Hybrid identification techniques for rigid aircraft

A series of studies has been undertaken at ONERA/DCSD/IDCO since 1998 in order to enhance the identification tools used by AIRBUS FRANCE for adjusting their rigid aircraft models. The current procedures followed by AIRBUS engineers for processing the flight test data are in fact encountering several difficulties, namely :

• the high number of non linear coefficients, necessary for a good fitting of complex aerodynamic phenomena (like pitch-up, stalls, ...);
• the simulator databases often tabulated in terms of several variables (Mach number, angle of attack, sideslip, surfaces deflection), which require to deal with multidimensional lookup tables for which the automated adjustment can be difficult;
• the consistency of the intermediate results, obtained at the close of each of the successive steps in the identification process, with the final result validated by means of an ultimate replay (dynamic simulation of the global model using the flight data inputs).

To improve the existing tools, both for longitudinal and lateral motions, a hybrid approach has been developed combining the usual identification methods with neural techniques. The first straightforward applications involved static modeling, such as ground effects or hinge moment identification from flight and wind tunnel tests. This results in different software packages, for example CINEMACH ("Codes pour l'Identification NEuronale des Moments Aérodynamiques de CHarnière"), which were used by AIRBUS for processing the latest A340-600 and A318 flight tests. Benefits are obtained in automation of the procedure as well as in improvement of the hinge moment matching. Significant savings are also achieved in terms of engineering effort and processing delays.

Continuing within the framework of static modeling, an interesting first step in the process of rigid body identification, currently followed by AIRBUS, consists of working on a time history reconstruction of the aerodynamic forces and moments, derived from the measured accelerations. From these estimated and filtered data, the expected initial coefficients can be improved for the following identification steps, by means of an equation error approach. An illustrative example is given in figure 1 for the longitudinal case. A special type of neural model is used, different from the usual multilayer perceptron, known as the Radial Basis Function Network. This architecture has strong localization properties which enables to implement constructive approaches (growing networks during self-organization stages), incremental learning (adjusting only a subset of parameters) and structural optimization.

Although it is attractive due to its simplicity and the physical interpretation it provides, this static processing is often not sufficient because it doesn't really minimize the deviations of the simulated outputs from the measured ones. Therefore, it doesn't offer any guarantee of consistency on the outcome of a dynamic test replay.



To achieve this ultimate goal, the best way involves using a criterion expressed in terms of these deviations. The data processing becomes dynamic, and ad hoc developments are therefore necessary due to the specificities of the aircraft modeling which are:

• continuous time differential equations for the flight mechanics,
• use of a priori knowledge for the parameters expected values,
• compatibility with the pre-existing tools dealing with the linear coefficients.

These requirements prevent us from using blackbox models, and motivate the development of greybox architectures including only a restricted set of subnetworks for the nonlinear terms. Therefore, the hybridization scheme is based upon a separate processing of the different types of efforts appearing in the flight mechanics equations. The state and output equations of such an hybrid modeling take the following form:



where X represents the aircraft state vector, U the control inputs (control surface deflections) and Z the output variables (appearing in the criterion). F^NN corresponds to the forces components which are adjusted by means of a neural representation, whereas F^aero represents the set of the other aerodynamic components, which do not require identification at this stage and remain computed via the OSMA model of AIRBUS. Figure 2 provides a graphical representation of the hybrid mechanisms.



As far as the optimization process is concerned, and whatever method is employed (a simple gradient descent or a more elaborated second-order technique), the computation of the sensitivities is a crucial point. In our case, for an adjustable parameter w of any neural module included into F^NN, the state sensitivity equations obey the synthetic expression below :



introducing a matrix operator (-*-) involved in the computation of .

Due to the number of parameters induced by the nonlinearities, and to keep the computation time at a reasonable level, a trade-off has to be found between a numerical algorithm and an analytical derivation which take adavantage of the generic structure of the neural networks. Different solutions were developed and compared, from a standard backpropagation-through-time to a more simple spatial backpropagation. The compromise was established on a parallel but coupled integration of the aircraft state equations and the neural sensitivities, the linear parameters continuing to be processed separately and numerically.

The pre-indutrial developments of the software IDLON^NN and IDLAT^NN, with respect to the IDentification of LONgitudinal and LATeral models, are in progress. In 2003, longitudinal validations were carried out, to demonstrate the benefits in terms of accuracy as well as usefulness for a fast and automated processing of the flight tests. Different aerodynamic coefficients were successfully identified, related to low speed stalls in clean and high lift configurations, pitch-up phenomenon (including hysteresis effects) and speedbrake deflections. Figure 3 shows an example of the type of nonlinearity involved in these applications, a two-dimensional component of the pitching moment, function of the Mach number and the angle of attack. The simulation results for the angle of attack illustrates the interest of the dynamic approach, when very sensitive variables are integrated.



In the following studies, in 2004 and 2005, the work will focus on improving the interface with the OSMA simulation tool, developed and updated by AIRBUS. The main challenge will be to withdraw the interactions between the hybrid algorithm and the aerodynamic modeling, in order to preserve the former from future structural changes in the latter.




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