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Computers in Industry
journal homepage: www.elsevier.com/locate/compind
Correlation-based feature extraction from computer-aided design, case
study on curtain airbags design
Arjomandi Rad Mohammad
a,⁎
, Kent Salomonsson
b
, Mirza Cenanovic
a
, Henrik Balague
c
,
Dag Raudberget
a
, Roland Stolt
a
a
Department of Product Development, School of Engineering, Jönköping University, Jönköping, Sweden
b
Department of Mechanical Engineering, School of Engineering Science, University of Skövde, Skövde, Sweden
c
Autoliv AB, Vårgårda, Sweden
article info
Article history:
Received 22 June 2021
Received in revised form 7 January 2022
Accepted 11 February 2022
Available online xxxx
Keywords:
Feature extraction
CAD/CAE
Parametric models
Medial Axis
Design Automation
Machine Learning
Regression Analysis
Curtain Airbag
abstract
Many high-level technical products are associated with changing requirements, drastic design changes, lack
of design information, and uncertainties in input variables which makes their design process iterative and
simulation-driven. Regression models have been proven to be useful tools during design, altering the re-
source-intensive finite element simulation models. However, building regression models from computer-
aided design (CAD) parameters is associated with challenges such as dealing with too many parameters and
their low or coupled impact on studied outputs which ultimately requires a large training dataset. As a
solution, extraction of hidden features from CAD is presented on the application of volume simulation of
curtain airbags concerning geometric changes in design loops. After creating a prototype that covers all
aspects of a real curtain airbag, its CAD parameters have been analyzed to find out the correlation between
design parameters and volume as output. Next, using the design of the experiment latin hypercube sam-
pling method, 100 design samples are generated and the corresponding volume for each design sample was
assessed. It was shown that selected CAD parameters are not highly correlated with the volume which
consequently lowers the accuracy of prediction models. Various geometric entities, such as the medial axis,
are used to extract several hidden features (referred to as sleeping parameters). The correlation of the new
features and their performance and precision through two regression analyses are studied. The result shows
that choosing sleeping parameters as input reduces dimensionality and the need to use advanced regression
algorithms, allowing designers to have more accurate predictions (in this case approximately 95%) with a
reasonable number of samples. Furthermore, it was concluded that using sleeping parameters in regression-
based tools creates real-time prediction ability in the early development stage of the design process which
could contribute to lower development lead time by eliminating design iterations.
© 2022 The Authors. Published by Elsevier B.V.
CC_BY_4.0
1. Introduction
High-level technical products (such as airbags and jet engine
components) that are characterized by having iterative and simu-
lation-driven design processes, often suffer from long development
lead time. These products are associated with having a large number
of manual simulation loops in the early stages of the design process
(Arjomandi Rad, 2020). Supporting tools for simulation-driven de-
sign include knowledge management systems to capture both tacit
knowledge and knowledge objects and create an ability to mimic the
reasoning of experts in simulation and design (Fatfouta and Le-
Cardinal, 2021). Additional supporting tools include creating auto-
mated systems with CAD (Computer-aided design) and CAE (Com-
puter-aided engineering) to save time and reduce human error. This
common practice is widely investigated by the fields of design sci-
ence and design automation (Chakrabarti and Blessing, 2016; La
Rocca, 2012). However, running complex simulations repeatedly,
even in an automated manner is time and energy-consuming and
can be quite unfeasible. Increasing computational power, utilization
of parallel or cloud-based techniques are other effective methods to
decrease simulation time but they have not been used to solve the
lead time problem since in product development one simulation
iteration can be dependent on the previous iteration’s simulation
results.
https://doi.org/10.1016/j.compind.2022.103634
0166-3615/© 2022 The Authors. Published by Elsevier B.V.
CC_BY_4.0
]]]]
]]]]]]
⁎
Corresponding author.
E-mail address: mohammad.rad@ju.se (A.R. Mohammad).
Computers in Industry 138 (2022) 103634
Machine learning (ML) belongs to a larger family of algorithms
that are part of the Artificial Intelligence (AI) branch, depicted in
Fig. 1. ML is “A form of applied statistics with increased emphasis on
the use of computers to statistically estimate complicated functions
and a decreased emphasis on proving confidence intervals around
these functions” (Goodfellow et al., 2016). Within the design pro-
cesses as support, ML has been used to estimate the results of
iterative assessment tasks. For instance, a method called Kansei en-
gineering is a good example of the application of ML in the early and
conceptual phases of product design and development. The method
is used to generate the shape of the product by inputting specific
design elements. The attempt tries to map the form of the product as
the design variables to the feelings of consumers as an indication for
the output (Fan et al., 2014; Wang et al., 2016).
Individual and independent pieces of information, being input
into the system is called a feature in machine learning (Goodfellow
et al., 2016). A large body of theoretical literature deals with con-
siderations that ought to be made for selecting features when
building predictors or classifiers. Selecting the best features has been
done by measuring the relevance of the feature such as correlation
coefficient, and ranking them (filters), assessing features’ influence
on the performance of the predictor (wrapper), or incorporating the
feature selection as part of the training process (embedded) (Guyon
et al., 2008). Feature construction (feature extraction) is a method
that aims to build more compact features to increase prediction
performance and feature reduction reduces the number of them in-
tending to acquire better predictors by removing irrelevant and re-
dundant features to defy the curse of dimensionality (Guyon and
Elisseeff, 2003). All mentioned methodologies consist of many
methods that are used as a pre-processing step in machine learning
to improve prediction efficiency and accuracy. The proposed method
in this paper of correlation-based feature extraction which is used
for ranking features based on various correlation matrices (Guyon
et al., 2008) is found effective when used in the process of selecting
features and it best works with supervised learning methods
(Hall, 1999).
Using data-driven approaches in the engineering design of con-
sumer products has been reviewed recently (Chiarello et al., 2021).
By identifying the tools, algorithms, and data sources that have been
used in engineering design, the authors touch upon challenges and
gaps that need to be tackled in the future. For instance, one of the
listed challenges is “Identifying latent features (e.g. temporal fea-
tures, behavioral features) hidden in CAD data”. Indeed, real-time
analysis of the design is a common practice but collecting analyses of
the design and deriving performance or cost indicators, or in other
words ‘data mining’ for new product development is still not ad-
dressed in the literature (Bertoni et al., 2017). The research gap
which this paper tries to fill is to address common problems asso-
ciated with using ML-based predictors in the design of consumer
products, namely dimensionality and parameterization. The problem
arises when creating configurations of the geometry using CAD
model parameters as features (also known as inputs or variables).
Often to produce samples, designers are required to fully define the
CAD with many parameters and constraints and then to fully cover
design space in turn, leads in having cumbersome training process.
Being obliged to follow the standard parameterization conven-
tion through the designing process naturally limits the designer and
suppresses creative solutions because then the designers will be
forced to follow the same parameterization convention that is used
when training sets are created. Therefore, in complex geometries,
designers usually avoid using any constraints and parameterized
CAD models, because doing so will either limit the ability to ma-
nipulate the design shape or result in having a sparse training set in
the design space. Another practical problem is that CAD designers
are not the same as the CAE simulation engineers and they might not
sit in the same company or work environment. This becomes an
issue if a higher level of competence in each area is needed which is
often the case for a high-level technical product. This fact triggers a
back-and-forth work between several engineers or departments in
the company and thus negatively influences the development lead
time of the design processes. The conceptual phase of a design
process encompasses an evaluation stage (Pahl and Beitz, 2013) in
which having an independent prediction tool (A live prediction
model) could make CAD designers aware of the consequences of
their decisions on CAE results. This evaluation stage can significantly
increase the development speed by avoiding the costly simulation
loops, thus such a tool can fill the aforementioned gap. Therefore,
the presented concept in this paper is an effort to overcome the high
dimensionality in engineering design that is one of the common
problems in applying data science in engineering design (Chiarello
et al., 2021).
This paper introduces a correlation-based feature extraction ap-
plication in CAD for regression-based machine learning algorithms.
