NON-BASELINE DAMAGE DETECTION FROM CHANGES IN
STRAIN ENERGY MODE SHAPES. EXPERIMENTS ON ARMORED
VEHICLE LAUNCHED BRIDGE
E. S. Sazonov1, P. Klinkhachorn1, H. V. S. GangaRao2, and U. B. Halabe2
1
Lane Department of Computer Science and Electrical Engineering,
West Virginia University, Morgantown, WV 26506, USA
2
Department of Civil and Environmental Engineering, Constructed Facilities Center,
West Virginia University, Morgantown, WV 26506, USA
Abstract. There are several existing methods for damage detection based on identifying changes in
strain energy mode shapes. Most of these methods require knowing strain energy mode shapes for a
structure without damage in order to establish a baseline for damage detection. Usually, the mode shapes
from the structure under test should be compared to the baseline mode shapes to identify and locate
damage. However, these methods of damage detection are not very suitable for application on structures
where baseline mode shapes cannot be readily obtained, for example, structures with preexisting
damage. Conventional methods, like building a finite element model of a structure to be used as a
baseline might be an expensive and time-consuming task that can be impossible for complex structures.
A new (non-baseline) method for the extraction of localized changes (damage peaks) from strain energy
mode shapes based on Fourier analysis of the strain energy mode shapes has been developed and
analytically proved for the cases of a pinned-pinned and a free-free beam. The new method looks for
characteristic changes in the power spectrum of the strain energy mode shapes in order to locate and
identify damage. The analytical results have been confirmed both by the finite element model and impact
testing experiments on a free-free aluminum beam, including single and multiple damage scenarios. This
paper presents results of testing the non-baseline method on a complex structure — Armored Vehicle
Launched Bridge, which consists of loosely coupled hinged beams with variable cross-section. The
results of testing confirm applicability of the non-baseline method to damage detection in complex
structures and highlight certain particularities of its use.
INTRODUCTION
In the recent past, several methods for detecting and locating damage (usually
cracks) from changes in Strain Energy Mode Shapes (SEMS) have been developed. All
these methods attempt to detect and locate damage that produces localized changes in
elastic modulus without significant changes in mass. Such damage can be observed as
localized changes (damage peaks) on strain energy mode shapes.
The majority of these methods requires knowing strain energy distribution (mode
shapes) for the structure without any damage or so-called baseline SEMS. The comparison
to the baseline is used to enhance appearance of damage peaks that sometimes may not be
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
1415
observed otherwise. The need for baseline SEMS is especially obvious for identifying
small damages that produce very subtle changes in SEMS.
Unfortunately, such an approach often is not feasible for a class of structures where
undamaged state is unknown and cannot be acquired experimentally. This class of
structures primarily includes old structures where damage state is unknown but the need
for non-destructive testing is usually greater. Conventional methods, such as building a
Finite Element (FE) model of a structure may represent a tedious, expensive and timeconsuming task. Besides, it is difficult or sometimes impossible to reach required accuracy
of mode shape approximation by a FE model.
If applicability of non-destructive damage detection utilizing SEMS could be
extended by eliminating the need for baseline mode shapes and employing a non-baseline
approach, it would significantly increase the class of structures where non-destructive
damage detection could be performed.
Consider some of the recent work in this area. Shi et.al. [1] suggested using
changes in strain energy distribution to detect and localize damage. The recommended
method monitors changes in modal strain energy in each structural element comparing the
states before and after it was damaged. Farrar and Jauregui [2] conducted a comparative
study of different damage identification algorithms on a bridge. The strain energy methods
performed very well compared to other methods tested in the experiments, occupying the
top two places by the accuracy of detection. The authors also noted the methods' high
sensitivity to less severe damage cases. Osegueda, Carrasco and Meza [3] investigated
strain energy method on aluminum cantilever beams and honeycomb composite plates.
