=Paper=
{{Paper
|id=Vol-1638/Paper104
|storemode=property
|title=Intellectual data analysis in aircraft design
|pdfUrl=https://ceur-ws.org/Vol-1638/Paper104.pdf
|volume=Vol-1638
|authors=Valeriy A. Komarov,Semen A. Piyavskii
}}
==Intellectual data analysis in aircraft design ==
https://ceur-ws.org/Vol-1638/Paper104.pdf
Data Science
INTELLECTUAL DATA ANALYSIS IN AIRCRAFT
DESIGN
V.A. Komarov1, S.A. Piyavskiy2
1
Samara National Research University, Samara, Russia
2
Samara State Architectural University, Samara, Russia
Abstract. This article considers the use of confidence judgments method by de-
cision-makers to analyze the information contained in large databases. The
comparative analysis of passenger aircrafts shows that it allows flexibly and ob-
jectively allocating the most relevant information from the data array.
Keywords: data analysis, aircraft design, large databases, decision-makers,
confident judgments.
Citation: Komarov VA, Piyavskiy SA. Intellectual data analysis in aircraft de-
sign. CEUR Workshop Proceedings, 2016; 1638: 873-881. DOI:
10.18287/1613-0073-2016-1638-873-881
Introduction
The emergence of large corporate databases opens up new prospects in the field of
aircraft design, as well as in other subject fields of project activity. It becomes possi-
ble to estimate comprehensively, over a large number of characteristics, both quantita-
tive and qualitative, the efficiency of different variants of design decisions against a
background of a huge amount of analogues. It is also important to keep in mind that
the project activity has largely heuristic nature, based on a combination of objective
quantitative analysis within intuitive the designers’ ideas, arising impulses of which
may the expand and transfer the attention focus, and even change the design paradigm
itself. The mechanism of using large databases for the design of complex, multi-
function objects such as aircraft should be oriented towards these features.
In our opinion, it is advisable to use some advanced methods of complex decision
theory, such as multi-criteria optimization, during the formation of such mechanism.
One of the main advantages of these methods is that they provide an adequate active
role of decision-makers along with the use of axiomatic approach to the information
analysis. For all the variety of decision-making methods [1,2], a decision-making
method under irremovable uncertainly [3,4] and confident judgments method (CJM)
are the most efficient methods from this points of view. The article is aimed to
demonstrate opportunities offered by the application of these techniques during intel-
lectual data analysis. The considered examples are given with great simplifications.
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Each object, denoted by y in the following, is described by a set of data which is use-
ful to divide into two groups. In the first group it is advisable to include the data
which determine how an object is arranged and which can be changed by decision-
makers. In terms of non-linear mathematical programming, it is usually called design
variables. The data, which include the object’s behavior characteristics or properties,
should be contained in the second group. These data are of interest for products’ cus-
tomers, as a rule, in the form of maximum and minimum values. Further, we will
denote them as a particular optimal criterion f i (y). In most cases, the particular effi-
ciency criteria for complex technical objects are contradictory, which generates the
well-known problem of multi-disciplinary optimization.
In aviation, for example, two important characteristics are in such conflict: the aircraft
weight and aerodynamic efficiency. Increasing the aerodynamic quality is achieved
by the wing lengthening, but it increases its weight [7,8]. Introducing new non-
dimensional load-carrying coefficient of structural perfection into consideration al-
lows to carry out the optimization of aircraft appearance taking into account both
weight and aerodynamic efficiency [9]. However, the design of new aircraft and, par-
ticularly, the development of technical specification for its creation, needs analysis
and taking into account a variety of parameters, which can allow to predict the suc-
cess of a new project by the consumer.
Rating Estimation Method
Let us consider a corporate database for the aircrafts as a set Y of objects 𝑦 ∈ 𝑌,
which are characterized by m-dimensional vectors
f ( y ) { f 1 ( y ), f 2 ( y ), ..., f m ( y )} , y Y . The components of these vectors
are separate efficiency characteristics of the object, which are of interest from the
viewpoint of decision-makers. For example, a passenger aircraft has the following
characteristics considered from an operational point of view:
Cruise speed, km/h
Number of passengers, pers
Flight range, km
Service ceiling, m
Runway length, m
Minimum price in passenger version, million USD
Maximum price in passenger version, million USD
Starting year of manufacturing
Number of built aircrafts
Engine power, kgf
Fuel capacity, l
Traditionally, the simplest way to analyze this data array is to sort by the values of
j
any characteristics f , j 1,...,m . It allows to define the locations according to
solution variants for this characteristic among analogues. However, since the solution
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efficiency, in general, is determined mainly by its characteristics, the analytical value
of sorting is not high.
