Post on 12-Jul-2015
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”
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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
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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
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GA computationssample acquisition
samplingSTART
t
samplingEND
• Structuraldamagesmodify the frequencyspectrums of the accelerationsignalscollectedby the nodes
Why the GA for SHM? 2/2
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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)
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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:
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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:
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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
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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
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“Our” Bridge
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Testbed Setup
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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
D6: 55.2% stiffness reduction
Random noise excitation
Selection of the Critical Frequencies
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[32-35] Hz
[32-35] Hz
[27-30] Hz
DAMAGESIGNATURE
ExperimentalValidation (D1)
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ExperimentalValidation (D2)
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ExperimentalValidation (D3)
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ExperimentalValidation (D4)
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ExperimentalValidation (D5 and D6)
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D5: 27.6% stiffness reduction
D6: 55.2% stiffness reduction
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
20ICCPS 2011, Chicago, IL, USA, 14.4.2011
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.
GA vs Off-Line Modal Analysis (2/3)
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measurementperiod: 30 s, samplingfrequency: 125 Hz
GA vs Off-Line Modal Analysis (3/3)
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measurementperiod: 30 s, samplingfrequency: 125 Hz
Conclusions
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• By the embeddedGoertzelalgorithm, it is possible to correctlydetect and localizestructuraldamages
• The proposedsystem is low-latency and low-power