1. 1
Environmental Effects Compensation for
Ultrasonic Guided Waves
Shangheng Li
A53082157

2. 2
Content
Chapter 1:Background................................................................................................3
1.1 Ultrasonic Guided Waves.................................................................................3
1.2 Environmental effects on UGWs.....................................................................4
Chapter 2:Approach....................................................................................................5
2.1 Compensation Techniques ...............................................................................5
2.2 Scale-Invariant Correlation (SIC)....................................................................5
A. Purely Strecthing Signals compensated by SIC........................................6
B. Temperature effects compensated by SIC.................................................7
2.3 Improvement of SIC- Regressive Phase Coherence (RPC).............................8
2.4 Performance Metric .......................................................................................13
A. Normalized Root-Mean-Square Error.....................................................13
B. Local Phase Difference ...........................................................................14
Chapter 3:Experiment .............................................................................................16
3.1 Signal Processing...........................................................................................16
3.2 Dispersion Curve ...........................................................................................16
3.3 Temperature Experiment ...............................................................................18
3.4 Bending Experiment ......................................................................................19
3.5 Experiment Result and Discussion ................................................................20
A. Result of Temperature Experiment.........................................................20
B. Result of Bending Experiment................................................................23
Chapter 4:Summary ..................................................................................................27
References...................................................................................................................28

3. 3
Chapter 1: Background
1.1 Ultrasonic Guided Waves
Structural Health Monitoring (SHM) is the process of implementing a damage
detection and characterization strategy for engineering structures. The applications of
SHM rapidly develop in various industrial field (e.g. composite material in aerospace
and pipelines in oil). SHM has a distinct advantage over traditional inspection
techniques; they offer real-time, continuous analysis and detection of damage without
damaging the structure. Moreover, the embedded transducers of SHM systems
significantly reduce maintenance costs and inspection time, and also overcome the
accessibility challenges of unreachable structures.
Ultrasonic guided wave (UGW) is one of the most popular candidates for SHM systems.
UGW is constrained by the boundaries of structure that enables the waves propagate
a long distance without losing much energy, and this property also enables the waves
to propagate in large areas. In general, the range of frequencies used for SHM is
between 10~100 kHz. Although higher frequencies is used in some specific cases, it
reduces the detection range significantly. In the applications of SHM, the UGW is
acquired by traducers and turned into digital signals. The signals go through a
sequence of processes including data normalization and cleaning, extraction of
damage-sensitive features, statistical analysis of features, and then the current state
of system health could be determined.

4. 4
1.2 Environmental effects on UGWs
In ultrasonic guided wave structural health monitoring system, the changing
environmental conditions considerably influences the damage detectability. In
complex structures, the acquired signals always accompany with large number of
overlapping reflections in time-traces. To eliminate the need for interpretation of the
complex signals and to observe the defects clearly, baseline subtraction technique is
widely used to detect the defects in structures. Baseline subtraction technique is
mainly subtracting current signal from baseline. The amplitude of residual signal is low
if there are no damages in structures. On the contrary, if there are damages in
structures, the amplitude of residual signal increases in specific location in time-trace.
However, environmental effects change both phase and amplitude of the signal. These
changes result in large amplitude in residual signal which may mask the information
received from reflection of defects and severely decreases the damage detectability
Temperature effect has the greatest influence on ultrasonic guided waves among all
other environmental effects. Even a small amount of temperature change produces
significant changes in signal. When structure is under temperature effect, the elastic
properties and density changes, and the changes further affect velocity of wave
propagation in structure. The different wave velocities result in the phase shift
between baseline and signal with temperature effect. Not only the material of
structures, but also the transducers and bonding are affected by temperature effects.
The degradation of bond condition decreases the amplitude. However, the effects on
transducers and bonding are relatively small, so the following compensation will not
take these effects into account.

