=Paper=
{{Paper
|id=None
|storemode=property
|title=Conceptual Analysis of Complex System Simulation Data for Decision Support: Application to Aircraft Cabin Design
|pdfUrl=https://ceur-ws.org/Vol-972/paper17.pdf
|volume=Vol-972
|dblpUrl=https://dblp.org/rec/conf/cla/MessaiMHBA12
}}
==Conceptual Analysis of Complex System Simulation Data for Decision Support: Application to Aircraft Cabin Design==
https://ceur-ws.org/Vol-972/paper17.pdf
Conceptual analysis of complex system simulation data
for decision support: Application to aircraft cabin design
Nizar Messai1 , Cassio Melo2 , Mohamed Hamdaoui2 , Dung Bui2 , and Marie-Aude
Aufaure2
1 LI, University Franois Rabelais Tours, France
nizar.messai@univ-tours.fr
2 MAS - Ecole Centrale Paris, Châtenay-Malabry, France
{cassio.melo,mohamed.hamdaoui,dung.bui,marie-aude.aufaure}@ecp.fr
Abstract. This paper presents a conceptual approach for decision support ap-
plied in a collaborative complex system design project. The approach takes ad-
vantage of the use of Similarity-based Formal Concept Analysis (SFCA) to clas-
sify, visualize, and explore simulation data in order to help system designers to
identify relevant design choices. The approach is illustrated on an aircraft cabin
design case study which concerns the simulation of different configurations of
the ventilation system to study the passengers comfort in the cabin. The classi-
fication of simulation data with their corresponding comfort scores using SFCA
allows to derive for each simulated input parameter the maximal interval of values
which guarantee an acceptable comfort level. To evaluate the obtained results, the
extracted intervals are then used as ranges of the input parameters for new sim-
ulations which confirmed the already obtained comfort levels and showed the
convergence of the results.
1 Introduction
The design phase is one of the biggest challenges industrial companies are often facing
in complex system production process. During the design process, several aspects must
be studied to ensure the system performances as well as its compliance with the end-
user requirements. These aspects are reflected by a set of design parameters that must
be taken into account early from the design phase. Several simulations of design param-
eters are then performed before validating the design choices. In the case of complex
systems, simulations produce large datasets to be carefully studied and analysed in order
to identify optimal configurations. The analysis process simultaneously implies several
criteria and is usually defined as multiple criteria decision analysis (MCDA) task which
involves the comparison and ranking of a number of alternatives with respect to multi-
ple, potentially conflicting, criteria, with the ultimate objective of identifying the best
option from the available choices [1]. In this context, decision support tools are used
to aid decision-makers to make rational choices. The range of decision support meth-
ods is very large and covers several application domains such as economy, industry,
etc. [2, 3]. The choice of one method instead of another depends on several constraints
related to data characteristics (data format, data size, etc.) or to the method it-self as
generated result characteristics (visualization, analytics, etc.). In [1], a brief survey of
c 2012 by the paper authors. CLA 2012, pp. 199–210. Copying permitted only for
private and academic purposes. Volume published and copyrighted by its editors.
Local Proceedings in ISBN 978–84–695–5252–0,
Universidad de Málaga (Dept. Matemática Aplicada), Spain.
200 N. Messai, C. Melo, M. Hamdaoui, D. Bui and M.-A. Aufaure
the main decision support approaches in industrial contexts is given before introduc-
ing an approach based on rough sets for environmental decision support in industry. In
the current work we are particularly interested in decision support approaches based on
conceptual structures such as concept lattices derived based on Formal Concept Anal-
ysis (FCA) formalism [4]. These approaches are motivated by the richness of lattice
structures as well as by their well-established formal properties. Indeed, a concept lat-
tice is a conceptual representation of data that highlights its underlying structure and
implicit relationships. Its usefulness for data analysis purposes is proved by the large
number of derived approaches which used lattice structures as navigation support for
information retrieval, as condensed representation of itemsets, implications and associ-
ation rules for data mining, as a set of embedded decision trees for machine learning,
prediction and decision support, etc. [5]. However, FCA method is usually limited by
the rigidity of its input format (binary data). Some works have proposed to extend it to
complex data [6–8], among them Similarity-based Formal Concept Analysis (SFCA)
method which considers similarity to directly classify non-binary data into lattice struc-
tures called Many-Valued Concept Lattices (MV lattices) [8]. Besides extending FCA to
complex data and avoiding loose of information in transformation phases, SFCA clas-
sification process produces MV lattices with different granularity levels which allows
progressive data exploration [9].
