Nonlinear aeroelastic reduced order modeling by recurrent neural networks

Journal of Fluids and Structures

Volumn 48, Issue , 2014, Pages 103-121

  Mannarino, Andrea ^a   Mantegazza, Paolo ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Continuous time recurrent neural networks; Limit cycle oscillation; Nonlinear aeroelasticity; Periodic collocation method

Indexed keywords

CONTROL NONLINEARITIES; DELTA SIGMA MODULATION; RECURRENT NEURAL NETWORKS;

AUTOMATIC DIFFERENTIATIONS; COLLOCATION METHOD; CONTINUOUS TIME RECURRENT NEURAL NETWORKS; HIGH-FIDELITY SIMULATIONS; LIMIT CYCLE OSCILLATION (LCO); NONLINEAR AERODYNAMIC MODEL; NONLINEAR AEROELASTICITY; PERIODIC BOUNDARY VALUE PROBLEMS;

AEROELASTICITY;

EID: 84901250804     PISSN: 08899746     EISSN: 10958622     Source Type: Journal    
DOI: 10.1016/j.jfluidstructs.2014.02.016     Document Type: Article

References (42)

1. Bisplinghoff R.L., Ashley H., Halfman R.L. Aeroelasticity 1955, Dover, New York, NY.
2. Borri, M., Mantegazza, P., 1987. Nonlinear oscillation and limit cycles: a numerical approach by finite elements in time domain. In: Sixth International Conference on Mathematical Modelling.
3. Dowell E.H., Clark R., Cox D., Curtiss H.C., Edwards J.W., Hall K.C., Peters D.A., Scanlan R., Simiu E., Sisto F., Strganac T.W. A Modern Course in Aeroelasticity 2004, Kluwer Academic Publishers, Norwell, MA. 4th edition.
4. Epureanu B., Dowell E. Compact methodology for computing limit-cycle oscillations in aeroelasticity. Journal of Aircraft 2003, 40:955-963.
5. Gelb A., Vander Velde W.E. Multiple-Input Describing Functions and Nonlinear System Design 1968, McGraw-Hill Book Company, Columbus, OH.
6. Goldberg D.E. Genetic Algorithms in Search, Optimization and Machine Learning 1989, Addison-Wesley Publishing, Boston, MA.
7. Griewank A., Juedes D., Utke J. Algorithm 755. ADOL-C: a package for the automatic differentiation of algorithms written in C/C++. ACM Transactions on Mathematica Software 1996, 22:131-167.
8. Griewank A., Walther A. Evaluating Derivatives. Principles and Techniques of Algorithmic Differentiation 2008, SIAM. 2nd edition.
9. Hall K.C., Thomas J.P., Clark W.S. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA Journal 2002, 40:879-886.
10. Haykin S. Neural Networks and Learning Machines 2009, Pearson International Edition, London, UK.
11. Jordan D.W., Smith P. Nonlinear Ordinary Differential Equations 2007, Oxford University Press, New York, NY. 4th edition.
12. Kholodar D., Dowell E.H., Thomas J.P., Hall K. Limit-cycle oscillations of a typical airfoil in transonic flow. Journal Of Aircraft 2004, 41:1067-1072.
13. Li D., Guo S., Xiang J. Study of the conditions that cause chaotic motion in a two-dimensional airfoil with structural nonlinearities in subsonic flow. Journal of Fluids and Structures 2012, 33:109-126.
14. Lucia D.J., Beran P.S., Silva W.A. Reduced-order modeling: new approaches for computational physics. Progress in Aerospace Sciences 2004, 40:51-117.
15. Manetti M., Quaranta G., Mantegazza P. Numerical evaluation of limit cycles of aeroelastic systems. Journal of Aircraft 2009, 46:1759-1769.
16. Manetti, M., Quaranta, G., Mantegazza, P., 2009. Numerical evaluation of limit cycles of aeroelastic systems. In: IFASD, Seattle, WA.
17. Marquardt D.W. An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics 1963, 11:431-441.
18. Masarati, P., Lanz, M., Mantegazza, P., 2001. Multistep integration of ordinary, stiff, and differential-algebraic problems for multibody dynamics applications. In: XVI Congresso Nazionale AIDAA, Palermo, Italy.