More powerful tool for intellectual analysis is the allocation of the total array of ob-
jects which are Pareto efficient. The object is considered as Pareto efficient if there do
not exist at least one dominant object on the entire considered set. It means that any
object according to the characteristics not worse, and at least one - better. Thus,
among the aircrafts, whose characteristics are given in Table 1 (data are taken from
[7] and other sources, partly modeled and have purely methodological nature), Pareto
efficient are Boeing 737-200, Boeing 737-400, Boeing 737-500 and Boeing 737-200
Advance is not efficient as it is dominated by Boeing 737-500.
Table 1. Some characteristics of Boeing’s aircrafts
Aircrafts Flight Ceil- Run En- Fuel
range, km ing, m way gine capacity,
length, thrust, l
m kgf
Boeing 737-200 Ad- 2960 1067 183 1578 1953
vance 0 0 0 5
Boeing 737-300 4670 1020 194 1994 2010
0 0 0 5
Boeing 737-400 3870 1130 192 2134 2382
0 0 0 5
Boeing 737-500 5550 1130 153 1816 2010
0 0 0 5
The rigorous formulation of Pareto efficient object is the following:
y Y : ( f j ( y ) f j ( y ) j 1,..., m) (j {1,..., m} : f j ( y ) f j ( y ) ))
Analysis of Pareto efficiency allows decision-makers to exclude obviously inefficient
objects from consideration, but it does not provide information about how much the
objects which remain in consideration, are relatively effective. It is necessary to use
techniques that allow to proportion the comparative significance of individual objects
from the position of a holistic estimation of their efficiency. It means that we need to
find an adequate way of comparing the individual characteristics of objects s after
which the object’s comprehensive efficiency estimation y Y is determined by
purely mathematical way as F ( y ) Fs ( f ( y )) , y Y . There are a number of es-
tablished proportion methods in each subject field. In aviation, “fuel efficiency” and
“weight efficiency”, as well as several others are used as a complex criterion during
aircraft’s comparative estimation. The disadvantage of this approach is that the objec-
tive criteria are important, but they express only one property and are not universal.
Therefore, the conclusions obtained with their use are questionable, since the use of
other, to the same extend authoritative criterion, could lead to other conclusions.
The universal construction methods of criteria convolution are more reliable. The
most famous of these is the linear convolution method, in which various characteris-
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tics are assigned numerical weight coefficients of relative importance. It is consid-
ered, that they can be obtained by averaging the opinion of many experts, involved by
decision-makers for this purpose. Then
m m
F ( f ) j f j , j 0, j 1,..., m, j 1 ,
j 1 j 1
where , j 1,..., m - weight coefficients.
j
The use of this method cannot be recommended during the design of such important
objects as an aircraft for two main reasons.
Confident judgments
Let us notice, that the decision-maker made two judgments by choosing it:
First of all, exactly this kind of account method for uncertainty in the form of linear
convolution is fully adequate for this decision-making task,
Secondly, exactly the chosen experts, the examination organization and methods of
expert opinion processing load to absolutely reliable values of weight coefficients.
Fig. 1. Example of incorrect linear convolution
Both judgments can be challenged by reasonable positions. First of all, the linear con-
volution may not see some Pareto-optimal objects for any values of weight coeffi-
cients. For instance, on Figure 1 all objects for two minimized objects, images of
which lie above the dotted line in a criterion space, will not be recognized as the most
rational for any weight coefficient values in linear convolution, although they are
Pareto-optimal objects [4]. Thus, this example shows that the use of the linear convo-
lution penalizes a natural requirement for multiple comparison methods of individual
object’s characteristics S: any Pareto-optimal variant from the set of admissible solu-
tions must correspond to at least one function 𝐹𝑠 (𝑓) ∈ 𝑆, the use of which provide the
most rational solution. If this requirement is failure to comply, it reduces the select
possibilities of decision-makers by purely mathematical features of the aircraft, which
is unacceptable. The subjectivity of weight coefficients’ determination by means of
expert examination is evident. In addition, the need to attract qualified experts when-
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ever the decision-maker wants to take a new look at the situation, greatly reduces the
data analysis capabilities.
Actually, the decision-maker can reasonably make only two types of judgments.
The confident judgment of the first type. Decision-maker person (DMP) with his
confidence may include various particular criteria to different group of importance.
For example, “criteria 1 and 4 are the most important ones, criteria 2 and 6 are merely
importance, and criterion 5 has the lowest importance”. Let us note, that we do not
assume that decision-maker provide a qualitative estimation of the relative importance
degree for particular criteria, it refers only to the qualitative comparison which is
optional.