After an introduction that outlines the existing gap, the next section
explores the related works, and the case study used throughout this
paper is introduced in the third section. Using finite element simu-
lations in the next section, a parametric study is performed to study
the effect of each CAD parameter on the volume. Separately, the latin
hypercube sampling method is used to generate and study a group of
100 design samples and their volumes as an output. It was shown
that CAD parameters alone, would not lead to effective prediction
accuracy. In the fifth section, with utilizing the concepts of different
geometric entities (such as area, circumference, or the medial axis),
new parameters referred to as sleeping parameters are defined and
studied as a performance indicator for the inflated curtain airbag. It
was demonstrated that new features have better correlations with
the volume. And they can be extracted from geometry without any
need for model parameterization which maintains freedom in de-
sign. Two regression analyses performed in the sixth section, com-
pare and validate the performance of extracted parameters in a
regression model by showing the ability of these parameters in re-
ducing the prediction error margins. The discussion in the last sec-
tion explains the effectiveness of the sleeping parameters, such as
the ones studied in this paper. This will allow designers to build
simple but accurate regression models with a low number of fea-
tures and sample points (small training set).
2. Related works
Statistical approximating methods in engineering design (e.g.
response surface methodology, Taguchi methods, neural networks,
inductive learning, and kriging) has been used for a long time to
address computation-intensive design problems (Simpson et al.,
Fig. 1. A Venn diagram showing AI categorization with examples (Goodfellow
et al., 2016).
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
2
2001; Sun and Wang, 2019; Wang and Shan, 2007). One application
of these modeling techniques is to build regression models to reduce
the number of simulation iterations. But their focus is on reducing
computational cost rather than reducing problem dimension. Thus,
modeling techniques in engineering design do not address high di-
mensionality problems, and the literature in this section is very
scarce. (Wang and Shan, 2007). The first metamodeling techniques
to tackle High-dimensional Expensive Black box (HEB) problems
utilized radial basis functions with a high dimensional model re-
presentation which basically offers an explicit function expression
and thus shows the contribution of each design parameter (Shan and
Wang, 2010). Since then, other metamodeling techniques that
combat the curse of dimensionality are published, for instance, by
improving kriging surrogates of high-dimensional design models by
partial least squares dimension reduction (Bouhlel et al., 2016), by
using convolutional neural networks (CNN) to study over hundred-
dimensional and strong-nonlinear product design problems (Li et al.,
2017), etc. This area of research aims to find better metamodeling
techniques with proposing sophisticated algorithms yet due to the
scope of this paper, they are not reviewed extensively in this section.
The common ground for any metamodeling method is that they
require pre-performed simulation data or experiment data as input
for the approximation and this makes most of them a data-driven
approach. A data-driven solution is not only about the size of data
under study but also more about decisions making based on data
analysis and interpretation. This can be inferred from the consensus
definition for the data-driven approach “Using computational sys-
tems to extract knowledge from structured and unstructured data”
(Chiarello et al., 2021). As discussed in the Introduction, using CAD
model parameters as input with any data-driven approach to map-
ping CAD input to CAE output could pull forward problems such as
dimensionality and parameterization.
To overcome the mentioned problems many studies have tried
to simplify the geometry to reduce the number of parameters. For
instance, Wang et al. digitally created simple n-fold symmetric
shapes representing cohesive contact zone in stereo-lithography
(SLA) as input for a neural network. For output vector calculation
they used finite element simulation and proposed a network that
enabled a fast prediction model for stress distribution in the
separation of the 3D printed part during the pull-up process of the
bottom-up SLA technique. (Wang et al., 2018). Additionally, Yoo
et al. used a large number of CAD models and CAE results for
training a deep learning algorithm. The presented framework is
applied to the road wheel design process, in seven stages; starting
from 2D generative design based on topology optimization prin-
ciples and ending in analysis and visualization of the CAE results
(Yoo et al., 2020). In this framework, the ML algorithm first
generates a large number of 3D CAD models by minimizing the
distance from a reference design, and later the designers manually
verify and select suitable designs for further modifications. Using a
simple design geometry that has only three design parameters and
applicability of the framework on large datasets are among the
limitation of this study. Though, a simple geometry, as well as a
less computationally expensive CAE method (modal analysis),
contributes to the success of this approach. As mentioned earlier,
running thousands of finite element simulations to build large
machine learning databases will require a huge computational
power. Just, for instance, assuming 5 min simulation run time
for 10,000 simulations requires 35 days of run time. Other sim-
plification methods also exist in literature such as data mining
design methodology (Du and Zhu, 2018) which was suggested for
high-dimensional design problems and it essentially simplifies the
design space by shrinking the changing interval of the design
parameters, using the decision tree technique. Approaches with
simplifying geometry or abstracting problem dimensions are lim-
iting the design (Sun and Wang, 2019) in various forms and this
means the designer needs to follow certain limiting rules to have a
feasible design case.
As another approach to overcome the mentioned problems, some
studies in the literature have increased the number of variants
drastically. For example, Ramnath et al. investigated the potential of
applying data science into engineering design (Ramnath et al., 2019,
2020) by an automated method for creating big datasets of 3D CAD
models. Several approaches, such as design catalogs/tables, user-
defined features, and other variant creation techniques are used for
generating many variants (60,000) of an automotive hood in CAD
software. Their framework was based on creating a variety of con-
figurations and then filtering out the infeasible cases which fail
during CAD work (Ramnath et al., 2019). A workflow for correlating
geometric configurations according to several performance and
safety requirements was also demonstrated to attain validity for
created training data set (Ramnath et al., 2020). However, these two
studies do not propose any automatic FEA model for mesh genera-
tion, and corresponding simulations were not performed. More ex-
amples from increasing the size of samples can be found in the
literature. Secco et al. used input parameters such as the wing
planform, airfoil geometry, and flight condition as inputs to con-
struct a neural-network-based prediction model for aerodynamic
coefficients of transport airplanes. The output was calculated for a
huge library (100,000) with a full-potential multiblock structured
code with an average time of 21.8 s per airplane (Secco and de
Mattos, 2017). This could have not been possible to perform if the
computational time was over one minute for each simulation run
because of exhaustive run time.
More data-driven approaches exist in literature with less em-
phasis on geometrical CAD model parameters as features. Rahman
et al. used the designer's sequential design behavioral data stored in
the design action log file (.JSON) of a CAD program to train a ma-
chine-learning algorithm and predict the next stage in the process as
immediate design action (Rahman et al., 2019). This approach is a
novel way of using CAD software as a data source and clearly em-
phasizes the gap in engineering design literature to explore alter-
native ways of using CAD to extract features for data-driven
approaches (Chiarello et al., 2021). Yet, based on performed litera-
ture study, extraction of hidden features based on CAD geometry has
not been proposed. But many applications of feature extraction and
feature reduction exist in other domains and each of them is an
independent research topic backed with a substantial number of
publications. Such topics are vibration analysis and signal processing
with the aim of condition monitoring in mechanical systems like
bearings or gears (Caesarendra and Tjahjowidodo, 2017) or me-
chanical defect prediction models using either supervised or un-
supervised learning methods (Kondo et al., 2019) or image
processing and pattern recognition where the number of features
requires a lot of preprocessing on the input images (Kumar and
Bhatia, 2014) or electronic circuits design automation where feature
extraction is being practiced on generating new circuit topology
(structure) with reusing learned patterns (Huang et al., 2021). Sen-
sitivity analysis methods such as Principal Component Analysis
(Yuce et al., 2014) or analysis of variance (ANOVA) (Khalkhali et al.,
2017) together with Taguchi are widely used dimension reduction
strategies to select the most important parameters and reduce the
dimensionality of the model. Yet, considering how large the number
of parameters and constraints in a real CAD model and how small
their effect on simulation output can be, running higher-order Ta-
guchi arrays add up to existing computational complications.
