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CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
1
A COMPARATIVE STUDY ON MATERIAL SELECTION OF
AEROSPACE COMPONENTS FOR FUSED FILAMENT
FABRICATION
Tikhani, Farimah1,2, and Hubert, Pascal1,2*
1 Mechanical Engineering Department, McGill University, Montreal, Canada
2 Research Center for High Performance Polymer and Composite Systems (CREPEC), Montreal, Canada
* Corresponding author (pascal.hubert@mcgill.ca)
Keywords: Material selection, Aerospace, Multi-criterion decision-making, Fused filament fabrication
1 INTRODUCTION
Manufacturing of many aerospace structures from advanced composite materials has led to lighter and more fuel-
efficient aircraft which has boosted profits of companies in this sector [1]. Lack of toughness, low shelf life as well
as multi-step processing are among the reasons why thermoset composites are less preferred than thermoplastic
composites for replacement of the load-bearing components in which superior toughness and damage tolerance
are required [2]. An example of such improvements is structural components of aircraft like the clips used to attach
fuselage panels to its frame in the Airbus A350 XWB, which were reproduced in carbon fibre reinforced
thermoplastic composites [3]. The thermoplastic polymers introduce manufacturing flexibility due to their melt
processability and enable the production of highly integrated structures thanks to their fusion weldability [4].
Moreover, the variety of processing methods available for this type of material allows for choosing the
manufacturing process which works best considering the production rate and component size. That is one of the
reasons why aerospace companies have been moving toward using the additive manufacturing technologies to
decrease the production costs of low-production-rate parts [5]. However, selection of the most suitable material
among the numerous polymers available is a challenge that one should tackle each time a component is going to be
designed or upgraded. This is a crucial design aspect since minor errors in material selection of sensitive applications
like aerospace could cause structural issues which puts the safety and reliability of the aircraft in danger.
To meet the processing and performance requirements, a robust approach is required to balance all the interrelated
and sometimes conflicting attributes of a component that is going to be reproduced out of composite. One can take
advantage of multi-criterion decision-making (MCDM) methods to systematically evaluate and rank the alternatives
based on the relative importance of the criteria. A comprehensive review on the application of MCDM methods in
material selection was conducted in diverse fields and it was shown that the hybrid methods (a combination of two
or more MCDM methods) are the most common techniques for material selection studies [6]. For instance,
Alaaeddin et al. [7] applied analytical hierarchy process (AHP) method to prioritize different polymers for fabrication
of short sugar palm composites and integrated it with technique for order preference by similarity to ideal solution
(TOPSIS) and elimination and choice expressing reality (ELECTRE) ranking methods to find the most suitable
polymeric matrix for their application. In another study, Mansor et al. [8] used the same combination of methods
to select the thermoplastic polymer matrix for hybrid natural fibre composites formulation to develop a structural
automotive component. Another example is a study reported by Rao [9] that integrated AHP method with “vIse
kriterijumska optimizacija kompromisno resenja” (VIKOR) compromise ranking method to find the best material for
designing a component operating at high-temperature environment. One can realize that in the majority of the
studies, AHP method is used to assign the relative importance of attributes, especially for the methods like TOPSIS
and VIKOR which are incapable of determining decision criteria weights. AHP reflects the designer’s preferences on
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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the material ranking and it could potentially result in bias towards the final ranking result depending on the
designer’s knowledge [10]. Moreover, the distribution of data and the potential interdependency between the
decision criteria, which are usually disregarded in decision-making problems, play significant roles in determination
of the criteria weights. Jahan et al. [11] proposed a weighting framework consisting of subjective, objective and
correlation (SOC) weights which can cover those shortcomings in the material selection approaches.
