of 8
The 6th International Workshop on Advanced Smart Materials and Smart Structures Technology
ANCRiSST2011
July 25
-
26, 201
1, Dalian, China
A Damage Detection Method for Instrumented Civil Structures
Using Prerecorded Green’s Functions and Cross
-
Correlation
Vanessa Heckman, Monica Kohler, and
Thomas Heaton
Department of Mechanical and Civil Engineering
,
California
Institute of Tec
hnology
,
Pasadena, CA
91125
,
USA
ABSTRACT
Automated damage detection methods
have application to
instrumented structures that are
susceptible to types of damage that are difficult or costly to detect. The presented method has
application to the detecti
on of brittle fracture of welded beam
-
column connections in steel
moment
-
resisting frames (MRFs), where locations of potential structural damage are known a priori.
The method makes use of a prerecorded catalog of Green’s function templates and a cross
-
cor
relation
method to detect the occurrence,
location
, and time
of structural damage in an instrumented building.
Unlike existing methods, the method is designed to recognize and use mechanical waves radiated by
the
original brittle fracture event
, where
the
event
is not known to have occurred with certainty and the
resulting damage may not be visible.
An e
xperimental stud
y
is
conducted to provide insight into
applying the method to
a
building. A tap test is performed on a small
-
scale
steel
frame to
test
whether
cross
-
correlation techniques and catalogued Green’s function templates can be used to identify the
occurrence and location of an assumed
-
unknown event. Results support the idea of using a
nondestructive force to characterize the
building response to high
-
frequency dynamic failure such as
weld fracture.
INTRODUCTION
Acoustic damage detection methods rely on the comparison of a recent signal to an archived
baseline response function, known as a template. The template is recorded
at a time when the structure
is undamaged. The sensor network
has
a sampling rate
that is
high enough
to capture the propagation
of waves throughout the structure. Acoustic techniques have been explored experimentally and
numerically for thin plates and b
eams, which serve as waveguides that effectively carry information
from the location of structural damage to a receiver
[1
-
3]
. This information, namely differences in
waveform and amplitude between the current signal and the template, are used to diagnose
damage.
Acoustic methods can be passive or active, and sensor networks can be per
manently installed or
temporary
.
E
xisting methods include pitch
-
catch, pulse
-
echo, time
-
reversal, and migration
[4].
In this
paper, a
complementary
acoustic method is present
ed, that makes use of a prerecorded catalog of
Green’s functions and a matched filter method to passively detect the original failure event. This
technique is different from existing acoustic methods as it is designed to recognize seismic waves
radiated by
the original brittle failure event.
It is similar to t
he matched filter method
, which
has been
successfully used in other fields
[
5
-
6
]
.
T
he method has yet to be explored in the context of acoustic
damage detection of civil structures.
DESCRIPTION OF MET
HOD
The proposed method make
s
use of a prerecorded catalog of Green’s functions for an instrumented
building to detect structural damage during a later seismic event. Continuous data collected on a
passive network are screened for the presence of waveform
similarity to one of the Green’s function
templates. The method is outlined below.
1) Identify probable points of failure in an instrumented building before structural damage has
occurred. As pre
-
Northridge steel MRFs are susceptible to the brittle failur
e of welded beam
-
column
connections, these would be the locations of probable failure for this type of building.
2) At each labeled location, apply a short
-
duration high
-
frequency pulse (e.g. using a force
transducer hammer). The response of the building
at each instrument site is the Green’s function
specific to that source location
-
receiver pair. The Green’s functions are archived in the catalog of
templates to be used later to screen the high
-
frequency seismogram for a damage signal.
3) For each possi
ble source location k, perform a running cross
-
correlation between the Green’s
function templates for that source location and a moving window of the seismogram that recorded the
shaking event, stacking over the receivers. Cross
-
correlation between the k
th
Green’s function template
x
i
k
recorded by the i
th
receiver and the seismogram
x
i
recorded by the i
th
receiver is given by
Eq
(
1
)
.
(1)
Time T is the duration of the template, and the cross
-
correlation is normalized by the
autocorrelation value
s for the given time window.