3. Studied case
Since its invention in the early 1990s, the side curtain airbags
have become an important part of vehicle restraint systems and they
are widely used to prevent serious injuries by increasing head
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
3
protection for both front and rear seat occupants. For the US market,
one measurement is the safety criteria (Federal motor vehicle safety
standards, 2011) that include measuring the amount that a human
head can go out of the widows (in millimeters) and is called, Ejection
Mitigation (EjM). One of the principal requirements for inflatable
curtains is to shield the occupants from intruding objects (Evans and
Leigh, 2013). The coverage area must be communicated to airbag
manufacturers (Suppliers) from car manufacturers (OEMs) as re-
quirements to be met during the design process. This is considered
for various occupants and positioning of car pillars, roof rail, door
glass, occupant seats, and components in front of occupants such as
dashboard and steering wheel. A typical curtain airbag design for a
sedan class is shown in Fig. 2. The front and rear chambers (marked in
the figure) are responsible for cushioning the head of the occupant
by filling the space between the head and windows. Each chamber
has one or two so-called islands (inner sewing lines) to prevent the
cushion from becoming a balloon (or like a pillow). The non-inflated
fabric around the chambers is responsible for holding the integrity of
the whole bag and it protects the occupants from broken glass and
other intruding objects at the time of the crash.
The number of islands and the size of chambers depends on the
size of the designed bag which in turn is affected by the size of the
car. So, for a large SUV with three rows of seats, another chamber
could be added to the bag shape and a higher capacity of inflators
might be necessary to fill in the bag. Likewise, for a small coupe
vehicle, designers could design one big chamber instead of two and
consequently choose a lower capacity. It also influences the cost of
the bag as suppliers (airbag manufacturers/sellers) tend to sell the
bigger capacities while OEMs (car manufacturers/buyers) try to
settle on a smaller one. This is because it is easier to meet the safety
requirements with bigger capacities, but it will be also more costly.
The design process continues back and forth until a design case
meets all requirements (Dix et al., 2012).
The curtain airbag design process is characterized as being
iterative and simulation-driven (Arjomandi Rad, 2020). Meaning
that from early conceptual phases designers are front-loading si-
mulations to meet requirements such as volume and EjM, etc. Finite
element simulations are used with separate simulation models
(varying in complexity) for each requirement. Fig. 3 shows how
coverage requirement (req.) is met first in a CAD environment and
then volume and EjM are calculated within a separate finite element
simulation model. Looping between volume and coverage or looping
between EjM and coverage could happen as frequently as 50–60
loops and the design process will continue until all three are sa-
tisfied. This looping between requirement gates in the design pro-
cess is a common workflow for components in the automobile
industry (Fatfouta and Le-Cardinal, 2021). Considering the time
spent by engineers for pre-processing, processing, and post-pro-
cessing, the importance of an automated prediction model in early
phases is highlighted.
There has been a lot of research performed to study curtain air-
bags. Song et al. introduced three types of simplified models in
curtain airbags mainly intending to save modeling and simulation
time (Song et al., 2011). It was argued that due to a variety of re-
quirements from different safety organizations, there is a need for
different configurations with regards to positioning impactors and
dummies in the simulation models. In a different study, the airbag
shape design has also been studied (Chavare et al., 2013) to increase
Fig. 2. Typical curtain airbag design for sedan class.
(with copyright permission from MarkLines Co.).
Fig. 3. The inflatable curtain design process in the conceptual phase.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
4
the performance of curtain airbags by applying Knowledge-Based
Engineering (KBE) methodology on the packaging and positioning
dummy and seat with respect to a set of interior design require-
ments. The result was a curtain airbag module configuration that
ensures protection zones for occupant body regions. Furthermore,
they used 3D clearance/interference volume between dummy, seat,
and vehicle side combined to arrive at the airbag cushion geometry,
volume, and inflated chamber size. Yun et al. presented the curtain
airbag design procedure (Yun et al., 2014) with two phases to first
select important parameters affecting head impact criteria (HIC)
using sensitivity analysis, and second to optimize the function based
on Taguchi orthogonal arrays to minimize HIC. Another study (Park,
2017) aims to establish a design procedure and an optimization
process for airbags using CAE techniques mainly to minimize de-
velopment time. Parameterized airbag shape and morphing techni-
ques were used to generate surrogate sled models. The direct
optimization method (not meta-model-based) is used for airbag
shape optimization regarding multiple load cases.
In this paper, to study how parameters are affecting the volume
of the airbag and to find out the most influencing parameters on the
simulation output, a subsystem of an actual airbag is considered as a
generic prototype. The shape of the designed prototype is inspired
by the front chamber of an actual curtain airbag depicted in Fig. 2
and it holds most of the features necessary for full analysis of an
actual curtain airbag shape. Fig. 4 shows the designed prototype
with 14 selected parameters which is being studied in this paper.
Moreover, Table 1 presents the names of the parameters which are
tagged with numbers to ease the lookup.
Design parameterization guidelines including the Independence
axiom and Information axiom were used when selecting the men-
tioned 14 parameters (Suh, 1998). The Independence axiom main-
tains the independence of design intent, and the Information axiom
attempts to minimize the information content of the design intent
(Chang, 2016). To meet the independence axiom all 14 parameters
are bound into an interval that allows them to change between a
minimum and a maximum range. Table 1 presents all selected
parameters and their associated bounds. To meet the information
axiom all parameters are selected in a way that allows all possible
design cases with a minimum number of parameters. For example,
among all the variations of parameters that could have described an
island’s shape and position, 5 parameters are selected based on their
ability to create the most frequently used shapes and the rest of the
parameters are assumed constant. For instance, the radii and the
control points for the curves on top of the island are assumed con-
stant because they are rarely changed in the actual curtain airbag
design.
4. Problem definition, sampling techniques
This section deals with identifying the problem area. To study
parameters and investigate each parameter’s effect, two studies have
been carried out. One factor at a time study, where only one para-
meter at a time is changed, and latin hypercube study where all the
parameters are changed with the help of a latin hypercube sampling
method. In both studies utilizing macro tools in CATIA® and Visual
Basic for Applications (VBA) programming, a parameterized CAD
model is modified based on each design sample and the generated
geometry is exported as a ‘.igs’ file. The choice for this file format
was based on the experience of the designers in the industry. As for
the simulation technique, there are several finite element (FE) codes
in the literature to simulate airbag deployment but studying which
is superior over the other is out of this paper’s scope. Yet for the
current paper, the uniform pressure method is used mostly because it
is faster to create and run and it gives sufficient precision for early
design phases. This method assumes uniform pressure and tem-
perature everywhere inside the airbag. This is a close approximation
of the airbag after it is fully inflated and stabilized so the airbag
geometry is considered without any fold (Zhang et al., 2004). In this
way, All the generated geometries in both studies are used in this
finite element analysis (FEA). Meshing is done with ANSA® and
generated key files are submitted to the LS-DYNA solver. Post-pro-
cessing is carried out with META® and the volume-time curve is
extracted for each design sample. Fig. 5 shows one of the curves as
an example for the volume-time ratio.
In all the simulations the pressure is raised to 40 kPa with a
smooth step function and then kept constant until the simulations
end in 100 ms (ending criteria). From Fig. 5 it is clear that the
maximum volume (recorded as 33.7 Liters) is reached in the last
20 ms of the simulation. At this time where the maximum volume is
reached, the pressure is maintained constant at 40 kPa. The run time
for each design sample ranges between 10 and 15 min, depending on
Fig. 4. Studied prototype representing all curtain design features.
Table 1
Selected 14 CAD parameters and their varying bounds.
Parameter Name Min (mm) Max (mm)
1 Offset1 50 100
2 Offset2 50 100
3 Radius1 40 135
4 Offset12 40 135
5 Radius2 40 60
6 Offset22 35 70
7 Radius3 40 100
8 Radius4 60 100
9 IslandOffset 100 250
10 IslandR1 10 50
11 IslandR2 10 50
12 IslandAngle 40° 130°
13 IslandLength 150 220
14 IslandBottom 40 180
Fig. 5. Volume - time ratio for one of the performed simulations.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
5
the size of the bag. Fig. 6 shows one of the simulations performed on
a 25 ms interval.