The confident judgment of the second type. If desired, the decision-maker can con-
struct the pairs of Pareto-incomparable vectors of particular criteria, for which he is
certain that one of the vectors is better that another. It is not required that the vectors
represent the efficiency of any real objects. If 𝑓1 and 𝑓2 – in which 𝑓1 is surely better
than 𝑓2 , it implements the following restriction on the set S:
S {s )} : Fs ( f1 ) Fs ( f 2 ) s S .
Based only on these two types of judgments, the method which proportion particular
characteristics into a single numerical object’s characteristic, represented in the data-
base, was developed in [5,6]. It is called confident judgments method.
Stages of confident judgments’ method
Stage 1. The uncertainty profile is constructed for the solving problem. It shows the
range of complex efficiency criterion values for this decision within all possible ways
to take into account the uncertainty for each design solution. The uncertainty profile is
given by a pair of functions, which are defined on the set: minorant 𝑚(𝑦) =
min 𝐹(𝑓(𝑦)) and majorant𝑀(𝑦) = min 𝐹(𝑓(𝑦)).
sS sS
It should be noted, that obviously irrational decisions z Y , for which there are bet-
ter solutions z Y by complex criterion in all possible ways of uncertainty, can be
identified. The identify conditions for such solutions have the following form:
z Y : M ( z ) m( z) .
The main purpose of uncertainty profile is to give decision-makers information about
the impact of uncertainty during decision-making in the problem. Adding confident
judgments, he will be able to estimate how they reduce the uncertainty.
Stage 2. If it is possible, the set of uncertainties narrows by taking into account the
decision-maker’s confident judgments. The uncertainty accounting methods, which
do not correspond to this judgments, are eliminated when we are using confident
judgments of the first type. When we have got the confident judgments of the second
type, conditions (6) are added to the set description, which eliminates those uncertain-
ty accounting methods that do not carry out these judgments.
At the end of first two stages the initial set of uncertainties can be narrowed. This
affect the uncertainty profile of the problem, but it is unlikely to remain only a single
element in it, or all variants except one will be eliminated from the plurality of solu-
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tions. Thus, the uncertainty retained in the problem. This will be a fatal uncertainty.
All uncertainty account methods, which form this fatal uncertainty, are completely
equal to the decision-maker as he has already use his ability to make additional con-
tent in the problem description using judgments of the first and second types. It is
possible that the other types of confident judgments of decision-makers can be found,
but they did not fundamentally change the situation: after their usage, fatal uncertainty
will remain in the problem.
Stage 3. Rigid and soft ratings for solution variants are calculated, taking into account
unavoidable uncertainty. In order not to introduce the unnecessary for understanding
and application complex mathematical apparatus, we shall assume that the set con-
tains a finite number of uncertainty accounting methods S: S= {𝑆𝑘 } k 1,..., K .
Then the rigid rating 𝑅𝐺(𝑦) for 𝑦 ∈ 𝑌 solution is a fraction of uncertainty accounting
method, in which the solution is the best compared to the other solutions:
K
1
k 1
F ( y ) Fk ( z ) zY
RG ( y ) k , yY
K
1
(If any uncertainty accounting method has several best solutions, we should write
𝑝
instead of 1 in the numerator of rigid rating).
Soft Rating RM(y) for 𝑦 ∈ 𝑌 decisions displays the average comprehensive efficiency
if this solution compared with solutions, which are the best in different ways of uncer-
tainty concideration:
K Fsk ( f ( y ))
max F ( f ( y))
k 1 sk
yY
RM .
K
Stage 4. Decision-maker recognize that the possibility of further uncertainty reducing
is exhausted due to its confident judgments. Finally, he chooses a solution with the
best (lowest) rigid rating as the most efficient solution. If there are several solutions,
we will choose the one, which has the best (lowest) soft rating, as the most efficient
solution.
Data analysis using confident judgments method
Let us show the use of confident judgments method for data analysis of passenger
aircrafts in terms of their operational characteristics. Table 2 shows a fragment of the
database.
