Heat Transfer for NDE: Landmine Detection 9
solution of the heat equation and the use of inverse problems techniques, López (2003); López
et al. (2009; 2004). The process starts with the acquisition of a sequence of infrared images
of the surface of the soil under known heating and atmospheric conditions. As explained
before, sunrise and sunset are the preferred times for detection. We will also assume that
a pre-processing stage is run on a conventional PC in order to align the images and map
grayscale colors to temperature values on the surface. Next, the soil inspection procedure
itself starts. First, we run a detection procedure, as will be explained in the following section,
to obtain the mask of potential targets. Then, a quasi-inverse process operator is used to
identify the presence of antipersonnel mines among the potential targets. For those targets
that failed to be classified as mines (and are therefore labeled as unknown), a full inverse
procedure to extract their thermal diffusivity will be run in order to gain information about
their nature. The overall detection process is summarized in Fig. 3, where the processes
that require the use of the 3D thermal model are indicated with an ellipse. The detection,
quasi-inverse and full-inverse procedures are based on the solution of the heat equation for
different soil configurations. As explained, this is a very time consuming task that makes the
whole algorithm inefficient for real on-field applications.
2.3.1 Target detection
The use of IR cameras taking images of the soil under inspection gives us the exact distribution
of temperatures on the surface. On the other hand, the thermal model described previously
and extensively validated with experimental data permits us to predict the thermal signature
of the soil under given conditions, López (2003); López et al. (2004). The detection of the
presence of potential targets on the soil is then made by comparing the measured IR images
with the expected thermal behavior of the soil given by the solution of the forward problem
under the assumption of absence of mines on the field, mathematically,
α
(x, y, z)=α
soil
, ∀x, y, z. (21)
For this set of soil parameters, p, the application of the functional in Eq. (20) determines
the surface positions

Heat Transfer for NDE: Landmine Detection 11
classified as unknown (a procedure for the retrieval of further information about the nature
of the unknown targets will be explained in the next section). For the mine category, the
depth of burial will be also estimated. In general, this reconstruction is not possible unless
additional information on the solution is incorporated in the model by means of the so-called
regularization techniques Engl et al. (1996); Kirsch (1996). It is, however, possible to solve
the inverse problem without the explicit use of a regularization strategy under proper
initialization conditions and the use of iteration methods.
The iterative procedure is based on evaluating Eq. (20), which expresses the deviation between
the observed IR data, y
δ
, and the one given by the solution of the forward problem using
known parameter distributions, F
[p]. Therefore the heat equation needs to be solved for each
of these distributions during the time of analysis (usually one hour around sunrise). In the
case of mine targets, we will assume that their thermal evolution is driven by the thermal
properties of the explosive used, which is commonly TNT composition B-3 or, less frequently,
Tetryl. Our initial guess will be to assume that, (i) all the targets detected in the detection step
are mines, that is,
α
target
= α
mine
, (22)
and (ii) the possible depths of burial constitute a discrete set z
∈
˜
Z being,
˜
Z

δ
s
, is estimated by evaluating Eq. (20) for each pixel position (x, y);
2. For each time instant s, a global error map (J
s
) and a global classification map (Υ
s
)are
estimated iteratively by comparing the error maps J
s,k
, k = 0, , d, as follows:
• Initialization step: For each pixel
(x, y), we set J
s
(x, y)=ε (where ε is a predefined
threshold error value); and Υ
s
(x, y)=soil.
• Iterative update step: For each depth of burial, k, with k
= 0, , d, J
s
(x, y)=
min(J
s,k
(x, y), J
s
(x, y)) and Υ
s
(x, y)=ar g mi n
k

s
(x, y)). This is a very conservative approach aiming at reducing the
number of false negatives (failure to detect a buried mine) even at the cost of increasing
the false alarm rate of the system.
• To find a trade-off between the accuracy of the classification and the number of false
alarms, we define a cutoff error, e
max
. If the entry on the error map, J for a pixel exceeds
e
max
, the pixel will be automatically assigned to the category of Unknown. e
max
is
estimated empirically, however it could be estimated taking into account the pixels
classified as non-mine based their temperature variance using bootstrap techniques,
Zoubir & Iskander (2004).
2.3.3 Full-inverse procedure for the classification of non-mine targets
In this case, no assumption about the nature of the targets found in the detection phase is
made, although the set of possible depths at which the targets can be placed is still bounded
by Eq. (23). Under these assumptions, Eq. (22) does not hold and α
target
is unknown and could
take any value depending on the nature of the object. For this reason, it is necessary in this
case to use a systematic approach for the minimization of the functional J, which implies the
calculation of the gradient ∂J/∂p.
Let us consider the existence of a buried target in a 3D soil volume, Ω, with an unknown
α
= α(r), r =(x, y, z) ∈ Ω. The thermal experiment is the following: at time t = t
0
, the solid