The authors received positive damage detection results in experiments with beams and
negative results in experiments with composite plates. They also claimed that strain energy
methods not only can identify damage but also quantify it by accounting the energy
relations between damaged and undamaged states. Cornwell et. al. [4] performed a
comparative study of two vibration-based damage identification algorithms, including
strain energy method. The testing was conducted on a beam and a plate, comparing the
damaged vs. undamaged strain energy distribution. Strain energy method successfully
identified severe damage cases, but a masking effect was reported for lower level damages,
i.e. when the two damage locations had different levels of damage, the algorithm tended to
only conclusively identify the location with the largest amount of damage. Yoo, Kwak and
Kim [5] used difference in strain energy mode shapes between damaged and undamaged
cases to detect and locate damage in a plate. Yan and Deng [6] applied the strain energy
algorithm to nondestructive damage detection in bridges. They conducted numerical
experiments on a finite element model of a freely supported bridge T-beam. Pereyra et. al.
[7] studied damage detection in an aluminum stiffened-plate panel resembling aircraft
fuselage construction. As in most other studies, the damaged strain energy mode shapes
were compared to the undamaged strain energy mode shapes. Statistical methods were
employed to jointly analyze information from several mode shapes and to locate damage.
Napolitano [8] investigated quality of damage detection using reduced measurements and
the strain energy algorithm. The author concluded that the strain energy method performs
better when many response points are measured. Cornwell, Doebling and Farrar [9]
provided a detailed theoretical explanation on application of the strain energy method to
plate-like structures. They reported that the method was effective enough to detect areas
with 10% reduction in stiffness.
A method based on strain energy mode shapes was developed at West Virginia
University (WVU) [10]. Strain energy for an interval [a,b] was computed using the
following formula:
1416
C/r
(1)
,i = -
where El is the flexural stiffness of the cross-section; <P is the mode shape vector
(displacement mode shape).
Subtracting the baseline SEMS from the SEMS acquired from the structure under
test produces so-called Difference Strain Energy Mode Shapes (DSEMS) where crack
locations are identified as damage peaks (FIGURE 1). Again, this method requires a
baseline to extract and enhance appearance of damage peaks. An extension of the WVU
method is described in [11]. The suggested procedure performs extraction and
enhancement of damage peaks appearance through separation of damage information in
frequency domain rather than traditional spatial domain. It was shown that the damage
introduced into a beam creates additional harmonics in the amplitude spectrum of the
strain energy mode shapes that have not been present in the undamaged beam. These
additional harmonics can be extracted by filtering and restored to produce enhanced
damage peaks.
This paper attempts to test the suggested non-baseline procedure on a complex
structure, such as the AVLB. The goal of testing is to verify applicability of the suggested
methodology on hinged beams with variable cross-section.
Undamaged (baseline) structure
Structure under test
Acquired displacement mode shape
Acquired displacement mode shape
Strain energy calculations
Strain energy calculations
Baseline strain energy mode shape
Test strain energy mode shape
Difference strain energy mode shape.
Peaks indicate damage.
FIGURE 1. Traditional strain energy method.
1417
METHODS
The non-baseline strain energy procedure for simple beams
Consider an undamaged pinned-pinned beam of length L and a uniform crosssection with the flexural stiffness of EL The bending mode shapes of the beam for a variety
of the boundary conditions can be found in [12]. For a pinned-pinned beam, displacement
mode shapes for mode k are given by the following equation:
(2)
where Qk is the amplitude of mode k,
cok=—— is the angular frequency for
J-j
mode shape k.
It can be shown [11] that the frequency spectrum of the strain energy mode shapes
Uk ( x )
for a pinned-pinned beam is limited to two terms ( AkQ andB* ) in the
corresponding Fourier series of the general form:
00
00
fj (\x )I = Aon + *—*
y An smcon x + *—*
Y. Bn coscon x
n=l
J
^(3)
n=l
The Fourier series for
equation:
Uk ( x )
of a pinned-pinned beam is given by the following
CkA CkA
CkA
Uk(x) = —— -——coscokx = ——(l ~ coscokx) ,
where
EIQ2.a>
c
= ____ *_
*
(4)
and, thus, the bandwidth of the tfh strain energy mode shape is
32
limited by the £* harmonic.
