8CUEE
CONFERENCE
PROCEEDINGS
8
th International Conference on Urban Earthquake Engineering
March
7
-
8
, 201
1,
Tokyo Institute of Technology
, Tokyo, Japan
A
M
ETHOD TO
D
ETECT
S
TRUCTURAL
D
AMAGE
U
SING
H
IGH
-
F
REQUENCY
S
EISMOGRAMS
Vanessa
M.
Heckman
1)
,
Monica
D.
Kohler
2)
, and
Thomas
H.
Heaton
3)
1)
Graduate Student
,
Department of
Mechanical and
Civil Engineering
,
California Institute of Technology
,
U
S
A
2)
Professional Researcher
,
Center for Embedded Networked Sensing, University of California at Los Angele
s
,
U
S
A
3) Professor
of
Engineering Seismology
,
Department of Mechanical and Civil Engineering
,
California Institute of Technology
,
U
S
A
heckman
@
caltech.ed
u
,
kohler
@
ess
.
ucla
.edu
,
heaton
@
caltech.edu
Abstract
:
A numerical study is performed to gain insight into applyin
g a novel method to detect high
-
frequency dynamic
failure in buildings. The method
relies on
prerecorded catalog of Green's functions for ins
trumented building
s
. Structural
failure during a seismic event is detected by screening continuous data for the presence of waveform similarities to each
of the cataloged building responses. In the first part of th
is numerical
study, an impulse
-
like force
is applied to a beam
column connection in a linear elastic steel frame. A time
-
reversed reciprocal method is used to demonstrate that the
resulting
simulated
displacements can be used to determine the absolute time and location of the applied force. In the
second part of the study, a steel frame's response to two loading cases, an impulse
-
like force and a
n opening crack
tensile
stress, is computed on a temporal scale of microseconds. Results indicate that the velocity waveform generated by a
tensile crack c
an be approximated by the velocity waveform generated by an impulse
-
like force load applied at the proper
location. These results support the idea of using a nondestructive impulse
-
like force
(e.g. hammer blow)
to characterize
the building response to high
-
frequency dynamic failure
(e.g.
weld
fracture
)
.
1.
INTRODUCTION
There has been recent interest in
using
acoustic
techniques
to
detect
damage
in
instrumented
civil structures
.
An automated damage detection method
that analyzes
recorded data
has applic
ation to building types that are
susceptible to a signature type of
failure
, where locations of
potential
structural damage
are known a priori. Such a
method
would be
valuable if it could be used to
detect types
of
damage
that
are
otherwise
difficult
and c
ostly
to detect
.
I
n
particular,
this method has application to the detection of
brittle failure of welded beam
-
column connections in steel
moment resisting frames (
MRFs
)
.
The 1994 Northridge
earthquake exposed this type of damage
, which
can occur
without a
ccompanying damage to architectural finishes and
cladding;
in some cases, detection
requires
intrusive
inspections that can be costly and time
-
consuming (Rodgers
et al. 2007).
An automated damage detection
method could
be used to
located areas of probable
damage
to
guide
post
-
earthquake
building inspection
.
A
coustic 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 undam
aged.
The
sensor network
must have
a
high
sampling
rate
to
capture
the
propagation
of waves throughout the structure.
Acoustic
techniques
have been explored
experimentally and
numerically
for thin plates
and beams
(
Park et al. 2007
,
Wang and Rose 2003,
Wan
g et al. 2004)
, which serve as
waveguide
s
that effectively carry information from the
location of structural damage to a receiver. This information,
namely differences in waveform and amplitude between the
current signal and the template, are used to diagn
ose
damage.
Acoustic methods can be passive or active, and sensor
networks can be permanently installed or temporary.
Giurgiutiu (2005)
reviews
current
techniques
, including
embedded ultrasonic
non
-
destructive evaluation (
NDE
)
,
which
use
s
a
transmitte
r to
interrogate the structure while
a
receiver records the structural response.
1)
Pitch
-
catch
:
A pu
lse is emitted by a transmitter
and
travels through the material to a receiver. Differences in
guided wave shape, phase, and amplitude
are
used to detect
damag
e in the medium between the transmitter and receiver.
2
)
P
ulse
-
echo
:
A
pulse is emitted by a t
ransmitter
,
which
also acts as a receiver to detect
damage in the form of
additional echoes
.
3
)
Time
-
reversal
:
A
signal sent by a transmitter
arrives at a
receive
r, where the signal is time
-
reversed and
reemitted.
Structural d
amage
that causes
linear re
ciprocity to break
down leads
to discrepancy between the
original signal and
the final signal received by the transmitter.
4
)
M
igration
:
Recorded waves are back
-
pro
pagated through
the material
by systematically solving the wave equation
to
image reflectors
in the medium
.
In this paper, a
complementary
acoustic method
is
presented
,
that
makes use of a prerecorded catalog of
Green’s functions and a matched filter meth
od
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.
The matched
filter
method has been
successfully
used
in
other fields
(
Gibbons and Ring
dal 2006,
Anstey 1964
)
, but
the method h
as yet to be
explored
in th
e context of
acoustic
damage detection of
civil structure
s
.