5. 5
Chapter 2: Approach
2.1 Compensation Techniques
In general, there are two different methods widely used in the compensation for
environmental effects. One is optimal baseline selection (OBS) [1], and the other one
is baseline signal stretch (BSS) [2]. Essentially, the two approaches are based on
different philosophy. In OBS, a large set of baseline in different environmental
conditions is recorded and the best matched waveforms will be selected as the
baseline from the baseline set. In BSS, only single baseline data at an arbitrary
reference temperature is needed. BSS compensates the temperature effects by
stretching the baseline with a certain stretching factor which minimizes the difference
between baseline and temperature affected signals. BSS assumes that the
temperature influencing the velocity of waves is constant, which results in all the time
of flights of each wave packets to arrive with increasing delay. The following chapter
will introduce the Scale-Invariant Correlation (SIC) [3] which is a temperature
compensation technique based on BSS assumption, and it can well estimate the
optimized stretching factor. Another compensation technique is Instantaneous Phase
Correction (IPC) [4], and it will be compared with the result of SIC and the
improvement of SIC in the following chapters.
2.2 Scale-Invariant Correlation (SIC)
The model used to drive the development of this algorithm was a stretch-based
temperature model illustrated by the following equation
𝑇𝛼{ 𝑥( 𝑡)} ≈ 𝑥( 𝛼𝑡)
where 𝑇𝛼{. } is the change of temperature of the guided wave signal, { 𝑥( 𝑡)} ,
and 𝑥(𝛼𝑡) is the compensated stretched signal. The temperature effect is thought of
as a phase stretch to first order, where the stretch in the signal proportionally stretches
longer for later parts in the signal. In this case, the problem is defined as minimizing
the normalized squared error between the temperate affected signal and the baseline
signal to determine an optimal stretch factor 𝛼̂ which is defined as follow
𝛼̂ = 𝑎𝑟𝑔 min
𝛼
∫ |
𝑥(𝑡)
𝜎 𝑥
−
𝑠(𝛼𝑡)
𝜎𝑠/√ 𝛼
∞
0
|2
𝑑𝑡,

6. 6
where 𝑥( 𝑡) is the signal with temperature effect, 𝑠( 𝛼𝑡) is the compensated
baseline signal, 𝜎𝑥 and 𝜎𝑠 are the standard deviations of the two signals respectively.
The scale-invariant correlation method (SIC) will be used in order to efficiently solve
the optimization problem. The first step is to take both signals 𝑠( 𝑡) and 𝑥( 𝑡), and
resample each one exponentially in the time domain using a spline interpolation. It
enforces the algorithm to focus the optimization on the early parts of the signal. The
next step is to multiply both signals by an exponential envelope and then use the fast
Fourier Transform to arrive at the scale transform. To determine the optimal stretch
factor, we are going to maximize the scale cross-correlation and this could be
expressed by the following expression
𝛼̂ = 𝑎𝑟𝑔 min
𝛼
√ 𝛼
𝜎𝑥 𝜎𝑠
𝑒
−(
1
2
)τ
𝐹−1{ 𝑋∗( 𝑤) 𝑆( 𝑤); ln( 𝛼)},
where (.)* is the complex conjugate of the signal and F-1
{.} is the inverse Fourier
Transform. To solve the expression, determine the index in which maximizes the
argument. Lastly, the optimal stretch factor will equal to the specific index determine
of the exponential distribution, τ. (Cited from Richard Do’s Thesis)
A. Purely Stretching Signals Compensated by SIC
SIC can perfectly compensate the signal when the signal is purely stretched. To verify
this property of SIC, a sequence of sinusoids is generated in Matlab to simulate the
signal. The signal is stretched through resampling the sinusoids with stretching
factor=1.003 as shown in Figure (2.1). Then, the result is evaluated by normalized root-
mean-square error (NRMSE), and phase shift of peak; the two performances are
illustrated in chapter (2.4).
In the purely stretching case, SIC can perfectly compensate the signal. The original
signal after implementing SIC is totally matching the stretched signal, since the NRMSE
decreases from 46.33% to 0. The effect of SIC is shown in Figure (2.2) where you can
see the phase shift of peak originally increases with time, and then decreases to 0 after
implementing SIC. In addition, we can also observe that the phase shifts linearly when
the signal is purely stretched.

7. 7
Figure (2.1)-Original Signal and Stretched Signal
Figure (2.2)-Phase Shift of Stretched Signal (upper) and Compensated Signal (lower)
B. Temperature effects compensated by SIC
In real case, the signal cannot be perfectly compensated since the phase shift is not
perfectly linear increasing. In addition, the phase shift occurs in the beginning of signal;
however the SIC can perfectly compensated the single only when the shift is zero in
the beginning as shown in Figure (2.2, upper). If there is a phase shift in the beginning
of signal as in Figure (2.3), SIC will overestimate the stretching factor. This will result in
the mismatch in the beginning and the end of signal. Taking the Metis temperature
compensation test as an example. In the test, there are signals under different