In this work, we aim to compare the performance of two weighting frameworks of AHP and SOC in conjunction with
TOPSIS and VIKOR methods to rank a set of polymeric alternatives that can be used for manufacturing of a filament
for fused filament fabrication (FFF) of an aerospace component. This provides an insight about the effect of personal
judgment and interdependency of decision criteria on the final decision. The motivation behind choosing TOPSIS
and VIKOR ranking methods is the easy and efficient computational approaches for relatively high number of
alternatives and criteria in comparison to other MCDM methods. Although they share similarities in functioning
based on the measure of ‘closeness to the ideal solution’, they use different normalizations (linear normalization
for VIKOR and vector normalization for TOPSIS). On the other hand, TOPSIS best solution is the alternative that has
the shortest Euclidean distance from the ideal solution and farthest distance from the worst solution simultaneously
while VIKOR best solution is the one that is the closest to the ideal solution [12]. This comparison signifies the
importance of suitability of methodology and precision that should be determined considering the nature of the
material selection problem.
2 MATERIAL SELECTION ALTERNATIVES AND CRITERIA
The filaments used in FFF 3D-printing require a specific diameter, printability, and certain other mechanical,
physical, and chemical properties depending on the application of the final 3D-printed part. Much research has been
devoted to developing new composite feedstock materials with optimized properties to widen the material portfolio
for FFF manufacturing by the incorporation of fibres into the pure polymers [13]. The materials for aerospace
applications need to meet strict requirements in terms of safety and reliability in addition to their application
properties. The goal of this material selection study is to find the most suitable matrix systems for developing an
FFF filament that will demonstrate good processability and provide high mechanical properties while meeting the
aerospace requirements like flammability. A list of the important criteria and associated explanations to select those
criteria for this study are provided in Table 1.
The number of criteria has been kept low enough (less than 15 criteria) to avoid the unnecessary complications
while addressing as many material characteristics as possible. Moreover, an effort was made to choose the criteria
from the quantitative attributes of materials for the sake of simplicity since qualitative criteria need an additional
step for quantification [14]. For the goal of this study, the thermoplastic polymers were considered as candidates
that demonstrated the potential of meeting aerospace requirements in the literature. This includes eight high
temperature thermoplastics such as polyether ether ketone (PEEK), polyetherketoneketone (PEKK), polyimide (PI),
polysulfones (PSU), polyphenylene sulfide (PPS), polyether sulfone (PESU), polyphenyl sulfone (PPSU), and
polyetherimide (PEI), as well as polycarbonate (PC) which is an engineering polymer but has performed as an
aerospace-grade material for manufacturing of many aircraft components [15]. The data for material properties are
the average value and were collected from online databases [16], [17].
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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Table 1. The list of material selection criteria and the associated reasoning behind their selection.
Attribute
Unit
Explanation
Density (ρ)
g/cm3
It is important for light-weighting purposes.
Glass Transition Temperature
(T
g
)
C
High glass transition temperatures are preferred and is a measure of
service temperature of the material.
Processing Temperature (Tp)
C
Lower processing temperature reduces manufacturing costs.
Coefficient of Thermal
Expansion (CTE)
µm/m. C
Low CTE prevents the printed part from warpage.
Thermal Conductivity (K)
W/m. C
High thermal conductivity facilitates redistribution heat for polymer
sintering.
Specific Heat (C
p
)
J/kg. C
Higher specific heat is preferred since more heat can be added in the
system when extruding.
Young’s Modulus (E)
GPa
High modulus of the filament can result in components with high
modulus.
Tensile Strength at Yield (TS)
MPa
High strength of the filament can result in components with high
tensile strength.
Shrinkage (S)
%
Low shrinkage from melt prevents warpage and result in dimensional
stability.
Moisture Absorption (MA)
w.t.%
Moisture content should be low enough to maintain the quality and
performance.
Limiting Oxygen Index (LOI)
%O2
Low LOI is a measure of high flammability of materials.
Cost (C)
$/kg
The lower the material cost, the lower the final component’s cost.
3 MATHEMATICAL APPROACHES
The material selection was performed using two different multi-criterion decision-making methods of TOPSIS and
VIKOR. The selection criteria are required to be weighted based on a rational and comprehensive approach in order
to be incorporated in the decision-making methods. As stated previously, two different weighting approaches of
AHP and SOC are applied in order to strengthen the comparison.
