intelligent support for aircraft flight test data processing in problem of engine thrust estimation

Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 103 (2017) 82 – 87 XIIth International Symposium «Intelligent Systems», INTELS’16, 5-7 October 2016, Moscow, Russia Intelligent support for aircraft flight test data processing in problem of engine thrust estimation O.N Korsuna,*, B.K Poplavskyb, S.Ju Prihodkoc a State Institute of Aviation Systems, Viktorenko str., Moscow 125319, Russia Gromov Flight Research Institute, 2A Garnaeva str., Zhukovsky 140180, Russia c Moscow Aviation Institute (National Research University), Volokolamskoe shosse, Moscow 125310, Russia b Abstract The report deals with the design of the intelligent support for flight test data processing in the problem of separate estimation of aircraft thrust and drag forces in flight experiment The thrust and drag identification belongs to the class of incorrect inverse problems, for which reason it is not to be solved by general system identification methods and their applications to aerodyna mic parameter estimation from the flight data The paper considers the specific aspects of the intelligent support for thrust and drag identification from the automatic estimation viewpoint of identification accuracy The proposed algorithms are tested at the set of data generated using a modern aircraft simulation facility © 2017The TheAuthors Authors.Published Published Elsevier © 2017 by by Elsevier B.V.B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the XIIth International Symposium «Intelligent Systems» Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” Keywords: aircraft; engine; flight test data; engine thrust estimation; estimation of aircraft drag forces; flight experiment; thrust identification; aircraft simulation facility Introduction In the problem of separate estimation of aircraft thrust and drag forces in flight experiment the thrust and drag identification belongs to the class of incorrect inverse problems1, for which reason it is not to be solved by general system identification methods and their applications to aerodynamic parameter estimation from the flight data2,3,4 The report develops the approach proposed in5 The paper considers the specific aspects of the intelligent support for * Corresponding author E-mail address: marmotto@rambler.ru 1877-0509 © 2017 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” doi:10.1016/j.procs.2017.01.017 83 O.N Korsun et al / Procedia Computer Science 103 (2017) 82 – 87 thrust and drag identification from the viewpoint automatic estimation of identification accuracy The proposed algorithms are tested at the set of data generated using a modern aircraft simulation facility Statement of the problem The problem is formulated in the system of the coordinate axes related to the plane As an example, let us consider the equation of forces acting on the aircraft along the x-axis associated with the aircraft: Px (t ) mgn x ( t )  C x ( t ) qS (1) where Px ( t ) - the projection of thrust; n x ( t ) - component of the vector overload; C x ( t ) - coefficient of drag aerodynamic force; q (t ) 0,5UV - dynamic pressure; m - aircraft weight; S - wing area Let us substitute into equation (1) the results of measurements performed in flight, comprising measurement errors The result: Px (t ) mgn x (t )  C x (t )q(t ) S  H (t ) (2) where H (t ) - equation discrepancy Let us assume measurement discretization interval being constant and denominate it as 't h Then the discrete time moments for N successive measurements made on the processing interval are as follows: ti hi , i N To solve the problem let us define the sliding base interval containing 2m  measurements of each parameter for the time moments >tk  m tk tk  m @ To simplify the calculations let us regard the mid-point of the sliding base interval as its zero point, believing tk Then for all the points of this sliding interval it’s possible to form the system of equations Px (t j ) mgn x ( t j )  C (t j ) q (t j ) S  H (t j ), ( j m m) (3) To identify the separate estimates of thrust Px (0) and drag coefficients C x (0) at the midpoint of the sliding base interval it is necessary to make