8. 8
temperatures. The signal in 30 degree Celsius is set as baseline and then SIC is
implemented on baseline in order to match another signal in 50 degree Celsius. Since
there is a phase shift between the two signals in the beginning, the phase of
compensated signal falls behind the phase of the temperature affected signal at the
forepart as marked in Figure (2.3). Due to the stretching factor is over estimated, the
phase of compensated signal exceeds the phase of temperature affected signal in the
latter part.
Figure (2.3)-Phase Shift of Signal with Temperature Effect
2.3 Improvement of SIC-Regressive Phase Coherence (RPC)
SIC is an effective and convenience method to compensate the phase shift of signals
because it is less computationally expensive and signals can be compensated by one
stretching factor instead of a whole series of data (e.g. the analytic signal in IPC).
However, SIC can perfectly compensate the signal only when the phase shift is linear
increasing and zero phase shift in beginning. The property of SIC is demonstrated in
chapter (2.1&2.2). In real case, the phase shift occurs from the beginning of signal and
increases with time. Thus, if we use SIC method to compensate the signals directly, the
returns stretching factor will be larger than the one without phase shift in the
beginning even the increasing rate of phase shifts are identical.

9. 9
To improve the inaccurate stretching factor caused by shift in the beginning of signal,
a new technique- Regressive Phase Coherence (RPC) is implemented to make SIC more
precise and can be comprehensively used to compensate the environment effect for
ultrasonic guided waves. The main idea of RPC is to compensate shift in the beginning
of signal. In general, phase shift increases linearly under small range of temperature
effects which can be observed from regression line in Figure (2.3).
By using SIC, the signal will be stretched to compensate the linear phase shift. The level
of the linear phase shift can be thought of as the slope of phase shift regression line
which means if two signals have more linear phase shift in between, the slope of phase
shift regression line will be larger. Since SIC will calculate the most proper stretching
factor that makes the compensated signal has lowest phase shift. The effects of SIC
can be thought of as minimizing phase shift by rotating the phase shift regression line
where the original point in the first point of regression line.
However, the stretching factor will never be optimized if the first point of regression
line in not zero. Thus, as shown in Figure (2.4), the total phase shift caused by
temperature effect can be seen as the combination of one constant phase shift and
one linear phase shift which is given as follow.
∅ 𝒕𝒐𝒕𝒂𝒍 = ∅ 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 + ∅𝒍𝒊𝒏𝒆𝒂𝒓
Figure (2.4)-Phase Shift Caused by Temperature Effect

10. 10
The linear phase shift can be compensated through SIC while the constant phase shift
can use RPC to compensate. In RPC, the constant phase shift is derived from the linear
regression of phase shift. Since the local peaks have higher energy and is more likely
to stand out from noises, RPC takes the local peaks as the criteria for phase shift. The
phase shift is calculated from the difference of peaks in time domain which is
illustrated in chapter (2.4).
Although the phase shift caused by temperature effects increases smoothly, it will be
affected by reasons other than temperature, like noise, scattering, or the reflections
from different boundary conditions. Thus, the phase shift of first peak is unable to
represent the constant phase shift. To find the precise constant phase shift, it is
necessary to take the trend of the whole phase shifts into account instead of only
considering the first peak. The trend of phase can be derived through linear regression
[5] which is an approach for modeling the relationship between variables by fitting an
equation to observed data. A linear regression model assumes that the relationship
between dependent variable and explanatory variable is linear. The linear regression
model can be expressed as follow where 𝑥𝑖 is explanatory variable and 𝑦𝑖 is
dependent variable. 𝛽 is the regression coefficient with p-dimensions. 𝜀𝑖 is the error
term which captures the factors that influence 𝑦𝑖.
𝑦𝑖 = 𝛽1 𝑥𝑖1 + 𝛽2 𝑥𝑖2 + ⋯ 𝛽 𝑝 𝑥𝑖𝑝 = 𝑥𝑖
𝑇
𝛽 + 𝜀𝑖, 𝑖 = 1,2, … 𝑛
Since the phase shift of temperature effects is assumes to be linear, the liner regression
model can be simplified to simple linear regression [6] model which is given as follow.
𝑦𝑖 = 𝑎 + 𝛽𝑥 + 𝜀𝑖
The most common method for fitting a regression line is least-squares approach in
which the best-fitting curve is found by minimizing the sum of squares of offsets for a
given set of points. In other words, the least-squares approach is to minimize the 𝜀𝑖
in the above equation.
𝐹𝑖𝑛𝑑 min 𝑄(𝑎, 𝛽), 𝐹𝑜𝑟 𝑄 = ∑ 𝜀𝑖
2
= ∑(𝑦𝑖 − 𝑎 + 𝛽𝑥)2
𝑛
𝑖=1
𝑛
𝑖=1
The 𝑎 and 𝛽 that minimize the objective function Q in above quadratic expression
are written into 𝑎̂ and 𝛽̂ as follow

