Available online at www.sciencedirect.com
ScienceDirect
Procedia Engineering 188 (2017) 170 – 177
6th Asia Pacific Workshop on Structural Health Monitoring, 6th APWSHM
IMPACT LOCATION IN AN ISOTROPIC PLATE WITHOUT
TRAINING
Prasanna Rajbhandaria, Kenan Tautgesa, Sahithi Chatradia, Nathan Salowitza*
a
University of Wisconsin – Milwaukee, Department of Mechanical Engineering, 3200 N Cramer St #955, Milwaukee, WI 53211, U.S.A.
Abstract
Unexpected impacts are a major concern in the aerospace industry that can result in hard-to-detect damage.
Techniques have been developed to detect and locate impacts based on time difference of arrival of strain waves
propagating to piezoelectric sensors. Current systems typically utilize data from 4 sensors to calculate an impact
location and are dependent on the knowledge of the speed of wave propagation in the material or other training data.
Training data, like wave propagation velocity, can vary with temperature changes or frequency generated requiring
large databases of reference data that can be hard to collect.
This paper presents a method of impact detection and location based on hyperbolic positioning, suitable for isotropic
homogenous plates, that does not require training. A closed form solution to the underlying location equations is
presented which works for general, non-specific, layouts of omnidirectional sensors without knowledge of the wave
velocity in the structure. The lack of training data overcomes issues of variation in wave propagation velocity due to
temperature changes or other properties. The paper outlines the mathematical formulation, system hardware design
considerations, and experimental testing of the system. The calculation simultaneously produces impact location
and wave velocity results.
© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2016 The Authors. Published by Elsevier Ltd.
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the 6th APWSHM.
Peer-review under responsibility of the organizing committee of the 6th APWSHM
Keywords: Impact Detection; Training Free, Strain Wave, Time Difference of Arrival; TDOA; Hyperbolic Positioning; Multilateration
* Corresponding author. Tel.: +1-414-229-2228.
E-mail address: Salowitz@UWM.edu
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of the 6th APWSHM
doi:10.1016/j.proeng.2017.04.471
Prasanna Rajbhandari et al. / Procedia Engineering 188 (2017) 170 – 177
1. Introduction
The aerospace industry is particularly interested in detecting and locating impacts that can be caused by foreign
objects kicked up from a runway or those occurring in flight. If left unaddressed, impact damage can lead to
catastrophic failure. For example, during the launch of the space shuttle Discovery, STS-107, a piece of foam insulation
broke off from the space shuttle external tank and struck the left wing of the orbiter. A few previous shuttle launches
had seen minor damage from foam shedding and had survived atmospheric re-entry. However, in this case, the damage
resulted in the failure of the shuttle’s thermal protection panels and the orbiter broke apart upon re-entry [1]. An
embedded impact detection and location system could have confirmed the impact and guided inspection, potentially
preventing the loss.
Nomenclature
TDOA Time Difference of Arrival
PZT
Lead Zirconate Titanate piezoelectric transducer
1.1. Background
Significant previous research has been done on impact detection and location because of its potential benefit. Most
of the systems that have been developed use Time Difference of Arrival (TDOA) techniques for hyperbolic positioning
or multilateration. Time difference of arrival methods are based on measuring the difference in time of the arrival of
a strain wave, generated by the impact, at multiple sensors in known locations and varying distances from the impact
location. Lead Zirconate Titanate (PZT) piezoceramic sensors are typically used to detect the strain wave signal. In
these techniques, the actual time of impact is an unknown. Based on the difference in time of arrival, combined with
knowledge of the wave propagation velocity in the material, information from 2 sensors can map out a hyperbola of
possible locations. Adding a 3rd sensor generates another hyperbola of possible positions that can intersect the first
hyperbola at multiple points. Adding sensors adds hyperbolas, reducing possible locations. Prior work has depended
on knowledge of the strain wave propagation velocity in the structure to generate these hyperbolas to form a unique
solution. In anisotropic materials, tricks can be used to account for differing strain wave propagation velocities in
different directions. However, all of these techniques require foreknowledge of the structure’s properties either in the
form of wave propagation velocity or training data.
Many techniques have been developed to use the time of arrival of signals in isotropic plates with knowledge of
the velocity of wave propagation in the plate. Most common systems can locate an impact in an isotropic plate with
4 omni-directional sensors. More advanced methods have been developed for impact location, sometimes in
anisotropic material structures, using reduced sets of directional sensors for triangulation, using specific sensor
layouts, and/or using large sets of training data [2,3,4]. Some even overcome training requirements using these
techniques.
1.2. Challenges
Existing impact detection and location techniques require training data, knowledge of the velocity of wave
propagation in the structure, directional sensors, and/or specific sensor layouts. Unfortunately, this is time consuming
and it can be particularly challenging to collect data representative of impacts of interest in various structural states.
