interpolation capability of the resulting thrust model are demonstrated in predicting thrust values under all flight conditions for the Pratt & Whitne

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1 Journal of hina Institute of Technology Vol Fuzzy-ogic Thrust Model for a Twin-Jet Transport Aircraft Ray. hang Ting-Han in un-en Ye ,3 Aviation Mechanical Engineering Dept., hina Institute of Technology 2 Graduate School of Aircraft System Engineering, hina Institute of Technology (QAR) (Pratt & Whitney) (QAR) ABSTRAT The thrust values of aircraft are not directly measured during the flight in the current state of the art due to the bottleneck of sensor technology. Therefore, the flight data recorder does not have the recorded thrust data. The thrust terms are three forces, mainly the axial force, and pitching moment in flight dynamic equations. To set up an accurate thrust model is quite important for flight simulations in desktop simulator. The main objective of this paper is to present an engineering approach of thrust model development through a fuzzy-logic algorithm based on the flight data from Quick Access Recorder (QAR) and flight operation manual. The robustness and nonlinear 491

2 interpolation capability of the resulting thrust model are demonstrated in predicting thrust values under all flight conditions for the Pratt & Whitney engines powering a twin-jet transport aircraft will be illustrated in this paper. Keywords: fuzzy-logic algorithm, Fuzzy ogic Modeling, Thrust model, Quick Access Recorder (QAR) I. 95 [1] [2, 3] [4] (EPR) (M) (EPR) 492

3 Journal of hina Institute of Technology Vol [5] (IAS, Indicated air speed) (AS, alibrated air speed) (TAS, True air speed) (EAS, Equivalent air speed) (FM, Fuzzy-ogic Modeling) (FM) Takagi Sugeno 1985 [6] FM (Neural Nets) (Applied Artificial Intelligent Techniques) FDR(Flight Data Recorder) FM [7] FM (Fuzzy Variable) (Range) (Membership Function) (Input Variables) (Internal Functions) (Membership Grades) (Flight Profile) 493

4 II. (Pratt & Whitney) (EPR) (h) (W) (M) (AS) (EPR) (fuel flow rate) T = f (h, W, M, AS, EPR, fuel flow rate) (1) x 1 Fx A x T x 1 - (Nonlinear Dynamic Numerical Analysis Method) FDR (oupling Effects) [8, 9] 494

5 Journal of hina Institute of Technology Vol [10] F = ma = qs + T (2) x x x x F = ma = q S + T (3) y y y y F = ma = q S + T (4) z z z z M = m q S c = I yy q& I xz (r 2 p 2 ) (I zz I xx )rp T m (5) (2)~ (5) F x, F y, Fz x, y z ; T x, T, Tz y x, y z ; M T m (ompatibility heck) (Kinematic Equations) III

6 T install T install = f 1 (h, W, M, AS, EPR, fuel flow rate) (6) Thrust = f 1 (h, W, M, AS, N 1, fuel flow rate) (7) (6) (7) QAR(Quick Access Recorder) FDR (7) (GE, General Electric) (N 1 /D [10] A R B /D h(ft) W(lb) M AS(ft/sec) EPR fuel flow rate (lb/hr)

7 Journal of hina Institute of Technology Vol ( h ) (AS) (α ) ( δ e ) ( δ a ( δ r ) ( V w ) ( q ) = 2 D f (h, AS,α, T install, δ e, δ, a δ, V r w, q ) (8) =17.5 D D (thrust) 2 h(ft) W(lb) M AS (ft/sec) 2. EPR fuel flow rate(lb/hr) thrust(lb) /D=17.5 T D 17.5 (6) (7) D D D 497

8 = f (h, W, M, AS) (8) = f (M, ) (9) D D 0.65 (8) (9) M=0.65 (8) (9) D 3 4 D (8) (9) 3. h(ft) W(lb) M AS(ft/sec)

9 Journal of hina Institute of Technology Vol ( ) h(ft) W(lb) M AS(ft/sec) D M D

10 4. ( ) M D FDR QAR W g dv dt = T D W sinγ (10) D D T W D 1 dv sin γ = 0 (11) W g dt 500

11 Journal of hina Institute of Technology Vol D D = cos γ (12) W IV. 2 R 2 = h AOA MAH AS EPR fflow T/W D/ 2 5 1/5 Hz 5(c) 7(c) 8 Hz 8 Hz 2 501

12 3 3 EPR 4 502

13 Journal of hina Institute of Technology Vol

14 7 4 (AS) 5 EPR D/( ) 8,280 D/ T/W AS D/ 6 EPR 7 EPR 504

15 Journal of hina Institute of Technology Vol D/ V. (EPR) (N 1 ) EPR N 1 NS E [1] hang, Ray., hu, Kuang-Hua, Ye, un-en, an,. E., Guan, Michael, and ee, Yannian, Multi-Purpose Desktop Flight Simulator and Flying Qualities Evaluation System, NS E , National Science ouncil, Nov [2] hang, Ray., Ye, un-en, an,. Edward, and Guan, Wen-in, "Flying Qualities for a Twin-Jet Transport in Severe Atmospheric Turbulence," accepted for publication by the, AIAA Journal of Aircraft, March,

16 [3] hang, Ray., Ye, un-en, an,. Edward, and Guan, Wen-in, "Hazardous evels of ommercial Aircraft Response to Atmospheric Turbulence," accepted for publication by the, Transactions of the Japan Society for Aeronautical and Space Sciences, May [4] " EPR " Vol.10, No.8, Aug [5] an,. E. and Roskam, J., Airplane Aerodynamics and Performance, DAR corporation, awrence, KS 66044, 1981, 1988, 1997, [6] Takagi, T. and Sugeno, M., Fuzzy Identifications of Systems and Its Applications to Modeling and ontrol, IEEE Transactions on Systems, Man and ybernetics, Vol. SM-15, No. 1, January/February 1985, pp [7] Wang, Z., i, J., an,. E. and Brandon, J. M., Estimation of Unsteady Aerodynamic Models from Flight Test Data, AIAA Paper , August [8] Pan,. and an,. E., Estimation of Aerodynamic haracteristics of a Jet Transport Using Accident FDR Data, AIAA Paper , Aug [9] hang, Ray., an,. Edward, and Su, Shen-Jwu, "An Expert System for the FOQA Program," Journal of Aeronautics, Astronautics and Aviation, Series A, Vol. 39, No. 1, March 2007, pp [10] Roskam, J., Airplane Flight Dynamics and Automatic Flight ontrols, Part I, DAR orporation, awrence, Kansas, [11] " (A Study of Fuzzy-ogic Thrust Model for Jet Transport)" 2007 /

[9] R Ã : (1) x 0 R A(x 0 ) = 1; (2) α [0 1] Ã α = {x A(x) α} = [A α A α ]. A(x) Ã. R R. Ã 1 m x m α x m α > 0; α A(x) = 1 x m m x m +

[9] R Ã : (1) x 0 R A(x 0 ) = 1; (2) α [0 1] Ã α = {x A(x) α} = [A α A α ]. A(x) Ã. R R. Ã 1 m x m α x m α > 0; α A(x) = 1 x m m x m + 2012 12 Chinese Journal of Applied Probability and Statistics Vol.28 No.6 Dec. 2012 ( 224002) Euclidean Lebesgue... :. : O212.2 O159. 1.. Zadeh [1 2]. Tanaa (1982) ; Diamond (1988) (FLS) FLS LS ; Savic