Aircraft aerodynamic model identification: a semi-empirical neural network based approach

Аuthors

Egorchev M. V.^*, Kozlov D. S.^**, Tiumentsev Y. V.^***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mihail.egorchev@gmail.com
**e-mail: dmkozlov001@gmail.com
***e-mail: yutium@gmail.com

Abstract

The paper considers the problem of simulation and identification of the nonlinear controlled dynamical system on the example of angular motion of a highly agile airplane. The proposed semi-empirical dynamical neural network-based model combines theoretical knowledge about the simulated objects with the tools of model improvement, which perform training of artificial neural networks. The theoretical knowledge is initially presented in the form of differential equations, which describe aircraft angular motion. Afterwards this knowledge is transformed into modular dynamic neural network representation. Insufficient accuracy of the theoretical model is improved via identification of the (nonlinear) aerodynamic force and moment coefficients. These coefficients are represented by the MLP (multilayer perceptron) modules, which are embedded into the complete model. A representative training set is generated to achieve the acceptable generalization capability and reduce the time, which is required to collect the data. This set is generated via special procedures of control input signal optimization. Training of dynamical neural networks on long data sequences has proven to be very difficult. There are several reasons for these difficulties, which include the effects of vanishing and exploding gradients as well as presence of spurious the training of the dynamical neural network model is performed in incremental fashion as follows. In order for the gradient learning method to attain the deep enough minimum of the error surface the training must start with the parameter values, which are close to that minimum. The problem of obtaining such parameter values may be treated as a problem of searching for minimum of a similar error surface. Thus a sequence of error surfaces with the following properties is constructed: a) the first error surface is simple enough to search for minimum with any initial parameter values; b) each next error surface is similar to the previous one; c) the sequence converges to the original error surface. Thus the original training problem is decomposed into a sequence of more simple sub-problems. Computational experiments confirm the efficiency of the proposed approach: the modeling errors for the test set are

where ,  are the angles of attack and sideslip; p, q r are the angular velocities about X, Y, Z axes.

Aerodynamic coefficient estimation errors for the test set are

where are the coefficients of body-axis components of the aerodynamic forces and moments.

Keywords:

nonlinear dynamical system, aircraft angular motion, aerodynamic model identification, semi-empirical model, neural network learning

References

1. Egorchev M.V., Tyumentsev Yu.V. Sbornik nauchnykh trudov XV Vserossiiskoi nauchno-tekhnicheskoi konferentsii «Neiroinformatika-2013», Moscow, 2013, vol.2, pp. 22- 31.
   
2. Egorchev M.V., Kozlov D.S., Tyumentsev Yu.V., Chernyshev A.V. Vestnik informatsionnykh ikompyuternykh tekhnologii, 2013, no.9, pp. 3-10.
   
3. Egorchev M.V., Tyumentsev Yu.V. Sbornik nauchnykh trudov XVI Vserossiiskoi nauchno-tekhnicheskoi konferentsii «Neiroinformatika-2014», Moscow, 2014, vol.2, pp. 263- 272.
   
4. Haykin S. Neural networks: Acomprehensive foundation: 2nd Edition, Prentice Hall, 2006, 823p.
5. Ljung L. System identification — Theory for the User: 2nd Edition, Prentice Hall, 1999, 609p.
6. Berestov L.M., Poplavskii B.K., Miroshnichenko L.Ya. Chastotnye metody identifikatsii letatelnykh apparatov (Frequency-domain methods for aircraft identification), Moscow, Mashinostroenie, 1985, 184p.
7. Klein V., Morelli E.A. Aircraft system identification: Theory and practice, Reston, VA: AIAA, Inc., 2006, 498p.
8. Tischler M.B., Remple R.K. Aircraft and rotorcraft system identification: Engineering methods with flight-test examples, Reston, VA: AIAA, Inc., 2006, 558p.
9. Rivals I., Personnaz L. Black-box modeling with state-space neural networks, Neural Adaptive Control Technology, World Scientific, 1996, pp. 237-264.
   
10. Dreyfus G. Neural networks: Methodology and applications, Berlin, Springer, 2005, 515p.
11. OussarY., Dreyfus G. How tobeagray box: Dynamic semi-physical modeling, Neural Network, 2001, vol.14, no.9, pp. 1161-1172
    
12. Bochkarev A.F., Andreevskii V.V. Belokonov V.M., Klimov V.I., Turapin V.M. Aeromekhanika samoleta: Dinamika poleta (Aeromechanics ofairplane: Flight dynamics), Moscow, Mashinostroenie, 1985, 360p.
13. Nguyen L.T., Ogburn M.E., Gilbert W.P., Kibler K.S., Brown P.W., Deal P.L. Simulator study ofstall/post-stall characteristics of afighter airplane with relaxed longitudinal static stability, NASA TP-1538, Dec.1979, 223p.
14. Dietterich T.G. Machine-learning research: Four current directions, AI Magazine, 1997, vol.18, no.7, pp. 97-136.
    
15. Joshi P., Kulkarni P. Incremental learning: Areas and methods— asurvey, International Journal of Data Mining and Knowledge Managament Process, 2012, vol.2, no.5, pp. 43-51.
    
16. Horn J., DeJesus O., Hagan M.T. Spurious valleys inthe error surface ofrecurrent networks— analysis and avoidance, IEEE Transactions on Neural Networks, 2009, vol.20, no.4, pp. 686-700.
    
17. Pascanu R., Mikolov T., Bengio Y. On the difficulty of training recurrent neural networks, availableat: http://arxiv.org/abs/1211.5063, 2013.
    
18. Elman J.L. Learning and development inneural networks: The importance of starting small, Cognition, 1993, vol.48, pp. 71-99.
    
19. Ludik J., Cloete I. Incremental increased complexity training, Proceedings of ESANN 1994, 2nd European Symposium on Artificial Neural Networks, Brussels, Belgium, 1994, pp. 161-165.
    
20. Suykens J.A.K., Vandewalle J. Learning asimple recurrent neural state space model tobehave like Chuas double scroll, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1995, vol.42, no.8, pp. 499-502.
    
21. Bengio Y., Louradour J., Collobert R., Weston J. Curriculum learning, Proceedings ofthe 26th Annual International Conference onMachine Learning, ICML 2009, New York, NY, USA, pp. 41-48.