For example, temperature variations in the structure can vary the wave propagation velocity. Similarly, differing
compositions of colliding objects impacting with differing force and energy may also affect the strain waveform and
propagation velocity. Some techniques have sought to overcome this issue through the use of specific geometric
sensor configurations, functionally creating directional sensors requiring that events occur ‘far’ from the sensor array.
171
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2. Problem
An algorithm was developed to provide impact detection and location capabilities in an isotropic plate without
training data or knowledge of the speed of wave propagation in the structure using a general set of non-directional
sensors in unspecified configurations. While unknown, the velocity of wave propagation was assumed to be constant.
3. Approach
The approach pursued was to develop an algorithm based on the TDOA equations maintaining the wave
propagation velocity as a single unknown. To compensate for this additional unknown, an additional equation was
added to the algorithm based on data from an additional sensor. Sensor layouts were also limited such that no 3
sensors laid on a single line to ensure unique solutions. The algorithm was verified with simulations and experiments.
4. Major Tasks
Major tasks to accomplish this consisted of: 1) Algorithm development based on TDOA equations. 2) Algorithm
testing based on calculated/simulated data. 3) Experimental testing on multiple specimens. Experimental testing
required signal and data conditioning to ensure useful data was collected and meaningful results were produced.
4.1. Algorithm Development
TDOA systems are based on manipulation of the relationship between velocity, distance, and elapsed time with the
basic equation (1) where: ti is the time of signal arrival at sensor i, t0 is the time of signal initiation (impact), Di is the
distance between the impact location and sensor i, and V is the velocity the signal travels.
ti t0
Di
V
(1)
In the situation of interest t0, Di, and V are unknown. Manipulation of these equations for sensors 1 and 2 results
in equation (2), known as the time difference of arrival equation.
t 2 t1
D2 D1
V
(2)
Complicating matters, for impact location, Cartesian coordinates are usually desired as opposed to a distance. The
TDOA equations (2) for 5 sensors were manipulated in vector notation to solve for impact location in x-y coordinates
(X0 and Y0) and velocity (V) of wave propagation. The impact location was found in matrix form in equation (3) with
the terms defined in equations (4) to (9) where Xi is the X location of sensor i and Yi is the Y location of sensor i. after
calculating the impact location, calculating the wave propagation velocity was relatively straightforward based on
equation (11). The full mathematical derivation and manipulation was developed from first principles and can be
found in the thesis by Prasanna Rajbhandari using a methodology based on the work by Ezzat Bakhoum [5,6].
ª a11
«a
¬ 21
a12 º ª X 0 º
a 22 »¼ «¬ Y0 »¼
a11
2 X 3 X1
2 X 2 X1
2 X 2 X1
2 X 4 X1
t 2 t1 t 3 t 2
t 3 t1 t 3 t 2
t 2 t1 t 4 t 2
t 4 t1 t 4 t 2
ª b1 º
«b »
¬ 2¼
(3)
(4)
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Prasanna Rajbhandari et al. / Procedia Engineering 188 (2017) 170 – 177
a12
2 Y3 Y1
2 Y2 Y1
2 Y2 Y1
2 Y4 Y1
t 2 t1 t 3 t 2
t 3 t1 t 3 t 2
t 2 t1 t 4 t 2
t 4 t1 t 4 t 2
(5)
a 21
2 X 3 X1
2 X 5 X1
2 X 2 X1
2 X 2 X1
t 2 t1 t 3 t 2
t 3 t1 t 3 t 2
t 2 t1 t 5 t 2
t 5 t1 t 5 t 2
(6)
a 22
2 Y3 Y1
2 Y5 Y1
2 Y2 Y1
2 Y2 Y1
t 2 t1 t 3 t 2
t 3 t1 t 3 t 2
t 2 t1 t 5 t 2
t 5 t1 t 5 t 2
(7)
b1
X 22 Y22 X 12 Y12
X 2 Y22 X 12 Y12
2
t 2 t1 t 3 t 2
t 2 t1 t 4 t 2
(8)
X 2 Y32 X 12 Y12
X 2 Y42 X 12 Y12
3
4
t 3 t1 t 3 t 2
t 4 t1 t 4 t 2
b2
X 22 Y22 X 12 Y12
X 2 Y22 X 12 Y12
2
t 2 t1 t 3 t 2
t 2 t1 t 5 t 2
(9)
X 2 Y32 X 12 Y12
X 2 Y52 X 12 Y12
3
5
t 3 t1 t 3 t 2
t 5 t1 t 5 t 2
V
­ 2> X 2 X 0 Y2Y0 X 1 X 0 Y1Y0 @ 2> X 3 X 0 Y3Y0 X 1 X 0 Y1Y0
°
t 2 t1
t 3 t1
1 °
®
t 3 t 2 ° X 22 Y22 X 12 Y12
X 2 Y32 X 12 Y12
3
°¯
t 2 t1
t 3 t1
@½
°
°
¾ (10)
°
°¿
4.2. Testing with simulated data
The algorithm presented was tested on simulated data by selecting mock sensor locations, an impact location, and
signal propagation velocity. From this information the times of arrival of the signal at each sensor was calculated.
