TWINS II - gpradar.eugpradar.eu/onewebmedia/Anna Šušnjara Prezentation_ANNA_VICKO... · Rome,...
Transcript of TWINS II - gpradar.eugpradar.eu/onewebmedia/Anna Šušnjara Prezentation_ANNA_VICKO... · Rome,...
TWINS IIANNA ŠUŠNJARA, VICKO DORIĆ & DRAGAN POLJAK
Training School on Ground Penetrating Radar for civil engineering and cultural heritage managementRoma, Italy, May 14-18, 2018
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
University of Split, Croatia
Rome, Italy,
May 14-18,
2018
Training School on GPR for civil engineering and cultural
heritage management
2TWINS I = Thin WIre Numerical SolverSuzana = Sustav za analizu antena (Croatian)
Frequency domain solver (FD) Time domain solver (TD)
What is solved?
- Governing equations for a current distribution along the wire radiating above a half space
Numerical method?
- Galerkin-Bubnov scheme of Indirect Boundary Element Method (GB-IBEM)
Programming language:
- C++
- Used for educational purpose and scientific research
Rome, Italy,
May 14-18,
2018
Training School on GPR for civil engineering and cultural
heritage management
3TD vs. FD techniques
Time domain (TD) techniques:
Applied for a large frequency spectrum, but for single source
More complex formulation requiring more computational effort
Deeper physical insight
Frequency domain (FD) techniques:
Applied for more sources, but at a singlefrequency
Formulation is substantially less demanding
In general, regulatory standards are specified in FD form; convenient for analyzing EMC properties
Rome, Italy,
May 14-18,
2018
Training School on GPR for civil engineering and cultural
heritage management
4TWINS I – Frequency Domain (FD)
Rome, Italy,
May 14-18,
2018
Training School on GPR for civil engineering and cultural
heritage management
5TWINS I – Time Domain (TD)
Rome, Italy,
May 14-18,
2018
Training School on GPR for civil engineering and cultural
heritage management
6
Transmitted
wave
ϑ
x
z
h
T (x,z)
d1
d2
L
εr1 σ1
εr2 σ2
εr3 σ3
(0,h) (L,h)TWINS II
- Frequency Domain (FD)
- Presented on final GPR conference in Warsaw
What is solved?
Integral formulas for the electric field transmitted into
the subsurface.
NEW!
The subsurface is non-homogenous.
Talk Layout
• THEORETICAL
BACKGROUND
• Model geometry
• INSTALLATION PROCEDURE
• USER GUIDE:
• Antenna parameters
• Ground parameters
• Frequency domain (FD)
• Time domain (TD)
• Run the simulation
• EXAMPLES
• REFERENCES
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Model geometry
Transmitted wave
ϑ
x
z
h
T (x,z)
d1
d2
L
εr1 σ1
εr2 σ2
εr3 σ3
(0,h) (L,h)
Ground penetrating radar dipole antenna
above a lossy half space.
The half space is modeled as a three
layered medium.
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𝐸𝑥𝑒𝑥𝑐 = 𝑗 𝜔
𝜇
4𝜋න−𝐿2
𝐿2𝑰 𝒙′ 𝒈 𝒙, 𝒙′ 𝑑𝑥′ −
1
𝑗4𝜋𝜔𝜀0
𝜕
𝜕𝑥න−𝐿2
𝐿2 𝝏𝑰 𝒙′
𝜕𝑥′𝒈 𝒙, 𝒙′ 𝑑𝑥′
Pocklington’s integro-differential equation:
𝒈 𝒙, 𝒙′ = 𝑔0 𝑥, 𝑥′ − 𝑹𝑻𝑴 𝑔𝑖 𝑥, 𝑥′
𝑔𝑖 𝑥, 𝑥′ =
𝑒−𝑗𝑘0𝑹𝒊
𝑹𝒊
I(x’) ... the unknown current
g(x,x’) ... Green’s function
g0(x,x’) ... for free space
gi(x,x’) ... from image theory
x σ, 𝜀r 𝜇0
ε0, μ0ϑ
x
z
Wire above a lossy half-space:
x
𝐑𝐢
x
x
𝐑𝟎
h
-h
𝑔0 𝑥, 𝑥′ =𝑒−𝑗𝑘0𝑹𝟎
𝑹𝟎
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𝐸𝑥 =1
𝑗4𝜋𝜔𝜀0න0
𝐿 𝜕𝐼 𝑥′
𝜕𝑥′
𝜕𝒈 𝒙, 𝒚, 𝒛, 𝒙′
𝜕𝑥𝑑𝑥′ − 𝛾2න
0
𝐿
𝐼 𝑥′ 𝒈 𝒙, 𝒙′ 𝑑𝑥′
𝐸𝑦 =1
𝑗4𝜋𝜔𝜀0න0
𝐿 𝜕𝐼 𝑥′
𝜕𝑥′
𝜕𝒈 𝒙, 𝒚, 𝒛, 𝒙′
𝜕𝑦𝑑𝑥′
𝐸𝑧 =1
𝑗4𝜋𝜔𝜀0න0
𝐿 𝜕𝐼 𝑥′
𝜕𝑥′
𝜕𝒈 𝒙, 𝒚, 𝒛, 𝒙′
𝜕𝑧𝑑𝑥′
Electric field integral relations:
𝒈 𝒙, 𝒙′ = 𝑻𝑻𝑴 𝑔0 𝑥, 𝑥′
Numerical procedure:
Galerkin Bubnov scheme of
Indirect Boundary Element Method
(GB-IBEM)
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z
x
L
h
~
ε0, σ = 0
μ0,
ε0 εr1
σ1
μ0, d1
ε0 εr2
σ2
μ0
ϑ0
ϑ1
ϑ2
Reflection/transmission coefficients for three layered media configuration:
Air + Layer1 + Layer2
The plane wave approximation with oblique
incidence at interfaces.