In the One factor at a time study, 14 aforementioned parameters
(Table 1) on the geometry have been altered in five steps, so the
results for volume change are shown in Fig. 7 for the total of 70
simulations. During the study, only one parameter is changed, and
others are kept constant. In this figure, the vertical axis shows the
volume in terms of liter and the horizontal axis represents the 5
changes in each parameter, normalized with respect to the average
of the five steps (each parameter’s average). The length of steps and
in horizontal axis shows how much that parameter has been
changed in comparison to others. For example, the smaller length
(‘Radius2′) shows that the parameter had a smaller boundary to
change in CAD due to the defined constraints. The slope of the curves
shows the sensitivity of the volume to each parameter’s change. For
instance, ‘Offset12′ and ‘Offset22′ have more or less the same sensi-
tivity. As it can be inferred from the figure, length-like parameters
(e.x. Offset1, Offset2, etc.) are linearly correlated with the volume and
the radius-like parameters (e.x. Radius1, Radius2, etc.) are correlated
quadratically. As expected, the more a parameter is affecting the area
of the geometry, the more it is changing the volume. Another in-
teresting effect happens with the parameter ‘IslandOffset’ and ‘Is-
landAngle’ where the volume with their increase first decreases and
then increases. This behavior can be explained considering the
thickness of the bag (how much it becomes inflated).
It should be mentioned that throughout this paper, for evaluating
the correlation between two sets, Pearson coefficient (R
2
) which is a
popular method in machine learning for ranking features and fil-
tering them has been used (Guyon et al., 2008). This correlation
coefficient for a feature with values x and output with values y is
defined as Eq. (1).
=Rx x y y
x x y y
( )( )
( ) ( )
iii
iiii
2
2 2
(1)
Where
x
is the mean of feature data set, and
y
is the mean of the
output data set. If R
2
is 0, it means that there is no correlation, and
input parameters cannot predict the value of the output. Similarly, if
its value is 1, it means that input parameters will always be suc-
cessful in predicting the output. The
R2
value is always
< <0 R 1
2
and for this criterion 0.9 or above is considered as ex-
cellent precision, 0.8 or above good, and in some cases, 0.6 or above
is considered satisfactory (Rad and Khalkhali, 2018).
In the second study, a latin hypercube is used to generate design
samples. A python module called ‘diversipy’ (Wessing, 2018) is used
as an implemented version of latin hypercube to create 100 nor-
malized design samples between the aforementioned bounds for the
parameters. All cases are mapped into desired intervals and using
CATIA knowledge ware bench work, a parameterized model is
modified with a VBA script, and all the CATIA models are generated
the same as described before. Fig. 8 illustrates the three most cor-
related parameters (out of 14) with the volume for 100 design
samples generated with the latin hypercube. As can be seen, these
CAD parameters are correlating with the volume with the R
2
value of
0.037, 0.018, 0.044 which means almost no correlation. Other para-
meters are also similar to the depicted ones, so they were not in-
cluded as they don’t yield more information. This lack of correlation
among all CAD model parameters and the simulation output can be
explained by the effect of each parameter on the volume change. As
it can be inferred from Fig. 7 some parameters have so small effect
(for example, ‘Radius 3′ or ‘Radius 4′), and some have very high (for
example, ‘IslandLength’ or ‘IslandAngle’). If one parameter with high
impact increases the volume and one other parameter with low
impact reduces it. The effect of the one with low impact will be
faded or maybe even out with each other when they are changed
together. This problem with these parameters will affect the accu-
racy of the machine learning regression model negatively because
the regression function will not be able to properly map inputs to the
output.
In other words, the algorithm might have difficulties finding a
meaningful relation between input and output. Consequently, using
low correlated features will require either having large training sets
or having a higher number of features. As mentioned in the in-
troduction, filtering methods are a group of feature selecting
methods that are based on the increased correlation between fea-
tures and the output (or label tags in classification problems) (Cai
et al., 2018). The feature extraction on CAD proposed in the next
Fig. 6. Studied prototype simulation in a 25 ms step time.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
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section is using the filtering method as a base. Some new parameters
are extracted and ranked according to firstly being independently
(from the parameterization) measurable and secondly having a high
correlation with the volume as output. This will ensure their impact
when they are used to create a machine learning regression model
and will increase the accuracy of such a model which is proposed
and verified in the last section.
5. Sleeping parameters
The parametric study in the previous section shows how much
area can be effective in the final volume output, which is no surprise.
Yet, it refers to more possible geometrical entities associated with
the airbag shape which can show a correlation with the volume.
Therefore, a more in-depth study is carried out on finding more
parameters with the same characteristics, and the results are pro-
vided in this section. Overall, underlying parameters of this kind that
can be obtained independently and fast from the geometry are an
example of a feature extraction application for machine learning in
the CAD environment. In this paper, the term sleeping parameters is
used to address them and more examples of such parameters are
presented further in the text. They are called ‘sleeping’ because they
are not primely linked to the CAD model parametrization, and are
derived from the model without any special treatment before or
during the design process. The extraction can simply be done after
the design is finished and when the design is ready for the simula-
tion stage. To gather a handful of Sleeping parameters, a workflow as
illustrated in Fig. 9 has been used during the next sections. In this
figure, if a geometric entity or an extracted parameter satisfies two
conditions, it is added to a non-dimensional array (Ndarray). Later,
we use all extracted parameters to train a regression model and
measure its accuracy. This is looped until we reach the expected
accuracy.
5.1. Area and circumference
Using the 100 samples acquired from the latin hypercube in the
previous section, a CATIA VBA script is used to read out the area of
each model. The correlation between area and volume is studied and
depicted in Fig. 10 (top). The figure also demonstrates the correlation
coefficients between two sets. The amount of correlation in this
figure makes the area an interesting parameter to estimate the vo-
lume in the early design phases. The figure also shows when the area
is increased so does the volume. It has been proven that the increase
in volume is always greater than the increase in the surface area
(Emert and Nelson, 1997). This is true for cubes, spheres, or any other
polyhedron object whose size is increased without changing its
shape (only undergo geometric change and not topological change).
Additionally, two upper and lower boundary lines are obtained and
shown in the figure with their corresponding functions. Using the 70
samples from the parametric study in the previous section and the
same script Fig. 10 (bottom) is acquired, which shows the correlation
between the volume and the area for mentioned samples. In this
figure, the purple points show the area of the design samples in
Fig. 7. One factor at a time study on fourteen selected parameters.
Fig. 8. Three example parameters out of 14 in the second study with 100 design samples.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
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which only island-associated parameters have been changed. These
parameters are namely IslandOffset, IslandR1, IslandR2, IslandAngle,
and IslandLength. Blue points show samples associated with the
change of other parameters. Two differentiated sets of parameters
clearly display a different behavior with the volume.
As another instance, the circumferences of the 100 bags (same as
area) are studied, and the results for correlation between
circumference and volume are shown in Fig. 11 (top). Upper and
lower bounds are quadratic and with small deviation at the begin-
ning and end of the plot (small and large circumferences) and large
deviation in middle range circumferences.
Moreover, to find out the reason behind observed behavior, the
circumference of the design samples from the parametric study, are
separated into two sets in the same way with the same color code as
illustrated before and the results are presented in Fig. 11 (bottom).
Interestingly, the same island parameters, namely IslandOffset, Is-
landR1, IslandR2, IslandAngle, and IslandLength are the reasons for
this behavior. In this figure, purple points are associated with the
simulations where the island parameters are changed, and the blue
points are depicting the rest of the simulations (where other para-
meters are changed). To find out more parameters other geometric
entities have been taken into account in the next section.
5.2. Using medial axis to extract more parameters
To find out parameters that can represent thickness, the medial
axis length of the bag shape in 2D is studied. The medial axis (also
known as the topological skeleton) is a fundamental geometrical
entity, first proposed by Blum (Blum, 1967) to describe a shape.
