Journal of hina Institute of Technology Vol.40-2009.06 Fuzzy-ogic Thrust Model for a Twin-Jet Transport Aircraft 1 2 3 Ray. hang Ting-Han in un-en Ye 1 2 3 1,3 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
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
Journal of hina Institute of Technology Vol.40-2009.06 [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
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
Journal of hina Institute of Technology Vol.40-2009.06 [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. 3.1 495
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 17.5-18.0 [10] A-300-600R B-757-200 /D 17.5 1 1. h(ft) W(lb) M AS(ft/sec) EPR fuel flow rate (lb/hr) 23000. 230000. 0.584 252. 1.070 4163. 25000. 230000. 0.606 251. 1.085 4160. 27000. 230000. 0.648 258. 1.099 4300 31000. 230000. 0.713 262. 1.145 4408. 35000. 230000. 0.765 259. 1.209 4431 39000. 230000. 0.777 240. 1.316 4337. 23000. 240000. 0.591 255. 1.077 4318. 25000. 240000. 0.627 260. 1.090 4427. 23000. 250000. 0.607 262. 1.083 4557. 27000. 250000. 0.706 283. 1.117 4986. 31000. 250000. 0.720 265. 1.170 4705. 35000. 250000. 0.774 262. 1.244 4744. 39000. 250000. 0.790 245. 1.391 4839. 3.2 496
Journal of hina Institute of Technology Vol.40-2009.06 ( 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) 23000. 230000 0.58400 252.0 1.0700 4163.0 6571.4 0.40179 0.022959 25000. 230000 0.60600 251.0 1.0850 4160.0 6571.4 0.40688 0.023251 27000. 230000 0.64800 258.0 1.0990 4300.0 6571.4 0.38859 0.022205 31000. 230000 0.71300 262.0 1.1450 4408.0 6571.4 0.38448 0.021970 35000. 230000 0.76500 259.0 1.2090 4431.0 6571.4 0.40266 0.023009 39000. 230000 0.77700 240.0 1.3160 4337.0 6571.4 0.47294 0.027025 23000. 240000 0.59100 255.0 1.0770 4318.0 6857.1 0.40939 0.023393 25000. 240000 0.62700 260.0 1.0900 4427.0 6857.1 0.39661 0.022663 23000. 250000 0.60700 262.0 1.0830 4557.0 7142.9 0.40426 0.023100 27000. 250000 0.70600 283.0 1.1170 4986.0 7142.9 0.35583 0.020333 31000. 250000 0.72000 265.0 1.1700 4705.0 7142.9 0.40983 0.023419 35000. 250000 0.77400 262.0 1.2440 4744.0 7142.9 0.42756 0.024432 39000. 250000 0.79000 245.0 1.3910 4839.0 7142.9 0.49729 0.028417 3.3 /D=17.5 T D 17.5 (6) (7) D D D 497
= 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) 15000.00 250000.00 0.2500 124.6514 1.7088 10000.00 250000.00 0.2500 137.4709 1.4023 5000.00 250000.00 0.2500 151.0427 1.1590 5000.00 250000.00 0.2500 151.0427 1.1590 15000.00 300000.00 0.2500 124.6514 2.0505 10000.00 300000.00 0.2500 137.4709 1.6827 5000.00 300000.00 0.2500 151.0427 1.3908 5000.00 300000.00 0.2500 151.0427 1.3908 15000.00 350000.00 0.2500 124.6514 2.3923 10000.00 350000.00 0.2500 137.4709 1.9632 5000.00 350000.00 0.2500 151.0427 1.6226 5000.00 350000.00 0.2500 151.0427 1.6226 15000.00 250000.00 0.4500 226.0092 0.5274 10000.00 250000.00 0.4500 248.7290 0.4328 5000.00 250000.00 0.4500 272.6253 0.3577 5000.00 250000.00 0.4500 272.6253 0.3577 15000.00 300000.00 0.4500 226.0092 0.6329 10000.00 300000.00 0.4500 248.7290 0.5194 5000.00 300000.00 0.4500 272.6253 0.4293 5000.00 300000.00 0.4500 272.6253 0.4293 15000.00 350000.00 0.4500 226.0092 0.7384 498