The continuity conditions for the tangential
components of electric and magnetic fields at two
interfaces (01 and 12) and the Snell’s law for wave
propagation yield the following equations
𝐸0+ =
1
𝜏01𝐸1+ +
𝜌01𝜏01
𝐸1−
𝐸0− =
𝜌01𝜏01
𝐸1+ +
1
𝜏01𝐸1−
𝐸1+ =
1
𝜏12𝑒𝛾1 cos 𝜗1𝑑1𝐸2
+
𝐸1− =
𝜌12𝜏12
𝑒−𝛾1 cos 𝜗1𝑑1𝐸2+
01
12
𝐸0+, 𝐸1
+, 𝐸0− & 𝐸1
− ...the magnitude of electric field at the
layer interfaces for the wave propagating in the negative
and positive direction of z axis, respectively
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𝜌𝑚𝑛 =𝑍𝑛 cos 𝜗𝑛 − 𝑍𝑚 cos 𝜗𝑚𝑍𝑛 cos 𝜗𝑛 + 𝑍𝑚 cos 𝜗𝑚
𝜏𝑚𝑛 =2𝑍𝑛 cos 𝜗𝑚
𝑍𝑛 cos𝜗𝑛 + 𝑍𝑚 cos 𝜗𝑚
𝑚 = 0,1 𝑛 = 1,2
Fresnel’s reflection/transmission coefficient approximation at
interfaces
𝑍𝑘 =𝑗𝜔𝜇0
𝜎𝑘 + 𝑗𝜔𝜀0𝜀𝑟𝑘𝛾𝑘 = 𝑗𝜔𝜇0 𝜎𝑘 + 𝑗𝜔𝜀0𝜀𝑟𝑘 𝑘 = 0,1,2
z
x
L
h
~
ε0, σ = 0
μ0,
ε0 εr1
σ1
μ0, d1
ε0 εr2
σ2
μ0
ϑ0
ϑ1
ϑ2
mn = 01
mn = 12
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complex propagation constantImpedance of medium
𝐸0+
𝐸0− = 𝑀01
𝐸1+
𝐸1−
𝐸1+
𝐸1− = 𝑃12𝑀12
𝐸2+
𝐸2−
𝑀𝑚𝑛 =1
𝜏𝑚𝑛
1
𝜌𝑚𝑛
𝜌𝑚𝑛
1𝑚 = 0,1, 𝑛 = 1,2
𝑃12 =𝑒𝛾1 cos 𝜗1𝑑1
0
0
𝑒−𝛾1 cos 𝜗1𝑑1
... matching matrix
... propagation matrix
The layers k = 3, ... are readily included by adding the propagation and matching matrices :
... Matrix form for equations that solve for field values at
layer’s interfaces
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By setting 𝐸0+ = 1 𝑉/𝑚, all the other magnitudes 𝐸𝑚
+ and 𝐸𝑚−are easily determined.