a number of assumptions about the nature of changes of the parameters of flight within a sliding base interval, that is for time t  >t m tm @ Let's assume that T êt m ơô C x (t j ) tj t º, m »¼ Px (t j ) const C x (0)  C xa (0) ' a ( t j ), ( j Px (0) ,  m m ), where Px (0), C x (0), C D x (0), D (0) parameter values at the midpoint of the sliding 'D (t j ) D ( t j )  D (0) Then interval >t m tm @ , 84 O.N Korsun et al / Procedia Computer Science 103 (2017) 82 – 87 C x (t ) j C x (0)  C D x (0) 'D j , 'D j 'D ( t ), j Under these assumptions the system of equations (3) can be transformed into a system with the unknown parameters Px (0) , C x (0) , and CD x (0) : mgn x m  C x (0) q m S  C D x (0) 'D  m q m S  H  m , P (0) mgn x  C x (0) q j S  C D x (0) ' D j q j S  H j , j mgn x  C x (0) qm S  C D x (0) ' D m qm S  H m m P (0) P (0) In matrix form, this system may be presented as follows: Za Z mgN x  H , (4)  q m S ' D  m q m S 'D j q j S ; a q j S ' D m qm S  qm S P (0) C x (0) ; N x C xa n x m nx ;H n xm H m Hi Hm In the case of applying the method of least squares to find the unknown vector a the estimate a takes the form: a Z T Z 1 Z T N x mg (5) The dispersion matrix of vector a assuming the uncorrelated noises H j can be calculated using the formula: D >a @ V H2 Z T Z 1 (6) In a more detailed form the matrix Z T Z can be represented as: Z T Z  q m  q m ' D m S q S j q j S  q m S  qm S 1 q jS  qm ' D m S  qm S m m  S ¦ q j 'D j ¦ qj j m j m m m m 2 2 S ¦ q j S ¦ qj S ¦ q 'D j j m j m j m j m m m  S ¦ q j ' D j S ¦ q 2j ' D j S ¦ q 2j ' D 2j j m j m j m (2 m  1) S  q m ' D  m S  q 'D S j j  qm ' D m S 85 O.N Korsun et al / Procedia Computer Science 103 (2017) 82 – 87 This result shows that when q const the matrix Z T Z is singular, since, for example, rows and coincide with a constant factor  Sq Therefore, to ensure identifiability is necessary to change the dynamic pressure q , that is to change the velocity of the flight However, changes with respect to the mean value should be small (the exact value depends on the type of engine and flight mode) to satisfy the condition of constant thrust Px (0) in the interval of processing Velocity changes are performed at constant engine regime, by performing successive dives and pitching with a small angle of inclination of the trajectory Concretization of problems and solutions The above model is somewhat idealized In practical use, it is advisable to take into account that the aerodynamic coefficients of drag and lift forces are usually represented in a coordinate system, associated with the projection of the velocity vector to the aircraft symmetry surface The aerodynamic drag and lift coefficients in the vicinity of the horizontal flight as a steady path are defined by the formulas where с xe § D2 ·  ¨ c  cD x ˜D  cx ˜D ¸ , â x0 ye GB Đ Ã  ¨ c  cD y ˜D  c y ˜G B , y0 â (7) D - the angle of attack, degree; G B - deflection of the elevator In accepted coordinate system the overloads are expressed through the overload projections in the coordinate axes related to the plane by the formulas: n xe n x cos D  n y sin D , n ye n x sin D  n y cos D (8) It should also be appreciated that the engines are usually installed in such a manner that the engine axis forms with the longitudinal axis of the associated coordinate system installation angle of the engine M eng z In addition, the thrust vector, strictly speaking, is a sum vector of an input pulse Pin directed along the oncoming flow, and the pulse output vector Pout , directed along the axis of the engine nozzles We now obtain the final expressions for the projections overload on the axis, substituting the expansion of the aerodynamic coefficients (7): Pin Pout D2 qS ( c  cD cos(Ieng  D )  x D  cx D )  x0 mg mg mg n xe  n ye GB Pout sin(Ieng  D ) qS ( c  cD y D  cy GB )  y mg mg (9) To estimate the thrust and drag it’s enough to consider the first equation, since the effect of the output pulse in the second equation is insignificant at angles of attack appropriate to horizontal flight Using trigonometric ratio cos(Ieng  D ) cos Ieng cos D  sin Ieng sin D and approximation cos D |  (1 / 2)D , sin D | D , we obtain 86 O.N Korsun et al / Procedia Computer