User manual | Inverse Problem Solution in Landmines

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Inverse Problem Solution in Landmines Detection
Based on Active Thermography
Barbara SZYMANIK
West Pomeranian University of Technology in Szczecin, Faculty of Electrical Engineering,
Sikorskiego 37, 70-313 Szczecin, Poland
[email protected]
Abstract. Landmines still affect numerous territories in the
whole world and pose a serious threat, mostly to civilians.
Widely used non-metallic landmines are undetectable
using metal detector. Therefore, there is an urging need to
improve methods of detecting such objects. In the present
study we introduce relatively new method of landmines'
detection: active infrared thermography with microwave
excitation. In this paper we present the optimization based
method of solving inverse problem for microwave heating.
This technique will be used in the reconstruction of detected landmines geometric and material properties.
Keywords
Microwave heating, landmines detection, active
thermography, inverse problems.
1. Introduction
Nowadays, metal detector is still the most popular device used in demining. It is able to detect landmines containing metallic parts, nevertheless it is almost completely
useless in case of the most common, nonmetallic (with
bakelite, PVC, and polyethylene casings) devices. Therefore, it is extremely important to work on improving the
methods of landmines’ detection and removal. Currently
the intensive investigations of several new methods of
landmine detection are conducted [1]. In the present study,
we introduce the relatively new method of landmines’
detection: active infrared thermography with microwave
excitation [2], [3], which can be considered complementary
to the metal detector. Microwave enhanced infrared thermography combines two phenomena: microwave heating
and thermal imaging. The volumetric microwave heating
induces the thermal contrast between the landmine and
soil. Thermal patterns obtained at the ground’s surface are
observed using sensitive thermovision camera. This
method is able to detect an object, determine its size and
approximate its location.
Active infrared thermography with microwave excitation can be used to detect objects buried below the
ground, regardless of what material they are composed of.
It is undoubtedly the basic advantage of this method. However buried stones, branches, and various types of waste
can produce similar thermal signatures to antipersonnel
landmines while heated by microwaves. It is therefore
important to not only detect an object that can be possibly
a landmine, but also to determine some of its parameters to
classify the object to the group of potentially dangerous
[4]. In this paper the method of solving inverse problem for
microwave heating will be presented. The proposed technique will be used in estimation of chosen geometric and
material properties of landmines. Both numerical and experimental results will be shown.
2. Numerical Modeling − Forward
Problem
The phenomenon of microwave heating can be simulated using finite element method (FEM). The propagation
of microwave through a dielectric material is governed by
the electromagnetic wave equation [5]:
 
 1
  2
k E  0
  
  E     r  j
 0  0
 
 r
(1)
where μr is the relative permeability, ε0, εr are permittivity
of vacuum and material, respectively, σ is the material
conductivity, k0 is the wave number and E is electric field
vector. The heat transfer equation can be written as follows:
C p
T
  ( k  T )  p
t
(2)
where ρ, Cp, k indicate material’s density, specific heat
capacity and thermal conductivity, respectively and
p  2f 0 '' E 2 is the volumetrically dissipated power, dependent on wave frequency f and dielectric properties of
material.
2D simulations were conducted using commercial
software COMSOL Multiphysics to obtain the data which
may be used in inverse problem using optimization method
(described in the subsequent section). The proposed geometry is presented in Fig. 1.
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B. SZYMANIK, INVERSE PROBLEM SOLUTION IN LANDMINES DETECTION BASED ON ACTIVE THERMOGRAPHY
is the distribution obtained in every iteration, t indicates
the time step, x − coordinate of the measurement point, N
is the number of measurement points.
Fig. 1. 2D numerical model geometry.
3. Inverse Problem in Infrared
Landmine Detection
Fig. 2. Estimated geometrical properties: A - width, B height, C - depth of burial, D - position against the
waveguide.
The chosen parameters of the landmine can be reconstructed by solving the inverse problem [6]. In our case, the
inverse problem is to determine the parameters of the landmines buried in the sand on the basis of the temperature
distribution along the sand surface. This distribution can be
obtained from the sequence of thermal images. In Fig. 1
one may see black line indicating the boundary from which
the temperature distributions were read. The main assumption of our method is a strong relationship between the
geometric parameters and material properties of buried
landmines and the shape of lines presenting temperature
distributions along marked boundary.
The total time of observation was set to 1200 seconds,
with 600 seconds of microwave heating. The temperature
distribution was measured during the whole time every 40
seconds. As the result we received 30 linear temperature
distributions to work with. Reconstructed parameters are:
object’s size (width and height), the depth at which the
object is buried and the position of the object in the relation
to the centre of waveguide aperture (geometric parameters
are shown in Fig. 2). Additionally, one material parameter
− the value of imaginary part of complex dielectric permittivity, was also taken into account. This parameter was
chosen after the study of the system’s sensitivity to modification of all of the material parameters (i.e. density, specific heat, thermal diffusivity, complex dielectric permittivity).
The optimization algorithm, composed of combined
Genetic Algorithms (GA) [7] and Pattern Search (PS), is
presented in Fig. 3. The minimized function is defined as
summed minimal square errors between the optimal temperature distribution and the distributions obtained in every
iteration of the algorithm:
1N
2
   f desT ( xk , l  t )  fT ( xk , l  t )   (3)
N
l 1  k 1