11. 11
𝛽̂ =
∑ (𝑥𝑖 − 𝑥̅)(𝑦𝑖 − 𝑦̅)𝑛
𝑖=1
∑ (𝑥𝑖 − 𝑥̅)2𝑛
𝑖=1
, 𝑎̂ = 𝑦̅ − 𝛽̂ 𝑥̅
Eventually, the regression line can be expressed as follow where 𝛽̂ and 𝑎̂ are
respectively the slope and intercept of regression line. Then, constant phase shift can
be figure out by substituting the x value of first peak into the function. The constant
phase shift will be converted from degrees into the shift of samples in baseline based
on central frequency and sampling rate. Then, the constant phase shift can be
compensated through shifting the baseline a certain samples.
𝑓 = 𝑎̂ + 𝛽̂ 𝑥
Moreover, since the squares of offset is used to calculate the regression line, the
outliers in phase shift which is caused by reasons other than temperature effects may
have significant influence on fitting curve. In RPC, a point will be defined as an outlier
if the distance between the point and regression line exceeds certain value. Then, a
new regression line will be calculated based on the signal without outliers.
After the compensation of constant phase shift through RPC, SIC will be implemented
to compensate the linear phase shift. To compensate the signal physically, it is
necessary to consider the energy dissipation of signals with temperature effect. In
general, there are two reasons that may cause energy dissipation. One is absorption
in which the energy of wave motion is absorbed by material; the other one is scattering
which is caused by the irregular geometry of plate. Because the increasing
temperature will somehow change material properties, the energy dissipation of
signal with temperature effect will be different from baseline. Thus, the compensated
signal is modified by an energy correction factor 𝑎 𝑒𝑛𝑒𝑟𝑔𝑦 which coheres the energy
between temperature affected signal and baseline. The energy correction factor is
given as follow.
𝑎 𝑒𝑛𝑒𝑟𝑔𝑦 = √
( 𝑆𝑖𝑔𝑛𝑎𝑙[𝑛])2
(𝑆𝑖𝑔𝑛𝑎𝑙 𝑐𝑜𝑚𝑝.[𝑛])
2
where 𝑆𝑖𝑔𝑛𝑎𝑙 𝑐𝑜𝑚𝑝. is the compensated signal, and 𝑆𝑖𝑔𝑛𝑎𝑙 is the goal of
compensated signal. The amplitude of compensated signal will be modified after
multiplying the energy correction factor to compensated signal. Although, energy
dissipations of each wave packets which comes from either transducers or reflections

12. 12
are different due to the environmental effects change the material properties unevenly,
we still use one energy correction to modify the energy of whole signal. Otherwise,
the amplitude of wave packets should be compensated individually.
Figure (2.5) shows the peak of A0 mode; it demonstrates that implementing PRC
before SIC returns the better result than using SIC directly. The curve of RPC/SIC (green)
is closer to baseline with temperature effect than the curve of SIC (black). The
improvement is also shown in phase shift. In Figure (2.6), the phase shift of RPC/SIC is
well compensated where its regression line almost matches zero. It solves the problem
that the forepart of signal are not compensated while the latter part of signal are over
compensated if there is a phase shift in the beginning of signal.
Figure (2.5)-Compensated Signals by SIC and RPC/SIC
Figure (2.6)-Phase Shift of Compensated Signals by SIC and RPC/SIC