Displacement mode shapes for mode k of a free-free beam are given by the
following equation [12]:
^(^)-cosh(^) + cos(^)-^(sinh(-^) + sin(^))
LJ
I-*
1^1
ff
k
(5)
JLi
where L is the length of the beam, Ak and
are the mode shape coefficients
dependent on k: *>k = { 4.730040739999998, 7.853204619999998, 10.9956078,
14.1371655, 7.27875969999999, (2k+l)7i/2 for k>5}) and crkk=
^
'
cosh X , — cos /Ik
*
.
k
k7
For the case of a free-free beam it can be shown [11] that the cut-off frequency that
limits the energy of strain energy mode shapes at 95% of the total energy has a welldefined dependency on k:
n
c«-off=k+1'
(6)
Thus, the amplitude spectrum of SEMS for a beam with free-free boundary
conditions is band-limited by the k+l harmonics.
Therefore, the amplitude spectrum of strain energy mode shapes for pinned-pinned
and free-free boundary conditions of a beam is limited to the first k+l harmonics (as the
most general case) in the Fourier series representation.
It can also be shown [11] that the amplitude spectrum of a damage peak on the
strain energy mode shapes is significantly wider than the amplitude spectrum of an
undamaged strain energy mode shape. Additionally, all damage peaks of the same shape
and amplitude have the same amplitude spectrum but different phase spectrum. Therefore,
1418
it is possible to separate mode shape information from damage information in the
frequency domain and avoid using a baseline by removing the first k+1 harmonics in the
frequency spectrum of a strain energy mode shape. The procedure is illustrated in FIGURE
it isnon-baseline
possible to method
separatehas
mode
information
in theof a
2. The
beenshape
successfully
testedfrom
bothdamage
on finiteinformation
element models
frequency
domain
and
avoid
using
a
baseline
by
removing
the
first
k+l
harmonics
in the
free-free beam and experimental data.
frequency spectrum of a strain energy mode shape. The procedure is illustrated in FIGURE
2. The non-baseline method has been successfully tested both on finite element models of a
Modal data acquisition on the AVLB
free-free beam and experimental data.
Acquisition of modal parameters on the AVLB
Modal data acquisition on the AVLB
AVLB is
a folding
scissors-type
aluminum-steel combination bridge
Acquisition
of modal
parameters
on thelightweight
AVLB
with the maximum span of 60ft. (18.3m) [13]. Structurally the bridge consists of the 4
hinged girders
(FIGURE
3) with
the deck lightweight
plates attached
on top of each
girder pair.
Each
AVLB
is a folding
scissors-type
aluminum-steel
combination
bridge
withhas
the6 maximum
span
60ft.
(18.3m)
[13].
Structurally
of the span,
4
girder
hinges: one
topofand
bottom
hinge
pair
located atthe
thebridge
center consists
of the bridge
girders (FIGURE
3) with
deck platesofattached
on top of each
girder
pair.and
Each
andhinged
two off-center
hinge pairs.
Thethe
acquisition
the displacement
mode
shapes
other
girder
has 6 hinges:
onethe
top AVLB
and bottom
pair located
at the
center of the
bridgedetection
span,
model
parameters
from
washinge
performed
by an
automated
damage
and
two
off-center
hinge
pairs.
The
acquisition
of
the
displacement
mode
shapes
and
other
system designed specifically for AVLB [14]. The system utilizes a non-contact
laser
model
parameters
from
the
AVLB
was
performed
by
an
automated
damage
detection
vibrometer mounted on a computer-controlled robotic gantry as the measurement sensor.
system data
designed
specifically processed
for AVLB to[14].
Thestrain
systemenergy
utilizes
a non-contact
laser are
Acquired
is automatically
obtain
mode
shapes, which
vibrometer mounted on a computer-controlled robotic gantry as the measurement sensor.
used as the damage indicator. The analysis of the strain energy mode shapes is performed
Acquired data is automatically processed to obtain strain energy mode shapes, which are
by aused
fuzzy
expert
system.