Utilizing this concept allows representing a virtual shape by geo-
metric location of the center of circles inscribed inside instead of its
outer boundary. The medial axis is represented in a 2D planar as a
line and in 3D, as a surface. What follows is the mathematical de-
finition of the medial axis for a 2D object (a simple polygon). Let G
denotes the boundary of a 2D object, then the medial axis M(G) is
defined by a set of points like y (see Equation 2) which is tangent to
the boundary G at two unique points like
x
and
x
. And as such, these
points must be equidistant to the medial axis point y. This distance
can be measured by using a distance function
d y( )
x
which shows the
distance between any x and y (Ramamurthy and Farouki, 1999) as
shown and Fig. 12.
Distance function d y x y: ( ) min
xx
(2.1)
Fig. 9. The process used in this section to extract Sleeping parameters.
Fig. 10. Correlation between area and volume (top: latin hypercube study, bottom:
One factor at a time study).
Fig. 11. Correlation between circumference and volume (top: latin hypercube study,
bottom: One factor at a time study).
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
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= =Medial Axis M G y x x X d y x y x y: ( ) { ; , ( ) }
x
(2.2)
Voronoi diagram (VD) which is another fundamental geometrical
entity associated with a closed bounded planar domain, can be used
to obtain the medial axis. As defined in the mathematical definition
shown in Equation 3. Let
ei
denotes a nonempty site in a collection of
sites, E in the space
2
. The Voronoi regions
VR e( )
i
, is the set of all
points whose distance to
ei
is not greater than the distance to any
other site
e E
j
, where
j i
. Consider a distance measure
d x A( , )
shown in Fig. 13 which denotes the distance between point x and the
subset A, this is typically the Euclidean distance (Fabbri et al., 2002).
The Voronoi region is then given by the definition
Voronoi regions VR e x d x e d x e e e: ( ) { , ( , ) ( , ), }
i i j i j
2
(3.1)
The Voronoi diagram is then given by the union of the bound-
aries of the Voronoi regions
Voronoi diagram VD E VR e: ( ) ( )
i
i
(3.2)
Voronoi diagram and its close associates such as the medial axis
are typically grouped under the term ‘Skeletons’. They have been
extensively studied and used in a wide range of applications such as
shape matching, surface reconstruction, dimensional reduction
(Suresh, 2003), morphing (Ilies, 2006), mesh generation (Yan et al.,
2013), etc.
In this paper, the Voronoi component in commercial software
Rhino/Grasshopper has been used to create the medial axis of the
100 design samples generated by the latin hypercube sampling
method. Grasshopper is a visual programming tool that has been
used in several applications, such as in design science to solve design
automation transparency problems by displaying input/output re-
lations on a canvas (Heikkinen, 2021). Using the built-in component
for python scripting in grasshopper, each design sample is imported
as a ‘.igs’ file and the boundary of the shape which is a closed-loop
curve is split into 300 points (Fig. 14-A). Using these points as the
center of circles for Voronoi regions and by increasing the radius, it is
possible to create Voronoi regions with all the center points in the
edge of the geometry (Fig. 14-B–E). Within higher radii, two meeting
regions create a curve that has two close points on the geometry and
correctly approximates the medial axis (Fabbri et al., 2002). Through
a selection procedure in grasshopper, the medial axis is isolated and
measured for its length (Fig. 14-F). The length of the medial axis is
studied to find out the correlation with the volume of the bag when
being inflated.
Fig. 15 shows the plot for the length of the medial axis in cor-
relation with volume for 100 design samples created by the latin
hypercube sampling method. As it can be seen, when the length of
the medial axis increases so does the volume.
Although the derived medial axis length for each design sample
due to its correlation with volume is a good feature to be used in
regression models. However, it does not represent the largeness of
the areas that are inflated ‘balloon-ability’. Another drawback is that
it is not sensitive to the small changes on the island. If the island
moves a little bit toward the right side (change in parameter 9 of
Fig. 4), it has a negligible effect on the length of the medial axis but
since the left area gets bigger, the pressure could create a bigger
balloon in that region and the volume could increase. To solve these
problems the maximum radii among the circles that are used to
generate the medial axis is derived and the result is plotted with
respect to volume in Fig. 16. The figure shows ‘maximum radius’ is a
better representative of the balloon-ability since it can have a better
reflection of the island’s movement on the volume, and thus it can
be useful in the regression analysis.
As it is demonstrated in Fig. 14 medial axis is the collection of
points that are created when two circles meet each other in the
middle of the geometry. To study the characteristics of the circles
that construct the medial axis, all circles inscribed in the geometry
are drawn as illustrated in Fig. 17-A. As it is shown in this picture, the
medial axis is exploded into equally distanced points and circles are
drawn on the x-z plane to be tangent with the nearest edge. Then, all
circles are flipped around the x-axis making their plane change from
the x-z plane to x-y. This is like drawing them in a perpendicular
plane to the bag’s geometry which is shown in a perspective view in
Fig. 17-B. The new circles prove that they are representing the vo-
lume better (since they are correlating better) than previously ex-
tracted parameters, this representation is clear in Fig. 17-C which is
the top viewport of the same circles in Fig. 17-B. The top view
(looking into the x-y plane from above) shows that whenever one
side of the bag has an opportunity to get bigger, the size of the radius
of the circles inscribed also grows, and this aligns well with de-
picting the degree to which the bag becomes balloon-like. Inter-
estingly, the radius of the circles inscribed (see Fig. 17) in the
geometry has a potential application to be extracted as an in-
dependent feature. However, for ease of the process, the cir-
cumferences of all the circles are calculated as a coefficient of the
radius.
Additionally, the maximum radius from Fig. 15 only represents
one side of the island (the bigger one), and thus, the effect of in-
scribed circles in the smaller chamber is not represented with this
parameter. To address this problem, and to fully benefit from the
radius of these circles, the sum of the circumference of all the circles
inscribed in the geometry is plotted against the volume in Fig. 18.
To illustrate how much building a regression analysis on ex-
tracted features (sleeping parameters) can increase the efficiency
and precision of the regression models, the next section presents a
comparison and analyses on the performance of these parameters in
regression models.
5.3. Regressions and analyses
The presented framework in the previous section for extracted
sleeping parameters is all about finding independent (from para-
meterization), and measurable features that show a high correlation
with the output volume. To illustrate this, a comparison between 3
sleeping parameters with the 3 CAD parameters is presented in
Table 2 which shows a big improvement in the correlation of the
extracted features with the volume as simulation volume.
In addition, a Multivariate Linear Regression (MLR) analysis to-
gether with the gradient descent method is used to create a pre-
diction model for the simulation output (volume) using extracted
Fig. 12. Medial Axis definition.
Fig. 13. A simple Voronoi diagram defined by three sites.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
9
features. The reason for using this method is that multivariate ana-
lysis is one of the simplest machine learning algorithms available. If
sleeping parameters with such a simple model result in good ac-
curacy, then it proves and validates the hypothesis about how these
features are better inputs than direct CAD parameters in regression-
based machine learning for envisioned prediction models. Another
advantage with choosing this method is that a simple regression can
be easily implemented by any CAD designer or industrial designer
utilizing ready-made libraries and modules. The applicability serves
the aim of being utilized as a tool for the early phases of the design
process.
Two models are trained through multivariant linear regression.
One model with 14 CAD parameters is introduced in Table 1 and the
other model with 3 of the extracted sleeping parameters from the
previous section (the selection was based on better correlation cri-
teria) namely: Area (Fig. 10 top), Length of the medial axis (Fig. 15),
and Sum of circumferences of all circles inscribed (Fig. 18). In the
training process, for minimizing the cost function, gradient descent
is chosen because of its performance in convergence. The cost
function (J) is used with both models, where it deducts y (the ori-
ginal output) from the hypothesis
h
(the predicted output) in
Equation 4. In the
h x( )
, the weights of the prediction model are
denoted by
. .. n0
and
x x. .. n0
are the response variables. n is the
number of variables, m is the number of data points and is the
learning rate.