In this paper we study the usefulness of MV lattices to provide a support for com-
bining numerical values (quantitative) analysis together with qualitative analysis to aid
decision makers in the process of complex system Design. More precisely we show how
MV lattices can be used to highlight crucial information a designer may need to vali-
date design choices. The proposed approach is applied to an industrial case study: the
design of the ventilation system of an aircraft cabin. Simulation data for this case study
are classified and analysed using MV lattices to identify relevant design configurations
regarding the obtained passengers comfort in the cabin. The analysis is facilitated by
two visualization techniques proposed in this work: score-based and interval-based vi-
sualization. The rest of the paper is organized as follows: Section 2 presents the context
of the study and the aircraft cabin design test case. Section 3 recalls basic definitions
of SFCA. Section 4 briefly describes the two visualization techniques to aid decision
making in MV lattices. Section 5 details the application of SFCA to the aircraft cabin
case, the obtained results and an evaluation of these results followed by the conclusion
in Section 6.
2 Context of the Study: Collaborative Complex System Design
The present research work is part of the Complex System Design Lab (CSDL)3 project
which involves 27 industrial and academic partners and aims at providing a collabora-
tive environment for complex system design. Since the simulation of design choices,
which is one of the more strategic steps of complex system design, usually outputs
large and high dimensional datasets, the CSDL platform should allow efficient analysis
of such datasets to identify the right conception choices. In this project, simulations are
3 http://www.systematic-paris-region.org/fr/projets/csdl
Analysis of Aircraft Simulation Data with SFCA 201
performed following a Design of Experiment procedure which consists in computing
the systems outputs for a set of chosen design points of parameter space. Moreover, ad-
ditional data dealing with the systems performances such as performance criteria, cost
functions and constraints are computed. Then the objective of the analysis step is to
identify interesting regions of the parameters space which correspond to the appropri-
ate design configuration.
Parameter Range
Alpha 1 (◦ ) [-90, -80]
Alpha 2 (◦ ) [-100, -45]
Alpha 3 (◦ ) [-135, -90]
Alpha 4 (◦ ) [-120, -80]
Uair 1 (m/s) [0.2, 0.7]
Uair 2 (m/s) [0.2, 0.7]
Uair 3 (m/s) [0.2, 0.7]
Uair 4 (m/s) [0.2, 0.7]
Uair In (m/s) [0.6, 3]
Tair In (◦C) [22, 25]
Tair P (◦C) [22, 25]
T ext (◦C) [-65, -50]
Kappa F (W /K) [1 e−4 , 4 e−4 ]
Fig. 1: Aircraft cabin schema and
the main simulated input parame- Table 1: Ranges of the simulated
ters parameters
CSDL industrial partners have provided a use case which corresponds to a com-
mercial aircraft cabin air control system. In this use case the goal is to identify relevant
design configurations which ensure comfort conditions in terms of air temperature and
velocity inside the cabin. Typical fields of temperature and velocity are obtained us-
ing the same fluid model as in [10] and the comfort design problem is parametrized
by 13 continuous parameters each evolving in a range interval of possible values (see
Table 1). These design parameters are: angles of air injection at 4 passengers’ personal
fan (Alpha 1..4), blown air speed at 4 passengers’ personal fan (Uair 1..4), temperature
of blown air at main inlet (Tair In), temperature of blown air at 4 passengers’ personal
fan (Tair P), blown air speed at main inlet (Uair In), external temperature (T ext), and
fuselage thermal conductivity (Kappa F). The mean values of temperature and velocity
for each of the four passengers’ seats (see Figure 1) have been computed to assess the
passengers’ comfort, which resulted in eight output criteria (two per passenger) related
to the comfort. Moreover, a measure of the energy consumed by the air-conditioning
system is also considered to estimate the price at which this comfort comes.
