Application of Fuzzy Abduction Technique in Aerospace Dynamics

The purpose of this paper is to apply Fuzzy Abduction Technique in aerospace dynamical problem. A model of an aeroplane is proposed for consideration at different air density level of the atmosphere and at different speed of the plane. Different air density of the atmosphere, angle of wings and speed of the plane are selected as parameters to be studied. In this paper a method is developed to determine the angle of wings of the plane with respect to its axis at different air density level of the atmosphere and at different speed of the plane. Data are given to justify our proposed method theoretically. Keywords—Fuzzy logic; Fuzzy abduction; Aerospace dynamics; Inverse Fuzzy relation


INTRODUCTION
Recently a good number of researchers had introduced abduction technique in aerospace dynamical problem.Abduction is an important tool to solve various problem including diagnosis and natural language understanding [4] , [ 7] .Also it is applicable in high level reasoning such as hypothetical reasoning [10] and default reasoning [ 3 ] .Pople [ 1 ] bases his discussion of firstorder logic and defined abduction as the procedure for derivation of hypothesis which explain a conjecture using an axiom set.Reggia [ 2 ] proposed abduction for diagnosis based on a relation between two sets .Bylander, et.al.[ 8 ] introduced plausibility (a map from the power set of hypothesis to a partially ordered set ) to abduction based on relation.K.Yamade,et.al.[9] studied fuzzy abduction based on multivalued logic and Y.Tsukamoro [11] has introduced fuzzy logic base on Lukasiewicz logic and its application to diagnosis and control .W.Pedrycz [ 13 ] has investigated numerical and applicational aspect of fuzzy relation equations and henceforth W.pedrycz [ 14 ] has introduced inverse problem in fuzzy relation equation .

Afterwards
Arnould, et.al.[15] have introduced -if…..then…..‖ rule in case backwardchaining with fuzzy .Bugarin, et.al.[16] have investigated fuzzy reasoning supported by Petri nets.When an aircraft moves through the air it passes through different atmospheric layers.Density varies due to change of atmospheric layers.So the aircraft passes through different air density level.The goal of the present paper is to determine what would be the angle the wings and aircraft velocity to keep constant forward velocity at a certain height of the aircraft for a certain air density level However, similar problems, as indicated above, in case of application of fuzzy abduction technique in aerospace dynamics have not been invested by any researcher in a similar approach.The authors considered when the air density is low then the speed of the aeroplane and angle of the wings are high and if air density is high the speed of the aeroplane and angle of the wings are low.If medium density of air is considered the speed of the aeroplane and angle of the wings are medium.Despite of importance of inference the concept has no standard definition.
In this paper authors propose a fuzzy abduction [18][19][20][21][22][23] method in aerospace dynamics.At first authors investigated modus pones and modus tolens in specific situation and showed that the inferred results were obtained as a truth value.Then the concept of derivation, fuzzy explanation and fuzzy abduction are introduced based on inference.Furthermore, the authors discussed necessary and sufficient conditions for the existence of fuzzy explanation and proposed a procedure to obtain approximate solution when the conditions are not satisfied.
In fine, the authors have illustrated this method by numerical examples.

II. DETERMINATION OF WING ANGLE AND SPEED USING FUZZY ABDUCTION
When an aircraft moves through the air, it propagates through different air density level because the atmospheric layers are changing.Suppose, at takeoff region the flight velocity is ω Km/m and air density level is medium.For this situation both the wings of the aircraft are at 90ᵒ from the axis of its body, shown in fig.www.ijacsa.thesai.orgIf the aircraft moves from this medium air density level to a lower air density level, it will moves down and the forward velocity will be decreased.To balance the height of the aircraft from the earth surface, the wings should be kept down to block more air and to develop a downward thrust so as to prevent the aircraft from moving down.Hence, both the wings of the aircraft should have an obtuse angle (i.e., >90ᵒ) from the axis of its body, shown in fig.B Fig. 2. Both the wings of the aircraft are at 120ᵒ angle from the axis of its body On the other hand, if the aircraft moves from the medium air density level to a higher air density level, it will move upward and the forward velocity will be decreased.To balance the height of the aircraft from the earth surface, the wings should be kept up to pass more air and to release air thrust so as to prevent the aircraft from moving upward.Hence, both the wings of the aircraft should have an acute angle (i.e., < 90ᵒ) from the axis of its body, shown in fig.C.Fig. 3.Both the wings of the aircraft are at 60ᵒ angle from the axis of its body

III. RESULTS
From above discussion, we refer the problem as, what would be wings angle and aircraft velocity to keep constant forward velocity and the height of the aircraft for a certain air density level?To solve this problem it is needed to know about the relationship between the wings angle and air density level, and also the aircraft velocity and air density level.For that we set 6 fuzzy rules which are given below.In Fuzzy Abduction technique, when we consider Aerospace Dynamics problem we faced several uncertainities.In this case,we consider when the plane goes through different layers we can see several changes have been occurred.Consider all of these problems we consider here fuzzy abduction method.
When the air density varied from low to high then the angle of wings also changed with the speed.wings angle and aircraft velocity to keep constant forward velocity and the height of the aircraft for a certain air density level we follow several rules of fuzzy abduction.From our simulation results we can calculate the wing's angle at different atmosphere.

Fig. 1 .
Fig. 1.Both the wings of the aircraft are perpendicular (90ᵒ) from the axis of its body

Rule 1 :
If wings angle is HIGH, air density will be LOW.Rule 2: If speed is HIGH, air density will be LOW.Rule 3: If speed is MEDIUM, air density will be MEDIUM.Rule 4: .If speed is LOW, air density will be HIGH.Rule 5: If wings angle is MEDIUM, air density will be MEDIUM Rule 6: If wings angle is LOW, then air density will be HIGH.Now, fuzzy membership curves for speed, wings angle and air density are defined.90̊ 120 www.ijacsa.thesai.org