30
MSET  
where fdes T indicates the desired temperature distribution, fT
Fig. 3. Flowchart of optimization algorithm.
4. Results − Numerical Data
In order to verify the proposed algorithm’s efficiency,
the analysis including four sets of numerical data was conducted. The optimization goal in the first case was a landmine of width 0.2 m, height 0.01 m, buried at 0.2 m below
the ground and located 0.1 m from the waveguide aperture
centre, and in the second case a landmine of width 0.14 m,
height 0.03 m, buried at 0.05 m below the ground and
located centrally under the waveguide. The imaginary part
of complex dielectric permittivity was set to 0.23 in the
second case. The first set of numerical data was used to
prove the efficiency of the proposed algorithm of estimating the landmine properties in case when there is an offset
between the feed and the landmine. In the second case
besides the geometric properties complex dielectric permittivity was also estimated. In the third and fourth case
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the Gaussian noise of 5 % was added to both previous data
sets. In Fig. 4 the optimal temperature distributions obtained as a result of forward problem solution for all of the
cases are presented.
Fig. 4. The optimal temperature distributions. a) and b) for the
mine of width 0.2 m, height 0.01 m, buried at 0.2 m
below the ground and located 0.1 m from the waveguide aperture centre for the case without noise and
with noise, respectively c) and d) for the mine of width
0.14 m, height 0.03 m, buried at 0.05 m below the
ground and located centrally under the waveguide for
the case without noise and with noise, respectively.
In all cases, the genetic algorithm using the population of 10 individuals was used. The generations number
for GA was set to 10. The solution from GA was used as
the starting point in the pattern search algorithm, which ran
in 50 iterations. As the result of the optimization process is
the reconstructed geometrical object parameters. Additionally, for the second case (the mine of width 0.14 m, height
0.03 m, buried at 0.05 m below the ground and located
centrally under the waveguide) the imaginary part of complex dielectric permittivity was found. Figure 5 presents
the comparison between optimal temperature distribution
and those obtained in the optimization process for all sets
of data. The results for the four test cases are gathered in
Tab. 1–4. It may be noticed that in the case of data with
added noise the results are significantly worse: especially
the object width was estimated with maximum 90% error.
However, in the case of relatively large objects like landmines, the correct estimation of location parameters (depth,
position against the aperture center) seems to be more
important. Moreover the imaginary part of dielectric permittivity was estimated with error of absolute value equal
to 4 %. Therefore, it can be expected that the method of
parameter estimation may be used not only for the exact
location of the object, but also to verify the type of material
from which the object is constructed.
Fig. 5. Comparison between goal temperature (blue line) and
reconstructed temperature (black line) distributions
along ground surface. a) and b) for the mine of width
0.2 m, height 0.01 m, buried at 0.2 m below the ground
and located 0.1 m from the waveguide aperture centre
for the case without noise and with noise, respectively.
c) and d) for the mine of width 0.14 m, height 0.03 m,
buried at 0.05 m below the ground and located centrally under the waveguide for the case without noise
and with noise, respectively.
Parameter
Width [m]
Height [m]
Depth [m]
Position against
aperture [m]
Desired value
0.2 m
0.01 m
0.025 m
Estimated value
0.19 m
0.01 m
0.025 m
Error
-5%
0%
0%
0.1 m
0.1 m
0%
Tab. 1. Estimated parameters for the mine of width 0.2 m,
height 0.01 m, buried at 0.2 m below the ground and
located 0.1 m from the waveguide aperture centre.
Without noise.
Parameter
Width [m]
Height [m]
Depth [m]
Position against
aperture [m]
Desired value
0.2 m
0.01 m
0.025 m
Estimated value
0.38 m
0.01 m
0.026 m
Error
90%
0%
4%
0.1 m
0.108 m
8%
Tab. 2. Estimated parameters for the mine of width 0.2 m,
height 0.01 m, buried at 0.2 m below the ground and
located 0.1 m from the waveguide aperture centre.
With noise.
Parameter
Width [m]
Height [m]
Depth [m]
Position against
aperture [m]
''