In the reminder of this paper we propose an approach based on SFCA for data
analysis and decision support in industrial contexts through the classification and visu-
alization of simulation datasets. The approach is illustrated on the previously introduced
CSDL use case.
202 N. Messai, C. Melo, M. Hamdaoui, D. Bui and M.-A. Aufaure
3 Similarity-Based Formal Concept Analysis Basic Notions
SFCA [8, 9] is a classification and data analysis method which extends FCA definitions
and results to complex data represented by many-valued contexts [4]. Formally, an MV
context is denoted by (G, M,W, I) where G is a set of objects, M is a set of attributes,
W is a set of attribute values, and I is a ternary relation between G, M and W (i.e.,
I ⊆ G × M ×W ). (g, m, w) ∈ I denotes the fact that “the MV attribute m takes the value
w for the object g”. This fact is also denoted by m(g) = w. Table 2 gives an example
of MV context corresponding to a part of simulation results for the aircraft cabin test
case (Figure 1). In this example, objects correspond to the first 5 simulations and the
attributes correspond to a part of simulated input parameters, namely T Ext, Tair In,
Tair P, and Uair In, and two output parameters T1 and V1 respectively corresponding
to the air temperature and velocity in seat1.
Table 2: An example of Many-valued Context corresponding to a part of simulation results for
seat1 in the aircraft cabin test case.
T Ext Tair In Tair P Uair In T1 V1
(◦C) (◦C) (◦C) (m/s) (◦C) (10−2 m/s)
1 -57.41 23.89 23.31 2.56 23.86 1.31
2 -56.68 22.71 23.11 1.95 22.34 3.47
3 -59.38 24.27 23.39 2.72 24.01 6.68
4 -51.11 22.06 23.95 1.78 21.42 2.38
5 -55.93 24.28 23.70 2.25 23.91 3.43
The basic intuition of SFCA is to group together objects which are sufficiently sim-
ilar (i.e. have similar attribute values). Therefore, a set of objects A shares an attribute
m when all values of m for the objects in A are similar. The similarity is defined in the
common intuitive way: two values are similar when their difference is not significant.
In the case of numerical data, computing similarity is straightforwardly given by a com-
paraison of the numerical values. Two values are said to be similar if their difference is
less than a given similarity threshold θ which expresses the maximal variation allowed
between two similar values. Formally, given a numerical MV context (G, M, I,W ) and
wi , w j ∈ W , wi ≃ w j iff |wi − w j | ≤ θ. More generally, two intervals [α1 , β1 ] and [α2 , β2 ]
are similar iff max(β1 , β2 ) − min(α1 , α2 ) ≤ θ. Given a similarity threshold θ, the set of
all possible possible intervals of similar values that can be defined on W , denoted by
Iθ , is the set of intervals of the form [wi , w j ] such that wi , w j ∈ W and w j − wi ≤ θ.
The choice of θ reflects the precision requirements to be considered during the data
analysis process. Lower values of θ mean that only the closest values will be considered
as similar whereas higher values of θ mean that more distant values can be considered as
similar. Depending on considered datasets and on the analysis processes, it is possible
to choose either the same similarity thresholds for all the context attributes or a separate
Analysis of Aircraft Simulation Data with SFCA 203
threshold for each attribute. In the later case, θ denotes a vector (θi )0≤i<|M| of |M|
elementary thresholds respectively corresponding to the context attributes.