This system
was successfully
testedmode
on a shapes
full-scale
AVLB with
as the
damage
indicator.
The analysis
of the strain energy
is performed
different
damage
scenarios.
by a fuzzy expert system. This system was successfully tested on a full-scale AVLB with
different damage scenarios.
Structure under test
Structure under test
60 FT
Girder 1
Acquired displacement mode shape
Girder 2
Girder 3
Girder 4
Strain energy calculations
Deck plates
(a)
Test strain energy mode shape
30 FT
20 FT
Off-center
Off-center
hinges
hinges
DFT, High-pass filtering, IDFT
DFT, High-pass filtering, IDFT
x
Center hinge
Center hinge
(b)
(b)
Modified spectrum strain energy mode shape.
Peaks indicate damage.
FIGURE 3. (a) Structural composition of AVLB
Modified spectrum strain energy mode shape.
FIGURE
2. Non-baseline damage
Peaks
indicate damage.
of a girder.
FIGURE 3. (b)
(a)hinges
Structural
composition of AVLB
(b) hinges of a girder.
detection procedure.
FIGURE 2. Non-baseline
damage
detection procedure.
1419
TESTING
TESTING
The mode shapes for the first three bending modes of AVLB were acquired by the
automatedThe
damage
4). Next,
strain energy
computations
mode detection
shapes forsystem
the first(FIGURE
three bending
modesthe
of AVLB
were acquired
by the
were
computed
from
the
bending
mode
shapes.
The
strain
energy
mode
shapes
from the
automated damage detection system (FIGURE 4). Next, the strain energy computations
undamaged
AVLBfrom
werethe
stored
as themode
baseline.
were computed
bending
shapes. The strain energy mode shapes from the
Three
damage
cases
were
simulated
by removing the central bottom hinge pin and
undamaged AVLB were stored as the baseline.
either of the
off-center
bottom
hinge
pins.
These
three simulated
casesbottom
of damage
Three damage cases were simulated by removing
the central
hingerepresent
pin and
different
of damage
According
to simulated
the AVLBcases
manual,
if therepresent
bottom
either ofdegrees
the off-center
bottomseverity.
hinge pins.
These three
of damage
central
pin
is
missing
or
cracked
(regardless
of
length),
or
damaged,
or
even
missing
different degrees of damage severity. According to the AVLB manual, if the bottom
retainer
pins,orthecracked
AVLB (regardless
is considered
Mission
Capable.orIf even
an off-center
centralclips/
pin ishinge
missing
of Not
length),
or damaged,
missing
bottom
hinge
pin
is
removed,
the
AVLB
is
still
considered
Mission
Capable.
strain
retainer clips/ hinge pins, the AVLB is considered Not Mission Capable. If an The
off-center
energy
mode
shapes
from
the three
also stored
for further
bottom
hinge
pin is
removed,
thedamaged
AVLB iscases
still were
considered
Mission
Capable.processing.
The strain
A mode
side-by-side
ofdamaged
the difference
strainalso
energy
mode
shapes processing.
obtained by
energy
shapes comparison
from the three
cases were
stored
for further
the subtracting
the baseline
strain energy
mode shapes
the mode
test strain
mode
A side-by-side
comparison
of the difference
strainfrom
energy
shapesenergy
obtained
by
shapes
(traditionalthe
strain
energy
method)
the shapes
modified
mode
the subtracting
baseline
strain
energyand
mode
fromspectrum
the test strain
strain energy
energy mode
shapes
by removing
firstmethod)
k+1 harmonics
the frequency
of themode
test
shapesobtained
(traditional
strain energy
and the in
modified
spectrumspectrum
strain energy
strain
energy
modeby
shapes
(non-baseline
energy
was conducted
shapes
obtained
removing
first k+l strain
harmonics
in method)
the frequency
spectrum toofcompare
the test
energy
mode shapes
(non-baseline strain energy method) was conducted to compare
thestrain
quality
of damage
peak expression.
the quality
of damage
peak expression.