Sensor locations and the calculated time data were input into the algorithm, which then re-constructed the impact
location and propagation velocity. Multiple sensor geometries were tried in a loop that simulated an impact every cm
of the geometry. The resulting calculated location and velocity were within machine precision of the simulated
location for every trial.
4.3. Experimental Testing
Experimental testing was significantly more complicated than simulated testing due to the realities of sensing,
signals, and measurement. Two different test specimens were created made of 6061-T651 aluminum, measuring 30.5
cm by 30.5 cm. One sample was 1 mm thick and the other was 5 mm thick. Circular disk piezoelectric sensors
composed of APC-850 PZT material and measuring 6 mm in diameter and 0.5 mm thick were adhered to the plates in
differing locations with circuit works CW2400 conductive epoxy and cured at 60ºC for a minimum of one hour [7]
[8]. Impacts at multiple locations on each specimen were performed with multiple impact materials including stainless
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Prasanna Rajbhandari et al. / Procedia Engineering 188 (2017) 170 – 177
steel and polyester. Data acquisition was performed with a pair of Tektronix MDO 3014 oscilloscopes that recorded
the electrical response of the PZTs in tandem at a sampling rate of 10 MHz [9].
Two 4 channel oscilloscopes were necessary to collect data from the minimum of 5 sensors necessary for this
algorithm. This introduced the first challenge; synchronizing the data on a single time scale. This was achieved by
connecting sensor 1 to both oscilloscopes and data from one oscilloscope was shifted to minimize the scatter signal
energy between the two different records of channel 1. Signals were also shifted to have zero average voltage before
strain wave arrival (pre-trigger points). In addition, some impacting objects appeared to have a small electrical
discharge that appeared as a simultaneous single point spike in all of the signals, while this completely synchronized
the signals it could also serve as a false threshold in the algorithm and therefore this errant data point was identified
and set to zero as well.
After signal conditioning, analysis required a signal feature to measure the time of arrival. Crossing of an absolute
threshold voltage was selected. It was found the different threshold voltages produced differing results, but in general
low threshold voltages provided more accurate results. Therefore, an approach of averaging the calculated location
across a range of threshold voltages was pursued, e.g. 0 to ±50 mV or ±40 to ±80 mV (to stay out of the noise). Post
calculation data processing was also used to remove errant or outlier solutions. Results produced by noise (typically
a few milliVolts) were identified by a combination of low Voltage threshold and arrival times within a few sample
points. Results from this data were ignored. Similarly, it was found that there was a moderate to strong correlation
between high calculated wave velocity and high error. Therefore, solutions with a calculated wave velocity above the
mean calculated wave velocity were also ignored. The remaining solutions were averaged to provide a unique impact
location. It is important to emphasize that, while knowledge of the actual impact location was used to develop, refine,
and improve these algorithms, knowledge of the actual impact location was not used in the actual algorithms. The
algorithms are based exclusively on signal data and calculated results. Additionally, results were not ignored because
of calculated location.
To further increase accuracy, a 6th PZT sensor was applied to the 5 mm thick specimen providing 6 combinations
of 5 sensors that could be used to calculate an impact location. It was initially hoped that data from this extra sensor
could be used to identify a single threshold voltage that produced minimal error in calculated impact location for each
individual impact but this effort has not been successful yet. Alternatively, simply averaging across the increased set
of calculated impact locations has shown increased accuracy. A photograph of the setup is shown in Fig. 1.
Fig. 1 – Setup of 5 mm thick Al 6061-T651 impact specimen with two oscilloscopes
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Prasanna Rajbhandari et al. / Procedia Engineering 188 (2017) 170 – 177
PZT sensors
10 cm
Fig. 2 – 1 mm thick plate of 6061 - T651 aluminium with 5 PZT sensors mounted
on it.
Sensor locations, actual measured impact location,
and calculated impact location on a 5 mm thick Al 6061-T651 plate
0.3
sensor
measured impact
calculated impact
Y coordinate
(m) (m)
Y dimension
of plate
0.25
0.2
0.15
0.1
0.05
0
0
0.05
0.1
0.15
0.2
0.25
0.3
X coordinate
X dimension
of (m)
plate (m)
Fig. 3 - Example output from 5 sensor impact location system showing
dimensions of the plate, sensor locations, a calculated impact location, and the
manually measured impact location. Linear error was 2.7 cm.