13. 13
2.4 Performance Metric
In order to evaluate the performance for different compensation method, it is
important to establish a reliable performance metric. Since the goal of compensation
methods is to recover signals under environment effects through baseline, the
difference between baseline and compensated signal are the closer the better. Two
method is used for the performance metric in the report. One is the normalized
root-mean-square error (NRMSE), and the other one is the phase shift of peaks.
A. Normalized Root-Mean-Square Error (NRMSE)
The Root-mean-square Error (RMSE) [7] is widely used to measure the difference
between the values from predicted models and the values from actually observed
models. The difference of individual values between two models are called residuals,
and the RMSE serves to aggregate them into a single measure of predictive power. The
equation of RMSE is given by
𝑅𝑀𝑆𝐸 = √
∑ (𝑥 𝑜𝑏𝑠. − 𝑥 𝑝𝑟𝑒.)
2𝑛
𝑡=1
𝑛
where 𝑥 𝑜𝑏𝑠.is the observed values and 𝑥 𝑝𝑟𝑒. is the predicted values. The result of
RMSE values will have units and can be used to distinguish the performance only when
the models are in same scale. However, different experiment results comes from
different specimens are evaluated together in the following experiment results. The
evaluation will be more meaningful if the result can be compared in same criteria. Thus,
the normalized root-mean square error (NRMSE) [7] is used to evaluate the
performance of compensation. Since the NRMSE is Non-dimensional form, the results
from temperature experiment, bending experiment, and simulations which originally
have different amplitudes can be compared together. The equation of NRMSE is given
as follow
𝑁𝑅𝑀𝑆𝐸 = √
∑ (𝑆𝑖𝑔𝑛𝑎𝑙 𝑐𝑜𝑚𝑝.[ 𝑛] − 𝑆𝑖𝑔𝑛𝑎𝑙[𝑛])
2𝑛
𝑡=1
( 𝑆𝑖𝑔𝑛𝑎𝑙[𝑛])2
Since the gold of environmental effects compensation is not only to recover the signals
with environmental effects through baseline. Most importantly, the compensated
signal should remind the features of damages after compensation. The low NRMSE of
environmental effects cannot guarantee the high NRMSE of damage. It may be a

14. 14
situation that both of them have the same low NRMSE, and then the compensation
approach fails to distinguish the damages from environmental effects. Thus, the
normalized root-mean-square error ratio (NRR) [8] is used to evaluate the weight of
different NRMSEs, and its equation is as follow.
𝑁𝑅𝑅 =
𝑁𝑅𝑀𝑆𝐸
1
𝑁
{∑ 𝑁𝑅𝑀𝑆𝐸[𝑖]𝑁
𝑖=1 }√ (𝑁 + 1)
2𝑁
where N is the ensemble size which is only two in the our case. They are respectively
the signals with and without damages. Essentially, the NRMSE ratio (NRR) is a measure
that estimates if the spread in the predictive distribution is fitting for the amount of
error in the model. When NRR<1, the ensemble spread is too large, while in cases that
NRR>1, the ensemble spread is too small. When evaluating the effects of different
approaches, the approach is considered to be the best by finding the high NRR in
damage signal and low NRR in signal without damage because high NRR represents
that the difference between signal and baseline is more distinguishable.
B. Phase Shift of Peaks
During the data acquisition, the acquired signals sometimes accompany with electrical,
environmental, or operational noise. Although the noises have frequencies out of band
pass are filtered, some of them superpose with original signal are reminded. Instead
of taking phase shifts from each sample points, only phase shift of peaks are taken into
account in the performance metric because the peaks have higher energy which is
more likely to stand out from noises. The phase shift of peaks can directly reflects the
trend of phase shift in time-trace. In addition, it can also be used to evaluate the result
of compensated signal by observing that if the phase shift of the compensated signal
is close to zero.
In Figure (2.7), there are 45 degrees phase shift between two sinusoids which are
generated by Matlab. The phase shift can be observed from the figure if the sampling
rate and frequency are known. Through the difference of peaks as marked in Figure
(2.7), delta t can be derived from dividing the difference of samples (62 samples points)
by the sampling rate (10*E6 Hz)). And then the phase angle is given as follow.
∅o
= 360o
∙ 𝑓 ∙ ∆𝑡

15. 15
where f is the frequency of signal (20000Hz). The calculated phase shift is 44.64
degrees which is precise. It is due to the fact that the resolution of phase shift relates
to number of samples in each sinusoids while the number of samples in each sinusoids
depends on sampling rate and central frequency. Although high sampling rate is used
in temperature experiment, the central frequency is also very high. After calculation,
each sinusoids is compose by 125 samples which means the resolution is only 2.88
degrees. With this low resolution, although the trend of phase shift can be observed,
it is not precise enough to predict the phase shift when the temperature differences is
lower than five degrees. In the bending experiment, due to the limitation of data
acquisition system, the resolution decreases to 11.52 degrees. Thus, the interpretation
will be exploited in Matlab to increase the resolution.
Figure (2.7)-Signals with 45 degrees phase shift in between