, t)=q
net
(r

, t) r

∈ Γ, t ∈ [t
0
, t
f
]. (24c)
We look at the reconstruction of α
(r) from the knowledge of the surface response of
temperature, y
δ
= θ(r

, t), to prescribed flux applied on the boundary q
net
(r

, t). We call data
the pair
(
θ(r

, t), q
net
(r

)=u
0
, r ∈ Ω (25b)
∂
∂n
u(r, t)=q
net
(r

, t) r

∈ Γ, t ∈ [t
0
, t
f
]. (25c)
The solution of Eq. (25) is a well-posed problem, as opposed to Eq. (24), and will be denoted
by u
(r, t; p). Our aim will be to control p in such a way that the difference between the model
and the observed data tends to zero. This goal is quantified by an objective function J to be
32
Developments in Heat Transfer
Heat Transfer for NDE: Landmine Detection 13
minimized. The functional to be minimized is the L
2
norm of the misfit between the model
and the observation given by,
J
(u(p)) ≡
1

Γ
q
net
(r

) v(r

) dS
a
p
< u, v >=

Ω
p gradu gradvdΩ,
then the model problem, Eq. (25), is equivalent to the variational problem,

t
f
t
0
<
∂u
∂t
, v
>
Ω
dt +

t
f

Ω
+a
p
< u, λ > − < q
net
, λ >
Γ
} dt. (28)
Note that L
= J if u is the solution of the model problem, Eq. (25), since Eq.(27) holds for
any λ. Thus, the minimum of J under the constraints in Eq. (27) is the stationary point of
the Lagrangian L. Conversely, if δL
= 0 for arbitrary δλ, u and p being held fixed, it follows
necessarily that Eq. (27) holds. We consider,
δL
=
∂L
∂u
δu
+
∂L
∂p
δp, (29)
where,
∂L
∂u
δu ≡

t
f

∂L
∂u
δu
= 0. (31)
This condition can be written as,

t
f
t
0
< u − θ, δu >
Γ
dt +

t
f
t
0
{− < δu,
∂λ
∂t
>
Ω
+a
p
< δu, λ >} dt+ < δu, λ >
Ω
|
t
f


t
f
t
0

Ω
∂p gradu gradλ dΩ dt. (35)
It results from Eq. (35) that the derivative of J in the p
(r) direction is known explicitly by
solving two problems, the direct problem for the field u and the adjoint problem for the field
λ. That is, the Z-integral,
∂J
∂p
≡ Z =

t
f
t
0
gradu gradλ dt. (36)
Solving Eq. (25) and Eq. (34), both of them well-posed forward problems, and using Eq. (36),
the expression of the update of Eq. (17)) can be calculated in a straightforward manner. With
respect to the number of iterations of the Landweber method, the selection of the stopping
criteria of the algorithm must be made according to the discrepancy principle in Eq. (18)). The
bigger the η, the lower the number of iterations is, and the higher the error is. The selection
of η for a particular application must then be a trade-off between computational time and
accuracy of the solution.
2.4 Estimation of the computational cost
The algorithm described above is based on iterative procedures involving multiple solutions

during one hour using C++ (optimized for speed using O2 flag from Microsoft Visual C++
compiler) on a Intel Core2Duo 2.8GHz takes 30 seconds if single precision arithmetic is used to
represent the temperatures. Taking into account that the proposed inverse procedure requires
the solution of the model for multiple soil configurations, the total computing time assuming
that only 100 iterations are needed (a soft approach) will add up to 50 minutes. As this
jeopardizes its use for field experiments we have developed a hardware implementation of a
34
Developments in Heat Transfer
Heat Transfer for NDE: Landmine Detection 15

  


  