Science 103 (2017) 82 – 87 mg ˜ n xe  qSc x0 D2 2  qScD x D  qSc x D  Pin  Pout cos Ieng  Pout cos Ieng ˜ D  Pout sin Ieng ˜ D (10) The research method of mathematical modeling showed that, to ensure the identifiability of the system the input pulse Pin should be taken according to a priori data Then estimates of the drag coefficients, and the output pulse Pout can be determined by the standard method of least squares Testing the proposed method The proposed method was tested at the set of data generated using a modern aircraft simulation facility First the test maneuver was carried out as described above at a constant regime of engine operation The velocity change (the number of Mach) is shown in Figure The parameter estimates were calculated using the formula (5), parameters variance estimates from the formula (6) The calculations were performed on a sliding base interval 15 seconds long, moving step interval was set equal to the sampling interval 't / f reg , where f reg 32 Hz the registration rate The estimates of an output pulse Pout and estimates (6) of their variance are shown in Figures and From the set of estimates was chosen the one that corresponds to the minimum variance estimation (time 3.2 s) In this experiment, the estimation error was 1.7% Thus it is shown that variance estimates (6) enable to find the best thrust estimates in the sense of the minimum estimation error It is assumed that the correction of systematic measurement errors of angle of attack is carried out according to the method6,7 Fig Change in the Mach number Fig The true value of output pulse Pist and its estimate Poc O.N Korsun et al / Procedia Computer Science 103 (2017) 82 – 87 Fig The standard deviations of the output pulse estimates Conclusion In the article the method is proposed for the separate estimation of aircraft thrust and the aerodynamic drag coefficient using the results of measurements carried out in the flight tests It should be noted that the proposed approach does not require the use of mathematical models of a gas turbine engine, which gives it the advantages of flexibility and relative ease On the other hand, the individual results of bench tests or calculations for gas-dynamic engine models can be used to improve the robustness of evaluation results Acknowledgements This work was supported by the Russian Foundation for Basic Research (RFBR), 15-08-06237-a project References Krasovsky AA, editor The Theory of automatic control Manual Moscow: Nauka; 1987 Klein V, Morelli EA Aircraft system identification: Theory And Practice Reston: AIAA; 2006 Korsun ON, Poplavsky BK Approaches for flight tests aircraft parameter identification Proc of the 29 Congress of International Council of the Aeronautical Sciencies 2014; paper 2014-0210 Jategaonkar RV Flight vehicle system identification: A time domain methodology Reston: American Institute of Aeronautics and Astronautics; 2006 Korsun ON, Poplavsky BK, Prihodko S Ju Identification of the absolute value of the engine effeciency thrust based on the maximum likelihood method and customized models Proc of the VIII Aerospace International Congress 2015; p 106-107 Korsun ON, Poplavskii BK Estimation of systematic errors of onboard measurement of angle of attack and sliding angle based on integration of data of satellite navigation system and identification of wind velocity J Comp Syst Sci Intern 2011;50(1):130-43 Korsun ON, Nikolaev SV, Pushkov SG An algorithm for estimating systematic measurement errors for air velocity, angle of attack, and sliding angle in flight testing J Comp Syst Sci Intern 2016;55(3):446-57 87 ... thrust Px (0) in the interval of processing Velocity changes are performed at constant engine regime, by performing successive dives and pitching with a small angle of inclination of the trajectory... that the engines are usually installed in such a manner that the engine axis forms with the longitudinal axis of the associated coordinate system installation angle of the engine M eng z In addition,... facility Statement of the problem The problem is formulated in the system of the coordinate axes related to the plane As an example, let us consider the equation of forces acting on the aircraft along