Desired value
0.14
0.03
0.05
Estimated value
0.14
0.06
0.06
0
0
0.23
0.24
Error
0%
100%
20%
4%
Tab. 3. Estimated parameters for the mine of width 0.14 m,
height 0.03 m, buried at 0.05 m below the ground and
located centrally under the waveguide. Without noise.
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B. SZYMANIK, INVERSE PROBLEM SOLUTION IN LANDMINES DETECTION BASED ON ACTIVE THERMOGRAPHY
Parameter
Width [m]
Height [m]
Depth [m]
Position against
aperture [m]
''

Desired value
0.14
0.03
0.05
Estimated value
0.07
0.06
0.04
0
0
0.23
0.19
Error
-50%
100%
20%
-4%
Tab. 4. Estimated parameters for the mine of width 0.14 m,
height 0.03 m, buried at 0.05 m below the ground and
located centrally under the waveguide. With noise.
5. Results − Experimental Data
The next stage of the study was devoted to evaluate
the effectiveness of the proposed algorithm for the case of
experimental data [8]. The experimental setup, shown in
Fig. 6, consists of a microwave heating device and thermovision camera (computer controlled FLIR A325, able to
record thermal images and videos). The microwave heating
device system is based on a magnetron, generating microwaves (frequency 2.45 GHz) of maximum power of
1000 W. The magnetron is connected to the rectangular
waveguide with a proper flange. The waveguide is placed
above the container with sand, in which the inert landmines
are buried. Sand surface is observed using a thermovision
camera FLIR A325.
Fig. 7. Exemplary thermogram obtained for PMA-1 landmine.
Temperature values were collected from marked green
line.
procedure of filtering out the noise is used. In the first step,
the Matlab Curve Fitting Toolbox was used to approximate
the temperature distribution curves. Data were approximated by Fourier functions, defined as follows:
f ( x )  a0  a1  cos( wx )  b1 sin( wx )  ... 
 a5 cos(5wx)  b5 sin(5wx )
(4)
where the parameters a0,…, a5, b1,…, b5, w were selected
using non-linear least squares method.
Fig. 6. Experimental setup.
In the experiment, inert landmine PMA-1 (width
0.14 m, height 0.03 m), with bakelite casing was used. The
landmine was buried to a depth of five centimeters. The
sand with buried landmine was heated for 10 minutes and
then the system was observed with themovision camera for
another ten minutes of natural cooling. During this time,
the sequence of 600 thermograms, presenting the temperature distribution on the surface of the sand, was recorded.
In each thermogram, the temperature values were collected
along a single line passing through the central part of the
heated space, as shown in Fig. 7. As a result, the 600 temperature distributions (shown in Fig. 8) were obtained.
It can be noticed, that obtained linear distributions are
noisy. As it was observed in the previous section, the proposed algorithm of parameters estimation gives distinctly
worse results for data with added noise. Therefore, the
Fig. 8. Temperature distributions collected from thermograms.
As a result of approximation, 600 curves presented in
Fig. 9 were obtained. Presented data was used as input to
the optimization procedure.
The parameter estimation procedure was carried out
just like in the case of numerical data, described in the
previous section. Again the genetic algorithm using the
population of 10 individuals was used. The generations
number for GA was set to 10. The solution from GA was
used as the starting point in the pattern search algorithm,
which ran in 50 iterations.
Figure 10 shows the comparison between the exemplary temperature distributions obtained in the optimization
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6. Conclusions
It was shown, that the proposed algorithm may be
