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Identification of nonlinear aerodynamic systems with application to transonic aeroelasticity of aircraft structures

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Abstract

In this study, identification of nonlinear aerodynamic systems based on an improved nonlinear state-space modeling approach is presented to predict transonic aeroelastic behaviors of aircraft structures. It starts with identifying a linear state-space aerodynamic model by using the eigensystem realization algorithm and observer/Kalman filter identification methods. Subsequently, the remaining parameters of the nonlinear state-space aerodynamic model are determined through an output error-minimization procedure, based on a new training data generation methodology. To illustrate the approach, two- and three-dimensional transonic aeroelastic configurations are studied. The transonic aeroelastic behaviors predicted via the proposed approach agree well with those obtained via computational fluid dynamics technique in the interested range of dynamic pressure.

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References

  1. Livne, E.: Aircraft active flutter suppression: state of the art and technology maturation needs. J. Aircr. 55(1), 410–452 (2017)

    Article  Google Scholar 

  2. Huang, R., Qian, W., Hu, H., Zhao, Y.: Design of active flutter suppression and wind-tunnel tests of a wing model involving a control delay. J. Fluids Struct. 55, 409–427 (2015)

    Article  Google Scholar 

  3. Huang, R., Zhao, Y., Hu, H.: Wind-tunnel tests for active flutter control and closed-loop flutter identification. AIAA J. 54(7), 2089–2099 (2016)

    Article  Google Scholar 

  4. Chen, G., Zhou, Q., Ronch, A.D., Li, Y.: Computational-fluid-dynamics-based aeroservoelastic analysis for gust load alleviation. J. Aircr. 55(4), 1619–1628 (2018)

    Article  Google Scholar 

  5. Hall, K.C., Thomas, J.P., Dowell, E.H.: Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows. AIAA J. 38(10), 1853–1862 (2000)

    Article  Google Scholar 

  6. Amsallem, D., Farhat, C.: Interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA J. 46(7), 1803–1813 (2008)

    Article  Google Scholar 

  7. Chen, G., Li, Y., Yan, G.: A nonlinear POD reduced order model for limit cycle oscillation prediction. Sci. China Phys. Mech. Astron. 53(7), 1325–1332 (2010)

    Article  Google Scholar 

  8. Cowan, T.J., Arena, A.S., Gupta, K.K.: Accelerating computational fluid dynamics based aeroelastic predictions using system identification. J. Aircr. 38(1), 81–87 (2001)

    Article  Google Scholar 

  9. Raveh, D.E.: Identification of computational-fluid-dynamics based unsteady aerodynamic models for aeroelastic analysis. J. Aircr. 41(3), 620–632 (2004)

    Article  Google Scholar 

  10. Silva, W.A.: Identification of nonlinear aeroelastic systems based on the Volterra theory: progress and opportunities. Nonlinear Dyn. 39(1–2), 25–62 (2005)

    Article  MathSciNet  Google Scholar 

  11. Kim, T., Hong, M., Bhatia, K.G., Sengupta, G.: Aeroelastic model reduction for affordable computational fluid dynamics-based flutter analysis. AIAA J. 43(12), 2487–2495 (2005)

    Article  Google Scholar 

  12. Silva, W.A.: Simultaneous excitation of multiple-input/multiple-output CFD-based unsteady aerodynamic systems. J. Aircr. 45(4), 1267–1274 (2008)

    Article  Google Scholar 

  13. Lucia, D.J., Beran, P.S., Silva, W.A.: Reduced-order modeling: new approaches for computational physics. Prog. Aerosp. Sci. 40(1–2), 51–117 (2004)

    Article  Google Scholar 

  14. Liu, H., Hu, H., Zhao, Y., Huang, R.: Efficient reduced-order modeling of unsteady aerodynamics robust to flight parameter variations. J. Fluids Struct. 49, 728–741 (2014)

    Article  Google Scholar 

  15. Huang, R., Li, H., Hu, H., Zhao, Y.: Open/closed-loop aeroservoelastic predictions via nonlinear, reduced-order aerodynamic models. AIAA J. 53(7), 1812–1824 (2015)

    Article  Google Scholar 

  16. Liu, H., Huang, R., Zhao, Y., Hu, H.: Reduced-order modeling of unsteady aerodynamics for an elastic wing with control surfaces. J. Aerosp. Eng. 30(3), 04016083 (2017)

    Article  Google Scholar 

  17. Thomas, J.P., Dowell, E.H., Hall, K.C.: Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver. AIAA J. 48(1), 19–24 (2010)

    Article  Google Scholar 

  18. Yang, Z., Huang, R., Zhao, Y., Hu, H.: Design of an active disturbance rejection control for transonic flutter suppression. J. Guid. Control Dyn. 40(11), 2905–2916 (2017)

    Article  Google Scholar 

  19. de Paula, N.C.G., Marques, F.D.: Multi-variable Volterra kernels identification using time-delay neural networks: application to unsteady aerodynamic loading. Nonlinear Dyn. 97, 767–780 (2019)

