Evaluation/Validation of Linear Flight Dynamics Models

Evaluation of a flight dynamic model implies checking the accuracy and adequacy of the identified model against the real system and to ensure that, to the extent possible, it is a true representation of the system. Evaluation methods can give valuable clues to the possible sources of error that might lead to discrepancies between the model output and flight measured response. Having done the model evaluation, one can use it to evaluate the aircraft dynamics, performance, and handling qualities. Such models are also useful in evaluating and updating flight-control systems or investi­gating aircraft design modifications.

Evaluation of the dynamic models can be done at two levels: (1) adequacy of the model structure and (2) adequacy and accuracy of the identified derivatives.

Since the dynamic models for fixed-wing aircraft and rotorcraft are based on phenomenological considerations, there is limited scope of making changes as far as the model structure is concerned. However, the set of derivatives to be identified from flight data is not always obvious, particularly if the system under consideration is operating in nonlinear regions.

The presence of too many secondary derivatives can lead to correlations among parameters, which can adversely affect the identification results. On the other hand, too few parameters can cause the model to produce an inadequate response match. There is no unique method to arrive at a reduced parameter model. One approach to recognize and retain significant parameters in the estimation model is to use stepwise linear regression [12]. Another approach is based on the Cramer-Rao bounds (CRB) of the derivatives. The CRB of the identified parameters are obtained from the information matrix, which is anyway computed by the output error algorithm during the estimation process. Derivatives that are secondary in nature and show exception­ally high standard deviations are dropped (fixed to zero) from estimation each time
the model is reconverged. Though time consuming, this approach helps to provide a reduced parameter set for identification.

Compared to fixed-wing aircrafts, helicopters pose greater modeling problems because of their highly cross-coupled and nonlinear dynamic behavior. Nonlinea­rities in helicopters could arise from compressibility effects, tip vortices, blade elasticity, inflow dynamics, lead-lag effects, torsion, etc. and significantly alter the flow field over the blades. The aerodynamic forces and moments generated at the main rotor strongly influence helicopter dynamics. At the basic level, classical 6DOF models are used assuming the blades to be rigid. The 6DOF model treats the rotor dynamics in quasi-steady form. This may, at times, lead to degradation of the estimated results. Including additional degrees of freedom due to blade flapping and inflow dynamics allows for better representation of rotorcraft dynamics at higher frequency leading to improved estimates.

The adequacy and accuracy of the identified models can be assessed by any one of the following methods:

• Comparing the estimated values of the identified derivatives with values obtained from other sources, like analytical values, CFD results, or wind tunnel data.

• Comparing the estimated derivative values from different sets of flight data gathered from similar maneuvers at the same flight condition.

• Comparing the model responses with the data not used in identification of the derivatives. Normally, it is advised to keep half the data for model development and half for model validation.

• Assessing based on the physical plausibility of the identified derivatives. Physical knowledge of the system being modeled is essential to correctly interpret the results and validate the model.

It needs to be emphasized here that no mathematical model is perfect. Therefore, model evaluation, to some extent, is subjective. Comparative plots of the estimated and measured time histories alone are not sufficient to evaluate a model. A combin­ation of the above-mentioned criteria should be used. Fully evaluated and validated dynamic models are essential for flying quality evaluation, piloted simulations, and for the design and upgradation of aircraft flight-control system.