Based on the similarity of attribute values, SFCA extends the definition of attribute
sharing between objects as follows. Given two objects gi , g j ∈ G and an attribute m ∈ M
such that m(gi ) = wi and m(g j ) = w j , gi and g j share m whenever wi ≃ w j . The interval
of values [min(wi , w j ), max(wi , w j )] is called similarity interval of attribute m for objects
gi and g j . Then gi and g j are said to share m w.r.t to [min(wi , w j ), max(wi , w j )] written
as (m, [min(wi , w j ), max(wi , w j )]). More generally, a set of objects A shares (m, [α, β])
where α = ming∈A (m(g)) and β = maxg∈A (m(g)) whenever ∀gi , g j ∈ A, m(gi ) ≃ m(g j ).
In this case, A is said to be valid w.r.t. m and [α, β] is the similarity interval of m for
A. In the same way, A shares a set of attributes B whenever A shares all attributes in B.
In the MV context given in Table 2 objects 1 and 3 share attribute T1 for a similarity
threshold θ4 = 1. However these two objects do not share attribute V1 for θ5 = 1.
A many-valued concept is defined as (i) maximal sets of objects having in common
(ii) maximal sets of attributes with intervals of similar values. These sets are formally
defined as follows.
(i) Maximal valid sets of objects: Given an attribute m and a set of objects A valid
w.r.t. m. SFCA defines the set of reachable objects from A w.r.t. m as :
R(A, m) = {gi ∈ G | m(gi ) ≃ m(g), ∀g ∈ A}
R(A, m) is the maximal set containing all objects similar to those in A w.r.t. m. This set
may not be valid w.r.t. m because of the non transitivity of “≃”. The maximal valid set
of objects containing A is the subset of R(A, m) obtained by removing from R(A, m) all
pairs of objects which do not share m. Formally this set is defined as follows:
Rv (A, m) = R(A, m) \ {gi , g j ∈ R(A, m) | m(gi ) 6≃ m(g j )}
More generally, the maximal valid set containing A with respect to B ⊆ M is:
\
Rv (A, B) = Rv (A, m)
m∈B
(ii) Maximal intervals of similar attribute values: When A ⊆ G shares an attribute m ∈
M, the largest interval of similar values of m for A is the interval of similar values of m
for the objects in Rv (A, m) obtained as follows:
γ(A, m) = [ming∈Rv (A,m) (m(g)), maxg∈Rv (A,m) (m(g))]
Then A is said to share (m, γ(A, m)). For example, for θ0 = 1, the set of objects {1,3,5}
shares (T 1, [23.86, 24.01]).
Based on these maximal sets, SFCA defines the following derivation operators for
A ⊆ G and B ⊆ M × Iθ :
A↑ = {(m, γ(A, m)) ∈ M × Iθ | γ(A, m) 6= Ø}
B↓ = Rv ({g ∈ G | ∀ (m, [α, β]) ∈ B, m(g) ≃ [α, β]}, B)
204 N. Messai, C. Melo, M. Hamdaoui, D. Bui and M.-A. Aufaure
A↑ is the maximal set of MV attributes shared by all objects in A and B↓ is the maximal
set of objects sharing all MV attributes in B. It has been shown in [8, 9] that ↑ and ↓
form a Galois connection between (G, ⊆) and (M × Iθ , ⊆θ ).
In the example of MV context in Table 2, and for θ = (10, 10, 10, 10, 1, 1), we have:
{1, 3, 5}↑ = {(T 1, [23.86, 24.01]), (T Ext, [−59.38, −55.93]), (Tair In, [23.89, 24.28]),
(Tair P, [23.31, 23.7]), (Uair In, [2.25, 2.72])}
and
{(T 1, [23.86, 24.01]), (T Ext, [−59.38, −55.93]), (Tair In, [23.89, 24.28]), (Tair P,
[23.31, 23.7]), (Uair In, [2.25, 2.72])}↓ = {1, 3, 5}.
