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IEEE MULTIDISCIPLINARY ENGINEERING EDUCATION MAGAZINE, VOL. 2, NO. 2, JUNE 2007 1
Design of Optimal GPR Antennas for Concrete
Evaluation
L. Travassos, Student Member, IEEE, S. Avila, N. Ida, C. Vollaire and A. Nicolas
Abstract—In order to resolve closely spaced targets in a planar
surface normal to the beam, the antenna used in the radar
assessment of concrete structures should have a narrow beam
width which means a higher directivity. To optimize the field
pattern of an antenna it was implemented a procedure that
unifies multi-objective genetic algorithms (MGA) and a moment
method (MoM) direct solver with the goal of implementing a tool
capable to choose optimal parameters to achieve the design of
an improved antenna to the radar testing of concrete structures.
Index Terms—Optimization, antennas, non-destructive testing.
I. INTRODUCTION
SINCE the success of the maintenance of a nation in-
frastructure depends on the ability of government policy
makers to strike a balance between available funds and the
need for repair or replacement, the Ground Penetrating Radar
(GPR) inspection of concrete structures is increasingly being
recognized as an effective way of maintenance.
This is due to the fact that tools for detecting distress that
results from deterioration have had undesirable limitations in
the past and these same limitations extend to the detection of
cracks and flaws. These limitations include requirements for
prolonged structures and significant measurement uncertainty.
Meanwhile, the life cycle cost of maintaining concrete
structures increases when distress is not detected before it
becomes too severe for effective repair or rehabilitation.
Antennas are one of the most critical parts in GPR systems.
They substantially determine the quality of the obtained GPR
raw data [1].
For work on concrete two main types of antenna are used,
generally described as either dipoles that operate in close
proximity to the material to be surveyed or TEM horns
that operate at least one wavelength from the material. Most
commercial GPR antennas are bow-tie dipoles given their loss
weight, low cost and broadband characteristics.
However bow-tie antenna provides a dipole-like omnidirec-
tional pattern with broad main beams perpendicular to the
plane of the antenna. Consequently, the image created by a
radar assessment could not correspond to the actual target,
and closely-space objects can not be detected.
In this paper, we present an alternative way to design
more efficient bow-tie dipole antennas using multi-objective
optimization process [2].
X. L. Travassos, C. Vollaire and A. Nicolas are with the Ecole Centrale de
Lyon (ECL), Ecully, France (phone: +33-4-72186105; fax: +33-4-78433717;
e-mail: lucas.travassos@ec-lyon.fr). S. Avila, was with the ECL. He is now
with the CTAI, Florianopolis, Brazil (e-mail: avila@senai.ctai.br). N. Ida is
with The University of Akron, Ohio, EUA.
Multi-objective optimization seeks to optimize the compo-
nents of a vector-valued cost function. Unlike single objective
optimization, the solution to this problem is not a single point,
but a family of efficient points called Pareto optimal front
which represents the trade-off among objective functions.
This procedure searches to attend two objectives: to mini-
mize the metal area of the antenna (in order to reduce the size)
and to maximize the gain in the plane normal to the antenna.
The moment method (MoM) with Rao-Wilton- Glisson (RWG)
basis functions [3] is used to calculate the electromagnetic
characteristics of the antenna.
II. MODELING NEEDS
Computers have had a significant impact on the modeling
of non-destructive testing (NDT) phenomena. In the method
of numerical modeling a physical phenomenon under inves-
tigation is represented by a mathematical system which can
be solved numerically. The results obtained from the mathe-
matical investigation of such a model are then interpreted in
terms of the original phenomenon and serve to develop an
understanding of the physical processes involved. The most
important task in NDT modeling is the prediction of faults or
inclusions in the physical parameters characterizing the region
under test.
NDT modeling involves calculating a physical magnitude
i.e. electromagnetic field, force, radiation, in a model defined
by a postulated distribution of parameters in the medium under
study, together with the exciting source. This calculus can be
done by solving finite-difference and finite-element equations.
Concerning this work, the fundamental mathematical model
is represented by Maxwell’s equations, which prescribe the
analytical relationship in the form of a system of first order
vector equations between the components of electric and
magnetic fields and the parameters of the medium under test.