19. Mastroddi F., Dessi D., Eugeni M. POD analysis for free response of linear and nonlinear marginally stable aeroelastic dynamical systems. Journal of Fluids and Structures 2012, 33:85-108.
20. Morton S.A., Beran P.S. Hopf-bifurcation analysis of airfoil flutter at transonic speeds. Journal of Aircraft 1999, 36:421-429.
21. Nelles O. Nonlinear System Identification 2001, Springer, New York, NY.
22. Paduart J., Lauwers L., Swevers J., Smolders K., Schoukens J., Pintelon R. Identification of nonlinear systems using polynomial nonlinear state space models. Automatica 2010, 46:647-656.
23. Pearlmutter B.A. Learning state space trajectories in recurrent neural networks. Neural Computation 1989, 1:263-269.
24. Petersen, K.B., Pedersen, M.S., 2008. The Matrix Cookbook. 〈〉. http://matrixcookbook.com.
25. Rivers, J., Dansberry, B., Bennet, R., Durham, M., Silva, W., 1992. NACA 0012 benchmark model experimental flutter results with unsteady pressure distributions. In: 33rd Structures, Structural Dynamics and Material Conference. Paper 92-2396.
26. Romanelli, G., 2012. Computational Aeroservoelasticity of Free-Flying Deformable Aircraft (Ph.D. thesis). Politecnico di Milano.
27. Romanelli, G., Castellani, M., Mantegazza, P., Ricci, S., 2012. Coupled CSD/CFD non-linear aeroelastic trim of free-flying flexible aircraft. In: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI.
28. Romanelli, G., Serioli, E., Mantegazza, P., 2010. A "free" approach to computational aeroelasticity. In: 48th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL.
29. Rowley C. Model reduction for fluids, using balanced proper orthogonal decomposition. International Journal on Bifurcation and Chaos 2005, 15(3):997-1013.
30. Schilders W.H., van der Vorst H.A., Rommes J. Model Order Reduction: Theory Research Aspects and Applications 2008, vol. 13. Springer, New York, NY.
31. Seyab, R.K.A., 2006. Nonlinear Model Predictive Control Using Automatic Differentiation (Ph.D. thesis). Cranfield University.
32. Seydel R. From Equilibrium to Chaos. Practical Bifurcation and Stability Analysis 1988, Elsevier, Amsterdam, The Netherlands.
33. Stanford B., Beran P. Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization. Journal of Fluids and Structures 2013, 36:111-123.
34. Suykens J.A.K., Vanderwalle J. Learning a simple recurrent neural state space model to behave like Chua[U+05F3]s double scroll. IEEE Transactions on Circuits and Systems 1995, 42:499-502.
35. Thomas J.P., Dowell E.H., Hall K.C. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations. AIAA Journal 2002, 40:638-646.
36. Thomas J.P., Dowell E.H., Hall K.C. Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver. AIAA Journal 2010, 48:19-24.
37. Timme S., Badcock K.J. Transonic aeroelastic instability searches using sampling and aerodynamic model hierarchy. AIAA Journal 2011, 49:1191-1201.
38. Timme S., Marques S., Badcock K.J. Transonic aeroelastic stability analysis using a Kriging-based Schur complement formulation. AIAA Journal 2011, 49:1202-1213.
39. VV.AA., 2010. OpenFOAM v.1.7.1 User[U+05F3]s Guide. 〈〉. http://www.opencfd.co.uk.
40. Wasnak, M.R., 1996. Modeling the benchmark active control technology wind-tunnel model for application to flutter suppression. In: 21st AIAA Atmospheric Flight Mechanics Conference, San Diego, CA. Paper 96-3457.
41. Yao, W., Liou, M., 2012. Reduced-order modeling for flutter/LCO using recurrent artificial neural network. In: 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSM, Indianapolis, IN.
42. Zhang, W., Wang, B., Ye, Z., 2010. High efficient numerical method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order-model. In: 51st AIAA, ASME, ASCE, AHS, ASC Structures, Structural Dynamics and Materials Conference, Orlando, FL.