= + + + …+h x x x x( ) n n0 1 1 2 2
(4.1)
… =
=
Jmh x y( , , , , ) 1
2( ( ) )
ni
mi i
1 2 3 1
2
(4.2)
=J( )
j j
j
(4.3)
For both problems, the training was performed in 5 folds. In this
way, data for 100 design samples are normalized and then divided
into 5 sections. Minimum (worst) accuracy among all sections is
reported as the output precision. Each section with a total of 20
samples is used as a training set and one section with 80 as a testing
set. The low number of training samples was chosen to make the
training a little challenging and show the performance difference
between the two problems clearly. As for learning rate, 5 different
learning rates were chosen based on best practices in literature and
subsequently were tried out and one was chosen as
=0.2
, based
on its performance in minimizing the cost function for both pro-
blems. The convergence rate of the algorithm using three sleeping
parameters is compared to its rate when using 14 CAD parameters
and the result shows slightly better convergence for the sleeping
parameters as depicted in Fig. 19.
For the regression model trained by sleeping parameters, final
values for were extracted according to Eq. (5) where y implies the
output volume and the
x
1
is the area,
x2
is the length of the medial
axis and
x
3
is the sum of circumferences of all circles inscribed.
= + +y x x x33.36 1.87 1.26 3.35
1 2 3
(5)
Fig. 14. Using Voronoi diagram to calculate medial axis in Rhino/Grasshopper.
Fig. 15. Correlation between length of medial axis and volume.
Fig. 16. Correlation between maximum radius and volume.
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To maintain a high level of interpretability and to further de-
monstrate the effectiveness of the proposed approach a Support
Vector Regression (SVR) is applied to the same training data. In
contrast to MLR that fits a line, SVR tries to fit a street of lines (hy-
perplanes), a characteristic that equally penalizes high and low
misestimates and makes the algorithm robust to outliers. It also
enables SVR to free computational complexity from the di-
mensionality of the input space (Awad and Khanna, 2015). Even
though the underlying optimization is complex, but the application
is easy to employ if one uses ready-made implementations. The
python module ‘scikit-learn’ (Pedregosa et al., 2011) implementation
of SVR was used throughout this study since it is a free and open-
source library and has good interoperability with other python li-
braries. Three different kernels namely, polynomial, radial basis, and
linear are tried out and the best performance that belonged to
polynomial was chosen with commonly used hyperparameters from
literature. Other model hyperparameters are also selected based on
best practice from literature and trial and error on the dataset.
Each regression model (MLR and SVR) is fed one time by all 14
CAD model parameters and the second time by the selected 3
sleeping parameters and the results are compared. The error be-
tween the result of the volume from the prediction model with the
result acquired from FEA models (i.e testing data) is studied with
common accuracy matrices in machine learning, the MSE, and R
2
coefficient and the result is shown in Table 3.
Mean Squared Error (MSE) is taken into account to make sure the
difference between two compared sets is significant. The MSE metric
measures the squared and averaged number of differences between
predicted and expected sets. Since this metric is on the scale of the
data point, its high number shows higher error or lower accuracy
(Rad and Khalkhali, 2018). In this criteria, since there is no optimal
range, the lower the error rate the better, and 0 means the model is
perfect.
6. Discussion
In this section, the results from two previous sections will be
discussed, and some important design keynotes will be highlighted.
The correlation coefficient for area and volume is R
2
= 0.829 as is
depicted in Fig. 10 (top). It can be inferred that with calculating area
from CAD software (without any FEA simulation) using two equa-
tions for lower and higher bounds shown on the figure, designers
will be able to have a rough estimation on volume, however, the
error margin will be high according to error criteria. Moreover,
Fig. 10 (bottom) reveals that without islands or inner sewing lines
the ‘area’ would be sufficient in predicting the ‘volume’ since there is
a highly linear correlation between them. And this is expected be-
havior since without the inner sewing lines (the ones that create the
inner island) the bag shape will become similar to a box shape with
round edges. Moreover, it can be inferred that the deviation from the
trend line in Fig. 10 (top) is the result of a change in these island-
associated parameters. This information can enable designers to
have a better understanding of the decisions that they are making in
the concept phase when meeting requirements over coverage and
volume. Overall, independence from other CAD parameters when
measuring the area and high correlation with the volume makes the
Fig. 17. Study of the circles inscribed in geometry that are used to generate medial axis.
Fig. 18. Correlation between the sum of circumferences of all circles inscribed and
volume.
Table 2
Comparison of the correlation between CAD and Sleeping parameters.
Name of the parameter (refer) R
2
Correlation with the
output (Volume)
Offset1 (Fig. 8) 0.037
Island Length (Fig. 8) 0.0183
Island Angle (Fig. 8) 0.0441
Area (Fig. 9 top) 0.829
Length of the medial axis (Fig. 14) 0.752
Sum of circumferences of all circles
inscribed (Fig. 17)
0.8816
Fig. 19. Convergence of gradient descent with learning rate = 0.15 using sleeping
parameters.
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area an interesting sleeping parameter to be used in regression
analysis.
As it can be inferred from Fig. 11 (top), circumference with vo-
lume shows a weak correlation R
2
= 0.37 but the study is interesting
from the design perspective. This parameter gives intuition on the
behavior of the island and can help the designers have a better es-
timation when working with island design. As shown in this picture,
if the change in bag dimensions results in increasing circumference,
the volume increases rapidly which verifies previous findings. Yet
from Fig. 11 (bottom) it is inferred that with increasing the cir-
cumference in the island's dimensions the volume is decreasing. This
can be explained since the bigger size of the island limits how much
the bag can get larger which in turn means less thickness for the bag.
The medial axis length also shows a good correlation with vo-
lume with R
2
= 0.75 as depicted in Fig. 15. This parameter also is
interesting because it is possible to calculate it like area with the
help of a raw geometry independent from the parameters that are
used to generate the shape. And therefore, has been considered as
another sleeping parameter to build regression models for pre-
dicting volume in the previous section. The high correlation can be
explained since longer the medial axis naturally means that the
geometry has narrow and twisted chambers and in other words,
smaller chambers will lead to having a lower thickness. However, if
the geometry has a big open area that can be inflated and become
thickened, the medial axis length will become shorter.
The correlation between maximum radius and volume is de-
picted in Figure16. However, the figure shows a lack of precision for
design samples that have a maximum radius between 180 and
230 mm. This can be inferred from R
2
= 0.52 which is due to a clear
higher deviation from the trend line over the mentioned region. To
fully understand the relation of circles that are used to create medial
axis their circumferences are added up as described The sum of all
the circles inscribed in the geometry and the volume demonstrate an
excellent correlation with R
2
= 0.88 and thus it can be argued that it
is a better feature and can increase the precision in regression
analysis.
All extracted features can be obtained independently from other
CAD parameters and this allows designers to have freedom when
designing. The reason is when creating a parameterized CAD model,
the designers need to always follow a unique convention and use the
same features (such as curves, constraints, etc.) in the geometry.
Obtaining these independent features can be done very fast and in
an automatic way within the CAD environment. Moreover, correla-
tion with simulation output will increase the accuracy and efficiency
of the regression models in the machine learning process and will
facilitate a live prediction model concerning decision-making in the
design process.
As discussed in the introduction, the literature conveys that
correlation can be a good criterion for selection features in machine
learning. Therefore, Table 2 can be used to argue that the 3 extracted
features in this table, with 80 + correlation, are superior in building a
regression model than using direct CAD parameters. Another com-
parison between the two regression models is presented in Table 3.
As it can be seen from the table, the accuracy for the model trained
by sleeping parameters is R
2
= 0.95 and for the model trained by 14
CAD parameters is R
2
= 0.63. The maximum range for this error
criteria is R
2
= 1, so it can be interpreted that the use of these
parameters helps to get to an excellent regression precision over the
estimated values. To make sure of the performed R
2
error compar-
ison results, the MSE of the two sets is also performed and depicted
in Table 3 which confirms the findings. For the model trained by 3
sleeping parameters, MSE is almost 7 times smaller than the one for
the model that is trained by CAD parameters. Since smaller values
for MSE shows better performance, we can once again confirm that
the model trained by sleeping parameters is more accurate than the
one trained by usual CAD parameters. Thus performed analysis
proves the benefit of using sleeping parameters and its ability to
perform accurate regressions with a small number of samples and
with no need for complex machine learning algorithms.
