A numerical study is performed to gain insight into applying a novel method to detect high-frequency dynamic failure in buildings. The method relies on prerecorded catalog of Green's functions for instrumented buildings. 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 this 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 an opening crack tensile stress, is computed on a temporal scale of microseconds. Results indicate that the velocity waveform generated by a tensile crack can 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)

Heaton, Thomas H.

Heckman, Vanessa M.

Kohler, Monica D.

Caltech Authors - Main

A Method to Detect Structural Damage Using High-Frequency Seismograms

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 application to building types that are susceptible to a signature type of failure, where locations of potential structural damage are known a priori. In particular, this method has application to the detection of brittle fractures in welded beam-column connections in steel moment-resisting frames (MRFs). Such a method would be valuable if it could be used to detect types of damage that are otherwise difficult and costly to identify. 



The method makes use of a prerecorded catalog of Green's function templates and a matched filter method to detect the occurrence and location of structural damage in an instrumented building. This technique is different from existing acoustic methods because it is designed to recognize and use seismic waves radiated by the original brittle failure event where the event is not known to have occurred with certainty and the resulting damage may not be visible. 



The method is outlined as follows. First, identify probable locations of failure in an undamaged building. In pre-Northridge steel MRFs, which are susceptible to brittle failure of welded beam-column connections, those connections would be the locations of probable failure for this type of building. Second, obtain a Green's function template for each identified location of probable failure by applying a short-duration high-frequency pulse (e.g. using a force transducer hammer) at that location. One underlying assumption of this method is that the Green's function template specific to a potential location of failure can be used to approximate the dynamic response of the structure to structural damage at that location. Lastly, after a seismic event, systematically screen the recorded high-frequency seismograms for the presence of waveform similarities to each of the catalogued Green's function templates in order to detect structural damage. This is achieved by performing a running cross-correlation between each Green's function template and a moving window of the continuous data recorded during the earthquake. Damage that occurs at one of the catalogued potential locations is expected to result in a high cross-correlation value when using the correct Green's function template. This method, also known as the matched filter method, has seen recent success in other fields, but has yet to be explored in the context of acoustic damage detection in civil structures. 



Preliminary experimental results from tap tests performed on a small-scale laboratory frame are presented. Cross-correlation calculations highlight similarities among events generated at the same source location and expose differences among events generated at different source locations. Finally, a blind tap test is performed to test whether cross-correlation techniques and catalogued Green's function templates can be used to identify the occurrence of and pinpoint the location of an assumed-unknown event

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ABSTRACT 
 
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 application to building types that are susceptible to a signature type 
of failure, where locations of potential structural damage are known a priori. In 
particular, this method has application to the detection of brittle fractures in welded 
beam-column connections in steel moment-resisting frames (MRFs). Such a method 
would be valuable if it could be used to detect types of damage that are otherwise 
difficult and costly to identify. 
The method makes use of a prerecorded catalog of Green’s function templates 
and a matched filter method to detect the occurrence and location of structural damage 
in an instrumented building. This technique is different from existing acoustic 
methods because it is designed to recognize and use seismic waves radiated by the 
original brittle failure event where the event is not known to have occurred with 
certainty and the resulting damage may not be visible.  
The method is outlined as follows. First, identify probable locations of failure in 
an undamaged building. In pre-Northridge steel MRFs, which are susceptible to brittle 
failure of welded beam-column connections, those connections would be the locations 
of probable failure for this type of building. Second, obtain a Green’s function 
template for each identified location of probable failure by applying a short-duration 
high-frequency pulse (e.g. using a force transducer hammer) at that location. One 
underlying assumption of this method is that the Green’s function template specific to 
a potential location of failure can be used to approximate the dynamic response of the 
structure to structural damage at that location. Lastly, after a seismic event, 
systematically screen the recorded high-frequency seismograms for the presence of 
waveform similarities to each of the catalogued Green’s function templates in order to 
_____________ 
 