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Prasanna Rajbhandari et al. / Procedia Engineering 188 (2017) 170 – 177
5. Results
The algorithm was tested with numerous impacts in many locations on the two specimens, with widely varying
impact forces, and with multiple impacting materials ranging from tool steel to polyester. The felt tip of a marker was
even used and produced results within the normal range. A typical example is presented here to illustrate the system,
and a summary of the results from many tests is presented.
The 5 mm thick plate was impacted with a steel impactor at a (X,Y) location of (0.100,0.200). Location results
were calculated and averaged using 6 sensors with absolute thresholds from 40 to 80 mV in 1 mV steps. The result is
shown in Fig. 3. The calculated location was (0.0886, 0.2092) giving a linear error of 0.0147. It should be noted that
this is on the boarder of the accuracy of the impact location measurement.
Table 1 shows error in impact location calculation for multiple impacts at different locations made with steel and
polyester impactors. This data was collected on a 5 mm thick plate using data from 5 sensors and averaging solutions
produced with absolute thresholds from 40 to 80 mV in 1 mV steps. The average error in calculated impact location
for both impactor materials was 0.037 m. Table 6 shows data from a different set of impacts on the 5 mm thick plate
where all 6 sensors were used. Similarly, averaging solutions produced with absolute thresholds from 40 to 80 mV
in 1 mV steps, but in this case the solution error is shown for each of the combinations of 5 out of 6 sensors. Then, in
the last column, the location solutions of the 6 combinations are averaged to produce a single solution and the error
of that solution is shown. The average error of the 6 sensor solutions is 0.029 m.
Polyester
Impactor
Steel
Impactor
Table 1
Impact location
X (m)
Y (m)
0.152
0.152
0.200
0.150
0.070
0.100
0.140
0.240
0.100
0.200
0.152
0.152
0.200
0.150
0.070
0.100
0.140
0.240
0.100
0.200
Table 2
Impact location
Error for a single sensor combination
X (m)
0.200
0.063
0.100
0.135
0.182
1
0.024
0.010
0.040
0.047
0.009
Y (m)
0.150
0.170
0.200
0.240
0.100
2
0.027
0.040
0.034
0.037
0.008
3
0.022
0.023
0.043
0.044
0.023
4
0.002
0.059
0.043
0.026
0.009
Error (m)
0.01705
0.02699
0.02940
0.05339
0.05920
0.04571
0.01521
0.05502
0.04578
0.02295
5
0.011
0.060
0.041
0.061
0.050
Error with location averaged
across combinations
6
0.026
0.042
0.033
0.044
0.022
0.019
0.023
0.039
0.043
0.022
6. Conclusion
An impact location algorithm based on hyperbolic positioning techniques, that does not require knowledge of the
wave velocity in an isotropic plate, training data, or specific sensor layouts was developed from first principles. This
algorithm was codified with matlab and experimentally tested on aluminum plates with multiple thicknesses and
multiple sensor layouts. Multiple impact materials were used and no control was made for impact force or energy.
Experimental results showed comparable to error to other published work.
Prasanna Rajbhandari et al. / Procedia Engineering 188 (2017) 170 – 177
7. Future Work
The elimination of the need for reference data opens new opportunities for development. For example, this system
should work on any isotropic material independent of global environmental effects, such as temperature variation.
Though theoretically viable, experimental validation is necessary on isotropic structures composed of different
materials and at different temperature. Similarly, microfabricated, non-directional sensors should be able to provide
the data reducing parasitic effects on the host structure [10,11]. Stretchable network fabrication techniques can address
this but would need to overcome the issue of linear extension, resulting in multiple sensors in a single line which can
lead to non-unique solutions [12,13,14,15].
A similar approach to what was presented in this paper can also be employed in an attempt to address more complex
systems. For example, using 6 sensors it may be possible to identify a unique optimal marker of time of arrival in the
signals for each individual impact that results in the minimum error solution. Data from the 6th sensor could also be
employed to solve for other complicating factors. For example, if the speed of wave propagation can be adequately
correlated to perpendicular propagation directions in an orthotropic material, it may be possible to employ a baseline
free system with an additional sensor to provide an equation to solve for the additional unknown. The linear set of
equations this produces also provides an opportunity to include more sensor/data into the system in a nearly unlimited
manner and perform analysis on the effect of error. Similar systems could be applied to any emitter-receiver location
system, as long as the emitter signal travels at the same velocity in every direction.
8. Acknowledgement
This work was supported through department funds from the University of Wisconsin – Milwaukee
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