3.1 Weighting Methods
3.1.1 Analytical Hierarchy Process (AHP)
AHP is a pair-wise comparison of decision criterion in which the designer judges the attributes by assigning a value
of 1, 3, 5, 7, or 9 corresponding to the verbal judgments of “equal importance”, “moderate importance”, “strong
importance”, “very strong importance”, and “absolute importance”, with values of 2, 4, 6, and 8 for compromising
between the previous values. This gives a square matrix of An×n (Eq. 1) where aij denotes the comparative importance
of attribute i with respect to attribute j. In this matrix, aij=1 when i=j and aji=1/aij. Here n is the number attributes.
12 13 1
11 12 13 1
12 23 2
21 22 23 2
13 23 3
31 32 33 3
123
123
123 1
11/ 1
21/ 1/ 1
3
1/ 1/ 1/ 1
n
n
n
n
nn n
n
nnn
n n n nn
Attributes n aa a
aaa a a aa
aaa a
A aa a
aaa a
aaa
n aaa a
×
= =
(1)
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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The relative normalized weight of each criterion can be obtained by calculating the geometric mean of each row
and normalizing them in the comparison matrix following the equation below [18]:
1
1
1
11
nn
ij
j
s
j
n
nn
ij
ij
a
w
a
=
==
=
∏
∑∏
(2)
The inconsistency in judgments of the analyst about the problem can be evaluated by calculation of consistency
ratio (CR) according to Eq. 3. The consistency index (CI) in this equation is defined based on the maximum eigen
value (λmax) of comparison matrix as in Eq. 4. Also, random index (RI) is defined for every number of attributes [19].
A CR of 0.1 or less is considered as acceptable and it reflects an informed judgment that could be attributed to the
knowledge of the analyst about the problem under study.
CI
CR RI
=
(3)
max
1
n
CI n
λ
−
=−
(4)
3.1.2 SOC Weighting Framework
This weighting framework proposed by Jahan et al. [14] consists of different objectives, subjective and inter-criterion
correlation weights. These weights are obtained using entropy method, AHP, and standard deviation methods,
respectively, after identifying the selection attributes for the application. The entropy method determines the
weights of the m attributes for n alternatives through the equation below:
1
11,..., ; 1,...,
(1 )
j
o
jn
j
j
E
w i mj n
E
=
−
= = =
−
∑
(5)
where,
1
11
1ln
ln( )
mij ij
jmm
i
ij ij
ii
xx
Emxx
=
= =
= −
∑∑∑
(6)
Here xij represents elements of the decision matrix and i and j indicate the number of alternatives and criteria,
respectively. In this method, the attributes with performance ratings that are very different from each other have
higher importance for the problem due to their higher influence on the ranking outcomes.
In order to calculate the effect of the correlation among criteria, correlation (R) is calculated according to Eq. 7 and
is applied in Eq. 8 to obtain the corresponding weights for m alternatives. A value of R near 0 indicates little
correlation between criteria, while a value near 1 or −1 indicates a high level of correlation.
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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( )
( )
( )
( )
( )
( )
( )
( )
1
22
11
1
22
11
If objectives of criteria and are same
and =1,...,n
If objectives of criteria and are different
m
ij j ik k
i
mm
ij j ik k
ii
jk
m
ij j ik k
i
mm
ij j ik k
ii
xxx x
jk
xx x x
R jk
xxx x
jk
xx x x
=
= =
=
= =
−−
−−
=
−−
−
−−
∑
∑∑
∑
∑∑
(7)
( )
( )
1
11
1
1
n
jk
ck
jnn
jk
jk
R
w
R
=
= =
−
=
−
∑
∑∑
(8)
The subjective weights in this framework are obtained based on the AHP method which was elaborated in section
3.1.1. The final weights of criteria are obtained using Eq. 9 which will be used in ranking procedures as explained in
the next section.