The design of radar systems has been subjected to funda-
mental changes. Electronic devices are no longer designed on a
simple desk using tables and calculators with inevitable design
errors eliminated tediously on prototypes. Today, the design is
computer aided, and both highly complex radars and complete
electronic systems are simulated immediately. Design errors
are excluded by a great deal by simulation. In reality, no
designer and no simulation is perfect, so failures will still be
detected on prototypes. However, the number of redesigns at
the prototype stage has dropped in a sensible scale.
Traditionally the NDT modeling seeks at improving the
systems’ sensors design and provide data for imaging. Imaging
of defects in concrete structures plays an important role in
NDT. They are usually applied to pulse-echo data carried out
by either acoustic, elastic or electromagnetic waves.
1558-7908 c
2007 IEEE Education Society Student Activities Committee (EdSocSAC)
http://www.ieee.org/edsocsac
IEEE MULTIDISCIPLINARY ENGINEERING EDUCATION MAGAZINE, VOL. 2, NO. 2, JUNE 2007 2
Antenna design is a topic of great importance to electromag-
netics. It involves the selection of antenna physical dimensions
to achieve optimal gain, pattern performance, voltage standing-
wave ratio, bandwidth, and so on, subject to some specified
constraints.
A trial and error process is typically used for antenna
design and consequently the designer is required to have great
experience and intuition.
In the last decade, several investigators have reported en-
couraging results from the coupling of gradient-free methods
with method of moments. The combination of various opti-
mization methods and numerical techniques further enables
the optimization of planar antennas such as a bow-tie shape
using gradient or gradient-free optimization methods.
Gradient-free methods, or direct-search methods, are gen-
erally robust and particularly effective for problems with a
large number of design variables, but require fast objective
function evaluations for their practical implementation. They
are largely independent of the initial design and solution
domain. Therefore, global optima are more likely to be found.
As is generally understood, gradient-free methods work very
well when many local optima exist, whereas gradient-based
methods break down in these cases.
III. MULTI-OBJECTIVE GENETIC ALGORITHM
The Genetic Algorithm (GA) is a stochastic procedure based
on the concepts of natural selection and genetics. There are
many papers showing the effectiveness of the GA to solve
engineering optimization problems.
In most real-world problems, several goals must be satisfied
simultaneously in order to obtain an optimal solution. As these
objectives are usually conflicting, no single solution may exist
that is best regarding all considered criteria.
Multi-objective optimization (also called multicriteria, mul-
tiperformance or vector optimization) seeks to optimize the
components of a vector-valued cost function. Unlike single
objective optimization, the solution to this problem is not a
single point, but a family of efficient points.
Each point in this set is optimal in the sense that no
improvement can be achieved in a cost vector component that
does not lead to degradation in at least one of the remaining
components. Each element in the efficient set constitutes a
non-dominated (non-inferior or non-superior) solution to the
multi-objective problem.
The main action of the multi-objective optimization is to
determine the efficient front. With this set of solutions, it is
possible to understand the dependence between each objective,
which allows making efficient choices for the final solution
decision.
The analysis of the Pareto-front behavior permits to under-
stand the tradeoff between the different objectives. Compared
with the deterministic optimization methods, which lead to
unique solution, multi-objective genetic algorithms (MGA)
offers the possibility to the designer to make the final choice
among the set of solutions by considering additional con-
straints not included in the initial steps [2,4].
The MGA used in this work is based on three current
populations. Basically, the algorithm starts with a set of
Initial
Solutions
?
#
"
!
Evaluation
MoM Analysis
?
#
"
!
Pareto’s
Condtion
?
@@@
@
@
@
@
@
Efficient
Solution ? Y
N
?
Dominated
Solutions
?
Real
Population -Sampling
+ Tournament -Crossover
and Mutation
6
Variable
Reflexion
6
Children
Evaluation
6
Global Elitism
-Non Dominated
Solutions
?
Clearing
and Niche
Fig. 1. Multi-objective Genetic algorithm.
solutions randomly created. These solutions are evaluated
and the Pareto-optimal condition is tested, giving two groups
of solutions: one formed by efficient solutions, called non-
dominated population (NDOM); and another by non-efficient
solutions, called dominated population (DOM).