Vanessa M. Heckman, California Institute of Technology Mail Code 104-44, 1200 East 
California Blvd, Pasadena, CA 91125, U.S.A.  
Monica D. Kohler, California Institute of Technology, 1200 East California Blvd, Pasadena, CA 
91125, U.S.A.  
Thomas H. Heaton, California Institute of Technology, 1200 East California Blvd, Pasadena, 
CA 91125, U.S.A.  
detect structural damage. This is achieved by performing a running cross-correlation 
between each Green’s function template and a moving window of the continuous data 
recorded during the earthquake. Damage that occurs at one of the catalogued potential 
locations is expected to result in a high cross-correlation value when using the correct 
Green’s function template. This method, also known as the matched filter method, has 
seen recent success in other fields, but has yet to be explored in the context of acoustic 
damage detection in civil structures.  
Preliminary experimental results from tap tests performed on a small-scale 
laboratory frame are presented. Cross-correlation calculations highlight similarities 
among events generated at the same source location and expose differences among 
events generated at different source locations. Finally, a blind tap test is performed to 
test whether cross-correlation techniques and catalogued Green’s function templates 
can be used to identify the occurrence of and pinpoint the location of an assumed-
unknown event.  
 
 
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 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, Wang et al. 2004), which serve as 
waveguides 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 diagnose 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 uses a 
transmitter to interrogate the structure while a receiver records the structural response. 
1) Pitch-catch: A pulse 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 damage in the medium between the transmitter and receiver. 
2) Pulse-echo: A pulse is emitted by a transmitter, 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 receiver, where the 
signal is time-reversed and reemitted. Structural damage that causes linear reciprocity 
to break down leads to discrepancy between the original signal and the final signal 
received by the transmitter.  
4) Migration: Recorded waves are back-propagated 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 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. The matched filter method has been successfully used in other fields 
(Gibbons and Ringdal 2006, Anstey 1964), but the method has yet to be explored in 
the context of acoustic damage detection of civil structures.  
 
 
METHOD 
 
The proposed method would make 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 is 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 failure 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 possible 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 kth Green’s function template xik recorded by the ith receiver 
and the seismogram xi recorded by the ith 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 kth source location, the stacked cross-
correlation function given by Eq. (2) should peak at a value close to one 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 one at the 
corresponding times, provided the correct Green’s function templates are used. This 
procedure could be extended to the three-dimensional case. 
    
! 
Cik (t) =
xik (")xi(t +")d"
0
T
#
xik (")( )
2d"
0
T
# xi(t +")( )
2d"
0
T
#
$ 
% 
& 
' 
( 
) 
1/ 2 .
! 
Ck (t) = 1R Ci
k (t)
i=1
R
" .
Figure 1. Instrumented steel frame (right) and beam-column connection (left).  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
EXPERIMENTAL TESTING 
 
Tap tests were conducted on a small-scale steel frame to study the feasibility 
of the proposed method. Resulting Green’s functions were analyzed using cross-
correlation techniques to verify the similarity between events generated at the same 
source location and to expose the difference between events generated at different 
source locations. Finally, a blind tap test was performed to confirm whether the 
prerecorded Green’s functions could be used to determine where and when a later 
hammer blow occurred.  
 
Experimental Setup  
 
A small-scale steel frame instrumented with four accelerometers, as shown in Fig. 
1 and 2, was subjected to hammer blows at beam-column connections by using a force 
transducer hammer. The experimental setup includes:  
• Small-scale steel frame 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 
 
(Right) Steel frame instrumented 
with four uniaxial accelerometers 
is subjected to hammer blows at 
the eight anterior beam-column 
connections. The base is pinned to 
the floor. 
 
(Left) The hammer blow is applied 
out-of-plane at the center of the 
bolted beam-column connection.  
 
Figure 2. Steel frame dimensions and accelerometer locations. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Experimental Method  
 
Green’s functions were generated by using a force transducer hammer to apply 
an impulsive force load at each of the eight connections shown in Figures 1 and 2 
above. Four accelerometers captured the response of the frame. The sample frequency 
was 200kHz and the record time duration was 2.5 seconds. A total of 7 trials were 
repeated at each source location. The recorded Green’s functions were then cross-
correlated by using autocorrelation normalization and stacking over the four receivers, 
as was done in Equations 1 and 2. The time delay from the cross-correlation is 
compared to the relative time difference of the hammer blows, to see how precise the 
cross-correlation timing is. A blind tap test was performed to determine whether the 
prerecorded Green’s functions could be used to pinpoint the locations of the taps. A 
sample recording is shown in Figure 3. 
 
