a new algorithm for more accurate estimation of …...a new algorithm for more accurate estimation...
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A New Algorithm for More Accurate Estimation of Wave Propagation Velocity by Common-Offset Survey Method
Janet F.C. SHAM, Wallace W.L. LAI*
Department of Land Surveying and Geo-informatics, The Hong Kong Polytechnic University,
Hong Kong
Phone: +852 3400-8960; Fax:; email: [email protected]
Abstract
This paper presents a new algorithm to estimate electromagnetic (EM) wave propagation
velocity (v) with high-frequency 2GHz ground penetrating radar (GPR)’s shielded antenna. The
data collection makes use common offset method with particular consideration of antenna’s
separation distances and its corresponding triangulation geometry. This method calculates the
distribution of discrete velocities at each point oblique to the embedded target object, analogous
to the similar yet ambiguous curve fitting process of hyperbolas in most software. Validation test
in air and a steel bar in concrete media were conducted and the results were satisfactory.
Comparison with the tradition hyperbola geometry method was conducted and the results show
that error on velocity analysis is significantly reduced by the proposed method. Based on the
result, works on next stage will be about differentiation of velocity variations in concrete as a
result of water seepage and leakage.
Keywords: ground penetrating radar (GPR), velocity analysis
1. Introduction Object identification and mapping in concrete has been the focus of GPR community working on
concrete structures in past decade. With the advent of electronics and signal processing
techniques, this task is much easier and more accurate results have been produced. The next
stage of work will be about characterization of long term concrete serviceability which means
corrosion, cracks, spalling and delaminations. On one hand, mechanical wave is the best
candidate to measure mechanical properties while electromagnetic wave works best for
aforementioned parameters of concrete serviceability, in which the root cause is water seepage. It
is an enduring and complex issue for the residents and also the Hong Kong government. In
Singapore, which has similar weather condition and environment as Hong Kong, [1] revealed
that water seepage is the most significant building maintenance problems in high-rise buildings.
It causes corrosion and eventually induces cracks and delamination in reinforced concrete
structures. Besides, it is also a threat to hygiene. Water seepage causes damp environment which
enhances the development of defects [2]. Therefore, it is crucial to develop more accurate
moisture mapping technique which helps to locate the source and extent of water seepage.
Amongst non-metallic materials, water is the single most influential factor affecting radar wave’s
traveling velocity and reflection strength, and absorbing high-frequency portion in spectral
content [3-11]. Therefore, presence of water seepage/leakage can be found by investigating the
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
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change of wave propagation velocity. However, as mentioned in HKIS [12], the major problem
on using GPR technique for water seepage measurement is data interpretation. Skilled operator is
required for better and more accurate data interpretation. This paper proposed a new developed
mathematical algorithm and software which allow more accurate estimation of EM wave
propagation velocity from GPR by adding suitable constraints and calculates the distribution of
discrete velocities at each point oblique to the embedded target object. In this paper, we
attempted to measure GPR wave velocity traveling in concrete, and validate our result in air and
concrete.
2. Principle of Velocity Analysis In ground penetrating radar survey, there is a rule of thumb relating velocity to dielectric
constant (ε’) for rough estimation of velocity [13]:
士 噺 算√資 Equation 1
where v is the EM wave propagation velocity, c is the propagation velocity in free space
(3x108m/s) and ε is the dielectric constant of the material which the EM wave propagate. The
condition for applying the above equation is dielectric constant of the material (where the EM
wave propagate) is known. Dielectric constant of the material can be estimated by applying time-
domain reflectometry (TDR). However, access of taking sample from the interested region for
TDR examination is always difficult and challenging.
2.1. Depth to the known reflector method
Another more reliable method for estimating velocity of the EM wave propagation from GPR is
when depth of the object (i.e. reflector) is known. This method is called ‘depth to the known
reflector method’ which bases on a general relationship of the time taken for a travelled distance:
士 噺 匝拶嗣 Equation 2
where D is the depth of the reflected object and t is the two-way travel time of the signal
reflected from the object which can be obtained directly by GPR. This is a simple method to
estimate the EM wave propagation velocity. However, the main problem of this method is that
the depth of the inspected object is unknown. Therefore, velocity estimation by depth to known
reflector method is not always applicable. Besides, only a single wave velocity can be obtained.
Detection of a rounded object by GPR renders the reflected signal as a hyperbola due to a certain
beam width affected by antenna design, frequency and material properties. While the only signal
for calculating the wave velocity make use of the fastest time (which is the peak of the reflected
hyperbola signal), the reflection events of the hyperbola tails are not used. Therefore, the
following hyperbolic geometry method is normally used for determining discrete velocities using
every point of the hyperbola in GPR commercial software.