( )
( )
1
3
1
3
1
osc
jjj
jn
osc
jjj
j
www
W
www
=
=
∑
(9)
3.2 Multi-Criteria Decision-Making Methods
3.2.1 TOPSIS Approach
The TOPSIS method is a powerful tool for dealing with high number of decision criteria and alternative materials
involved in the decision-making process. This method requires reasonable quantitative weights for the attributes to
maintain the correct trade-offs among the objectives. The first step in this method is to normalize the decision
matrix (Xm×n) after determination of the criteria weights. Consequently, the weighted normalized matrix can be
obtained according to the equation below which shows vector normalization for all n criteria:
ij ij j
V MW=
(10)
where,
2
1
ij
ij n
ij
j
x
M
x
=
=
∑
(11)
In this equation, xij are the elements of Xm×n design matrix and are referring to the value of each attribute for each
alternative. Also, i and j indicate the number of alternatives (from 1 to m) and criteria (from 1 to n), respectively. In
the next step, the ideal (best) and negative ideal (worst) solution should be determined according to the Eq. 12 and
Eq. 13 considering the weighted normalized V [18].
{ }
max min
12
/ , / ' 1,2,..., , ,...,
ij ij n
ii
V V jJ V jJ i m VV V
+ ++ +
= ∈ ∈= =
∑∑
(12)
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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{ }
min max
12
/ , / ' 1,2,..., , ,...,
ij ij n
ii
V V jJ V jJ i m VV V
− −− −
= ∈ ∈= =
∑∑
(13)
where in ={| {1,2, . . . , }} , j is associated with beneficial attributes and in ʹ={| {1,2, . . . , }} , j is
associated with non-beneficial attributes. Based on these values, the “separation measures” of each alternative (Si)
from the ideal one is achieved by calculation of the Euclidean distance expressed as:
( )
0.5
2
1
, 1, 2,...,
n
i ij j
j
S VV i m
−−
=
=−=
∑
(14)
()
0.5
2
1
, 1, 2,...,
n
i ij j
j
S VV i m
++
=
=−=
∑
(15)
The final ranking of the alternatives is obtained by calculation of the relative closeness (C) of alternatives to the ideal
solution according to Eq. 16. The higher the value of relative closeness of a particular alternative, the higher the
ranking of that alternative in the material selection list.
i
i
ii
S
CSS
−
+−
=+
(16)
3.2.2 VIKOR Approach
The straightforward mathematical procedure and the ease of implementation are among the reasons why VIKOR
has been the topic of many studies for decision-making problems. This approach can be considered as an updated
version of TOPSIS method in which the best solution is obtained based on the same rule of ‘closeness to the ideal
solution’ but the worst case is not viewed as a reference point. The VIKOR method aims to minimize the individual
regret and maximize the group utility for decision makers [6]. The mathematical procedure is explained as follows.
As previously indicated, VIKOR approach applies the linear normalization for calculating the weighted normalized
index according to the Eq. 17 which is known as the “utility measure”. Also, R index is obtained by Eq. 18 which
shows the “regret measure”.
*
*
1
nj ij
ij
jjj
ff
Sw
ff
−
=
−
=−
∑
(17)
*
*
max[ ]
j ij
ij
jjj
ff
Rw
ff
−
−
=−
(18)
where
,
and
are elements of design matrix, best and worst values of for all criteria, respectively. Also,
represents the weights of criteria which is defined as explained in section 3.1. Consequently, the Q indices can be
calculated according to the Eq. 19.