Compute the stacked cross
-
correlation function by summing over the R receiver locations to
obtain
Eq (2).
(2)
4) If damage occurred at or near the k
th
source location, the stacked cross
-
correlation function
given by Eq.
(2) should peak at a value close to
unity
at the correct time of the structural damage event.
In the case of multiple locations of damage, then the stacked cross
-
correlation functions should each
peak at a value close to
unity
at the corresponding times,
provided the correct Green’s function
templates are used. This procedure could be extended to the three
-
dimensional case.
C
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)
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R
!
EXPERIMENTAL
STUDY
To study the feasibility of the proposed method, e
xperimental
tests were conducted on
the
small
-
scale steel frame
shown in Fig. 1.
T
hree different source mechanisms were applied
to
beam
-
column connection
s
:
impulsive hammer blow,
bolt fracture,
and impulsive h
ammer blow to a
frame with a
“damaged”
beam
-
column connection
.
The similarities and differences
between the
th
ree
cases were analyzed using
waveform
cross
-
correlation
normalized by the autocorrelation value and
stacked over the eight receiver locations. R
esults were averaged over 15
-
25
trials.
Experimental Setup
A small
-
scale steel frame instrumented with
eight
uniaxial (y
-
axis)
accelerometers, shown in Fig.
2,
was subjected to hammer blow
s
and bolt fracture
at beam
-
column connections
.
A
sample frequency
of
1
00kHz and record
duration
of
2.0
seconds
were used
.
The experimental setup i
ncluded
:
Small
-
scale steel f
rame with a pinned base and bolted beam
-
column connections
High sensitivity low mass accelerometers and power supply
Force transducer hammer and power supply
USB multifunction data acquisition device
Laptop for data logging
Experimental Method
and Resul
ts
Green’s functions were generated by using a force transducer hammer to apply an
impulsive force
load
along the y
-
axis to
each of the eight
beam
-
column connections
(A
-
H) shown in Fig. 2. A total of
Fig.
1
.
Instrumented s
teel frame
(left), close
-
up of bolted beam
-
column connection (top right), and
notched bolts before and after failure (bottom right).
Dimensions are shown in Fig. 2.
Fig.
2
.
Experimental Setup
:
Steel frame dimensions,
receiver
(accelerometer)
locations
,
and source
(hammer blow and bolt fracture)
locations
five
hammer blows
were
delivered
at
each source location.
Fig. 3
displays
the Green’s function that
was generated by applying an impulsive hammer blow at source location C.
The cross
-
correlation of
e
ach possible pair of Green’s functions was
computed.
Cross
-
correlations we
re
first
calculated
at each
receiver location
,
using the two different r
ecords
and autocorrelation normalization, as in Eq. (1)
. The
cross
-
correlations we
re then stacked, or summed, over a
ll eight receivers, as in Eq. (2).
An example is
presented
in Fig. 4, where the cross
-
correlations
of
Green’s functions
generated by
impulsive hammer
blow
s
applied
at
identical
source location
s
C
-
C
are plotted on the left
, and those generated by
hammer
b
lows
applied
at
different source locations
are plotted on the right
.
The maximum amplitude of the
stacked cross
-
correlation
is
recorded
,
averaged over the total
number of
pairs
(20
total for
pair
s
consisting
of
two
identical source locations and 25
total
f
or
pair
s
consisting
of
two distinct source
locations)
,
and
presented
in Table 1.
In
Fig. 4,
the maximum value of the stacked cross
-
correlation is
0.87 for source location pair C
-
C, and 0.11 for source loc
ation pair C
-
F.
Fig.
3
.
Acceleratio
n time series for a hammer blow (left) and a bolt fra
cture (right) shown for four
receiver locations
(R
1
, R
3
, R
5
, R
7
)
and the same source location
(C)
.
Fig.
4
.
Cross
-
correla
tions
of Green
s functions
generated by
hammer blows at the same source
location (left) and
of
Green
s functions
generated by
hammer blows at two different source locations
(right) shown at four receiver locations, as well as the stacked cross
-
correlation
s
(bottom)
.