2.2. Hyperbolic geometry method
In this paper, shield antenna is used i.e. transmitter and receiver are shielded with a fixed
separation. It is called common-offset survey method. Therefore, velocity sounding method
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
cannot be applied and the following velocity estimation method – hyperbolic geometry is used.
The general equation for hyperbolic geometry is shown as below: 懸 噺 2捲紐建掴態 伐 建待態 Equation 3
Where to refers to the two-way travel time of EM wave transmitted to the target and reflected
back and received by the receiver when the shielded antenna is located normal to the target. On
the other hand, tx refers to the two-way travel time of the EM wave transmitted to the target and
reflected back and received by the receiver when the shield antenna is located position x, oblique
to the target. This method is only valid when the reflector is round-shaped. Both velocity
sounding and hyperbolic geometry can be used to estimate EM wave propagation velocity from
GPR without the information of dielectric constant and depth of the object. Therefore, they are
widely applied in the commercial software which make use of hyperbolic geometry method as
curve fitting for estimating velocity of EM wave propagation as shown below (from Software
Reflexw):
Figure 1: Sample of velocity estimation by curve-fitting method
However, it is biased by human judgment and become very subjective. As shown in Figure 1, it
is only based on curve-fitting the bands of colors (as a result of polarity) by the reflections. The
velocity estimation may not be consistent and hence significant deviations may be induced when
different analysts are handling the data. There is no systematic guideline on this hyperbola fit.
Besides, Equation 3 assumes that the subsurface object is a point reflector. However, this
assumption does not hold in real case, e.g. in reinforced concrete wall with small concrete cover.
The effect of size of the reinforcement becomes very significant because the size and cover are in
comparable magnitude. Moreover, the equation does not take into account the effect of antenna
separation which changes the triangulation geometry of wave emission and reflection. This
causes significant error when the targeted object is located at a shallow level where the size of
the targeted object is comparable to the antenna separation.
3. Formulation and implementation In each signal received by the GPR antenna, it records the whole waveform (A-scan) with
amplitude at discrete time. The location of reflector is recognized by locating the time at which
stronger (either positive or negative polarity) reflective amplitude is recognized. This time of
stronger signal can be converted to the estimated distance between the reflector and antenna if
velocity is known. In this study, shielded antenna with common separation of transmitter and
receiver is used i.e. transmitter and receiver are enclosed within one casing. The basic geometry
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
of signal travel with the antenna (enclosed with transmitter and receiver) is represented in the
following figure:
Figure 2: Schematic diagram of the geometry of common-offset survey by shielded antenna
By referring to the above figure, the equation of geometric analysis for velocity estimation based
on hyperbola reflection obtained by common-offset survey (using shielded antenna) on
subsurface round-shaped target is shown below:
For any ‘x’,
懸岫捲岻 噺 経態 髪 経戴建掴 Equation 4
経態 噺 俵峪岫経墜 髪 堅岻 伐 岫経墜 髪 堅岻堅紐岫経墜 髪 堅岻態 髪 捲態崋態 髪 峪峭捲 伐 堅 抜 捲紐岫経墜 髪 堅岻態 髪 捲態嶌 伐 稽崋態
Equation 5
経戴 噺 俵峪岫経墜 髪 堅岻 伐 岫経墜 髪 堅岻堅紐岫経墜 髪 堅岻態 髪 捲態崋態 髪 峪峭捲 伐 堅 抜 捲紐岫経墜 髪 堅岻態 髪 捲態嶌 髪 稽崋態
Equation 6
Substitute Equation 5 and Equation 6 into Equation 4
懸岫捲岻 噺 俵峪岫経墜 髪 堅岻 伐 岫経墜 髪 堅岻堅紐岫経墜 髪 堅岻態 髪 捲態崋態 髪 峪峭捲 伐 堅 抜 捲紐岫経墜 髪 堅岻態 髪 捲態嶌 伐 稽崋態 髪俵峪岫経墜 髪 堅岻 伐 岫経墜 髪 堅岻堅紐岫経墜 髪 堅岻態 髪 捲態崋態 髪 峪峭捲 伐 堅 抜 捲紐岫経墜 髪 堅岻態 髪 捲態嶌 髪 稽崋態建掴
Equation 7
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
The above velocity equation (Equation 7) allows calculation of the wave velocity of discrete
travelling time of signal reflected from the embedded object. This modified equation is
especially designed for GPR survey on rounded object by common-offset method. Better than
the “depth to the known reflector method”, instead of giving single value for wave velocity on a
reflected hyperbola (based on the fastest reflection time at the peak of the hyperbola), it gives
discrete velocity values which consider the signals of the whole hyperbola (i.e. including the tail
region of the hyperbola). In the equation, it requires the input of ‘Do’ as the depth of the object,
radius of the object ‘r’, ‘x’ the horizontal distance of the antenna from any oblique relative to the
normal position of the target; ‘tx’ the two way travel time of the reflection from the
transmitting/receiving antennae to the target at any distance ‘x’ and ‘B’ the antenna separation.