The goal of the presented feature extraction framework is to
simplify the problem so the regression can be done with any simple
and easy-to-handle estimation model. To ensure that a more ad-
vanced algorithm can not perform better with the 14 CAD para-
meters, and also to ensure how good a job is MRL is doing on the
sleeping parameters, the Support Vector Regression model is applied
on both datasets. As it is shown in Table 3 the CAD parameters are
giving R
2
= 0.8 when applied on 14 parameters, which is considered
relatively underperformed. The model however reports the accuracy
R
2
= 0.95 as seen from the same table when it is trained with
sleeping parameters. The MSE error criterion is also showing an
improvement from 14.34 to 1.77 which is considered substantial.
The fact that MLR and SVR have very close accuracy rates when
trained with sleeping parameters, proves that these new features
have successfully reduced the model order so it is now actually
possible to regression the problem with MLR as good as SVR. This
shows that sleeping parameters by increasing the quality of training
features, have made it possible to get an acceptable result with MLR
and there is no need for advanced and complicated regression al-
gorithms such as SVR. Which was the aim from the beginning and is
indeed an advantage and justification for pursuing feature extraction
on CAD using the proposed framework.
The calculated simple regression will empower designers in the
early stage of airbag design to have a real-time prediction model and
therefore potentially will reduce the development lead time. This
model can be added to a CAD environment so when designers
change a length and/or a radius and/or an offset they can quickly see
the impact of their decisions on the volume of the bag without any
need to perform a complex finite element analysis. Moreover, in-
dependence from conventional parametrization in CAD will provide
the flexibility for being creative with new solutions since they will
not be forced to follow one standard parameterization in complex
geometries which is very much needed in today’s industry.
The proposed methodology is transferable to all volume simu-
lations in airbag models that are using 2D geometries as inputs such
as knee and side airbags that deploy from the passenger seat.
Additionally, this methodology can be utilized by other simulations
that use 2D shapes as inputs such as the design of wire patterns for
seat heaters in the automotive industry. Other inflatable structures
that require volume simulation can benefit from the finding of this
paper, such as high-pressure vessels, inflatable tunnel plugs, in-
flatable rubber dams, different kinds of inflatable boats, etc. The
methodology is also scalable to any performance evaluation that
requires good enough accuracy but fast evaluation for decision-
making in the early stages of the design process.
Table 3
Comparison of the accuracy between the regression model trained by two sets of parameters.
Multivariant Linear Regression Support Vector Regression
Accuracy of the regression model among
predicted and expected sets
All 14 CAD model
parameters
Selected 3 Sleeping
parameters
All 14 CAD model
parameters
Selected 3 Sleeping
parameters
R
2
0.6318 0.9505 0.8027 0.9544
MSE 14.7304 1.8802 14.3419 1.7784
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
12
7. Conclusion
This paper applies correlation-based feature extraction on CAD
model parameters. The aim is to have better features as input in
machine learning which will in turn help to build more accurate
regression-based models. Performed literature study, confirms the
identified gap in the literature for lack of novel ways of utilizing CAD
as input for data-based tools. It also confirms that potentially such
tools could add to the efficiency of design processes by removing
iterative loops (such as metamodels) in early development phases.
First, the inefficiency of using CAD parameters alone, as input for
estimation tools was investigated by showing how these parameters
lack correlation with volume. Finite element simulation was used to
study the effect of each parameter alone on the volume output
through a parametric study. Using the concept of fundamental
geometrical entities such as area, circumference, and medial axis, a
group of parameters that are referred to as sleeping parameters are
extracted. Rhino/Grasshopper was employed for creating the medial
axis and measuring the parameters. Utilizing a correlation coeffi-
cient, it was shown that these parameters have a better correlation
with volume as simulation. Multivariate Linear Regression as an
example of a simple, and Support Vector Regression as an example
of sophisticated machine learning algorithms are used on sleeping
parameters and the usual CAD geometry parameters. The compar-
ison between the two trained models proves that these extracted
parameters are superior to be used in regression models. In future
work, the generalization of this method on other case products will
be carried out to show that it is possible to extract such sleeping
parameters from other products’ CAD models. A framework to ex-
tract and rank features from CAD models can be developed for de-
signers in the next study.
CRediT authorship contribution statement
Mohammad Arjomandi Rad: Conceptualization, Methodology,
Study design, Software, Validation, Formal analysis, Investigation,
Resources, Data curation, Writing – original draft, Writing – review &
editing, Visualization. Kent Salomonsson: Methodology, Study de-
sign, Investigation, Data curation, Supervision. Mirza Cenanovic:
Software resources, Resources, Writing – review & editing,
Supervision. Henrik Balague: Validation, Resources, Writing – re-
view and editing, Supervision, Visualization. Dag Raudberget:
Resources, Writing – review and editing, Supervision, Project ad-
ministration, Funding acquisition, Roland Stolt: Conceptualization,
Writing – review & editing, Supervision, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing fi-
nancial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgement
This work has been carried out within the project Butterfly Effect
in the school of engineering, Jönköping University. The authors
would like to acknowledge the staff in Autoliv company in Sweden
who were involved in the research projects and the Swedish
Knowledge Foundation (‘KK-Stiftelsen’ with grant number
20180189) for the financial support as well as our former colleagues
Dr. Joel Johansson and Dr. Tim Heikkinen who made this work
possible. Finally, we also thank and acknowledge the editor and
reviewers of the journal for valuable comments, which indeed has
helped to improve the quality of this manuscript.
References
Arjomandi Rad, M., 2020. Reducing development lead time in iterative, simulation-
driven design processes. Jönköping Univ.
Awad, M., Khanna, R., 2015. Support vector regression. Efficient Learning Machines.
Springer, pp. 67–80.
Bertoni, A., Larsson, T., Larsson, J., & Elfsberg, J., 2017. Mining data to design value: A
demonstrator in early design. Paper presented at the DS 87–7 Proceedings of the
21st International Conference on Engineering Design (ICED 17) Vol 7: Design
Theory and Research Methodology, Vancouver, Canada, 21–25.08. 2017.
Blum, H., 1967. A Transformation for Extracting New Descriptors of Shape. 4 MIT
Press, Cambridge.
Bouhlel, M.A., Bartoli, N., Otsmane, A., Morlier, J., 2016. Improving kriging surrogates
of high-dimensional design models by Partial Least Squares dimension reduction.
Struct. Multidiscip. Optim. 53 (5), 935–952.
Caesarendra, W., Tjahjowidodo, T., 2017. A review of feature extraction methods in
vibration-based condition monitoring and its application for degradation trend
estimation of low-speed slew bearing. Machines 5 (4), 21.
Cai, J., Luo, J., Wang, S., Yang, S., 2018. Feature selection in machine learning: a new
perspective. Neurocomputing 300, 70–79.
Chakrabarti, A., Blessing, L., 2016. A review of theories and models of design. J. Indian
Inst. Sci. 95 (4), 325–340.
Chang, K.-H., 2016. e-Design: Computer-Aided Engineering Design. Academic Press.
Chavare, A.P., Khare, P., Bhise, A., Belanke, P., 2013. Performance Driven Package
Feasibility of Side Restraints Using KBE Tools. SAE Technical Paper
(0148–7191).
Chiarello, F., Belingheri, P., Fantoni, G., 2021. Data science for engineering design: State
of the art and future directions. Comput. Ind. 129, 103447. https://doi.org/10.1016/
j.compind.2021.103447
Dix, J., Hammoud, S., Cardinali, A., Mitchell, A., Fulk, D., 2012. Influence of complying
with FMVSS 226 (ejection mitigation) on side airbag occupant out of position
injury assessment. SAE Int. J. Passeng. Cars Mech. Syst. 5 (2012-01–0466),
358–368.
Du, X., Zhu, F., 2018. A new data-driven design methodology for mechanical systems
with high dimensional design variables. Adv. Eng. Softw. 117, 18–28.