As FIGURE
5 shows,
expression of the damage peaks is approximately equal for
As FIGURE
shows,
expressionstrain
of theenergy
damage
peaks isThe
approximately
equal
for
both the traditional
and5 the
non-baseline
methods.
dissimilarities
in the
both
the
traditional
and
the
non-baseline
strain
energy
methods.
The
dissimilarities
in
the
resulting difference strain energy mode shapes and modified strain energy mode shapes are
resulting
difference
strain energy
shapesof
and
energy mode shapes are
minor
and cannot
drastically
changemode
the results
themodified
damagestrain
detection.
minor and cannot drastically change the results of the damage detection.
CONCLUSIONS
CONCLUSIONS
The experiments on the AVLB have shown that the damage indicators extracted
have shown that
the energy
damage methods
indicators have
extracted
either byThe
theexperiments
traditional on
or the
byAVLB
the non-baseline
strain
the
either by the
or ofbyexpression
the non-baseline
strain
energy the
methods
have the
approximately
the traditional
same degree
and provide
essentially
same amount
of
approximately
the same damage.
degree ofThese
expression
provide essentially
same amount
of
information
for detecting
resultsand
practically
justify the the
applicability
of the
information
for
detecting
damage.
These
results
practically
justify
the
applicability
of
the
non-baseline method to complex structures, thus significantly expanding the class of
non-baseline
to complex
thus significantly
the class of
structures
wheremethod
the damage
detectionstructures,
by strain energy
mode shapesexpanding
can be applied.
structures where the damage detection by strain energy mode shapes can be applied.
1
3 5 7
9
11 13 15 17 19 21 23 25 27 29 31
1
3
5
7
S
1
11 13 15 17 19 21
3
5
23 25
7
27
FIGURE
First
three
mode
shapesacquired
acquiredononthe
theAVLB.
AVLB.
FIGURE
4. 4.First
three
mode
shapes
1420
9 11 13 15 17 19 21 23 2S 27 29 31
29 31
First mode, ~ 8Hz, Traditional method
First mode, ~ SHz^Traditional method
1
4
7
10
13
16
19
22
25
28
A
31
34
37
40
43
46
49
52
First mode, ~ 8Hz,
Traditional
method
First mode,
~ 8Hz,
A
55
58
61
1
4
7
10
Second mode, ~ 27Hz, Traditional method
Second mode, ~ 27Hz, Traditional method
13
Traditional method
16
19
22
25
28
31
34
37
Jv
40
43
46
49
52
55
58
61
37
40
43
46
49
52
55
58
61
37
40
43
46
49
52
55
58
61
Second mode, ~ 27Hz,
Traditional
method
Second mode,
~ 27Hz,
Traditional method
1
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
4
First mode, ~ 8Hz, Non-baseline method
First mode, ~ 8Hz, flon-baseline method
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
Second mode, ~ 27Hz, Non-baseline method
Second mode, ~ 27Hzj Non-baseline method
4
7
^A_
10
13
16
.——^—..
19
22
....
.
25
..
28
31
f\
34
;>-^ ._->*.
1
37
40
43
_
46
49
52
55
58
1
4
^
7
4
16
19
22
25
28
10
13
16
4
7
10
10
13
13
16
16
4
7
10
13
16
19
22
25
28
Second mode, ~ 27Hz,
Second mode,
~ 27Hz,
Non-baseline
method
Non-baseline method
1
61
19
,•x^
22
25
19
4
7
10
13
16
19
22
25
28
19
V
22
-, /
10
13
16
31
34
A A
31
34
37
40
43
19
22
46
49
A
52
55
58
61
28
r\/ —'"\-~— —T
31
34
37
40
43
46
49
^^-^^^
52
55
58
61
Second mode, ~ 27Hz,
Second mode,
~ 27Hz,
Traditional
method
Traditional method
V
22
' ^--^V^,,
7
34
First mode, ~ 8Hz,
First mode,
- 8Hz,
Traditional
method
Traditional method
25
28
31
34
__
37
40
^
43
46
/x
49
52
55
58
61
First mode, ~ 8Hz,
First mode, - 8Hz,
Non-baseline method
Non-baseline method
^_A- ^
25
28
31
34
37
40
-
43
46
49
-^^^ 52
55
58
61
Second mode, ~ 27Hz
Second mode, ~ 27Hz
Non-baseline method
Non-baseline method
\
\
4
31
•U
I
/s ,
7
•W'
1
13
VL -*^\.