The new developed equation concerns many parameters and hence the discrete velocities derived
by the new equation are very similar to the wave velocity obtained by the tradition depth to the
known reflector method. The new algorithm was used to build up a velocity analysis program
and validated the steel bar reflections from two media: (1) air and (2) concrete wall.
4. Development of New GPR Velocity Analysis (GPR-VA) Program As mentioned before, another problem for unreliable velocity estimation by various software in
the market is that they rely on human judgment for curve-fitting the bands of colors by the
reflections. In order to minimize the human interference on examining the velocity analysis
process, a statistical method for GPR velocity analysis (GPR-VA) has been developed by using a
virtual programming platform - LabVIEW. The mathematical algorithm developed in the
previous session is applied in the GPR-VA program. This program enables calculation of
distribution of discrete velocities at each point oblique to the embedded target. The interface of
the developed program is shown below at Figure 3. It includes figures of selected (A) A-scan,
(B) radargram (B-scan) generated by combining all A-scans captured when moving the antenna
horizontally., (C) distance-time curve of the selected hyperbola signal and also (D) the
corresponding discrete velocities at each point of the hyperbola. The only human judgment is to
identify the region of interest (ROI), after specifying the ROI, the program will select only the
relevant points to form the hyperbola signal (graph (C) in Figure 3). At this stage, the program is
compatible to file format in either 16bit or 32bit.
Figure 3: Interface of GPR-VA program build up by LabVIEW Instrument.
(B)
(A)
(C)
(D)
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
According to the assumption of velocity analysis in both the traditional Equation 3 and the
developed equation (Equation 7), the velocities along the whole hyperbola signal should have the
same velocity. However, sometimes the calculated velocities can be quite fluctuate, therefore,
statistical method (i.e. setting standard deviation (SD) limit) is applied to regulate the amount of
discrete velocity for velocity analysis. The program will stop selecting the velocities along the
hyperbola signal when the SD of the batch of selected velocities exceeds the designated SD set
before analysis. It shows that by restricting the required SD, the program can automatically select
the most suitable data set and avoid erroneous data for velocity analysis. The proposed statistical
method enables automatic calculation of more reliable wave velocity of GPR survey.
5. Validation of Velocity Analysis
5.1. Validation test in AIR
In order to validate the results obtained by the modified velocity analysis equation and GPR-VA
program, hyperbola signal was collected by transmitting and receiving reflected signal of a
reinforcement bar through a unique medium, i.e. air. Y25 steel bar is used as the target. The
experimental setup is shown in the following photographs:
Figure 4: Experimental setup of the calibration process
The above figures show the experimental setup of the calibration process. A frame was built for
holding a steel bar. The steel bar was placed at different levels apart from the GPR antennae:
2GHz antennas was used for the calibration. The media for the travelling of GPR wave is air, in
which the travelling velocity of EM wave is known as 0.2998m/ns. The speed of EM wave in air
is a constant because air is a non-dispersion media for EM wave propagation, and will not be
affected by the frequency of antenna used for the experiment, angle, distance of the target etc.
Therefore, it is the most suitable and stable media to be used to calibrate the proposed method for
estimating wave velocity by GPR. The following table shows the mean wave velocity calculated
by the proposed VA method and the hyperbola geometry method. The selected data are all
collected with set standard deviation of less than 0.03 and data larger than 0.29979m/ns are
treated as invalid and hence disregarded in calculating mean wave velocity.
Table 1: Wave velocity obtained by the proposed method and by the hyperbola geometry method
Reference velocity (m/ns)
Depth of Steel
Bar (m)
Proposed VA method Hyperbola geometry method Mean Wave
Velocity
Standard Deviation
% error with respect to the
reference
Mean Wave Velocity (m/ns)
Standard deviation
% error with respect to the
reference velocity
Y25 Steel bar 2G GPR Antenna
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
(m/ns) velocity 0.29979 0.2 0.288 0.004 -5% 0.282 0.016 -6%
0.29979 0.3 0.287 0.003 -4% 0.280 0.017 -7%
0.29979 0.4 0.288 0.002 -4% 0.280 0.015 -7%
0.29979 0.5 0.289 0.003 -4% 0.266 0.023 -11%
The following figures show the discrete velocity data of the reflected hyperbola by different
methods:
0.200
0.220
0.240
0.260
0.280
0.300
0.320
-80 -60 -40 -20 0 20 40 60 80
Velocity Analysis (Air with 200mm object depth)
New method (Equation 7) Speed of Light Hyperbola (Equation 3)
Apex of hyperbola
0.200
0.220
0.240
0.260
0.280
0.300
0.320
-80 -60 -40 -20 0 20 40 60 80
Velocity Analysis (Air with 300mm object depth)
New method (Equation 7) Speed of Light Hyperbola (Equation 3)
Apex of hyperbola
0.200
0.220
0.240
0.260
0.280
0.300
0.320
-80 -60 -40 -20 0 20 40 60 80 100
Velocity Analysis (Air with 400mm object depth)
New method (Equation 7) Hyperbola (Equation 3) Speed of Light
Apex of hyperbola
Vel
ocity
(m
/ns)
V
eloc
ity (
m/n
s)
Vel
ocity
(m
/ns)
Position
Position
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
Figure 5: Velocity analysis of the reflected hyperbola signals with different object depth in air by different methods.