MV concepts are then defined as pairs (A, B) where A ⊆ G and B ⊆ M × Iθ such that
A↑ = B and B↓ = A. A and B are respectively the extent and the intent of (A, B). For θ =
(10, 10, 10, 10, 1, 1) in the MV context given in Table 2, ({1, 2, 3}, {(T 1, [23.86, 24.01]),
(T Ext, [−59.38, −55.93]), (Tair In, [23.89, 24.28]), (Tair P, [23.31, 23.7]), (Uair In,
[2.25, 2.72])}) is an example of MV concept.
The MV concepts of an MV context can be partially ordered based on the inclusion
of their extents (and, dually, intents) and form the hierarchy structure called MV concept
lattice and denoted by Bθ (G, M,W, I). The Hasse diagram of the MV concept lattice of
the MV context given in Table 2 for θ = (10, 10, 10, 10, 1, 1) is shown in Figure 2. In
this graphical representation, MV attributes in the form (m, [α, β]) are written m : [α, β]
for a better readability.
Fig. 2: The MV lattice Bθ (G, M,W, I) corresponding to the MV context given in Table 2 for
θ = (10, 10, 10, 10, 1, 1).
4 Visualization of MV Concepts
Finding patterns within MV concepts may be assisted with the use of visualization
techniques. In this work we propose two techniques to assist the analyst in determining
Analysis of Aircraft Simulation Data with SFCA 205
the similarity threshold, filtering and selecting concepts of interest. The proposed tech-
niques follow the so called “information-seeking mantra” - Overview first, zoom and
filter, then details-on-demand [11].
First we propose a visualization technique that consists on the filtering and coloring
of concepts based on user-defined scores. In Section 2, we show how certain inter-
vals in the temperature and the air speed are used to determine comfort classes in the
cabin according to international standards. A color gradient is assigned according to the
“global score” of a concept (Figure 2). For instance, the score of “maximum comfort”
is attributed when the scores of velocity and and temperature are equal to 2 and the
color. This simplification is important because in Complex System Design the number
of parameters are usually overwhelming to the analyst to overview and compare. Alter-
natively, user can filter concepts that are below a score threshold. This is particularly
important during the extraction of comfort classes as explained in Section 2.
When the relevant concepts are identified, i.e. the comfort classes in our case, the
analyst will take decisions based on concepts that fit best to his or her goals. To help
the analyst to quick identify intervals in the concepts and compare with other concepts
in the lattice, we created a new visualisation based on a “conceptual heat map” where
each concept is depicted as an array of rectangles (Figure 3). Each rectangle represents
an attribute, its color indicates the interval of the attribute value in a continuous color
scale from blue to red. Its width is proportional to the size of the range. If an attribute
is not present in the concept the corresponding rectangle is empty in order to keep the
order of attributes consistent.
5 Applying SFCA to Aircraft Cabin Test Case
5.1 Using Similarity Threshold to Express Constraints to Guide Data
Exploration Process
In the previous section, SFCA formalisation is given from a numerical data perspec-
tive. Such a formalisation can also be done on other data formats which makes SFCA
approach generic and flexible. In this case, appropriate similarity measures need to be
defined accordingly to handle complex data. Once similarity measures are defined, the
application of SFCA follows the intuition of “grouping together similar data”. As shown
above, this operation also needs the definition of threshold which can be a subjective
task strongly related to the data analysis process. The variation of similarity thresholds
yields a variation in the obtained MV lattices in terms of number of MV concepts as
well as in terms of concept granularity and it has been shown that both aspects are
related [9].
In the current work, we are interested in identifying the input requirements which
guarantee a convenient output situations based on a set of simulation data. This means
that we first need to formulate “convenient” output situations in terms of constraints.