\
V
1
10
First mode, ~ 8Hz,
First mode, ~method
8Hz,
Non-baseline
Non-baseline method
1
1
7
61
25
28
31
34
37
40
43
46
49
52
55
58
61
, , , „ .N^J, A^X » « » « « « « « « .. «
FIGURE
5. 5.Damage
indicators
FIGURE
Damage
indicatorsofofthethefirst
firsttwo
twobending
bendingmodes
modesofofthe
theAVLB
AVLBextracted
extractedby
by
traditional
and
non-baseline
traditional
and
non-baselinestrain
strainenergy
energymethods.
methods.
AtAtthethepresent
presenttime,
time,the
theanalytical
analyticalproof
proofofofthe
thenon-baseline
non-baselineprocedure
procedureexists
existsonly
only
forfora limited
number
of
boundary
conditions
of
a
simple
beam.
The
results
obtained
a limited number of boundary conditions of a simple beam. The results obtainedon
onthe
the
AVLB
AVLBshow
showthat
thatit itmay
maybebepossible
possibletotoextend
extendthe
theanalytical
analyticalcoverage
coveragetoto more
more complex
complex
beams,
beams,such
suchasashinged
hingedbeams
beamsofofvariable
variablecross-section.
cross-section. Such
Such analytical
analytical work
work should
should
establish
establishthetheproper
properprocedure
procedureand
andinterpretation
interpretationofofthe
theresults
resultsobtained
obtainedon
onthe
thecomplex
complex
structures.
structures.Indeed,
Indeed,a special
a specialcase
casemay
mayexist
existwhen
whena astructure
structurehas
hasan
anabrupt
abruptchange
changeinincrosscrosssection
that
can
be
falsely
identified
as
a
damage
peak.
Baseline
methods
section that can be falsely identified as a damage peak. Baseline methodswould
wouldprovide
provide
relatively
relativelygood,
good,although
althoughnot
notcomplete,
complete,cancellation
cancellationofofsuch
suchpeaks,
peaks,while
whilethe
theproposed
proposed
non-baseline
non-baselineapproach
approachdoes
doesnot
nothave
havesuch
suchcapability.
capability.AApossible
possiblesolution
solutiontotothis
thisproblem
problem
might
mightbebeininmatching
matchingofofthe
themodified
modified strain
strainenergy
energy mode
mode shapes
shapes toto the
the geometric
geometric
configuration
configurationofofthethestructure
structureand
anddiscarding
discardingthe
thefalse
falsepeaks.
peaks.
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
The
Theauthors
authorswish
wishtotoacknowledge
acknowledgethe
thefinancial
financialsupport
supportprovided
providedby
bythe
theU.S.
U.S.Army
Army
(contract
(contract# #DAAE07-96-C-X226).
DAAE07-96-C-X226).
1421
REFERENCES
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strain energy change," Journal of Sound and Vibration , vol. 218, n.5, pp. 825-844
2. Farrar C.R., Jauregui D.A. (1998). "Comparative study of damage identification
algorithms applied to a bridge," Smart Materials and Structures, n.7, pp. 704-719
3. Osegueda R.A., Carrasco C.J., Meza R. (1997). "A modal strain energy distribution
method to localize and quantify damage", Proceedings of International Modal Analysis
Conference (IMAC-XV), Orlando, Florida, pp. 1298-1304
4. Cornwell P., Kam M., Carlson B., Hoerst B., Doebling S., Farrar C. (1998).
"Comparative study of vibration-based damage ID algorithms", Proceedings of
International Modal Analysis Conference (IMAC-XVI), Santa-Barbara, California, pp.
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