**
**
(1 )
ii
i
SS RR
Qv v
SS RR
−−
−−
= +−
−−
(19)
In this equation, and are the minimum values of and , respectively, over all alternatives. Similarly, and
are the maximum values over all values of and , respectively. Here is known as the weight of the decision-
making strategy of ‘‘the maximum group utility’’. It is usually considered to be equivalent to 0.5 which means the
compromise solution is obtained by consensus. Here the material with the best ranking has the minimum value of
Q and in case it meets the following conditions, it can be proposed as the compromise solution; First condition is
the acceptable advantage which requires the satisfaction of () ()1/( 1) inequality. The second
condition is known as the acceptable stability in decision-making and states that the top-ranked alternative should
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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also be ranked first based on values. Here and are the alternatives ranked as the first and second
solutions. If only the first condition is not met, all the alternatives that follow the inequality of () ()<
1/( 1) are considered as the compromise solutions for maximum K. On the other hand, if only the second
condition is not satisfied, the alternatives with the first and second positions are the solutions [12], [20].
4 RESULTS AND DISCUSSION
For selecting the best thermoplastic polymer in developing an aerospace-grade FFF filament, the design matrix was
established by collecting the average value of each of 12 criteria reported in Table 1 for every material, as explained
in Section 2. Following the weighting procedures discussed in Section 3.1, the decision matrix was devised according
to AHP procedure for calculating the subjective weights. With RI being equal to 1.54, the value of CR was calculated
to be 0.061 which validates the designer’s informed judgment. The objective weights were calculated through
entropy method and the correlation’s weights of criteria were determined following Eq. 7 and 8. All the weighting
results are defined in Table 1.
As can be observed in Figure 1, the moisture absorption, cost and shrinkage obtained the highest objective weight
factors since the data for these criteria is more scattered than the other criteria in the design matrix [21].
Similarly, the objective weight of density is almost zero since the density of polymeric materials are very close
to each other. The most important criteria from the designer’s point of view are cost, tensile strength, and
Young’s modulus. This shows that the designer is interested in an FFF filament that shows good mechanical
properties at a low cost. This is to the desire to improve the mechanical properties of 3D-printed parts to
replicate the performance of metallic components while keeping them light and affordable. Considering the
correlation’s weight factors, one can realize that the correlation values are almost equal for all criteria, and
attributes are slightly correlated for this set of data. Thus, it can be concluded that the correlation concept is
not decisive in this decision-making problem. Finally, the SOC weights are reflecting the effect of all three
factors on the final decision and together with AHP weights, are used for material ranking by TOPSIS and VIKOR
approaches.
Figure 1. The results of weighting frameworks for different criteria.
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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The ranking lists obtained by each method are demonstrated in Figure 2. The ranking list of AHP-VIKOR and SOC-
VIKOR approaches, reported in Table 2, were obtained having = 0.5 and they both satisfied the conditions
explained in Section 3.2.2. Therefore, the results can be considered as the compromise solutions. Looking into the
Figure 2, one can observe that the polymers of PEI and PPS achieved the first and second positions in three methods
and in the last approach, SOC-TOPSIS, these two are ranked among the top three materials. Thus, it can assertively
be concluded that the best material for meeting the objectives of this study is PEI. This is in line with the results of
studies existing in the literature that were in pursuit of replacing the metallic components of aircraft with
thermoplastic composite materials [22]. For instance, researchers attempted to 3D-print aircraft vanes using a
carbon fibre reinforced ULTEM1000 composite filament which is an aerospace grade of PEI [23]. Moreover, we can
see that PC appears in the three highest-ranked alternatives in approaches involving TOPSIS method. It can be stated
that when being far from the worst condition is important, PC can be a good choice for the application of interest.
This means that by choosing PC as the polymeric matrix, we might not achieve the maximum performance, but it is
assured that the material stands far enough from the worst-case scenario.