Further experimentation was
conducted
t
o determine whether pr
erecorded Green’s functions
could
be
used as an approximation
to
the
frame’s
response to
structural
damag
e
(i.e. a fracture event)
at the same source location. A notched stainless steel socket cap screw was introduced into a
beam
-
column connection. The screw
replaced the bottom bolt shown in Fig. 1. It was then loaded by
torque tightening to the point of failure
, and the response of the frame
to the fracture
was recorded on
the eight accelerometers
.
A
n example
acceleration time series generated by bolt fractu
re is shown in
Fig. 3.
Three trials were repeated at each of the four source locations
A, C, E, and G
.
Cross
-
correlation
s
were
computed
to determine the similarity between the
prerecorded
Green’s
function
s
and the frame’s response to
bolt failure
.
Specific
ally, the frame’s response to the prerecorded
Green’s functions
was
cross
-
correlated with the response of the frame to bolt
failure
.
Each
possible
pair
of
bolt
failure
source location and Green’s function source location
w
as
considered.
Results
presented i
n Table 2
were averaged over
15
total
pair
s
.
Finally, a tap test was performed
on a
frame
with a “damaged” beam
-
column connection
.
Damage
was introduced by removing a
ll three bolts from
the
connection
(A, C, E, or G)
,
with
t
he stiffness of
the rest of the
structure
holding
the
beam and column
in place.
An impulsive hammer blow was
applied
to
each of t
he eight source locations
, for each of the four
damaged
connection
cases
.
This was
performed
a total of three
times
.
To highlight
difference
s
in structural res
ponse before and after
damage occurred, the prerecorded Green’s functions were cross
-
correlated with the
response of the
damaged frame to an impulsive
hammer blow
applied at the same source location, for
each of the
four
damaged
connection
cases
. Results
w
ere
averaged over 15 total trials and are presented in
Table 3.
Table 1.
Stacked cross
-
correlation
of
Green’s functions
:
averaged
maximum
value
over
20
-
25
trials
. T
he table is symmetric.
Hammer Blow
Source Location
A
B
C
D
E
F
G
H
Hammer Blow
Source Loc
A
0.78
0.17
0.14
0.09
0.15
0.10
0.13
0.10
B
0.85
0.09
0.15
0.08
0.08
0.08
0.07
C
0.80
0.14
0.16
0.10
0.20
0.11
D
0.83
0.09
0.22
0.10
0.11
E
0.81
0.10
0.30
0.10
F
0.83
0.12
0.18
G
0.80
0.13
H
0.85
Table
2
.
Stacked cross
-
correlation
of Green’s function and
structural
response to bolt
failure
: averaged maximum
value
over 15 trials
.
Hammer Blow
Source Location
A
B
C
D
E
F
G
H
Bolt Fracture
Source Loc
A
0.17
0.07
0.11
0.07
0.07
0.06
0.08
0.05
C
0.07
0.05
0.16
0.06
0.12
0.05
0.09
0.05
E
0.08
0.06
0.07
0.07
0.17
0.06
0.14
0.07
G
0.06
0.05
0.07
0.06
0.11
0.07
0.15
0.07
Table
3
.
Stacked cross
-
correlation
of
the
Green’s function
generated by
applying
a
hammer blow at
one source location
and
the
r
esponse of
the
damaged frame to a
hammer blow
applied
at the same
location. F
our different damaged connection
cases
are shown
: averaged maximum
value
over 15 trials
.
Hammer Blow Source Location
A
B
C
D
E
F
G
H
Damaged
Connection
A
0.11
0.44
0.46
0.53
0.51
0.56
0.51
0.56
C
0.52
0.50
0.41
0.48
0.44
0.51
0.51
0.51
E
0.60
0.57
0.46
0.54
0.33
0.45
0.47
0.53
G
0.60
0.60
0.52
0.60
0.45
0.54
0.31
0.50
DISCUSSION
The maximum value of the stacked cross
-
correlation record is used as an indicator of how similar
the two correlated waveforms are, e.g. how similar the building responses are to
different source
mechanisms and locations. Stacked cross
-
correlation values range from
-
1 to 1, with a higher value
corresponding to a higher degree of similarity.
In Table 1, t
he stacked cross
-
correlation
values are
greatest
along the diagonal
,
where
the two
Green’s function
source locations are
the same
.