Then, we use such constraints to guide the SFCA classification process in order to
obtain the appropriate values of input parameters satisfying these constraints. In the
previously shown example (Table 2 and Figure 2) the choice of the threshold θ =
(10, 10, 10, 10, 1, 1) follows the idea of defining constraints on the output parameters T 1
206 N. Messai, C. Melo, M. Hamdaoui, D. Bui and M.-A. Aufaure
Fig. 3: The MV concept view for the lattice in Figure 2. Color indicates position in the range
(from blue to red), width shows the length of the interval.
and V 1 in order to extract the appropriate ranges of the input parameters T Ext, Tair In,
Tair P and Uair In. Indeed, value of θi = 10 defined as threshold for each input pa-
rameter exceeds the difference between the minimal and the maximal values of each
of the four input parameters. Consequently, there is no effective constraint in group-
ing together these parameters while forming the MV concepts. However, the thresholds
θi = 1 for T 1 and V 1 mean that values of T 1 (respectively V 1) can be grouped together
if and only if their difference is less than 1. This constraint is expressed to obtain a
lattice formed by MV concepts where intervals of values of T 1 and V 1 are not larger
than 1 and without any constraint on the other attributes. Having such a MV lattice one
can directly read the maximal range of each input parameter which allows to obtain
a temperature in given interval. For example, MV concept with extent {2, 4} in Fig-
ure 2 shows that values of Uair In, Tair P, Tair In and T ext respectively in intervals
[1.78,1.95], [23.11,23.95], [22.6,22.71], and [-56.68,-51.11] ensure to obtain a value of
T1 in [21.42,22.34]. Knowing intervals of temperature values corresponding to a com-
fort situation, it is then possible to deduce the required inputs to ensure such a comfort.
Based on this idea we develop and apply a data analysis strategy to deal with the aircraft
cabin design test case.
5.2 Simulation Dataset of the Aircraft Cabin Test Case
In the reminder of this paper we will consider the previously introduced aircraft design
case study. The considered dataset corresponds to the simulation results of 100 ran-
domly chosen configurations of design parameters (the 13 input parameters). 9 output
criteria have been defined to assess the quality of each configuration in terms of passen-
gers comfort and energy cost. The mean values of temperature and velocity of each of
the four seats are computed which resulted in 8 criteria associated with the comfort of
the passengers. The dissipated energy is computed based on the velocity as a measure
of the loss of energy due to the fluid viscosity.
In order to quickly appreciate the comfort in each seat and hence simplify the dataset
exploration and the experiments evaluation, comfort scores were computed for the val-
ues of the comfort output criteria (temperature and velocity). The scores are in a three
points scale (0: uncomfortable, 1: acceptable, 2: comfortable) computed according to
Analysis of Aircraft Simulation Data with SFCA 207
ANSI/ASHRAE Standards [12] as follows:
0 if T < 21 or T > 24
0 if V > 1
score(T) = 1 if 21 ≤ T < 22.5 or 23.5 < T ≤ 24 score(V) = 1 if 0.2 < V ≤ 1
2 if 22.5 ≤ T ≤ 23.5 2 if V ≤ 0.2
These scores are then used instead of their corresponding values of temperature and
velocity in the classification process by SFCA.
5.3 Extracting Comfort Classes and Their Corresponding Design Parameters’
Ranges
Our objective is to determine the design parameters that are important to qualify the
experiments such that all of the four passengers are satisfied. We make the assumption
that the temperature is more important than the velocity to define the thermal comfort
of the passengers. Therefore, we focus our analysis on the experiments that offer the
maximum comfort for the passengers from the temperature point of view only: we keep
only the experiments such that the score for the temperature is 2 and we called this
subset Ssilver . Then, following the previously detailed strategy for thresholds choice, we
applied SFCA to build the corresponding MV lattice shown on Figure 4.