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Table 2. A fragment of database for passenger aircrafts
Year of serial manufactur-
Weight of empty aircraft,
Min. price in passengers
Max.price in passengers
Aircraft Built in Total
Cruise speed, km/h
Engine power, kgf
Runway length, m
Service ceiling, m
Take-off weight, t
variant, mil. USD
variant, mil. USD
Flight range, km
Passengers, pers
Fuel capacity, l
Aircrafts
ing
t
Boeing 905 120 2960 10670 49,40 27,17 1830 3,00 11,00 1967 3660 13160 10790
737-200
Boeing 905 120 3700 10670 58,00 31,90 1830 3,00 11,00 1984 865 15780 16250
737-200
Advance
Boeing 910 128 4670 10200 62,80 34,54 1940 10,50 44,00 1984 1102 19940 20105
737-300
Boeing 910 168 3870 11300 68,10 37,46 1920 18,50 48,00 1988 456 21340 23825
737-400
Boeing 910 108 5550 11300 60,55 33,30 1530 33,00 39,00 1990 385 18160 20105
737-500
Boeing 925 108 5910 12500 65,09 35,80 1880 32,00 39,00 1998 20 18160 26035
737-600
Boeing 925 128 5920 12500 69,40 38,17 2040 39,00 46,00 1997 15 21830 26035
737-700
Boeing г 925 189 5370 12500 78,24 43,03 2040 48,00 54,00 1998 20 23860 26035
737-800
Tu-204 850 210 3700 12600 94,60 52,03 1550 20,00 25,00 1994 15 32280 32000
Tu-204- 850 210 5200 12600 103,0 56,65 1750 22,00 27,00 1995 20 32280 32000
100 0
Tu-204- 850 210 5200 12100 103,0 56,65 1800 25,00 29,00 1997 26 39000 29900
120 0
Tu-204- 850 210 6200 12100 110,7 60,91 2050 30,00 35,00 1996 23 32280 32000
200 5
Tu-204- 850 210 3400 12600 86,00 47,30 2050 35,00 40,00 1997 22 32280 32000
300
Airbus 900 124 4910 11275 68,00 37,40 1750 35,00 35,00 1996 15 21340 23860
Industry
А319-110
Airbus 900 185 5000 10676 89,00 48,95 2000 46,20 51,00 1996 1000 29960 23700
Industry
А321-200
Analyzing this data, first of all, we will use one on the traditional comprehensive
performance criteria – fuel efficiency. In this case, the only Pareto-optimal object is
Tu-204-200, which rigid rating is equal to 100% (Column 2, Table 3). Its fuel effi-
ciency is equal to 19,66 44 grams/pass*km, while the nearest Tu-204-120 it is 23.44
grams/pass*km. At the same time, we can use the other criteria – weight efficiency,
which is calculated as the aircraft’s ration of takeoff weight to the number of passen-
gers. In this instance, the only Pareto-optimal variant with 100% rigid rating is anoth-
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er one object – Boeing Боинг 737-400 (Column 3 of Table 3), the weight efficiency
of which is 0,41 t/pass, whereas Tu-204-120 has 0,49.
Table 3. The result of data analysis for passenger aircrafts
Aircraft Rigid aircraft rating (%)
Complex Complex CJM (Fuel CJM (six characteristics
criterion – criterion – and weight distributed by three sig-
fuel efficien- weight effi- efficiency) nificance groups)
cy ciency
1 2 3 4 5
Boeing 737- 4
200
Boeing 737-
200
ADVANCE
Boeing 737- 0,1
300
Boeing 737- 100 2,9 8
400
Boeing 737-
500
Boeing 737-
600
Boeing 737-
700
Boeing 737- 86,2 67,6
800
Tu-204
Tu-204-100
Tu-204-120
Tu-204-200 100 4,1
Tu-204-300
Airbus Indus-
try А319-110
Airbus Indus- 2,8 24,3
try А321-200
Total 100 100 100 100
Let us use confident judgments method to analyze the data. If we suppose that the
decision-maker wants to use both of complex criteria, which were mentioned above,
without giving preferences to any of them in order to organize data, we will receive
the results shown in column 4 of Table 3. In this case, fire aircrafts are worthy of
consideration (Pareto-optimal): Boeing 737-800, Tu-204-200, Boeing 737-200, Boe-
ing 737-400 and Airbus Industry A321-200, while their efficiency was compared in
relative scale. According to this, Boeing737-800 leads by a wide margin – its rigid
rating is equal to 86,2%. Each of other listed aircrafts has only few percent of rigid
rating.
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However, applying confident judgments method, there is no need to bring subjectivity
in the data analysis, coupled with the use of traditional complex criteria. It is enough
to list the primary characteristics which are significant to the maintenance viewpoint.
They are:
Cruise speed,
Number of passengers,
Range,
Minimum price in passenger variant,
Maximum price in passenger variant,
Fuel capacity.
Cruise speed and number of passengers are the most significant criteria. Taking into
account the variety of routes for various distances, on which aircrafts are operated
within its capabilities, the range and fuel capacity are the following on the im-
portance. They also influence on the running costs, as they are transferred to the min-
imum and maximum ticket price of an aircraft. Thus, the criteria are distributed into
three groups of significance. The results are shown in column 5 of Table 3. Boeing
737-800 saves leading positions, and Airbus Industry A321-200 follows it with a
considerable margin.
Conclusion
Thus, the article shows that the application of confident judgments method for analy-
sis of large databases opens new flexible opportunities for its users.
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