INTELLECTUAL DATA ANALYSIS IN AIRCRAFT DESIGN V.A. Koarov 1, S.A. Piyavskiy 2 1 Saara National Research University, Saara, Russia 2 Saara State Architectural University, Saara, Russia Abstract. This article considers the use of confidence judgents ethod by decision-akers to analyze the inforation contained in large databases. The coparative analysis of passenger aircrafts shows that it allows flexibly and objectively allocating the ost relevant inforation fro the data array. Keywords: data analysis, aircraft design, large databases, decision-akers, confident judgents. Citation: Koarov VA, Piyavskiy SA. Intellectual data analysis in aircraft design. CEUR Workshop Proceedings, 216; 1638: 873-881. DOI: 1.18287/1613-73-216-1638-873-881 Introduction The eergence 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 becoes possible to estiate coprehensively, over a large nuber of characteristics, both quantitative and qualitative, the efficiency of different variants of design decisions against a background of a huge aount of analogues. It is also iportant to keep in ind that the project activity has largely heuristic nature, based on a cobination of objective quantitative analysis within intuitive the designers ideas, arising ipulses of which ay the expand and transfer the attention focus, and even change the design paradig itself. The echanis of using large databases for the design of coplex, ultifunction objects such as aircraft should be oriented towards these features. In our opinion, it is advisable to use soe advanced ethods of coplex decision theory, such as ulti-criteria optiization, during the foration of such echanis. One of the ain advantages of these ethods is that they provide an adequate active role of decision-akers along with the use of axioatic approach to the inforation analysis. For all the variety of decision-aking ethods [1,2], a decision-aking ethod under irreovable uncertainly [3,4] and confident judgents ethod (CJM) are the ost efficient ethods fro this points of view. The article is aied to deonstrate opportunities offered by the application of these techniques during intellectual data analysis. The considered exaples are given with great siplifications. Inforation Technology and Nanotechnology (ITNT-216) 873
Each object, denoted by y in the following, is described by a set of data which is useful to divide into two groups. In the first group it is advisable to include the data which deterine how an object is arranged and which can be changed by decisionakers. In ters of non-linear atheatical prograing, 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 custoers, as a rule, in the for of axiu and iniu values. Further, we will denote the as a particular optial criterion f i (y). In ost cases, the particular efficiency criteria for coplex technical objects are contradictory, which generates the well-known proble of ulti-disciplinary optiization. In aviation, for exaple, two iportant characteristics are in such conflict: the aircraft weight and aerodynaic efficiency. Increasing the aerodynaic quality is achieved by the wing lengthening, but it increases its weight [7,8]. Introducing new nondiensional load-carrying coefficient of structural perfection into consideration allows to carry out the optiization of aircraft appearance taking into account both weight and aerodynaic efficiency [9]. However, the design of new aircraft and, particularly, the developent of technical specification for its creation, needs analysis and taking into account a variety of paraeters, which can allow to predict the success of a new project by the consuer. Rating Estiation Method Let us consider a corporate database for the aircrafts as a set Y of objects y Y, which are characterized by -diensional vectors 1 2 f ( y) { f ( y), f ( y),..., f ( y)}, y Y. The coponents of these vectors are separate efficiency characteristics of the object, which are of interest fro the viewpoint of decision-akers. For exaple, a passenger aircraft has the following characteristics considered fro an operational point of view: Cruise speed, k/h Nuber of passengers, pers Flight range, k Service ceiling, Runway length, Miniu price in passenger version, illion USD Maxiu price in passenger version, illion USD Starting year of anufacturing Nuber of built aircrafts Engine power, kgf Fuel capacity, l Traditionally, the siplest way to analyze this data array is to sort by the values of f j, j 1,...,. It allows to define the locations according to any characteristics solution variants for this characteristic aong analogues. However, since the solution Inforation Technology and Nanotechnology (ITNT-216) 874