Journal of hina Institute of Technology Vol.40-2009.06 3. ( ) h(ft) W(lb) M AS(ft/sec) 10000.00 350000.00 0.4500 248.7290 0.6059 5000.00 350000.00 0.4500 272.6253 0.5008 5000.00 350000.00 0.4500 272.6253 0.5008 4. D M D 0.2500 0.3500 0.0239 0.2500 0.4500 0.0272 0.2500 0.5500 0.0314 0.2500 0.6500 0.0363 0.2500 0.7500 0.0421 0.2500 0.8500 0.0487 0.2500 0.9500 0.0561 0.2500 1.0500 0.0644 0.2500 1.1500 0.0734 0.2500 1.2500 0.0834 0.2500 1.3500 0.0941 0.2500 1.4500 0.1056 0.2500 1.5500 0.1180 0.2500 1.6500 0.1312 0.2500 1.7500 0.1452 0.2500 1.8500 0.1601 0.2500 1.9500 0.1758 0.2500 2.0500 0.1923 0.2500 2.1500 0.2096 0.2500 2.2500 0.2278 0.4500 0.3500 0.0239 0.4500 0.4500 0.0272 0.4500 0.5500 0.0314 0.4500 0.6500 0.0363 0.4500 0.7500 0.0421 499
4. ( ) M 0.4500 0.8500 0.0487 0.4500 0.9500 0.0561 0.4500 1.0500 0.0644 0.4500 1.1500 0.0734 0.4500 1.2500 0.0834 0.4500 1.3500 0.0941 0.4500 1.4500 0.1056 0.4500 1.5500 0.1180 0.4500 1.6500 0.1312 0.4500 1.7500 0.1452 0.4500 1.8500 0.1601 0.4500 1.9500 0.1758 0.4500 2.0500 0.1923 0.4500 2.1500 0.2096 0.4500 2.2500 0.2278 3.4 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
Journal of hina Institute of Technology Vol.40-2009.06 D D = cos γ (12) W IV. 2 R 2 = 0.99986 h AOA MAH AS EPR fflow T/W D/ 2 5 1/5 Hz 5(c) 7(c) 8 Hz 8 Hz 2 501
3 3 EPR 4 502
Journal of hina Institute of Technology Vol.40-2009.06 5 6 503
7 4 (AS) 5 EPR D/( ) 8,280 D/ T/W AS D/ 6 EPR 7 EPR 504
Journal of hina Institute of Technology Vol.40-2009.06 D/ V. (EPR) (N 1 ) EPR N 1 NS 97-2221-E-157-002 [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 95-3114-E-157-002, National Science ouncil, Nov. 2007. [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, 2009. 505
[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 2009. [4] " EPR " Vol.10, No.8, Aug.1989. [5] an,. E. and Roskam, J., Airplane Aerodynamics and Performance, DAR corporation, awrence, KS 66044, 1981, 1988, 1997, 2003. [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. 116-132. [7] Wang, Z., i, J., an,. E. and Brandon, J. M., Estimation of Unsteady Aerodynamic Models from Flight Test Data, AIAA Paper 2001-4017, August 2001. [8] Pan,. and an,. E., Estimation of Aerodynamic haracteristics of a Jet Transport Using Accident FDR Data, AIAA Paper 2002-4494, Aug. 2002. [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. 29-36. [10] Roskam, J., Airplane Flight Dynamics and Automatic Flight ontrols, Part I, DAR orporation, awrence, Kansas, 2003. [11] " (A Study of Fuzzy-ogic Thrust Model for Jet Transport)" 2007 / 2007.11 506