Figure 3. Recorded hammer data (top) and R1 acceleration (bottom) for source location A. 
0 0.5 1 1.5 2 2.5
?1
0
1
2
Am
pli
tu
de
 (V
)
0 0.5 1 1.5 2 2.5
?2
0
2
Time (s)
Am
pli
tu
de
 (V
)
 
FE
R4R3
Second Floor
BA
R2R1
Fourth Floor
x
y
HG
FE
A B
C D
0.8 m
1.
1 
m
x
z
x
y
Accelerometer
Receiver Locations
R1 R2 R3 R4
Hammer Blow
Source Locations
A B C D E F G H
Column C-SBeam C-S
1 cm5 cm
5.
5 
cm6 mm
The steel frame is 
subjected to hammer 
blows directed along 
the positive y-axis at 
each of the eight 
locations shown to 
the right.  
 
A total of 4 uniaxial   
(y-direction) 
accelerometers are 
located on the fourth 
and second floors. 
They record positive 
acceleration along 
the positive y-axis. 
 
Figure 4. Comparison of A-A and A-H stacked cross-correlations. 
 
?2.5 ?2 ?1.5 ?1 ?0.5 0 0.5 1 1.5 2 2.5
?0.5
0
0.5
1
Time (s)
Am
pli
tu
de
 
 
Experimental Results 
 
The cross-correlation statistics were computed and shown in Tables I and II on 
the following page. The maximum amplitude of the cross-correlation, as shown in 
Figure 4 above, is used as an indicator of how similar the two waveforms are. The 
maximum amplitude is highest when comparing Green’s functions generated at the 
same source location. The hammer time series is used to compute the reference time 
difference between the two taps, and the time error is calculated as the difference 
between the reference time difference and the cross-correlation time delay. The time 
error is smallest when the same source location is used for the two signals.  
A blind tap test, shown in Figure 5 below, was performed using three taps in 
unknown locations. A number of tap tests were performed. One of these tap tests was 
selected at random, and analyzed to see if the tap locations could be determined. 
Stacked cross-correlations between the test data and the Green’s function for each 
source location were computed and compared to determine the three locations. Three 
cross-correlation peaks stand out in the comparison: B, A, and A. The actual locations 
were revealed at the end, after the selection had been made. The chosen locations were 
indeed the three locations used for the blind test. Note that the cross-correlation values 
no longer range from 0 to 1 due to the multiple peaks in the blind tap test record. The 
time errors fell between -10 µs and 10 µs. 
 
Figure 5. Blind tap test consisting of three taps at unknown locations. Recorded hammer data (top), R1 
acceleration (middle), stacked cross-correlation comparison (bottom).  
0 0.5 1 1.5 2 2.5
?1
0
1
2
3
0 0.5 1 1.5 2 2.5
?2
0
2
Am
pli
tu
de
 (V
)
?2.5 ?2 ?1.5 ?1 ?0.5 0 0.5 1 1.5 2 2.5
?0.2
0
0.2
0.4
Time (s)
A-A and A-H stacked cross- 
correlations have maximum 
amplitudes of 0.94 and 0.10, 
respectively.  
TABLE I. STACKED CROSS-CORRELATION MAXIMUM AMPLITUDE VALUE: 
           MEAN, STANDARD DEVIATION, AND NUMBER OF PAIRS 
     Source Location    
   A B C D E F G H 
So
ur
ce
 L
oc
at
io
n 
 µ 0.85 0.22 0.12 0.10 0.12 0.09 0.09 0.10 
A ! 0.06 0.01 0.02 0.01 0.01 0.01 0.01 0.01 
 N 21 49 49 49 49 49 49 49 
          
 µ 0.22 0.83 0.10 0.12 0.10 0.10 0.10 0.09 
B ! 0.01 0.06 0.01 0.03 0.01 0.01 0.01 0.01 
 N 49 21 49 49 49 49 49 49 
          
 µ 0.12 0.10 0.86 0.12 0.19 0.12 0.19 0.12 
C ! 0.02 0.01 0.05 0.01 0.01 0.01 0.01 0.01 
 N 49 49 21 49 49 49 49 49 
          
 µ 0.10 0.12 0.12 0.83 0.09 0.18 0.11 0.15 
D ! 0.01 0.03 0.01 0.05 0.01 0.02 0.01 0.02 
 N 49 49 49 21 49 49 49 49 
          
 µ 0.12 0.10 0.19 0.09 0.82 0.11 0.17 0.14 
E ! 0.01 0.01 0.01 0.01 0.05 0.01 0.03 0.01 
 N 49 49 49 49 21 49 49 49 
          