efficiency, in general, is deterined ainly 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 objects which are Pareto efficient. The object is considered as Pareto efficient if there do not exist at least one doinant object on the entire considered set. It eans that any object according to the characteristics not worse, and at least one - better. Thus, aong the aircrafts, whose characteristics are given in Table 1 (data are taken fro [7] and other sources, partly odeled and have purely ethodological nature), Pareto efficient are 2, 4, and 2 Advance is not efficient as it is doinated by. Table 1. Soe characteristics of s aircrafts Aircrafts Flight range, k Ceiling, 2 Advance 296 167 3 467 12 4 387 113 113 Run way length, 183 194 192 13 Engine thrust, kgf 178 1994 2134 1816 Fuel capacity, l 193 21 2382 21 The rigorous forulation of Pareto efficient object is the following: j j j j y Y : ( f ( y) f ( y) j 1,..., ) ( j {1,..., }: f ( y) f ( y))) Analysis of Pareto efficiency allows decision-akers to exclude obviously inefficient objects fro consideration, but it does not provide inforation about how uch the objects which reain in consideration, are relatively effective. It is necessary to use techniques that allow to proportion the coparative significance of individual objects fro the position of a holistic estiation of their efficiency. It eans that we need to find an adequate way of coparing the individual characteristics of objects s after which the object s coprehensive efficiency estiation purely atheatical way as F y) Fs ( f ( y)), y Y y Y is deterined by (. There are a nuber of established proportion ethods in each subject field. In aviation, fuel efficiency and weight efficiency, as well as several others are used as a coplex criterion during aircraft s coparative estiation. The disadvantage of this approach is that the objective criteria are iportant, 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 sae extend authoritative criterion, could lead to other conclusions. The universal construction ethods of criteria convolution are ore reliable. The ost faous of these is the linear convolution ethod, in which various characteris- Inforation Technology and Nanotechnology (ITNT-216) 87
tics are assigned nuerical weight coefficients of relative iportance. It is considered, that they can be obtained by averaging the opinion of any experts, involved by decision-akers for this purpose. Then F ( f ) j 1 j j j j f,, j 1,...,, 1, j, j 1,..., where - weight coefficients. The use of this ethod cannot be recoended during the design of such iportant objects as an aircraft for two ain reasons. j 1 Confident judgents Let us notice, that the decision-aker ade two judgents by choosing it: First of all, exactly this kind of account ethod for uncertainty in the for of linear convolution is fully adequate for this decision-aking task, Secondly, exactly the chosen experts, the exaination organization and ethods of expert opinion processing load to absolutely reliable values of weight coefficients. Fig. 1. Exaple of incorrect linear convolution Both judgents can be challenged by reasonable positions. First of all, the linear convolution ay not see soe Pareto-optial objects for any values of weight coefficients. For instance, on Figure 1 all objects for two iniized objects, iages of which lie above the dotted line in a criterion space, will not be recognized as the ost rational for any weight coefficient values in linear convolution, although they are Pareto-optial objects [4]. Thus, this exaple shows that the use of the linear convolution penalizes a natural requireent for ultiple coparison ethods of individual object s characteristics S: any Pareto-optial variant fro the set of adissible solutions ust correspond to at least one function F s (f) S, the use of which provide the ost rational solution. If this requireent is failure to coply, it reduces the select possibilities of decision-akers by purely atheatical features of the aircraft, which is unacceptable. The subjectivity of weight coefficients deterination by eans of expert exaination is evident. In addition, the need to attract qualified experts when- Inforation Technology and Nanotechnology (ITNT-216) 876