Table 2. Ranking results for different thermoplastic polymers
Materials
Ranking Methods
AHP-TOPSIS
AHP-VIKOR
Ci
Rank
Si
Ri
Qi
Rank
PI
0.4839
7
0.4936
0.1192
0.3786
3
PEEK
0.3100
9
0.5756
0.1668
0.7566
8
PEKK
0.4223
8
0.4134
0.2000
0.5369
4
PSU
0.6232
5
0.5890
0.1346
0.6522
6
PPS
0.6496
2
0.4070
0.1645
0.3754
2
PESU
0.6002
6
0.5550
0.1306
0.5609
5
PPSU
0.6327
4
0.5584
0.1590
0.6863
7
PEI
0.6623
1
0.3967
0.0795
0.0000
1
PC
0.6409
3
0.6236
0.1645
0.8526
9
SOC-TOPSIS
SOC-VIKOR
Ci
Rank
Si
Ri
Qi
Rank
PI
0.3546
9
0.5495
0.1514
0.7387
8
PEEK
0.4404
8
0.5918
0.1559
0.8648
9
PEKK
0.5604
6
0.4073
0.1869
0.5351
7
PSU
0.6331
5
0.5337
0.0723
0.3538
4
PPS
0.6838
3
0.4069
0.0997
0.1536
2
PESU
0.5180
7
0.5335
0.0972
0.4616
6
PPSU
0.6780
4
0.4838
0.0822
0.2709
3
PEI
0.6902
2
0.3933
0.0745
0.0096
1
PC
0.6989
1
0.5211
0.0946
0.4191
5
Other than the difference in normalizations, the different performance of SOC-TOPSIS approach can be related to
the effect of weighting results. It can be understood from Figure 1 that cost is among the most significant criteria
for all objective, subjective, and correlation weights and it becomes even stronger when they are multiplied to form
the final weight in the SOC framework. Knowing that PC is the most affordable material among all the alternatives,
it can be realized that PC is a more conservative candidate among all when cost is of great significance.
Moreover, when the weighting framework of AHP is applied, we observe that PI rises to the top three materials.
This is due to the high importance of mechanical properties and LOI as well as low importance of Tg from the
designer’s point of view since PI is known to have high modulus, tensile strength, and LOI with the highest Tg among
all the alternatives. Yet, it cannot compete with the overall performance of the PEI and PPS regarding the selection
priorities. Lastly, it can be said that there is a good agreement between the methods, however, the weighting
CANCOM2022 ‒ CANADIAN INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS
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framework should be validated before further attempt toward manufacturing of the desired component. This can
be pursued by consulting several knowledgeable experts of the field and/or collecting material properties in a more
precise manner.
Figure 2. Comparison of the ranking results of the four ranking approaches for material selection.
5 CONCLUSION
In this paper, we sought to find the most suitable thermoplastic polymer to be used for manufacturing of a
composite filament for FFF 3D printing of an aerospace component. To solve this material selection problem, nine
thermoplastic polymers were chosen as the set of alternative materials which were ranked considering the
importance of 12 decision criteria. Their significance was quantified using two different weighting frameworks of
(1) AHP that demonstrates the designer’s preferences, and (2) SOC which combines the AHP weights with correlation
effect of criteria and objectivity of the decision matrix. The weights obtained from these methods were then
implemented in two common MCDM methods, namely TOPSIS and VIKOR, to achieve the final ranking lists of
materials. Although there are some differences between the performance of the methods, they all agree that PEI is
the most suitable material for this application and PPS stands in the second position. However, the SOC-TOPSIS
approach gives more priority to PC and ranks it as the best material. This might be due to the strong contribution of
the cost criterion as a result of SOC weighting framework together with the nature of TOPSIS approach to provide a
solution that not only is it the closest to the ideal solution but also stands far from the worst case. In conclusion, this
study provides a good insight about the effect of different weighting methods on the final decision. Objectivity and
the effect of correlation among data are not involved in the most of decision-making processes and the introduced
methodologies can encourage more robust and reliable decisions, specifically for sensitive applications like
aerospace. This study was conducted based on the average property of the materials. The robustness of the ranking
results can be improved by using the exact properties of the materials of interest or more precise databases. Also,
the results of selection should be verified in a real-case design problem to confirm the better performance of the
alternatives suggested by these methods.
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6 ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial support provided by our partners at the Natural Sciences and
Engineering Research Council of Canada (NSERC), PRIMA Québec, and the McGill Engineering Doctorial Awards
(MEDA).
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