An index (IDOM) indicating how many times each solution
is dominated by others is created. After the Pareto’s check,
it is time to apply the Clearing technique, whose purpose is
to obtain a sparse and well-established Pareto front. If simi-
larities among individuals are detected (in parameters or/and
objectives spaces [5]), one or some of them are punished. The
penalty consists in moving the penalized individual to DOM
(by changing IDOM from 0 to 1).
This approach makes easier the attainment of a well-
established Pareto set. Crossover and mutation operators based
on real coding representations are then applied to create the
children of a generation.
To control that all design variables always remain inside
the feasible bounds and are not affected by the evolutionary
process, a procedure of ”adjustment by saturation” is applied.
Design variables outside their prescribed limits are automati-
cally adjusted to the limit values.
1558-7908 c
2007 IEEE Education Society Student Activities Committee (EdSocSAC)
http://www.ieee.org/edsocsac
IEEE MULTIDISCIPLINARY ENGINEERING EDUCATION MAGAZINE, VOL. 2, NO. 2, JUNE 2007 3
The children are evaluated and associated with the non-
dominated solution of REAL to form the new initial popula-
tion. This elitism process guarantees the preservation of effi-
cient parent solutions. The process is iterated until an ending
criterion is met (typically a fixed number of generations).
IV. RESULTS
Bow-tie antennas are not isotropic radiators or receivers and
exhibit directionality of wavefields. High directivity adversely
affects wide angle surveys used to determine velocity and other
physical attributes.
In addition, directivity becomes even more important for
imaging applications used to accurately determine the shape,
location, and size of subsurface targets and becomes essential
when inverting GPR data to extract target’s physical properties.
The design of an effective planar bow-tie antennas requires
balancing the antenna length, the flare angle and the radiation
pattern produced. Therefore, there is an issue of optimization
in determining the antenna parameters for best performance.
To address the issue of optimization, we considered the
problem where an antenna is in free-space and evaluated in
the far-field region.
Most antenna characteristics that are relevant to GPR appli-
cations such as the wave polarisation, radiation field pattern
and beam width are commonly defined in the far-field region
of an antenna.
However, notwithstanding the complexity of the electromag-
netic radiation in the near-field region, most civil engineering
applications using surface contact antennas are concerned with
radar measurements in the near-field region [6].
Considering this complexity, edge finite elements (FEM)
are used to investigate the behaviour of the optimized antenna
in the near-field region of a concrete GPR assessment to the
location of reinforced bars.
The goal in the optimized design of this antenna is to
reduce the metal area (and consequently a minimal length and
weight) and to improve the gain in the plane perpendicular to
the antenna. The MGA are then coded to find multiple non-
dominated solutions (the Pareto-front) using a fixed frequency
of 1 GHz. The antenna parameters to adjust are:
Pg=
Lg,1αg,1Eg,1
.
.
..
.
..
.
.
Lg,np αg,np Eg,np
(1)
where each line represents a feasible solution, g is the current
generation and np is the population size. The variables to be
optimized are then the antenna length, the flare angle and
the percentage of antenna elements that can be erased. They
are adjusted to minimize the metal area of the antenna. This
becomes the first objective function. The second objective
function is to maximize the gain in the direction perpendicular
to the antenna plan.
In order to find the antenna configuration with a higher
directivity and a smaller metal area we implemented a MGA
to accomplish two conflicting objectives with the following
limits: the length L[0.1λto 1λ] (with frequency equal to 1
Fig. 2. Pareto front for the planar bow-tie antenna.
Fig. 3. H-plane field pattern of the planar bow-tie antenna.
GHz), the flare angle [30◦to 120◦], and the void spaces in
the antenna structure.
The antenna first is created with 256 elements and then a
percentage of this total between 0 and 20%is replaced from
metal to air according to the objectives. The feed region is
obviously protected to avoid numerical errors.
Figure 1 shows the pareto-front and the modifications ap-
plied to a given solution in order to improve the radiation
pattern. The optimized antenna proposed by the algorithm with
a maximal gain has α=79◦and L=26cm with 11%of the
elements erased.
The radiation pattern shown in the Figure 2 presents the
gain obtained in the plane normal to the antenna. The gain
obtained was 6.37 dB against 3.40 dB of a common structure
with improvement of the half-power beam width from 57.6◦
to 43.2◦. In this case, the area presented is maximal. Other
soulutions can be found according with the designer’s needs.
The convergence has been attained in about 50 generations
with a population of 50 individuals in several GA executions.