16. 16
Chapter 3: Experiment
3.1 Signal Processing
Demeaning and Band-pass filter are the common signal processing methods that
people implements them before analyzing the signals. Demean is to subtract the mean
of signals from each samples in order to cohere the mean of each signals. Band-pass
filter is the filter that only a certain range of frequencies in the signal can go through
it; the other frequencies which are either higher or lower than the bound will be
filtered. Thus, the useful signals are reminded and the noises from environment and
electrical devices can be removed. In the experiment, the central frequency is 80 kHz,
and the range of band pass is from 50 kHz to 11 kHz which is also named as cutoff
frequency.
3.2 Dispersion Curve
The propagation of ultrasonic guided waves is different from longitudinal and shear
waves; it is more similar to Lamb waves or Rayleigh waves that they propagate on
surface of materials. In longitudinal and shear waves, the propagation velocity only
dependents on the material properties while the velocity of guided waves is influenced
by materials, thickness, and frequency. Thus, dispersion curve [?] can describe the
relation between frequency and velocity which includes phase velocities and group
velocities. Phase velocity is the speed of waves which can be considered as how fast
the particle moving and propagating the energy in material while Group velocity is the
speed that wave packet travels. In bending experiment, we use the dispersion curve
to find the group velocity, as in Figure (3.1), to confirm the accuracy of signal and the
location of A0 and S0 wave packet.

17. 17
Figure (3.1)-Dispersion Curve of Aluminum Plate (Thickness = 0.5mm)
In Figure (3.1), the velocity of different modes in different frequencies are displayed.
Since the central frequency in bending experiment is only 80 kHz (0.08 MHz) which
locates at the beginning of the x axis, theoretically only S0 mode and A0 mode will
occur in the acquired signals. In general, S0 mode is faster than A0 mode and the
amplitude of A0 mode is larger than the one of S0 mode. S0 mode is symmetric mode
which is also named as extensional mode when it is in low frequency range in which it
travels at the plate velocity. When the frequency increases and the wavelength
becomes comparable with the plate thickness, the group velocity drops dramatically
toward the minimum. After that, the group velocity increases with the increasing
frequency and converges towards the Rayleigh wave velocity. On the contrary, A0
mode is antisymmetric mode and is also named as flexural mode. In low frequencies,
the phase and group velocities are both proportional to the square root of the
frequency. This relationship breaks down when it increases to higher frequencies, and
both the phase and group velocities also converge towards Rayleigh wave velocity.
The A0 mode is verified in the following step. First, the piezoelectric transducers are
placed in the middle of aluminum plate in which the distance between the transducers
are 4 inches and 8 inches respectively. Then, difference in time of flight (Delta t in
Figure (3.2)) can be derived from dividing the difference of samples by the sampling
rate. Finally, velocity of A0 mode is the difference of distance between transducers
(8inches-4inches=4inches) divided by the delta t (90ms). In dispersion curve, the
velocity of A0 mode in aluminum plate is 1.186 m/ms when frequency is 80 kHz. In
bending experiment, the derived velocity is 1.128 m/ms. There is only 5% error in

18. 18
between. The result shows that the signals are reliable and also verify the assumption
that the used wave packet is A0 mode is correct.
Figure (3.2)-Signals with Different Distance between the Transducers
(4 inches and 8 inches)
3.3 Temperature Experiment
The test bed used in temperature experiment is an aluminum plate as show in Figure
(3.3). The test used two Metis MD7 nodes containing one actuator sensor in the
middle surrounded by six receiving sensors. The node was place near the center and
around 3.5’’ apart from one another. A thermistor was placed at the center of the plate
between the two nodes to monitor the mean temperature of the plate. This plate was
placed inside a thermal chamber where it remained untouched during the test. The
test protocol was as follows: heat the structure to 55°C, turn off the heating
mechanism and allow for self-cooling, continuously record the temperature using a
thermistor, and simultaneously take periodic UGW measurements until 30°C was
reached. (Cited from Richard Do’s Thesis)

19. 19
Figure (3.3)-Temperature Experiment Test Bed
3.4 Bending Experiment
In the experiment, the test bed is an aluminum plate with dimension of 610 mm x 380
mm x 0.5mm. The specimen is a constant thickness plate and the edges of plate are
flat in order to reduce the scattering. Two piezoelectric transducers are attached on
surface of the aluminum plate and the distance between them are from 4 inches to 10
inches. One short side of aluminum plate is fixed, and the other short side is movable.
The bending moment is generated by giving a certain force which is paralleled to the
plate to the moveable short side, and then the plate will have a slightly downward
bending.
The two piezoelectric transducers are 12 mm diameter. One of them serves as
transmitter and the other one is receiver. The data acquisition system used in the
experiment are NI PXIe-1073 and TB-2708. All of the parameters of signals (e.g. central
frequency, sampling rate, time delay, waveforms, and hamming window) can be real-
timely controlled in computer through LabVIEW. In addition, the signal is amplified to
15 voltage through amplifier 7602M.