As shown in
Figure 5, the calculated discrete velocities using the developed equation (Equation 7) are quite
constant when comparing to those velocities calculated by hyperbola geometry method
(Equation 3). According to Table 1, the standard deviation of the new VA equation is only
ranging from 0.002-0.004 while it is 0.015-0.023 by hyperbola geometry method. Also, it shows
that all data points by the proposed method are included under the two constraints (1) standard
deviation <0.03 and (2) calculated velocity <0.3m/ns while most of the data points derived by
hyperbola geometry method were lost. Besides, when considering the average percentage error,
the table shows that it is only -4% to -5% by new method while it is up to ranging from -6% to -
11% in hyperbola geometry method.
5.2. Validation test on Concrete
After validation in air, another validation test was done on a concrete wall as shown in the
following Figure 6:
0.220
0.230
0.240
0.250
0.260
0.270
0.280
0.290
0.300
0.310
-80 -60 -40 -20 0 20 40 60 80
Velocity Analysis (Air with 500mm object depth)
New method (Equation 7) Speed of light Hyperbola (Equation 3)
Apex of hyperbola
0.220
0.230
0.240
0.250
0.260
0.270
0.280
0.290
0.300
0.310
-80 -60 -40 -20 0 20 40 60 80
Velocity Analysis (Air with 500mm object depth)
New method (Equation 7) Speed of light Hyperbola (Equation 3)
Apex of hyperbola
Vel
ocity
(m
/ns)
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
Figure 6: Concrete wall for validation test.
Similar to the validation process in air, the selected data were collected with set standard
deviation of less than 0.03 except that the reference velocity was calculated by “depth to the
known reflector method”. The following table shows the mean wave velocity calculated by the
proposed method and the hyperbola geometry method:
Table 2: Wave velocity obtained in concrete by the proposed method and by the hyperbola
geometry method Reference
velocity (m/ns)
Proposed VA method Hyperbola geometry method Mean Wave
Velocity (m/ns)
Standard Deviation
% error with respect to the
reference velocity
Mean Wave Velocity (m/ns)
Standard deviation
% error with respect to the
reference velocity
0.106 0.106 0.003 5% 0.140 0.022 38%
Figure 7: Velocity analysis of the reflected hyperbola signals in concrete by different methods.
The above result shows that the new algorithm also gives a very satisfactory result in concrete. It
is very close to the estimation made by “depth to known reflector” method. According to
Table 2, the standard deviation of the new velocity analysis equation is only 0.003 while it is
0.022 by hyperbola geometry method. The percentage error of using the proposed method in
0.050
0.100
0.150
0.200
0.250
-25 -20 -15 -10 -5 0 5 10 15 20 25
Velocity Analysis (concrete with a steel bar with 50mm cover depth)
New method (Equation 7) Depth to known reflector Hyperbola (Equation 3)
Apex of hyperbola
50m
m c
over
Vel
ocity
(m
/ns)
International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany
concrete is only 5% while it is up to 38% error with respect to the “depth to the known reflector
method”. The error obtained by the hyperbola geometry method is still quite large even though
constraints were added for data selection.
6. Discussion and Conclusion
In conclusion, this paper proposed a new alogorithm and program for more accurate and
consistant velocity analysis for GPR survey with common-offset survey method. Several
highlights are listed as below:
1. A new equation was formulated by concerning parameters such as antenna seperation, depth
and size of the embedded object which are neglected in commercial software.
2. By applying the proposed method, discrete velocities can be obtained for better investigation
of variation of material properties since more data points can be used.
3. New program is build up in a virtual programming platform LabVIEW by applying the
developed equation.
4. Statistical method i.e. considering standard deviation among the calculated velocities of the
reflected hyperbola signal as a quality check of data, is proposed. This constraint can largely
reduce the error induced by human interference during signal post-processing.
5. Validation test of the proposed method and program have been tested in two environment (1)
air and (2) concrete wall. Satisfactory results were obtained by using the new method in
which only -4% to -5% percentage error with standard deviation of 0.002-0.004 in air while
only -1% to 5% percentage error with standard deviation of 0.001-0.005 in concrete are
observed.
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International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)
September 15 - 17, 2015, Berlin, Germany