    Article  Google Scholar 

  20. Kou, J., Zhang, W., Yin, M.: Novel Wiener models with a time-delayed nonlinear block and their identification. Nonlinear Dyn. 85(4), 2389–2404 (2016)

    Article  Google Scholar 

  21. Balajewicz, M., Dowell, E.H.: Reduced-order modeling of flutter and limit-cycle oscillations using the sparse Volterra series. J. Aircr. 49(6), 1803–1812 (2012)

    Article  Google Scholar 

  22. Huang, R., Hu, H., Zhao, Y.: Nonlinear reduced-order modeling for multiple-input/multiple-output aerodynamic systems. AIAA J. 52(6), 1219–1231 (2014)

    Article  Google Scholar 

  23. Yao, W., Liou, M.S.: Reduced-order modeling for flutter/LCO using recurrent artificial neural network. In: 12th AIAA Aviation Technology, Integration, and Operations Conference, Indianapolis, Indiana (2012)

  24. Zhang, W., Wang, B., Ye, Z., Quan, J.: Efficient method for limit cycle flutter analysis based on nonlinear aerodynamic reduced-order models. AIAA J. 50(5), 1019–1028 (2012)

    Article  Google Scholar 

  25. Mannarino, A., Mantegazza, P.: Nonlinear aeroelastic reduced order modeling by recurrent neural networks. J. Fluids Struct. 48, 103–121 (2014)

    Article  Google Scholar 

  26. Li, K., Kou, J., Zhang, W.: Deep neural network for unsteady aerodynamic and aeroelastic modeling across multiple Mach numbers. Nonlinear Dyn. 96(3), 2157–2177 (2019)

    Article  Google Scholar 

  27. Mannarino, A., Dowell, E.H.: Reduced-order models for computational-fluid-dynamics-based nonlinear aeroelastic problems. AIAA J. 53(9), 2671–2685 (2015)

    Article  Google Scholar 

  28. Huang, R., Liu, H., Yang, Z., Zhao, Y., Hu, H.: Nonlinear reduced-order models for transonic aeroelastic and aeroservoelastic problems. AIAA J. 56(9), 3718–3731 (2018)

    Article  Google Scholar 

  29. Quan, E., Xu, M., Xie, D., Li, G.: Efficient nonlinear reduced-order model for computational fluid dynamics-based aeroelastic analysis. AIAA J. 56(9), 3701–3717 (2018)

    Article  Google Scholar 

  30. Carrese, R., Joseph, N., Marzocca, P., Levinski, O.: Aeroelastic response of the AGARD 445.6 wing with freeplay nonlinearity. In: 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Grapevine, Texas (2017)

  31. Decuyper, J., De Troyer, T., Runacres, M.C., Tiels, K., Schoukens, J.: Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow. Mech. Syst. Signal Process. 98, 209–230 (2018)

    Article  Google Scholar 

  32. Silva, W.A.: AEROM: NASA’s unsteady aerodynamic and aeroelastic reduced-order modeling software. Aerospace 5(2), 41 (2018)

    Article  Google Scholar 

  33. Haykin, S.: Neural Networks and Learning Machines, 3rd edn, pp. 14–136. Prentice-Hall, Upper Saddle River, NJ (2008)

    Google Scholar 

  34. Kutz, J.N., Brunton, S.L., Brunton, B.W., Proctor, J.L.: Dynamic mode decomposition: data-driven modeling of complex systems. Soc. Ind. Appl. Math. (2016). https://doi.org/10.1137/1.9781611974508.bm

    Article  MATH  Google Scholar 

  35. Juang, J.N., Pappa, R.S.: An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guid. Control Dyn. 8(5), 620–627 (1985)

    Article  Google Scholar 

  36. Silva, W.A., Bartels, R.E.: Development of reduced-order models for aeroelastic analysis and flutter prediction using the CFL3Dv6. 0 code. J. Fluids Struct. 19(6), 729–745 (2004)

    Article  Google Scholar 

  37. Phan, M., Horta, L.G., Juang, J.N., Longman, R.W.: Linear system identification via an asymptotically stable observer. J. Optim. Theory Appl. 79(1), 59–86 (1993)

    Article  MathSciNet  Google Scholar 

  38. Landon, R.H.: NACA 0012 oscillating and transient pitching, data Set 3 in: Compendium of unsteady aerodynamic measurements. AGARDR-702 (1982)

  39. Beran, P.S., Khot, N.S., Eastep, F.E., Snyder, R.D., Zweber, J.V.: Numerical analysis of store-induced limit-cycle oscillation. J. Aircr. 41(6), 1315–1326 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (No. NS2019002).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, People’s Republic of China

    Haojie Liu

  2. School of Physical and Mathematical Sciences, Nanjing Tech University, 210016, Nanjing, People’s Republic of China

    Xiumin Gao

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  1. Haojie Liu
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Correspondence to Xiumin Gao.

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Liu, H., Gao, X. Identification of nonlinear aerodynamic systems with application to transonic aeroelasticity of aircraft structures. Nonlinear Dyn 100, 1037–1056 (2020). https://doi.org/10.1007/s11071-020-05553-2

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