ever the decision-aker wants to take a new look at the situation, greatly reduces the data analysis capabilities. Actually, the decision-aker can reasonably ake only two types of judgents. The confident judgent of the first type. Decision-aker person (DMP) with his confidence ay include various particular criteria to different group of iportance. For exaple, criteria 1 and 4 are the ost iportant ones, criteria 2 and 6 are erely iportance, and criterion has the lowest iportance. Let us note, that we do not assue that decision-aker provide a qualitative estiation of the relative iportance degree for particular criteria, it refers only to the qualitative coparison which is optional. The confident judgent of the second type. If desired, the decision-aker can construct the pairs of Pareto-incoparable 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 f 1 and f 2 in which f 1 is surely better than f 2, it ipleents the following restriction on the set S: S s)} : F ( f ) F ( f ) s S { s 1 s 2. Based only on these two types of judgents, the ethod which proportion particular characteristics into a single nuerical object s characteristic, represented in the database, was developed in [,6]. It is called confident judgents ethod. Stages of confident judgents ethod Stage 1. The uncertainty profile is constructed for the solving proble. It shows the range of coplex 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: inorant (y) = in F(f(y)) and ajorantm(y) = in F(f(y)). s S s S It should be noted, that obviously irrational decisions z Y, for which there are bet- z Y by coplex criterion in all possible ways of uncertainty, can be ter solutions identified. The identify conditions for such solutions have the following for: z Y : M( z) ( z). The ain purpose of uncertainty profile is to give decision-akers inforation about the ipact of uncertainty during decision-aking in the proble. Adding confident judgents, he will be able to estiate how they reduce the uncertainty. Stage 2. If it is possible, the set of uncertainties narrows by taking into account the decision-aker s confident judgents. The uncertainty accounting ethods, which do not correspond to this judgents, are eliinated when we are using confident judgents of the first type. When we have got the confident judgents of the second type, conditions (6) are added to the set description, which eliinates those uncertainty accounting ethods that do not carry out these judgents. At the end of first two stages the initial set of uncertainties can be narrowed. This affect the uncertainty profile of the proble, but it is unlikely to reain only a single eleent in it, or all variants except one will be eliinated fro the plurality of solu- Inforation Technology and Nanotechnology (ITNT-216) 877
tions. Thus, the uncertainty retained in the proble. This will be a fatal uncertainty. All uncertainty account ethods, which for this fatal uncertainty, are copletely equal to the decision-aker as he has already use his ability to ake additional content in the proble description using judgents of the first and second types. It is possible that the other types of confident judgents of decision-akers can be found, but they did not fundaentally change the situation: after their usage, fatal uncertainty will reain in the proble. 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 coplex atheatical apparatus, we shall assue that the set contains a finite nuber of uncertainty accounting ethods S: S= {S k } k 1,..., K. Then the rigid rating RG(y) for y Y solution is a fraction of uncertainty accounting ethod, in which the solution is the best copared to the other solutions: k 1 K 1 F k ( y) F k ( z) z Y RG( y), K y Y (If any uncertainty accounting ethod has several best solutions, we should write 1 p instead of 1 in the nuerator of rigid rating). Soft Rating RM(y) for y Y decisions displays the average coprehensive efficiency if this solution copared with solutions, which are the best in different ways of uncertainty concideration: K Fs ( f ( y)) k ax Fs ( f ( y)) y Y k RM 1 K k. Stage 4. Decision-aker recognize that the possibility of further uncertainty reducing is exhausted due to its confident judgents. Finally, he chooses a solution with the best (lowest) rigid rating as the ost efficient solution. If there are several solutions, we will choose the one, which has the best (lowest) soft rating, as the ost efficient solution. Data analysis using confident judgents ethod Let us show the use of confident judgents ethod for data analysis of passenger aircrafts in ters of their operational characteristics. Table 2 shows a fragent of the database. Inforation Technology and Nanotechnology (ITNT-216) 878
