shm in wsns by the embedded goertzel algorithm

Structural Health Monitoringin WSNs by the

Embedded Goertzel Algorithm

Maurizio Bocca, Janne Toivola, Lasse M. Eriksson,JaakkoHollmen, Heikki Koivo

Department of Automation and Systems Technology

Aalto University School of Electrical Engineering, Helsinki, Finlandwww.wsn.tkk.fi

1

Looking back at SHM

ICCPS 2011, Chicago, IL, USA, 14.4.2011

AIM: accurate diagnosis of the health of civil infrastructures from data collected by sensors

Brooklyn Bridge, NYCAfrican

Elephant

Few Facts about Finland

• It is extremely difficult to retrieve elephants…

• Extremely cold climate

Very rigid temperatures

Lots of snow and ice

• 187 888 lakes… 14 000 (approx.) public roads bridges

• 150-200 new bridges built every year

• Most of the bridges built in the 60’s and 70’s: Originally not engineered for the current volume and type of traffic

Approaching the critical “50-years maintenance check”

2ICCPS 2011, Chicago, IL, USA, 14.4.2011

The 4 levels of SHM

ICCPS 2011, Chicago, IL, USA, 14.4.2011

Damage detection

Damage localization

Damage quantification

Assessment of the remaining lifetime of the structure

COMPLEXITY

PATIENT:the monitored infrastructure

DOCTOR:the structural engineer

3

Outline of the Talk


Goertzel algorithm (GA) and Transmissibility Functions (TFs)

WSN architecture

Experimental evaluation

• Published in 1958. 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)

worksiteratively: no need to store the accelerationsignals in RAM orFlashmemory for off-lineprocessing

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

Why the GA for SHM? 1/2


GA computationssample acquisition

samplingSTART

t

samplingEND

• Structuraldamagesmodify the frequencyspectrums of the accelerationsignalscollectedby the nodes

Why the GA for SHM? 2/2


GA: Concept&Parameters

• The GA implements a 2nd-order IIR filtercentered at each frequency of interest:

• 3 keyparameters (set by the end-user):

Samplingfrequency(fs)

Distance (db) betweentwoconsecutivebins on the frequencyaxis(resolutionr = 1/db)

Vector of frequencies of interest (fi)


12

1 2

1

1 2cos 2

i

s

i

fZ

f

f

i

s

eH Z

fZ Z

f

From the Goertzel Algorithm...

• Before the sampling:

Number of samples (N) to be collected to obtain the fixed resolution (r = 1/db)

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

Coefficients (c) used in the GA iterations

• During the sampling:

• At the end of the sampling:


s

b

fN

d

0.5 i

s

N fk

f

2cos 2k

cN

0 1 2

2 1

1 0

iq c q q s

q q

q q

si: last collected sample

q1 and q2 store the results of thetwo previous iterations

2 2 2

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

Xi: squared magnitude of the spectrum

...to Transmissibility Functions

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

• TFsachieveenvironmentalinvariability

• Damage indicator:


2

1

2

1

2

1 22

,j

j

i

i

f

s

s f f

s f

s

f f

X f

T f f

X f

si and sj: sensor nodes

(fi ,f2): range of frequencies of interest

1 2 1 2

1 2

1 2

, ,,

,

j j

i ij

i j

i

TEST REFs s

s ss

r s REFs

s

T f f T f fD f f

T f f

REF: reference (undamaged)

TEST: current condition (damaged?)

Flow of the Application


Sink Node Sensor Node #1 Sensor Node #2 Sensor Node #N...

Goertzel Algorithm Parameters Broadcast

Accelerometer Sampling &

Goertzel Algorithm Computations

Results BroadcastTransmissibility

FunctionsComputations

TDMA ResultsSharing

Dam

age

Ind

icat

ors

t tt

• Sensinode’s U100 Micro.2420:

• MSP430 MCU,clock @ 8 MHz

• 500 kB external serialFlash

• CC2420 transceiver

• 3 axisaccelerometer:

• 2g/ 6g full scale

• 12/16 bit representation

• Highsensitivity: 76.4 mV/m/s2

• Temperature-humiditysensor

Sensor Nodes Hardware


“Our” Bridge


Testbed Setup


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

D1, D2, D3, D4: 500 g weight

sensor node

Electro-Dynamic Shaker

Damaged Cross Bar

D5: 27.6% stiffness reduction


Random noise excitation

Selection of the Critical Frequencies


[32-35] Hz

[32-35] Hz

[27-30] Hz

DAMAGESIGNATURE

ExperimentalValidation (D1)


ExperimentalValidation (D5 and D6)




GA vs Off-Line Modal Analysis (1/3)

• Modal analysis: study of the dynamic properties of structures under vibrational excitation

• Centralized off-line data analysis for identifying natural frequencies, mode shapes and damping ratios


M. Bocca, A. Mahmood, L.M. Eriksson, J. Kullaa, and R. Jäntti, A Synchronized Wireless Sensor Network for Experimental Modal Analysis in Structural Health Monitoring, Computer-Aided Civil and Infrastructure Engineering, 2011.



measurementperiod: 30 s, samplingfrequency: 125 Hz

Conclusions


• By the embeddedGoertzelalgorithm, it is possible to correctlydetect and localizestructuraldamages

• The proposedsystem is low-latency and low-power

Thankyou!

24

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

mailto:[email protected]

shm in wsns by the embedded goertzel algorithm

Technology

ga iterations

goertzel algorithm ga

concept parametersthe

frequency spectrums

collected sampleq1

dbvector of frequencies

frequency axis resolution

range of frequencies