Off
-
diagonal terms, where two d
ifferent source locations
are used,
have
a
much lower
stacked
cross
-
correlation value
.
T
he reason for this is illustrated in Fig. 4, which compares the
cross
-
correlation records for source location pairs C
-
C and C
-
F.
For source location pair
C
-
F, the
unstacked
cross
-
correlation
s
computed a
t each receiver location have
lower peak value
s
than t
he
corresponding C
-
C
unstacked
cross
-
correlations.
Furthermore, the
stacked
C
-
F
cross
-
correlation
attain
s
a peak value
of 0.11, which is lower
than
each of
the
peak values of
the un
stacked C
-
F
cross
-
correlation
s, which range from 0.15 to 0.32
.
T
here is a
r
elatively large
time
difference
(0.0087
sec)
at which
the peak values occur
in the unstacked C
-
F cross
-
correlations
.
For comparison, t
he
maximum time difference between unstacked
C
-
C
cross
-
correlation peaks
is
0.00002 sec
, which
results in much more coh
erent stacking
.
D
ifference
s
in
both
waveform as
well as arrival time
contribute
to the
smaller
off
-
diagonal terms
.
T
he sta
cked cross
-
correlation values
in Table 2
are
greatest
when the bolt fracture source location
is the same as the Green’s function sour
ce location
.
Hence
, the Green’s function
that best
approximates the frame’s response to bolt fracture is the one with the same source location.
This is a
necessary condition
for
the proposed method to be successful.
However, t
he stacked cross
-
correlation
v
a
lues in Table 2 are much lower than those in Table 1
.
Alternative cross
-
correlation
techniques
will
need to
be
explored
,
as a high
cross
-
correlation value
will be
essential
for robust detectio
n of structural
damage
.
Future
work
will
investigate
which prov
ides a better approximation to the structural response
to bolt failure: the prerecorded set of Green’s functions or the
post
-
event
set of
structural responses to
hammer blows.
This will be
accomplished
by cross
-
correlating t
he damaged structure’s response to an
i
mpulsive hammer blow with the struc
ture’s response to bolt failure.
The
change
in
the response of the
frame
to an impulsive hammer blow
at
the same
source location
after damage has occurred
is
apparent
in Table 3
.
The values
in Table 3
are much lower than
the
values along the diagonal
in
Table 1, falling from an average value of 0.82 to
0.49.
The values along
the diagonal
in Table
3
,
where the location of the damaged connection is the same as the source
location of the hammer blow,
give the lowest cross
-
co
rrelation value
s
, an average of
0.29 compared to
the
off
-
diagonal terms,
which
have an average
of
0.52.
Thus, there is significant change in the
response of the structure to
a hammer blow after damage has occurred, and this
change
becomes more
evid
ent
when the hammer blow is applied at the location of the damaged
connection
.
CONCLUSION
An experimental
stud
y
was
conducted to provide insight into
a damage detection method that
makes use of a prerecorded catalog of Green’s function templates and a c
ross
-
correlation method to
detect the occurrence and location of structural damage in an instrumented building
.
Impulsive
hammer
blows
and bolt
fracture
were applied to a small
-
scale steel frame to
test the
feasibility of
appl
ying
the method
to a
building
.
Results indicate that the Green’s function that best approximates
the frame’s response to bolt fracture at a beam
-
column connection is the Green’s function generated
by a hammer blow applied
to
the same connection
.
However, alternative cross
-
correlation t
echniques
will be explored, as a high
er
stacked
cross
-
correlation value
than the one obtained via waveform
correlation
will be essential for robust detection of structural damage.
S
uccessful damage detection
could be accomplished by employing
a mixed appro
ach
that
analyzes both
recorded
seismograms
for
the
presence of a
brittle fracture even
t
as well a
s post
-
event tap tests
that
expose
changes in building
response
.
Results support the idea of using a nondestructive force to characterize the building respons
e
to high
-
frequency dynamic failure such as weld fracture.
ACKNOWLEDGEMENTS
We would like to thank donors to the Hartley Fellowship
and
the
Lin Lab
for their support.
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