Fig. 5. GPU internal structure and memory hierarchy.
heat equation solver. In Pardo et al. (2009; 2010) we presented an FPGA-based implementation
of such a solver. However, the main drawback of an FPGA implementation is the requirement
of the system in terms of memory. The FPGA has a little amount of distributed memory
and the FPGA’s logic blocks can also be configured to behave like memory, however this is
an inefficient way of FPGA using. Some vendors offer cards where external memory and
FPGA are integrated on the same board, allowing to use the FPGA to deal with processing
issues. However, these are expensive solutions. GPUs offers a structure which perfectly
fits with the proposed problem and they have the advantage of being cheaper than FPGAs.
GPUs are present in all computers and therefore we avoid the necessity of having a dedicated
and expensive hardware to deal with our problem. Moreover, the GPU implementation is
hardware independent, in the sense that it can be used on GPUs from NVIDIA with none or
little changes, depending on GPU’s computing capabilities.
3. GPU thermal model implementation















 
















GPU programming required to understand the structure of the proposed system . Functions
in CUDA are called kernels and each kernel can be executed in parallel by several threads
1
,as
contrary to ordinary C/C++ functions that can only be executed by one processor. A kernel
is not executed as a single thread, but it is executed as a block of threads, each of them
processing the same function on different data, following a single-program multiple data
(SPMD) computing model. Each thread inside the block has a 1D, 2D or 3D identifier (ID),
depending on the applications, which distinguishes the concrete thread, to compute elements
from a vector, matrix or volume of data. All the threads of a block are executed on the same
multiprocessor and therefore they must fit within the available resources. This sets a limit
on the maximum threads per block, which is limited to 512 in current GPUs. To avoid this
limitation a kernel can be executed in several blocks of threads, which are organized as 1D or
2D groups of threads. The only requirement concerning the block of threads is that they must
1
The thread is the basic element of processing
36
Developments in Heat Transfer
Heat Transfer for NDE: Landmine Detection 17
CUDA cores 128
CUDA Multiprocessors 8
Graphics Clock 738 MHz
Processor Clock 1836 MHz
Global Memory 512 MB
Memory Clock 1100 MHz
Memory Bandwidth 70.4 GB/s
Table 1. GTS 250 NVIDIA GPU main characteristics.




Concerning the memory usage, the initial temperatures are stored in the global memory, and
they have been transferred from the HOST memory to GPU global memory prior to the
computation of the new temperatures. The temperatures are duplicated in the memory, as
during one iteration we need to use one location to read temperatures and the other to write
37
Heat Transfer for NDE: Landmine Detection
18 Will-be-set-by-IN-TECH















 


Fig. 8. Data memory transferences during the updating process.
the updated values and in the following iteration the roles are interchanged. The remainder
constant values needed in the computations, such as F
0
and values related to the boundary

acquired in a real test field. The scenario considered corresponds to the sand lane of the
38
Developments in Heat Transfer
Heat Transfer for NDE: Landmine Detection 19



























Table 2. Symbols used to represent the different categories of targets present in the test field
in Fig. 9.
test facilities of the TNO Physics and Electronics Laboratory. For the experimental setup
considered, the measured thermal diffusivity of the soil was α
sand
= 6 × 10
−7
m
2
/s. With
respect to the test mine targets present, they are surrogated mines and most of them have been
built at TNO-FEL. In all test mines the same substitute for the explosive has been used, RTV,
having the same relevant properties as the real explosive and particularly α
RTV
= 1.13 × 10
−7
m
2
/s. Fig. 9 shows a sample image of the sand lane acquired with the IR sensor and the
position of the different targets considered. Table 2 summarizes the symbols used for
the different categories of targets present. The total number of targets is 43, 34 of which
correspond to landmines. The remaining nine targets are five undefined test objects and four
shells used as markers. We will concentrate on the results of the quasi-inverse and full-inverse
procedures for the classification of mines and non-mine targets respectively.
39
Heat Transfer for NDE: Landmine Detection
20 Will-be-set-by-IN-TECH
Location Detected and classified Total
Surface 12 12
Buried at 1 cm 6 6