Electric field can be calculated using the following expressions:
𝐸0 = 𝐸1+ cos𝜗0 Ԧ𝑒𝑥 + sin 𝜗0 Ԧ𝑒𝑧 𝑒−𝛾0 𝑥 sin 𝜗0−𝑧 cos 𝜗0 + 𝐸0
− cos 𝜗0 Ԧ𝑒𝑥 − sin 𝜗0 Ԧ𝑒𝑧 𝑒−𝛾0 𝑥 sin 𝜗0+𝑧 cos 𝜗0
𝐸1 = 𝐸1+ cos 𝜗1 Ԧ𝑒𝑥 + sin 𝜗1 Ԧ𝑒𝑧 𝑒−𝛾1 𝑥 sin 𝜗1−𝑧 cos 𝜗1 + 𝐸1
− cos𝜗1 Ԧ𝑒𝑥 − sin 𝜗1 Ԧ𝑒𝑧 𝑒−𝛾1 𝑥 sin 𝜗1+𝑧 cos 𝜗1
𝐸2 = 𝐸2+ cos 𝜗2 Ԧ𝑒𝑥 + sin 𝜗2 Ԧ𝑒𝑧 𝑒−𝛾2 𝑥 sin 𝜗2−𝑧 cos 𝜗2
The reflection and transmission coefficients RTM and TTM appearing in the Green’s function
are calculated as the ratio between the field value at the ground surface and the field
value obtained from the equations above at the given observation point.
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ϑinc
T(x,z)
T(x’,z’)
The MIT approach assumes the normal incidence of
a propagating EM wave, therefore the incidence angles are zero: ϑm = 0º.
The expressions for the reflection and transmission
coefficients for the two adjacent media indexed
with m and n are given as:
𝜌𝑚𝑛𝑀𝐼𝑇 =
𝑍𝑚2 − 𝑍𝑛
2
𝑍𝑚2 + 𝑍𝑛
2
𝜏𝑚𝑛𝑀𝐼𝑇 =
2𝑍𝑚2
𝑍𝑚2 + 𝑍𝑛
2
𝑚 = 0,1 𝑛 = 1,2
Alternative simplified approach to calculate tranmission / reflection coeffiicients:
- Modified image theory based approach
- convenient for TD computations
- a comparison with the plane wave approximation in FD needed for benchmark
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ϑ=0
Installation procedure
Run transmitted_E_field_pkg.exe.
This action installs MATLAB Compiler Runtime (MCR) version 8.1. and
extracts the following files:
- transmitted_E_field.exe
- MCRInstaller.exe
- readme.txt file
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. . .
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User guide
▪ ANTENNA PARAMETERS
▪ GROUND PARAMETERS
▪ FREQUENCY DOMAIN (FD)
▪ TIME DOMAIN (TD)
▪ RUN THE SIMULATION
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1.
2.
3.
4.5.
Graphical user interface
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Antenna parameters
L
(0,h) (L,h)
Ground parameters
d1
d2
εr1 σ1
εr2 σ2
εr3 σ3
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Frequency domain (FD)
Figures generated:
- E vs. x (z) if only one z (x) point is defined
- contours if xz grid is defined
Figure generated:
- E vs. frequency
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Figure generated:
- None
- The results are saved in .txt file
Freq. (MHz) x(m) z(m) Real(Ex) Imag(Ex) Real(Ez) Imag(Ez)
Frequency domain (FD)
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Time domain (TD)
▪ The excitation is given as a Gaussian waveform
where the parameters tw and t0 represent the
half width and time delay of a pulse
▪ Figure generated upon the calculation:
- E vs. time for tangential component of electric
field
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Examples1. E vs. xz
2. E vs. z
3. E vs. freq
4. E vs. time
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1. E vs. xz25
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f = 10 MHz 26
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1. E vs. xz
f = 10 MHz 27
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1. E vs. xz
f = 300 MHz 28
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1. E vs. xz
f = 300 MHz 29
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1. E vs. xz
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1. E vs. xz
Freq. (MHz) x(m) z(m) Real(Ex) Imag(Ex) Real(Ez) Imag(Ez)
Freq. (MHz) x(m) Real(I) Imag(I)
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1. E vs. xz
2. E vs. z
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3. E vs. f
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3. E vs. f
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3. E vs. time
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36REFERENCES
[1] D. Poljak, “Advanced Modelling in Computational Electromagnetic Compatibility,” John Wiley andSons, New York 2007.
[2] D. Poljak, V. Dorić, “Transmitted field in the lossy ground from ground penetrating radar (GPR)dipole antenna”, Computational Methods and Experimental Measurments XVII 3, WIT Transactions onModelling and Simulation, Vol 59, pp. 3-11, 2015
[3] A. Šušnjara, D. Poljak, S. Šesnić, V. Dorić “Time Domain Integral Equation versus Frequency DomainBoundary Element model for calculation of Transmitted Electrical Field for Ground Penetrating Radar(GPR) Antenna
[4] A. Šušnjara, D. Poljak, V. Dorić, “Electric Field Radiated By a Dipole Antenna Above a Lossy HalfSpace: Comparison of Plane Wave Approximation with the Modified Image Theory Approach,”SoftCOM conference, Split, 2017
[5] A. Šušnjara, V. Dorić, D. Poljak, “ Electric Field Radiated By a Dipole Antenna and Transmitted Into aTwo-Layered Lossy Half Space,” submitted for SpliTECH conference, Split, 2018