The proposed method is
described
in greater detail in
the following section.
Two numerical stud
ies are performed
;
the first
compare
s
our method to
a
similar time
-
reversed
reciprocal method, and
the second
provide
s
a waveform
comparison between a
non
-
destructive
event
and a
failure
event.
2.
MATCHED
FILTER
METHOD
The
proposed method
would mak
e
use of a prerecorded
catalog
of Green’s functions
for an instrumented building to
detect
structural
damage
during a later seismic event
.
C
ontinuous data collected on a passive network
is screened
for the presence of waveform similarity to one of the
Gree
n’s function templates.
The
method is
outline
d
below
.
1)
Identify probable points of failure in a
n instrumented
building before structural damage has occurred. As
pre
-
Northridge steel MRFs are susceptible to the brittle
failure of
welded
beam
-
column connec
tions,
these would be
the locations of probable failure
for this type of building
.
2)
A
t each
labeled
location
, apply a
short
-
duration
high
-
f
requency
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 function
s are
archived in the catalog of
templates to be used later
to screen the high
-
frequency
seismogram for a damage signal.
3)
Fo
r each possible source location
k, p
erform
a running
cro
ss
-
correlation between
the
Green’s function template
s
for
that
source location
and a moving window of
the
seismogram
that recorded the shaking event
, stacking over
the receivers.
C
ross
-
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
(1)
Time
T
is the
duration
of the template,
and
the
cross
-
correlation is normalized by the autocorrelation values
for the given time window.
Compute the
stacked cross
-
correlation
function
by
summing
over
the
R receiver locations
to
obtain
(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 one
at the correc
t time of
the
structural damage
event
.
In the case of multiple locations of
dama
ge
, then
the
stacked cross
-
correlation functions should
each peak at a value close to one at the corresponding times
,
provided
the co
rrect
Green’s function template
s are used
.
This
procedure could be extended to the
three
-
dimensional
case
.
The proposed method makes some assumptions
.
The
first is
that the signal due to the
failure
event will be
observable over the predominant building response to
seismic loading.
Rodgers et al
. (2007) carried out
experimentation on
a
one
-
third scale model steel moment
frame
and found that “high
-
frequency high
-
amplitude
transient accelerations” were observable over the structural
response to shaking and
could be attributed to
connection
fracture
.
They further analyzed building records from the
1994 Northridge earthquake
by
identifying transie
nt signals
and classifying the
possible causes, and they
were able to
determine with a 67% success rate
whether each building
h
ad undergone connection fractu
re
.
A second assumption is that the template will not change
significantly over time.
However, it
has been shown that
changes in environment
al conditions as well as moderately
large local earthquakes can lead to
observed changes in a
building’s natural
frequency
(Clinton et al. 2006). T
his has
not been extended to
observed
changes in
wave propagation
through
the
structural components of the building
.
A similar
matched
filter
method has been
successfully
employed by
Gibbons
and Ringdal
(2006)
to
detect
s
imilar
low
-
magnitude
seismic
events
by cross
-
correlating
a
waveform template with successive time segments of
incoming data and stacking over the seismic array.
A third assumption is that the sensor network will
be
able
to capture waves propagating awa
y from the
damage
location
throughout the structure
. Kohler
et al. (2009)
ha
ve
carried out preliminary experimentation
on the UCLA
Factor building using hammer blow
s
to
generate
Green’s
function
templates
. T
he structural response to
the
hammer
blow was obs
ervable
well above
ambient noise
, and the
signal could be seen to propagate
awa
y from the source
location at a
downsampled
rate of 200 sps, achieved by
filtering the
500 sps accelerometer array data for
frequencies
between 10 and
95 Hz
.
A fourth assump
tion is that the Green’s function
template will be similar to the damage signal. This
assumption
is addressed
in
S
ection
4
.
3
.
A
TIME
-
REVERSED
RECIPROCAL
NUMERICAL EXPERIMENT
A time
-
reversed reciprocal method is applied to
demonstrate that the locat
ion of
a nondestructive
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impulse
-
like
force can be determined by using the
numerically computed
displacement records
to time
-
reverse
and retransmit the signal
.
First, the
response
of a
two
-
story
one
-
bay
steel frame
to an impulse
-
like force applied to a
beam
-
column connection
is computed
.
A
cross section of
the
three
-
dimensional
steel
model is
shown in Fig
ure
1
below
.
Each beam and column has a square cross section of
length 0.5 m.
The model parameters are
governed by
linear
elastic material properties of A36
structural steel (E = 200
GPa,
μ
= 80 GPa,
ρ
= 7850 kg/m
3
), which cor
respond to
seismic velocities of
c
s
=
3.2 km/s
and
c
p
=
5.6 km/s
. The
hex 8 mesh elements
have a
discretizat
ion length
of
2.5 cm
;
the total time is
4
ms
with a time step of
2
μ
s.
CUBIT i
s
used for mesh generation, PyLith for physics code, and
ParaView for visualization
(Aagaard
2008
)
.