 µ 0.09 0.10 0.12 0.18 0.11 0.78 0.13 0.16 
F ! 0.01 0.01 0.01 0.02 0.01 0.06 0.01 0.04 
 N 49 49 49 49 49 21 49 49 
          
 µ 0.09 0.10 0.19 0.11 0.17 0.13 0.80 0.18 
G ! 0.01 0.01 0.01 0.01 0.03 0.01 0.06 0.02 
 N 49 49 49 49 49 49 21 49 
          
 µ 0.10 0.09 0.12 0.15 0.14 0.16 0.18 0.80 
H ! 0.01 0.01 0.01 0.02 0.01 0.04 0.02 0.04 
  N 49 49 49 49 49 49 49 21 
 
TABLE II. STACKED CROSS-CORRELATION TIME ERROR:  MEAN AND STD DEVIATION 
     Source Location    
   A B C D E F G H 
So
ur
ce
 L
oc
at
io
n 
 µ (µs)  -7 1370 -1900 2500 -620 -840 2600 470 
A ! (µs) 15 15 2300 930 840 2700 5900 2200 
 µ (µs)  1370 5 -2100 2500 -2100 -1600 -2100 900 
B ! (µs) 15 17 1800 3900 2400 5400 1600 5800 
 µ (µs)  -1900 -2100 -20 -1200 190 -40 600 -2000 
C ! (µs) 2300 1800 33 2000 250 2100 30 1900 
 µ (µs)  2500 2500 -1200 14 -140 330 -830 420 
D ! (µs) 930 3900 2000 24 2700 27 2000 58 
 µ (µs)  -620 -2100 190 -140 4 950 280 -2300 
E ! (µs) 840 2400 250 2700 23 2700 69 1100 
 µ (µs)  -840 -1600 -40 330 950 -3 1300 520 
F ! (µs) 2700 5400 2100 27 2700 25 890 760 
 µ (µs)  2600 -2100 600 -830 280 1300 -1 1400 
G ! (µs) 5900 1600 30 2000 69 890 23 332 
 µ (µs)  470 900 -2000 420 -2300 520 1400 7 
H ! (µs) 2200 5800 1900 58 1100 760 332 12 
 
  
DISCUSSION 
 
Experimental results support the feasibility of the proposed method. However, it 
remains to be seen whether waveform cross-correlation will be successful when the 
source mechanism is different from a hammer blow, as is the case for structural 
damage at a beam-column connection. It is possible that a different cross-correlation 
method will be more robust, especially one that is weighted based on the amplitude of 
the acceleration record.  
 
 
CONCLUSION 
 
Preliminary experimental results from tap tests performed on a small-scale 
laboratory frame are presented. Cross-correlation calculations highlight similarities 
among events generated at the same source location and expose differences among 
events generated at different source locations. Finally, a blind tap test was performed. 
Cross-correlation techniques and catalogued Green’s function templates were used to 
successfully identify the occurrence of and pinpoint the location of an assumed-
unknown event. Experimental results pave the way for damage event detection 
experiments that cross-correlate pre-recorded Green's function templates with the 
response of the structure to damage. 
 
 
REFERENCES 
 
1. Park, H.W., Sohn, H., Law, K.H., and Farrar, C.R. 2007. “Time reversal active sensing for health 
monitoring of a composite plate,” Journal of Sound and Vibration 302(1-2): 50-66.  
2. Wang, C.H., and Rose, L.R.F. 2003. “Wave reflection and transmission in beams containing 
delamination and inhomogeneity,” Journal of Sound and Vibration, 264(4): 851-872. 
3. Wang, C.H., Rose, J.T., and Chang, F.K. 2004. “A synthetic time-reversal imaging method for 
structural health monitoring,” Smart Materials and Structures, 13(2): 415-423. 
4. Giurgiutiu, V. and Cuc, A. 2005. “Embedded Non-destructive Evaluation for Structural Health 
Monitoring, Damage Detection, and Failure Prevention,” Shock and Vibration Digest, 37(2): 83-10. 
5. Gibbons, S.J. and Ringdal, F. 2005. “The detection of low magnitude seismic events using array-
based waveform correlation,” Geophysical Journal International, 165(1): 149-166. 
6. Anstey, N.A. 1964. “Correlation Techniques – A Review,” Geophysical Prospecting, 12(4): 355-
382. 
 


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A Method to Detect Structural Damage Using High-Frequency Seismograms

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