Fig. 4: MV lattice generated on Ssilver
By analyzing this MV lattice, it turns out that Ssilver can be described using three
distinct main comfort classes: (i) ”Maximum comfort” (concept n◦ 3): maximum score
208 N. Messai, C. Melo, M. Hamdaoui, D. Bui and M.-A. Aufaure
for both temperature and velocity for the 4 seats, (ii) ”Intermediate comfort” (concepts
n◦ 2 and 5): the score for velocity for seat 4 is not maximum, and (iii) ”Poor comfort”
concept (concept n◦ 2, 4, and 6): the score for velocity for seats 2 and 4 is not maximum.
These three comfort classes can be directly read on Figure 4. Each class is given
by one MV concept in the lattice and the order defined on the MV concepts also holds
for the comfort classes : Concepts 3, 5 and 6 corresponding respectively to maximum,
intermediate, and poor comfort classes. The colors linked to concept scores in Figures 4
and 3 allow to quickly identify the concepts corresponding to the most relevant design
configurations and to extract ranges of variation of the corresponding design parame-
ters. These extracted ranges are given in Table 3.
Table 3: Extracted ranges of the 13 comfort design problem parameters for different classes of
comfort.
Parameter Range “Maximum comfort” “Intermediate comfort” “Poor comfort”
range range range
Alpha 1 (◦ ) [-90, -80] [-86.61, -83.05] [-89.83, -80.56] [-89.83, -80.56]
Alpha 2 (◦ ) [-100, -45] [-96.65, -54.66] [-96.65, -46.52] [-96.65, -46.52]
Alpha 3 (◦ ) [-135, -90] [-133.35, -100.3] [-134.22, -91.59] [-134.22, -91.59]
Alpha 4 (◦ ) [-120, -80] [-105.77, -87.14] [-105.77, -81.15] [-105.77, -81.15]
Uair 1 (m/s) [0.2, 0.7] [0.30, 0.69] [0.20, 0.69] [0.20, 0.69]
Uair 2 (m/s) [0.2, 0.7] [0.38, 0.67] [0.23, 0.67] [0.23, 0.67]
Uair 3 (m/s) [0.2, 0.7] [0.39, 0.63] [0.20, 0.63] [0.20, 0.63]
Uair 4 (m/s) [0.2, 0.7] [0.24, 0.64] [0.24, 0.68] [0.24, 0.68]
Uair In (m/s) [0.6, 3] [2.59, 2.82] [1.68, 2.98] [0.81, 2.98]
Tair In (◦C) [22, 25] [22.82, 23.45] [22.71, 23.53] [22.71, 24.65]
Tair P (◦C) [22, 25] [22.08, 22.88] [22.08, 24.29] [22.08, 24.74]
T ext (◦C) [-65, -50] [-64.84, -52.86] [-64.97, -50.25] [-64.97, -50.25]
Kappa F (W /K) [1e−4 , 4e−4 ] [1.03e−4 , 1.28e−4 ] [1.03e−4 , 1.99e−4 ] [1.03e−4 , 1.99e−4 ]
5.4 Evaluating the Extracted Design Parameters’ Ranges Through New
Simulations
In order to evaluate the obtained results, we considered the extracted ranges of input
parameters corresponding to the maximum comfort class for new simulations to check
wether the output values of temperature and velocity belong to the same comfort class.
We performed 12 new simulations for which input parameters take randomly chosen
values in the ranges of the maximal comfort class previously extracted. All of the twelve
simulations resulted in maximal comfort values for temperature and velocity mean val-
ues for each of the four seats. That is, in each seat, the mean value of temperature is
between 22.5◦C and 23.5◦C and the mean value of velocity is less than 0.2. The ob-
tained values are in the following ranges: T1: [22.57, 23.16], T2: [22.64, 23.30], T3:
[22.84, 23.40], T4: [22.76, 23.29], V1: [0.013, 0.041], V2: [0.016, 0.062], V3: [0.001,
0.004], and V4: [0.148, 0.2].