3
.1 Forward
Simulation
The
response
of
the
steel frame
to an impulse
-
like force
applied to a beam
-
column connection
is computed.
As
shown in Figure 1
above
,
the force is applied
along the
positive x
-
axis
to the close
-
up
section of the connection.
The
total force is distributed proportionally over nodes according
to the amount of surface area contained by each node.
The
force
-
time history is a Ricker
wavelet.
W
aves propagate away f
rom the location of the source,
reflecting off the edges of the
frame
,
as
shown
in Figure 2
below
. Resu
lting displacements
are recorded at
the twelve
receiver locations
approximately
evenly spa
ced
along the
cen
tral cross
section of the frame. A representative sample of
displacements is
provided in Figure 3(a)
below.
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Figure 1
Numerical Setup for Steel Frame: (a)
Impulse
-
like force is applied at beam
-
column connection in
a direction parallel to the x
-
axis (b) Ricker wavelet is used
for time
-
force history.
Figure
2
Re
sponse of Steel Frame to Nondestructive
Impulse
-
like
Force
Applied
to
Beam
-
Column
Connection.
125
μ
s
225
μ
s
325
μ
s
425
μ
s
525
μ
s
6m
8m
F
a
(t)
0.05 m
F
a
(t)
(a)
(b)
(a)
(b)
Figure
3
Receivers, Sources
, and Displacement
s
:
(a)
Receiver locations
and
examples of
recorded displacemen
ts
for forward simulation. (b)
Source l
ocations
and
corresponding
prescribed time
-
reverse displacements for
reverse simulation.
Due to symmetry, d
z
(t) = 0.
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3
.2 Reverse
Simulation
Following the time
-
reversed reciprocal method, the
rec
eiver and source locations are interchanged, and each of
the displacement records is time
-
reversed and applied at the
respective new source location as prescribed Dirichlet
conditions
, as shown in Figure 3(b) above
.
The retransmitted
signal propagates thro
ugh the frame
,
and
the waves
generated by the
twelve
new source locations interfere
constructively to
focus
at
the original
source
location
S
1
,
where the nondestructive load was applied
,
and at the correct
time
.
To simplify timing, the
reverse
simulation
b
egins
at
-
4
ms and ends at 0 ms, with waves focusing on the
beam
-
column connection at the correct time of
-
125
μ
s
,
demonstrated in Figure 4 below
.
Thus, by using a
time
-
reversed reciprocal method, the recorded displacements
are used to determine the absolu
te time and location of the
original applied force.
4
.
NUMERICAL APPLICATION OF
MATCHED
FILTER METHOD
A time
-
reversed reciprocal method
as presented in the
previous section is not application
-
realistic, as the location of
th
e receiver may not coincide with the location of damage,
and thus, the focusing of the transmitted time
-
reversed signal
could go undetected.
The purpose of this
section
is to
investigate
numerically
an alternat
ive
yet similar approach
that makes use of Gre
en’s functions, waveform similarity,
and wave
propagation reciprocity.
The
matched filter
method
is used to screen
data
recorded by
a passive seismic
network
for waveform similarities to an archived
template,
ultimately relying on experimental, not simulat
ed, building
response.
To validate the feasibility of the proposed method
,
it is
first
necessary to
provide justification
for
using the
structural response to an impulse
-
like force to approximate
the structural response to an opening crack tensile stress.
4
.1
Comparison of
Structural Response to
Two
Different Source Conditions
The response of a
steel frame to two
different
loading
cases, an impulse
-
like force and
an opening crack tensile
stress
, both shown in Figure 5
,
is compared
to determine
whe
ther th
e waveform generated by
a
nondestructive
source
can be used to approximate the waveform generated by
a
structural
ly damaging
source
.
The same material prope
rties
and dimensions
as in Sect
ion
3
are used.
A square notch is
introduced
in the opening crack ten
sile stress case, to
simulate crack initiation
at
the
beam
-
column connection.
The square notch has
a length
of
0.05 m
, consistent with the
dimensions used for the
unnotched
frame
.
Resulting displacements an
d velocities are recorded at
four receivers located along the central cross
section of the
frame
, shown in Figure 6 below
. The simulation is repeated
at each of the four source locations for both a force impulse
and a tensile crack.
The d
isplacement record
s
, provided in Figure 7 below,
generated by using the nondestructive source
differ
significantly
between the
displacement records generated by
using the
structurally damaging source
s, primarily
due to the
static
offset
across
the
notch.
The two sets of v
el
ocity
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Figure 5
Numerical Setup: (a) Impulse
-
like force using
Ricker wavelet force
-
time history applied to top left
beam
-
column connection in an unnotched frame
, and (b)
Opening crack tensile stress using error function force
-
time
history applied to the same connection in a notched frame.
-
125
μ
s
-
155
μ
s
-
185
μ
s
-
215
μ
s
-
245
μ
s
Figure
4
Response of Steel Frame to Pres
cribed
Time
-
Reversed Displacements. Waves generated at each of
the twelve source locations converge at the correct location
at the correct time.
F
a
(t)
F
b
(t)
(a)
(b)
F
a
(t)
F
b
(t)
F
b
(t)