the election of e
max
, being a trade-off between sensitivity and specificity, i.e. , between the
number of mine targets correctly classified and the number of false alarms. In humanitarian
operations, the stress is put on the correct location of mines, while reducing the number
of false alarms, although highly desirable, is a secondary goal. With respect to the global
performance, it is clearly a function of the particular value of e
max
. For e
max
= 2.6 we find
that 24 mines were correctly detected and classified over a total of 26.At the same time, the
number of false positives is 13 compared to the 27 after the application of the detection stage
alone.
4.1.2 Results of the full-inverse approach for the classification of non-mine targets
Now, we will illustrate the process of estimating the thermal parameters of non-mine targets
making use of the full inverse process previously described. To this aim, we will consider the
test object V82 present on the minefield (see Fig. 9). This target was classified as unknown by
the quasi-inverse operator and we now aim to infer what type of object it is by estimating its
thermal properties. If we estimate the measurement error to be δ
= 0.3
◦
C and setting η = 0.2,
we have,
μ
> 2
1
+ η
1 − 2η
= 4. (38)

(a) (b)
Fig. 10. Test target V82: (a) Evolution of the error in the estimation of α; (b) Evolution of the
value of α during the inverse problem procedure.
For μ
= 4.1, the discrepancy principle determines the stopping rule as,
y
δ
− F[p
δ
k
(δ,y
δ
)
]≤1.23 < y
δ
− F[p
δ
k
],0≤ k ≤ k(δ, y
δ
) (39)
The evolution of the error for the Landweber iteration method is shown in figure 10(a). The
stopping criteria in (39) corresponds to a number of iterations of the algorithm N
it
= 230.
Figure 10(b) shows the evolution of the estimation of the α parameter in this case. The final
result obtained for the non-mine target V82 is,
α
V82
= 170 × 10

Heat Transfer for NDE: Landmine Detection
22 Will-be-set-by-IN-TECH









   


(a) Throughput of GPU heat equation solver for different blocks’ size.









  


 
(b) Throughput of GPU and CPU heat equation solvers
implementations for different volume of simulated points. In

×16 1400.0 2 40
Table 4. GPU throughput for a given volume of points and varying block thread’s
dimensions.
Volume GPU throughput (Mpoints/s) CPU throughput (Mpoint/s) Speedup
32×32×50 332 39.3 8.4
64
×64×50 1289.33 39.3 32.6
256
×256×50 1476.67 39.3 37.0
512
×512×50 1496.02 39.3 39.3
1024
×1024×50 1402.8 39.3 36.7
Table 5. Throughput and CPU and GPU solvers of the heat equation solver for different size
volumes.
5. Conclusions
In this chapter, two inverse procedures for the inspection of soils by non-invasive means with
application in antipersonnel mines detection have been presented. The first quasi-inverse
procedure aims at the detection of surface-laid and shallowly buried mines, giving an
estimation of their depth of burial that will be of critical importance during the removal stage.
In the second approach, a full inverse procedure for the identification of the thermal properties
of other objects present on the soil was presented. Both procedures need the recursive solution
of the heat equation problem for different soil configurations, which constitutes a very time
consuming task on a conventional computer. The efficient solution of the aforementioned
procedures is successfully solved using a heat equation solver accelerator based on the use of
GPUs, obtaining speed-up factors over 40. The speedup obtained with the proposed system
with respect to nowadays computers, together with its low-cost and portability justifies the
implementation as it permits its use on the field during demining operations.
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López, P., Pardo, F., Sahli, H. & Cabello, D. (2009). Non-destructive soil inspection using an
efficient 3d softwareâ

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Heat Transfer for NDE: Landmine Detection
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Wang, T. & Chen, C. (2002). 3-D thermal-ADI: A linear-time chip level transient thermal
simulator, IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems 21(12): 1434–1445.
Zoubir, A. M. & Iskander, R. (2004). Bootstrap Techniques for Signal Processing, Cambridge
University Press.
46
Developments in Heat Transfer


Developments in Heat Transfer

48
pipe. The first method to enhance the thermal conductive performance is to improve the
liquid evaporation, the clotted phases transforming frequency, and intensity of phase

