Two biased estimation techniques in linear regression: Application to aircraft

Several ways for detection and assessment of collinearity in measured data are discussed. Because data collinearity usually results in poor least squares estimates, two estimation techniques which can limit a damaging effect of collinearity are presented. These two techniques, the principal components regression and mixed estimation, belong to a class of biased estimation techniques. Detection and assessment of data collinearity and the two biased estimation techniques are demonstrated in two examples using flight test data from longitudinal maneuvers of an experimental aircraft. The eigensystem analysis and parameter variance decomposition appeared to be a promising tool for collinearity evaluation. The biased estimators had far better accuracy than the results from the ordinary least squares technique

Analysis of flight data from a High-Incidence Research Model by system identification methods

Data partitioning and modified stepwise regression were applied to recorded flight data from a Royal Aerospace Establishment high incidence research model. An aerodynamic model structure and corresponding stability and control derivatives were determined for angles of attack between 18 and 30 deg. Several nonlinearities in angles of attack and sideslip as well as a unique roll-dominated set of lateral modes were found. All flight estimated values were compared to available wind tunnel measurements

On Problems Associated with Modeling Wing-Tail Configurations from Wind Tunnel Data

This paper considers factors that contribute to poor identification of unsteady aerodynamics from wind tunnel data for an airliner configuration. One approach to modeling a wing-tail configuration is considered and applied to both steady and large-amplitude forced pitch oscillation wind tunnel data taken over a wide range of angles of attack but a limited range of amplitude and frequencies. The identified models fit the measured data well but in some cases with inaccurate parameters. Only limited conclusions can be drawn from analysis of the current data set until further experiments can be performed to resolve the identification issues. The analysis of measured and simulated data provides some insights and guidance on how an effective experiment may be designed for wing-tail configurations with nonlinear unsteady aerodynamics

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

Transport Aircraft System Identification from Wind Tunnel Data

Recent studies have been undertaken to investigate and develop aerodynamic models that predict aircraft response in nonlinear unsteady flight regimes for transport configurations. The models retain conventional static and rotary dynamic terms but replace conventional acceleration terms with more general indicial functions. In the Integrated Resilient Aircraft Controls project of the NASA Aviation Safety Program one aspect of the research is to apply these current developments to transport configurations to facilitate development of advanced controls technology. This paper describes initial application of a more general modeling methodology to the NASA Langley Generic Transport Model, a sub-scale flight test vehicle

Transport Aircraft System Identification Using Roll and Yaw Oscillatory Wind Tunnel Data

Continued studies have been undertaken to investigate and develop aerodynamic models that predict aircraft response in nonlinear unsteady flight regimes for transport configurations. The models retain conventional static and dynamic terms but replace conventional acceleration terms with indicial functions. In the Subsonic Fixed Wing Project of the NASA Fundamental Aeronautics Program and the Integrated Resilient Aircraft Controls project of the NASA Aviation Safety Program one aspect of the research is to apply these current developments to transport configurations to facilitate development of advanced simulation and control design technology. This paper continues development and application of a more general modeling methodology to the NASA Langley Generic Transport Model, a sub-scale flight test vehicle. In the present study models for the lateral-directional aerodynamics are developed

Accuracy of Aerodynamic Model Parameters Estimated from Flight Test Data

An important put of building mathematical models based on measured date 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. An expression is developed for computing quantitatively correct parameter accuracy measures for maximum likelihood parameter estimates when the output residuals are colored. 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. 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, whereas conventional parameter accuracy measures were optimistic

Program of Research in Flight Dynamics, The George Washington University at NASA Langley Research Center

The program objectives are fully defined in the original proposal entitled Program of Research in Flight Dynamics in GW at NASA Langley Research Center, which was originated March 20, 1975, and in the renewals of the research program from January 1, 2003 to September 30, 2005. The program in its present form includes three major topics: 1. the improvement of existing methods and development of new methods for wind tunnel and flight data analysis, 2. the application of these methods to wind tunnel and flight test data obtained from advanced airplanes, 3. the correlation of flight results with wind tunnel measurements, and theoretical predictions

Estimation of Longitudinal Unsteady Aerodynamics of a Wing-Tail Combination From Wind Tunnel Data

This paper presents an initial step toward model identification from wind tunnel data for an airliner configuration. Two approaches to modeling a transport configuration are considered and applied to both steady and large-amplitude forced-oscillation wind tunnel data taken over a wide range of angles of attack. Only limited conclusions could be drawn from this initial data set. Although model estimated time histories of normal force and pitching moment agree reasonably well with the corresponding measured values, model damping parameters did not, for some cases, have values consistent with small amplitude oscillatory data. In addition, large parameter standard errors implied poor information content for model structure determination and parameter estimation. Further investigation of the modeling problem for more general aerodynamic models is recommended with close attention to experiment design for obtaining parameters with high accuracy

Determining the accuracy of maximum likelihood parameter estimates with colored residuals

An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data