20. 20
Since the Lamb waves radiate out from the source transducer, it propagate away from
the circle until it touch boundaries, defects or another transducers. After that,
reflections and scattering occur, and they will interact with each other or new
propagated signals. It make the received signal looks messy and hard to analyzing. To
reduce this phenomenon, the transducers are placed on the middle of the plate and
the distance between transmitter and receiver is less than the distance from the
transmitter to edges so that theoretically the A0 and S0 acquired by receiver will be
clear wave packets.
Figure (3.4)-Bending Experiment Test Bed
3.5 Experimental Results and Discussion
A. Result of Temperature Experiment
Figure (3.5) shows the phase shift for different effects including temperature changes,
bolt loss, and magnet. The regression line, as in Figure (3.5), has shown that the phase
shift of signal with temperature effects is linearly increasing, while the slope of
regression line is relatively flat in bolt loss and magnet effects. Based on the different
properties of phase shift, SIC is implemented to compensate the linear phase shift in
order to increase the detectability of damages. In addition, there are many peaks occur
in the phase shift of blot loss. These peaks can be considered as the features of
damages, and we can further exploit these features to implement damage localization

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or other analyses. The compensation results of SIC and RPC/SIC is shown is Figure (2.6)
where the RPC/SIC demonstrates the best performance since its regression linear
almost overlaps with zero. It shows that using RPC and SIC to compensate constant
phase shift and linear phase shift respectively is better than implements SIC to
compensate the whole phase shift directly.
Figure (3.5)-Phase Shift caused by Temperature, Bolt loss, and Magnet
Figure (3.6) demonstrates the performance of different methods which are
respectively, SIC, RPC/SIC, and IPC. The result is presented in NRMSE versus difference
of temperature values. Then, we can see that how the increment of temperature
changes the effects of different compensation methods. According to the result of
NRMSE, the figure shows that SIC, IPC, and PRC/SIC can well distinguish the damage
signals from signals without damages. It has clearly shown that signals without
damages have less NRMSE, signals with magnet effects have slightly higher NRMSE
and signals with bolt loss have severely higher NRMSE.

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Figure (3.6)-NRMSE of Different Effects by SIC, RPC/SIC, and IPC
Due to the gold of temperature compensation is to distinguish the damage effects
from temperature effect. It is important that the features of damages should be
reminded after implementing compensation methods. Thus, we use normalized root-
mean-square error ratio (NRR) to evaluate the NRMSEs of each effects. The higher NRR
of damage effects reflects the truth that the damage is more detectable than other
effects. In Figure (3.7), it is NRR versus difference of temperature values. When there
are not temperature effects in the signal, the damage is theoretically highly detectable.
Comparing to the black curve in Figure (3.7) which is the NRR of signals without any
compensation methods, the other three colored NRR curves present the results that
all the three methods (SIC, RPC/SIC, and IPC) improve the detectability of damages. In
addition, we can also observe that bolt loss is more detectable than magnet effect
because the bolt loss has higher NRR values. Note that the reason that NRR starts at
2.31 is because the number of N is two in the equation of NRR in chapter (2.4-A); one
is baseline and the other one is damage signal. When there is no temperature effects,
the NRMSE of baseline is zero and 𝑁𝑅𝑀𝑆𝐸/{∑ 𝑁𝑅𝑀𝑆𝐸[𝑖]𝑁
𝑖=1 } will be one. Thus, 2.31
comes from N/√ (𝑁 + 1)/2𝑁 where N=2.

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Figure (3.7)-NRR of Magnet and Bolt Loss Effects by SIC, RPC/SIC, and IPC
B. Result of Bending Experiment
In the bending experiment, the trend of phase shift under different effects can be
observed through Figure (3.8) where the blue curve is phase shift between
baseline with and without bending moment, and red curve shows phase shift
between baseline and damage signal which is simulated by adding the magnet on
the plate. We can observe that the bending effect has linear phase shift through
regression line, however, the linear trend is not as obvious as the one in
temperature effect since there are many outliers that far away from regression
line. Comparing to the bending effect, there is no linear trend for magnet effect
according to regression line whose slope is almost zero. In addition, unlike the
temperature experiment where the changing of amplitudes in each signals are
small; the amplitudes of each wave packets in bending experiment change a lot.
The severally changing in amplitude reflects that the energy dissipation for each
wave packets are quite different. This phenomenon illustrates the truth that the
bending effects changes the material property more unevenly than temperature
effects.