Analysis of Aircraft Simulation Data with SFCA 209
The ranges of the input parameters for the new simulations extracted from this lat-
tice are shown in Table 4 (column: New range).
Compared to the ranges previously obtained for the maximum comfort class (also
given in Table 4, column: Maximum comfort range), the new ranges are almost the same
as the maximum comfort ranges for all the input parameters. As the new simulations
resulted in values of temperature and velocity in full compliance with the maximum
comfort class values, this means that the simulations converge to the ranges obtained
for the maximum comfort class. These ranges can then be confirmed by the system de-
signer as one possible optimal solution for the multidimensional problem of passengers
comfort in the aircraft cabin.
We proceeded in the same way to evaluate the extracted ranges of the intermedi-
ate comfort class. The twelve simulations performed for values of input parameters
randomly chosen in the ranges corresponding to the intermediate comfort class have
produced values of temperature in the interval [22.5,23.5]. However velocity values in
seat 4 resulted in values in the interval [0.2,1] for eleven simulations which correspond
to intermediate comfort. These results also confirm the ones previously obtained. In ad-
dition, input parameter ranges are included or equal to the ones obtained in the previous
case which means that the simulations converge as in the case of maximum comfort
class.
The evaluation of the extracted parameters ranges for the poor comfort class in the
same way produced similar results and confirmed the convergence of the simulations to
the solution extracted from the MV lattice given in Figure 4.
These results show the usefulness of the presented approach for supporting a sys-
tem designer to improve and validate the choice for a design solution of a complex sys-
tem based on simulation results. In addition, the genericity and the flexibility of SFCA
formalism makes it possible to adapt the presented approach and apply it to similar
problems.
6 Conclusion
In this paper we presented an approach based on conceptual structures to support com-
plex system designers in the identification of relevant design configurations. The ap-
proach takes advantage of SFCA formalism to study the thermal comfort of 4 passen-
gers in an aircraft cabin whose ventilation system is parametrized by 13 design param-
eters. The design problem takes into account 9 decision criteria defining the passengers
comfort and energy consumption of the air ventilation system. A dataset of 100 ran-
domly chosen simulated configurations is considered for the aircraft case study. The
use of SFCA following a smart analysis strategy through the choice of appropriate sim-
ilarity thresholds allows to directly deduce the ranges of values of input parameters
which guarantee different levels of passengers comfort. In addition, an adapted visual-
isation of MV lattices delivers a tractable and easy way to read them easing the design
and decision making process. The obtained results are then evaluated by new simula-
tions which converged to the same solutions in terms of passengers comfort as well as
in terms of input parameters ranges.
210 N. Messai, C. Melo, M. Hamdaoui, D. Bui and M.-A. Aufaure
Table 4: Extracted ranges of the 13 comfort design problem parameters for the maximum comfort
class and for the new simulations.
Parameter “Maximum comfort” range New range
Alpha 1 (◦ ) [-86.61, -83.05] [-86.27, -83.30]
Alpha 2 (◦ ) [-96.65, -54.66] [-95.38, -56.82]
Alpha 3 (◦ ) [-133.35, -100.3] [-131.51, -103.58]
Alpha 4 (◦ ) [-105.77, -87.14] [-103.08, -87.87]
Uair 1 (m/s) [0.30, 0.69] [0.33, 0.68]
Uair 2 (m/s) [0.38, 0.67] [0.39, 0.60]
Uair 3 (m/s) [0.39, 0.63] [0.39, 0.63]
Uair 4 (m/s) [0.24, 0.64] [0.26, 0.59]
Uair In (m/s) [2.59, 2.82] [2.61, 2.82]
Tair In (◦C) [22.82, 23.45] [22.86, 23.42]
Tair P (◦C) [22.08, 22.88] [22.14, 22.88]
T ext (◦C) [-64.84, -52.86] [-64.27, -54.27]
Kappa F (W /K) [1.03e−4 , 1.28e−4 ] [1.07e−4 , 1.27e−4 ]
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