The object for this experiment is SEMOS Heat Pipes with closed loop, one is a SEMOS Heat
Pipe with a uniform cross-section of 3mm inner diameter, the other heat pipe based on the
uniform one with elliptic non-uniform cross-section is consisted of vertically intervened
heating section and insulating section of the pipes. As shown in figure 1 the material of the
heat pipe is brass, the working fluid in the pipe is distilled water with high purity, the
amount of working is
ϕ
=42%, the obliquity of the heat pipe is
θ
=55
0
, the pressure in the
heat pipe is
p
=1.8×10
-3
Pa.
Figure 2 shows the experiment set up for the thermal performance measurement consisting
of the main test apparatus, a laser supply and its cooler and its power supply system, a data
acquisition system combined with personal computer to show the data collected. As shown
in figure 2, the laser supply is consisted of eight passages Quantum Well Laser Diode
Arrays, the maximum output power of every single channel is 50W, the heating electrical
current range is 5~40A, the wave length of the laser is 94nm. The heat input comes from
continual laser heating while every single could work individually or together as heater,
and 20 K-type thermocouples were mounted on the surface at diameter of 1mm totaling 20
in number. Accordingly, the data acquisition frequency is 1/s based on the 20 data
collecting channels and the data acquisition precision is at ms.

1
2

and T
1
denote the output and input temperature of
cooling water, K.
As can be seen from the figure, the transfer rate of the heat pipe with non-uniform cross-
section is lower than that of the heat pipe with uniform cross-section when the heating
electrical current is relatively low, while the rate of heat pipe with non-uniform cross-section
would exceed that of the heat pipe with uniform cross-section as the heating electrical
current of laser supply increases. It is suggested from the trend of the graph of transfer rate
P
o
~I that the more heat input the more of the difference of transfer rate between the heat
pipe with non-uniform cross-section and the heat pipe with uniform cross-section becomes.
The transfer rate of heat pipe with non-uniform cross-section is 13.6% higher than that of the
heat pipe with uniform cross-section at the maximum heat input in this experiment, the
heating electrical current of every channel is 23A that is about 25.5W.

8 1012141618202224
0
10
20
30
40
50
60
70
80
90
100
110

=
−
(2)
Where,
o
P denotes transfer rate, W. l is the distance between the hot and cold end, m.
h
T

and
c
T Mean temperature of hot end and cold end, K. F Total heat transfer area, m
2
,

total
circulate cross section area for heat transfer, total cross section area for pure conductor.

8 1012141618202224
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000


52
section heat pipe is 19% higher than that of uniform cross-section one, 14 times higher than
that of the pure conductor one.
4.3 Heat transfer performance of the heat pipe with non-uniform cross-section
Theoretically, there are two reasons to answer that why non-uniform heat pipe consisted of
the heating section and insulating section could improve heat transfer rate. One is that the
portrait eddy formed for the Non-uniform Cross-Section of cross and adds parts of the
velocity on the pipe surface vertically, that means the temperature grads field and velocity
vector field co-operate together, then the heat transfer rate could be improved. Meanwhile
the resistance on the working fluid increases because of the non-uniformity of the cross-
section, certain amount of the heat input is needed for the SEMOS Heat Pipe with non-
uniform cross-section to improve heat transfer performance in word and deed. Because the
advantage of the SEMOS Heat Pipe with non-uniform cross-section on improving heat
transferring could be demonstrated easily when the portrait eddy becomes stronger and
circulating power becomes declining, the SEMOS Heat Pipe with non-uniform cross-section
is more suitable for the high density working fluid.
On the other side, as shown in figure 5 it could be found by monitoring the temperature of
the cold and hot end surface that the hot end surface temperature surging amplitude of the
non-uniform heat pipe is lower than that of the uniform one, while the surging frequency is
higher. In SEMOS Heat Pipe with non-uniform cross-section the circulating power increases
because of the alternation of liquid evaporation and gas clot. The accelerated motion inside
the pipe because of unsteady expanding and contracting process along with the vertical
velocity on the interface could finally improve the heat transfer performance.

0 100 200 300 400 500
85
90
95
100

6. Acknowledgement
This work was Supported by the Key Project of Chinese Ministry of Education (No: 210050).
7. Nomenclature
P heating power, W
G rate of mass flow, kg·s
-1
T temperature, K
T mean temperature, K
I heating electrical current, A
F
Total heat transfer area, m
2

c specific heat at constant pressure, J·kg
-1
·K
-1

l distance between the hot and cold end, m
λ heat transfer coefficient, W·m
-1
·K
-1

Subscripts
p pressure
o out
d equivalent
h hot end
c cold end