Table 2. A fragent of database for passenger aircrafts Aircrafts Cruise speed, k/h Passengers, pers Flight range, k Service ceiling, Take-off weight, t Weight of epty aircraft, t Runway length, Min. price in passengers variant, il. USD Max.price in passengers variant, il. USD Year of serial anufacturing Aircraft Built in Total Engine power, kgf Fuel capacity, l 737-2 737-2 Advance 737-3 737-4 737-9 12 296 167 49,4 27,17 183 3, 11, 1967 366 1316 179 9 12 37 167 8, 31,9 183 3, 11, 1984 86 178 162 91 128 467 12 62,8 34,4 194 1, 44, 1984 112 1994 21 91 168 387 113 68,1 37,46 192 18, 48, 1988 46 2134 2382 91 18 113 6, 33,3 13 33, 39, 199 38 1816 21 737-6 737-7 92 18 91 12 6,9 3,8 188 32, 39, 1998 2 1816 263 92 128 92 12 69,4 38,17 24 39, 46, 1997 1 2183 263 г 92 189 37 12 78,24 43,3 24 48, 4, 1998 2 2386 263 737-8 Tu-24 8 21 37 126 94,6 2,3 1 2, 2, 1994 1 3228 32 Tu-24-1 Tu-24-12 Tu-24-2 Tu-24-3 Airbus Industry А319-11 Airbus Industry А321-2 8 21 2 126 13, 6,6 17 22, 27, 199 2 3228 32 8 21 2 121 13, 6,6 18 2, 29, 1997 26 39 299 8 21 62 121 11,7 6,91 2 3, 3, 1996 23 3228 32 8 21 34 126 86, 47,3 2 3, 4, 1997 22 3228 32 9 124 491 1127 68, 37,4 17 3, 3, 1996 1 2134 2386 9 18 1676 89, 48,9 2 46,2 1, 1996 1 2996 237 Analyzing this data, first of all, we will use one on the traditional coprehensive perforance criteria fuel efficiency. In this case, the only Pareto-optial object is Tu-24-2, which rigid rating is equal to 1% (Colun 2, Table 3). Its fuel efficiency is equal to 19,66 44 gras/pass*k, while the nearest Tu-24-12 it is 23.44 gras/pass*k. At the sae tie, we can use the other criteria weight efficiency, which is calculated as the aircraft s ration of takeoff weight to the nuber of passengers. In this instance, the only Pareto-optial variant with 1% rigid rating is anoth- Inforation Technology and Nanotechnology (ITNT-216) 879
er one object Боинг 737-4 (Colun 3 of Table 3), the weight efficiency of which is,41 t/pass, whereas Tu-24-12 has,49. Table 3. The result of data analysis for passenger aircrafts Aircraft Rigid aircraft rating (%) Coplex criterion fuel efficiencciency Coplex criterion weight effi- CJM (Fuel and weight efficiency) CJM (six characteristics distributed by three significance groups) 1 2 3 4 4 2 2 ADVANCE,1 3 1 2,9 8 4 6 7 8 86,2 67,6 Tu-24 Tu-24-1 Tu-24-12 Tu-24-2 1 4,1 Tu-24-3 Airbus Industry А319-11 Airbus Industry А321-2 2,8 24,3 Total 1 1 1 1 Let us use confident judgents ethod to analyze the data. If we suppose that the decision-aker wants to use both of coplex criteria, which were entioned above, without giving preferences to any of the in order to organize data, we will receive the results shown in colun 4 of Table 3. In this case, fire aircrafts are worthy of consideration (Pareto-optial): 8, Tu-24-2, 2, 737-4 and Airbus Industry A321-2, while their efficiency was copared in relative scale. According to this, 737-8 leads by a wide argin its rigid rating is equal to 86,2%. Each of other listed aircrafts has only few percent of rigid rating. Inforation Technology and Nanotechnology (ITNT-216) 88
However, applying confident judgents ethod, there is no need to bring subjectivity in the data analysis, coupled with the use of traditional coplex criteria. It is enough to list the priary characteristics which are significant to the aintenance viewpoint. They are: Cruise speed, Nuber of passengers, Range, Miniu price in passenger variant, Maxiu price in passenger variant, Fuel capacity. Cruise speed and nuber of passengers are the ost 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 iportance. They also influence on the running costs, as they are transferred to the iniu and axiu ticket price of an aircraft. Thus, the criteria are distributed into three groups of significance. The results are shown in colun of Table 3. 737-8 saves leading positions, and Airbus Industry A321-2 follows it with a considerable argin. Conclusion Thus, the article shows that the application of confident judgents ethod for analysis of large databases opens new flexible opportunities for its users. References 1. Larichev O. Theory and ethods for decision-ethods. Logos, 2; 29. 2. Larichev O. Verbal decision analysis. ISI RAS, Science, 26; 181. 3. Sirnov O, Padalko S, Piyabskiy S. CAD: the foration and functioning of project odules. Mechanical engineering, 1987; 272. 4. Malyshev V, Piyavskiy B, Piyavsliy S. Decision-aking ethods taking into account the variety of uncertainty conditions. Izvestiya RAS, Theory and control systes, 21; 1: 46-61.. Piyavskiy S. Two new top-level concepts in the ontology of ulti-criteria optiization. Designing ontology, 213; 1(7): 6-68. 6. Malyshev V, Piyavskiy S. Confident judgents ethod for aking ulti-criteria decisions. RAS, Theory and control systes, 21; : 9-11. 7. World passenger aircrafts. Argus, 1997; 336. Inforation Technology and Nanotechnology (ITNT-216) 881