Vladislav Klein

Estimation of aircraft aerodynamic parameters from flight data

Abstract Several ways for obtaining aerodynamic parameters of an aircraft from flight data are presented with the emphasis on present problem areas. The paper starts with a brief description of data analysis from steady measurements. Then, a concept of system identification applied to aircraft is introduced with a discussion of various steps in this procedure. This is followed by a formulation of a mathematical model of an aircraft with aerodynamic forces and moments approximated either by polynomials or splines. The main part contains a rather detailed treatment of two more often used techniques for parameter estimation. The first method is based on linear regression which can be extended to a stepwise regression for model structure determination and to data handling procedure, known as data partitioning. The second technique applies the maximum likelihood principle to measured data. In this part, mainly the output error estimation method is considered. The problem of near linear relationship among measured time histories is mentioned in a separate section together with some diagnostic measures and two estimation techniques dealing with this problem. Because of a renewed interest in the frequency domain analysis, one section of the paper is devoted to this problem. All the methods explained in the paper are demonstrated in several examples using real flight data.

Application of System Identification to Aircraft at NASA Langley Research Center

The past, present, and future of system identification applied to aircraft at NASA Langley Research Center (LaRC) in Hampton, Virginia, are discussed. Significant research advances generated at NASA LaRC in the past are summarized, including some perspective on the role these developments played in the practice of system identification applied to aircraft. Selected recent research efforts are described, to give an idea of the type of activities currently being pursued at NASA LaRC. These efforts include real-time parameter estimation, identifying flying qualities models, advanced experiment design and modeling techniques for static wind-tunnel database development, and indicial function identification for unsteady aerodynamic modeling. Projected future developments in the area are outlined

Accuracy of Aerodynamic Model Parameters / Estimated from Flight Test Data

Eugene A. Morelli*Lockheed Martin Engineering and Sciences Company, Hampton, Hrginia 23681-0001andVladislav Klein tGeorge Washington University and NASA Langley Research Center, Hampton, Virginia 23681-0001An important part of building mathemalical models based on measured data iscalculating the accuracy associ-ated with statistical estimates of the model parameters. Indeed, witheut some idea of this accuracy, the Imrameterestimates themselves have limited value. An expression is developed for computing quantitatively conreet param-eter accuracy measures for maximum likelihood parameter estimates when the output residuals are colored. Thisresult i_ important because experience in analyzing flight test data reveals that the output residuals from maximumlikelihood estimation are almost always ce/orod. The calculations involved can be appended to conventional maxi-mum likelihood estimation algorithms. Monte Carlo simulation runs were used to show that parameter accaracymeasures from the new technique accurately reflect the quality of the parameter estimates from maaimum likefi.hood estimation without the need for correction factors or frequency domain analy_ of the output residuals. Thetechnique was applied to flight test data from repeated maneuvers flown on the F-I8 High Alpha Research Vehicle.As in the simulated cases, parameter accuracy measures from the new technique were in agreement with the scatterin the parameter estimates from repeated maaeuvers, whereas conventional parameter accuracy measures wereoptimistic.Nomenclature z(i) = ith measured scalara_ = vertical acceleration, g z(i) = measured no x 1 output vector at time ff - 1)AtCL = lift coefficient ct = angle of attack, radCu = pitching moment coefficient At = sampie time, sCz = vertical force coefficient _ij = Kronecker delta= mean aerodynamic chord, ft 6, = stabilator deflection, radD = dispersion matrix ® = pitch angle, taddj/ = jth diagonal element of D 0 = element of the parameter vector 0E{.} = expected value 0 = n e x 1 parameter vectore(i) = ith equation error residual tr = Cram6r-Rao bound for the standard error ofg = gravitational acceleration, 32.174 ft/s 2 v(i) = measurement noise vector at time (i - 1)Atly = pitch axis moment of inertia, slug-ft2 Vo = gradient with respect to 0J = cost function • = roll angle, radM = information matrix 0 = zero vectorm = mass, slugN = total number of sample times Subscriptsno = number of outputsnp = number of parameters c = correctedq = body axis pitch rate, rad/s m = measured= dynamic pressure, lbf/ft 2 o = initial or biasR = discrete noise covariance matrix w = wind axes_,, = autocorrelation matrix of vector vS = wing area, ft2 SuperscriptsS(i) = output sensitivity matrix at time (i - 1)At T = transposes = sample standard error - 1 = matrix inverset = time, s ^ = estimateu(t) = control vector - = mean valueV = airspeed, ft/sv(i) = output residual vector at time (i - l)At = time derivativex(t) = state vectory(i) = noxl output vector at time (i --1)At Introductiony(t) = no x 1 output vector

Optimal Input Design for Aircraft Parameter Estimation using Dynamic Programming Principles

A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.

Nonlinear Unsteady Aerodynamic Modeling Using Wind Tunnel and Computational Data

Extensions to conventional aircraft aerodynamic models are required to adequately predict responses when nonlinear unsteady flight regimes are encountered, especially at high incidence angles and under maneuvering conditions. For a number of reasons, such as loss of control, both military and civilian aircraft may extend beyond normal and benign aerodynamic flight conditions. In addition, military applications may require controlled flight beyond the normal envelope, and civilian flight may require adequate recovery or prevention methods from these adverse conditions. These requirements have led to the development of more general aerodynamic modeling methods and provided the impetus for researchers to improve analytical and experimental techniques and the degree of collaboration between them. In addition to more general mathematical model structures, dynamic test methods have been designed to provide sufficient information to allow model identification. This paper summarizes research to develop a modeling...

Determining the Accuracy of Aerodynamic Model Parameters Estimated from Flight Test Data

An important part of building mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of this accuracy, the parameter estimates themselves have limited value. In this work, an expression for computing quantitatively correct parameter accuracy measures for maximum likelihood parameter estimates with colored residuals is developed and validated. This result is important because experience in analyzing flight test data reveals that the output residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Monte Carlo simulation runs were used to show that parameter accuracy measures from the new technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for correction factors or frequency domain analysis of the output residuals. The technique was applied to flight test data from repeated maneuvers flown on the F-18 High Alpha Research Vehicle (HARV). As in the simulated cases, parameter accuracy measures from the new technique were in agreement with the scatter in the parameter estimates from repeated maneuvers, while conventional parameter accuracy measures were optimistic.