Emert, J., Nelson, R., 1997. Volume and surface area for polyhedra and polytopes.
Math. Mag. 70 (5), 365–371.
Evans, N.C., & Leigh, M.J., 2013. FMVSS 226 ejection mitigation: A review.
Fabbri, R., Estrozi, L.F., Costa, L.D.F., 2002. On Voronoi diagrams and medial axes. J.
Math. Imaging Vis. 17 (1), 27–40.
Fan, K.-K., Chiu, C.-H., Yang, C.-C., 2014. Green technology automotive shape design
based on neural networks and support vector regression. Eng. Comput. 31 (8),
1732–1745. https://doi.org/10.1108/EC-11-2012-0294
Fatfouta, N., Le-Cardinal, J.S., 2021. An ontology-based knowledge management ap-
proach supporting simulation-aided design for car crash simulation in the de-
velopment phase. Comput. Ind. 125, 103344.
Federal motor vehicle safety standards , 2011, Ejection mitigation; phase-in reporting
requirements; Incorporation by Reference, 76C.F.R.
Goodfellow, I., Bengio, Y., Courville, A., Bengio, Y., 2016. Deep Learning. Deep learning
1 MIT Press, Cambridge.
Guyon, I., Elisseeff, A., 2003. An introduction to variable and feature selection. J. Mach.
Learn. Res. 3, 1157–1182.
Guyon, I., Gunn, S., Nikravesh, M., Zadeh, L.A., 2008. Feature Extraction: Foundations
and Applications. 207 Springer.
Hall, M.A., 1999. Correlation-based feature selection for machine learning.
Heikkinen, T., 2021. Transparency of Design Automation Systems Using Visual
Programming–Within the Mechanical Manufacturing Industry.
Huang, G., Hu, J., He, Y., Liu, J., Ma, M., Shen, Z.,. Zhong, K., 2021. Machine learning for
electronic design automation: A survey. arXiv preprint arXiv:2102.03357.
Ilies, H.T., 2006. Parametric solid modeling. Paper presented at the ASME 2006
International Design Engineering Technical Conferences and Computers and
Information in Engineering Conference, American Society of Mechanical
Engineers.
Khalkhali, A., Noraie, H., Sarmadi, M., 2017. Sensitivity analysis and optimization of
hot-stamping process of automotive components using analysis of variance and
Taguchi technique. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 231 (4),
732–746.
Kondo, M., Bezemer, C.-P., Kamei, Y., Hassan, A.E., Mizuno, O., 2019. The impact of
feature reduction techniques on defect prediction models. Empir. Softw. Eng. 24
(4), 1925–1963.
Kumar, G., & Bhatia, P.K., 2014. A detailed review of feature extraction in image pro-
cessing systems. Paper presented at the 2014 Fourth international conference on
advanced computing & communication technologies.
La Rocca, G., 2012. Knowledge based engineering: between AI and CAD. Review of a
language based technology to support engineering design. Adv. Eng. Inform. 26
(2), 159–179.
Li, Y., Wang, H., & Liu, J., 2017. Can CNN Construct Highly Accurate Models Efficiently
for High-Dimensional Problems in Complex Product Designs? arXiv preprint
arXiv:1712.01639.
Pahl, G., Beitz, W., 2013. Engineering Design: A Systematic Approach (2nd, illustrated
ed.). Springer Science & Business Media, London.
Park, W., 2017. A study of airbag design and optimization methodology. Paper pre-
sented at the Proc. 25th Int. Technical Conf. Enhanced Safety of Vehicles (ESV)
National Highway Traffic Safety Administration.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
13
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Dubourg,
V., 2011. Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12,
2825–2830.
Rad, M.A., Khalkhali, A., 2018. Crashworthiness multi-objective optimization of the
thin-walled tubes under probabilistic 3D oblique load. Mater. Des. 156, 538–557.
Rahman, M.H., Xie, C., & Sha, Z., 2019. A deep learning based approach to predict
sequential design decisions. Paper presented at the International Design
Engineering Technical Conferences and Computers and Information in
Engineering Conference.
Ramamurthy, R., Farouki, R.T., 1999. Voronoi diagram and medial axis algorithm for
planar domains with curved boundaries I. Theoretical foundations. J. Comput.
Appl. Math. 102 (1), 119–141.
Ramnath, S., Haghighi, P., Kim, J.H., Detwiler, D., Berry, M., Shah, J.J.,. Menzel, S., 2019.
Automatically generating 60,000 CAD variants for big data applications. Paper
presented at the ASME 2019 International Design Engineering Technical
Conferences and Computers and Information in Engineering Conference, IDETC-
CIE 2019.
Ramnath, S., Haghighi, P., Ma, J., Kim, J.H., & Shah, J.J., 2020. Design Science Meets Data
Science: Curating Large Design Datasets for Engineered Artifacts. Paper presented
at the International Design Engineering Technical Conferences and Computers
and Information in Engineering Conference.
Secco, N.R., de Mattos, B.S., 2017. Artificial neural networks to predict aerodynamic
coefficients of transport airplanes. Aircr. Eng. Aerosp. Technol.
Shan, S., Wang, G.G., 2010. Metamodeling for high dimensional simulation-based
design problems. J. Mech. Des. 132 (5).
Simpson, T.W., Poplinski, J., Koch, P.N., Allen, J.K., 2001. Metamodels for computer-
based engineering design: survey and recommendations. Eng. Comput. 17 (2),
129–150.
Song, J.-Y., Lee,K., & Ahn, B.-J., 2011. Simplifiedmodels for optimization of curtain air
bag for US NCAP (0148-7191).Retrieved from.
Suh, N.P., 1998. Axiomatic design as a basis for universal design theory. Universal
Design Theory, 3–24.
Sun, G., Wang, S., 2019. A review of the artificial neural network surrogate modeling in
aerodynamic design. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 233 (16),
5863–5872.
Suresh, K., 2003. Generalization of the mid-element based dimensional reduction. J.
Comput. Inf. Sci. Eng. 3 (4), 308–314.
Wang, C.-C., Yang, C.-H., Wang, C.-S., Chang, T.-R., Yang, K.-J., 2016. Feature recognition
and shape design in sneakers. Comput. Ind. Eng. 102, 408–422. https://doi.org/10.
1016/j.cie.2016.05.003
Wang, G.G., Shan, S., 2007. Review of metamodeling techniques in support of en-
gineering design optimization. J. Mech. Des. 129 (4), 370–380. https://doi.org/10.
1115/1.2429697
Wang, J., Das, S., Rai, R., Zhou, C., 2018. Data-driven simulation for fast prediction of
pull-up process in bottom-up stereo-lithography. Comput. Aided Des. 99, 29–42.
Wessing, S., 2018. diversipy (Version 0.8). Retrieved from https://pypi.org/project/
diversipy/.
Yan, D.-M., Wang, W., Lévy, B., Liu, Y., 2013. Efficient computation of clipped Voronoi
diagram for mesh generation. Comput. Aided Des. 45 (4), 843–852.
Yoo, S., Lee, S., Kim, S., Hwang, K.H., Park, J.H., & Kang, N., 2020. Integrating Deep
Learning into CAD/CAE System: Case Study on Road Wheel Design Automation.
arXiv preprint arXiv:2006.02138.
Yuce, B., Mastrocinque, E., Packianather, M.S., Pham, D., Lambiase, A., Fruggiero, F.,
2014. Neural network design and feature selection using principal component
analysis and Taguchi method for identifying wood veneer defects. Prod. Manuf.
Res. 2 (1), 291–308. https://doi.org/10.1080/21693277.2014.892442
Yun, Y.-W., Choi, J.-S., Park, G.-J., 2014. Optimization of an automobile curtain airbag
using the design of experiments. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 228
(4), 370–380.
Zhang, H., Ma, D., Raman, S.V., 2004. CAE-based side curtain airbag design. SAE Trans.
488–494.
A.R. Mohammad, K. Salomonsson, M. Cenanovic et al. Computers in Industry 138 (2022) 103634
14
