 1 2

2 1

1 0

iq c q q sq qq q

si: last collected sample

q1 and q2 store the results of thetwo previous iterations

2 2 21 2 1 2i i i ii iX N q q q q c

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...to Transmissibility Functions

• Transmissibility is the result of the interference of vibrations propating and reflecting along the structure

• TFs achieve environmental invariability

• Structural damages modify the spectrums of the acceleration signals collected by the nodes

• Damage indicator:


2

1

2

1

2

1 22

,j

j

i

i

f

ss f fs f

sf f

X fT f f

X f

si and sj: sensor nodes(fi ,f2): range of frequencies of interest

1 2 1 2

1 21 2

, ,,

,

j j

i ij

i j

i

TEST REFs ss ss

r s REFss

T f f T f fD f f

T f f

REF: reference

(undamaged)TEST: current condition (damaged?)

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Flow of the Application


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• Sensinode U100 Micro.2420:• MSP430 MCU (10 kB RAM, 48 kB

Flash)• 500 kB external serial data Flash• CC2420 transceiver (ZigBee,

802.15.4 compatible, 2.4 GHz band, 250 kbps theoretical bandwidth)

• 3 axis digital accelerometer:• ±2g/±6g selectable full scale• 12/16 bit representation• Sensitivity: 76.4 mV/m/s2

Sensor Nodes Hardware


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Testbed Setup


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6

8

1

2

47

3

D3

D4

D1

D2

Electro-Dynamic Shaker

Damaged Cross Bar

WOODEN TRUSS STRUCTURE: 420 cm long, 65 cm wide, 34 cm high, 44 kg

D1, D2, D3, D4:500 g weight

D5: 27.6% stiffness reductionD6: 55.2% stiffness reduction

sensor node

Random noise excitation

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Experimental Validation


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D5: 27.6% stiffness reduction

D6: 55.2% stiffness reduction

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Centralized VS Distributed

• Life time increase: 52%


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Centralized VS Distributed

• Latency reduction: 80%


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Thank You!

[email protected]://autsys.tkk.fi/MaurizioBocca

Questions?

mailto:[email protected]

Structural Health Monitoring in WSNs by the Embedded Goertzel Algorithm

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