used to estimate chosen parameters of the landmines. Solution of the inverse problem allowed the estimation of geometric parameters and one material parameter of the object.
The imaginary value of the complex dielectric permittivity
may be used to approximate determination of the type of
material. It may be especially useful to distinguish between
variety types of plastic (used to landmines’ casings construction) and other materials, which often contaminate the
minefields (like rocks, metal parts and wood chunks). The
estimation of the burial depth seems to be very important,
since this information may be crucial for the safety of
deminers.
Fig. 9. Approximated temperature distributions.
References
[1] MACDONALD, J., LOCKWOOD, J. R. Alternatives for
Landmine Detection. RAND, 2003.
[2] MENDE, H., DEJ, B., KHANNA, S., APPS, R., BOYLE, M.,
ADDISON, F. Microwave enhanced IR detection of landmines
using 915 MHz and 2450 MHz. Defence Research Reports, no.
DRDC-OTTAWA-TM-2004-266. Ottawa (Canada): Defence
R&D, 2004.
[3] MALADEGUE, X. Theory and Practice of Infrared Technology
for Nondestructive Testing. New York (USA): John Wiley and
Sons, 2001.
[4] THANH, N. T., SAHLI, H., HAO, D. N. Infrared thermography
for buried landmine detection: Inverse problem setting. IEEE
Transactions on Geoscience and Remote Sensing, 2008, vol. 46,
p. 3987–4004.
Fig. 10. The comparison between the exemplary temperature
distributions obtained in the optimization process
(solid lines) and those obtained experimentally (dashed
lines).
process and those obtained experimentally. In Tab. 5 the
estimated parameters are gathered. The good agreement
between the results of estimation and the actual parameters
of the detected object may be noticed. In the case of the
geometrical parameters, the largest error occurs in the
estimation of the mine height, while the width, the depth of
burial and location of mine are estimated with a small
error. Imaginary part of the complex dielectric permittivity
was estimated to 0.28 (compared to ε’’= 0.23, for bakelite).
Estimation of material properties is essential in this study,
since it can be used to determine the approximate type of
material.
Parameter
Width [m]
Height [m]
Depth [m]
Position against
aperture [m]
''

Actual value
0.14
0.03
0.05
Estimated value
0.13
0.08
0.06
Error
-7%
167%
20%
0
0.02
5%
0.23
0.28
22%
Tab. 5. Estimated parameters for the case of experimental data.
[5] SZYMANIK, B., GRATKOWSKI, S. Numerical modelling of microwave heating in landmines detection. International Journal of
Applied Electromagnetics and Mechanics, 2011, vol. 37, no. 2-3,
p. 215–229.
[6] SZYMANIK, B. Objects’ parameters reconstruction in landmines’
detection based on active thermography. In International
Interdisciplinary PhD Workshop IIPhDW 2013. Brno (Czech
Republic), 8-11 September, 2013.
[7] GOLDBERG, D. E. Genetic Algorithms in Search, Optimization
and Machine Learning. Addison-Wesley Publishing Company Inc.
1989.
[8] SZYMANIK, B. Zastosowanie aktywnej termografii podczerwonej
ze wzbudzeniem mikrofalowym do wykrywania niemetalicznych
min lądowych. (The use of active infrared thermography with
microwave excitation for detection of non-metallic landmines.)
PhD Thesis. West Pomeranian University of Technology, Poland,
2013 (in Polish).
About Author ...
Barbara SZYMANIK was born in 1982. She received her
master’s degree in Mathematics in 2006 and in Physics in
2009. In 2013 she defended her doctoral thesis and received her PhD degree in Technical Sciences. Her scientific interests are mainly NDT of materials using active
infrared thermography.

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