The crossover and mutation probabilities were set to 0.9 and
0.05 respectively.
To take into account the coupling effects of the antenna on a
dielectric interface FEM are useful due to their correct physical
sense and accuracy. Considering this, the electromagnetic
propagation of a more realistic model of concrete structure
was realized using FEM.
1558-7908 c
2007 IEEE Education Society Student Activities Committee (EdSocSAC)
http://www.ieee.org/edsocsac
IEEE MULTIDISCIPLINARY ENGINEERING EDUCATION MAGAZINE, VOL. 2, NO. 2, JUNE 2007 4
TABLE I
DATA FOR T HE CONCRET E PROB LEM
Porosity of concrete 0.15
Degree of saturation 0.7
Salt content 52ppt
Temperature 20◦C
Fig. 4. Finite element analisys of the optimized antenna.
For the concrete electrical properties, the discrete model
proposed by Halabe [7] was used. This model deals with
complex conductivities instead of complex dielectric constants.
The discrete model is then used to compute the complex
pemittivity for each frequency component.
The concrete electrical properties used are shown in Table
I. In addition, it was added to the antenna a conductor shield
to improve the directivity. For 1 GHz the concrete slab was
simulated with ǫr= 8.37 and σ= 0.23S/m. First order
boundary conditions were used to truncate the domain of study.
The simulation was performed in a Pentium IV with 964Mb
in about 15 min for a domain of 25K nodes.
The scattered near field shown in Figure 3 illustrates a non-
destructive assessment to detect the presence of a conducting
bar buried 15 cm in the concrete and located parallel to the
antenna’s direction.
Figure 4 shows the modifications in the antenna’s input
impedance for three different scenarios. In the case where
the bar is perpendicular to the antenna, and consequentially,
located in the region more illuminated, the input impedance
is more affected indicating his presence.
In order to improve the results, it was added to the problem
the angle between the bow-tie wings as a new variable. The
pareto-front for the V-shaped bow-tie antenna is shown in
Figure 5 with the geometry of the solution with a maximal
gain. At this time, a new constraint was imposed to problem:
the return loss of the antenna.
Antennas with a return loss greater than -10 dB considering
a transmission line feed with 200 Ωwere penalized in the
optimization process. The gain obtained was of 8.77 dB with
a return loss of -13.5 dB for 1 GHz. The angle between the
bow-tie wings found was 97.88◦. In this case, the same antenna
without the holes would not fulfill the impedance criteria.
Fig. 5. Input impedance of the antenna in the radar assessment.
Fig. 6. Pareto front for the V-shaped bow-tie antenna.
V. CONCLUSION
The significance of this antenna pattern optimization ap-
proach is in the resolution that can be achieved in improving
the antenna design. The results show that a better field pattern
can be obtained with the optimized antenna which leads to
a better signal penetration and more realistic GPR images of
lossy concrete structures.
REFERENCES
[1] A. A. Lestari et al, ”Analysis and design of improved antennas for GPR,”
Subsurface sensing technologies and applications, vol. 3, pp. 295-326,
2002.
[2] K. Deb, Multi-Objective Optimization. John Wiley &Sons , 2002.
[3] S. Makarov, ”MoM antenna simulations, with Matlab: RWG basis func-
tions,” IEEE Antennas and Propagation Magazine, vol. 43, pp. 100-107,
2001.
[4] C. A. Coelho et al., Evolutionary Algorithms for Solving Multi-Objective
Problems (Genetic Algorithms and Evolutionary Computation). Kluwer
Academic Publishers, 2002.
[5] S. L. Avila et al., ”A Multi-Niching Multi-Objective Genetic Algorithm
for Solving Complex Multimodal Problems,” In: OIPE 2006, The 9th
Workshop on Optimization and Inverse Problems in Electromagnetics,
September 13 - 15, 2006, Sorrento (Italy).
[6] S. G. Millard et al., ”Field pattern characteristics of GPR antennas,”
NDT&E International, vol. 35, pp. 473-482, 2002.
[7] U. B. Halabe, Condition assessment of reinforced concrete structures
using electromagnetic waves, PhD thesis, Massachusetts Institute of
Technology, USA, 1990.
1558-7908 c
2007 IEEE Education Society Student Activities Committee (EdSocSAC)
http://www.ieee.org/edsocsac