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Figure (3.8)-Phase Shift Caused by Bending and Magnet Effect
Since the effect of bending and magnet make the phase changes differently. The
linear trend of bending effect is assumed that it could be compensated through
RPC/SIC which works well in the compensation of temperature effect. In Figure
(3.9), there are results for SIC and RPC/SIC. The compensated phase shift can be
observed through regression lines of SIC and RPC/SIC in Figure (3.9) where the
slopes of them are flatter and closer to zero phase shift. However, the
compensation effects did not work well in bending experiment because of the
large numbers of outliers in phase shift and highly different energy dissipation
between each wave packets. The normalized root-mean-square error between
baseline and baseline with bending moment is 40.87%, while the one between
compensated signal and baseline with bending moment is 36.01% which shows
that the compensation methods fail to decrease the NRMSE caused by bending
effects.

25. 25
Figure (3.9)-Phase Shift of Compensated Signals by SIC and RPC/SIC
Since constant increasing bending criteria is not yet setup, the data for bending
experiment is not as completed as the temperament experiment. The result of
bending experiment after different methods are shown in Figure (3.10) where
the blue line is signal without magnet effect, and red line is signal with magnet
effect. In X-axis, “zero” means there is no bending moment in plate and “one”
means the plate has a certain value of bending moment. Note that there are only
two values in both X-axis and Y-axis which means there is no other data between
“zero” and “one”, so the linear trend is meaningless. The reason that the results
is presented as follow is because it will be easier to compare it with results in
temperature experiment in Figure (3.6). According to Figure (3.10), it shows that
the magnet effect is easily to be detected when there is no bending moment in
the plate. However, the NRMSE of signals with or without magnet effects are
almost the same height when the plate is added the bending moment. All the
three methods (SIC, RPC/SIC, IPC) show poor results in the compensation of
bending effects, while IPC is relatively better than the other two ones. In Figure
(3.11), the normalized root-mean-square error ratio shows that the methods did
not well improve the detectability for damages meanwhile, SIC and RPC/SIC even
returns worse detectability.

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Figure (3.10)-NRMSE of Magnet Effect by SIC, RPC/SIC, and IPC
Figure (3.11)-NRR of Magnet effect by SIC, RPC/SIC, and IPC

27. 27
Chapter 4: Summary
According to the result in chapter (2.3), the combination of SIC and RPC gives the good
performance for temperature compensation. It illustrates the fact that if two signals
with linear phase shift in between and the phase shift starts from the beginning of two
signals, the total phase shift between the two signals could be thought of as the
combination of a constant phase shift and a linear phase shift as in Figure (2.4). The
constant phase shift can be compensated by RPC in order to make the first point of
phase shift regression line equals to zero. And then, the SIC can perfectly compensate
the linear phase shift.
In chapter (3.5-A), the results of temperature compensation by SIC, SIC/RPC, and IPC
is compared together base on normalized root-mean-square error (NRMSE) and
normalized root-mean-square error ratio (NRR) as in Figure (3.6&3.7). Although IPC
can perfectly compensate the phase of whole signal and gives the smallest NRMSE,
the characteristics of phase shift from damages are also compensated. However, the
goal of environmental effects compensation is to remind the features from damages
and compensates the changes of signal caused by environment effects. Thus, NRR is
another performance metric which shows the ratio of NRMSEs. The high NRR of
damage means that the NRMSE cause by damage is more likely to stand out from the
NRMSE due to environmental effects.
Since the phase shift of temperature effect is assumed to be linear in a small range
temperature change, theoretically, it is better to compensate the temperature effect
based on the characteristic of “liner phase shift” instead the phase shift of each points.
Moreover, linear phase shift can be consider as stretching of signal. Scale-Invariant
Correlation (SIC) is the method that exploits this property to compensate signals with
temperature effects. Thus, RPC/SIC gives the results better than IPC as in Figure (3.7)
In the bending experiment, although the bending effects also shows the linear phase
shift as in Figure (3.8) which is supposed to be compensated by SIC, the result shows
that the performances of SIC, and SIC/RPC are even worse than IPC as in Figure (3.11).
It is due to the fact that there are many outliers besides the regression line. Thus, even
the slope of regression line is close to zero after compensation; many phase shift
caused by outlier are still there. In addition, the extremely large NRMSE is also caused
by highly difference of amplitude in each wave packages. To further understand the
bending effects of UGW, a sequence of signals with constantly increasing bending
moment is needed.

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