A Modified Noise-Resistant Trend Estimation Method Based on EMD and SSA for Aeroelastic Aircraft Systems

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

2 Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, IRAN.

Abstract

Aimed at the nonlinear system identification of aeroelastic aircraft, the signal decomposition methods are required to extract the contributing natural and non-standard flight modes from flight test data, especially in the presence of flight noise. To this end, the SSA-EMD algorithm is proposed in this paper as a noise-tolerant signal decomposition method. The SSA-EMD is an improved Empirical Mode Decomposition (EMD) in which the sifting process is implemented by a direct approach to the signal trend extraction as a substitute for the envelope concept. In the proposed method, Singular Spectrum Analysis (SSA) is used for extraction of the signal trend in order to improve the mathematical foundation of the EMD. The proposed method is verified by decomposing some benchmark signals. Numerical results demonstrate that the proposed method outperforms the original one, especially in handling noisy signals. Afterwards, a novel gray-box non-parametric system identification method is proposed for considering extracted flight mode in the aircraft dynamics. The performance of the SSA-EMD is studied for the aircraft system identification from real flight test data of an aeroelastic aircraft in the transonic regime. It can be observed that the average fitness values of 60.01% and 88.41% are obtained for the lateral flight parameters using the EMD and SSA-EMD, respectively. Moreover, the RMSE values of the flight parameters predicted by the EMD and SSA-EMD are 1.85 and 0.65, respectively. Therefore, the SSA-EMD can achieve better results than the original EMD for the aircraft system identification due to its noise rejection properties.

Keywords

Main Subjects


  1. A. Mokhtari, and M. Sabzehparvar, Application of Hilbert–Huang Transform With Improved Ensemble Empirical Mode Decomposition in Nonlinear Flight Dynamic Mode Characteristics Estimation, J. Comput. Nonlin. Dyn. 14.1 (2019). doi: 10.1115/1.4042016.
  2. A. Bagherzadeh, Flight dynamics modeling of elastic aircraft using signal decomposition methods, P. I. Mech. Eng. G.-J. Aer. 233.12 (2019), pp. 4380-4395. doi:10.1177/0954410018821788.
  3. Brenner, Marty, and Chad Prazenica, Aeroelastic flight data analysis with the Hilbert-Huang algorithm, AIAA Atmospheric Flight Mechanics Conference and Exhibit, San Francisco, CA, 2005. doi:10.2514/6.2005-5917.
  4. Dai, Q. Chen, and H. Dai, De-Noising Algorithm for Flight Data Recording System Based on Modified Ensemble Empirical Mode Decomposition, J. Phys. Conf. Ser. 1267.1 (2019). doi:10.1088/1742-6596/1267/1/012024.
  5. Wang, X. Xu, T. Zhang, Y. Zhu, and J. Tong, An EMD-MRLS de-noising method for fiber optic gyro Signal, Optik183 (2019), pp.971-987. doi: 10.1016/j.ijleo.2019.03.002
  6. Zhang, Q. Jiang, B. Ma, Y. Zhao and L. Zhu, Signal de-noising method for vibration signal of flood discharge structure based on combined wavelet and EMD. Journal of Vibration and Control23.15 (2017), pp.2401-2417. doi: 10.1177/1077546315616551
  7. Zhou, H. Zhao, H. Xia, J. Zhang, Z. Liu, C. Liu, and F. Gao, De‚Äźnoising of photoacoustic sensing and imaging based on combined empirical mode decomposition and independent component analysis. Journal of biophotonics12.8 (2019). doi:10.1002/jbio.201900042
  8. Xiong, C. Zheng, J. Liu, and L. Song, ECG signal in-band noise de-noising base on EMD, Journal of Circuits, Systems and Computers28.01 (2019). doi:10.1142/S0218126619500178
  9. R. Smith, M. H. Al-Badrawi, and N.J. Kirsch, An Optimized De-Noising Scheme Based on the Null Hypothesis of Intrinsic Mode Functions. IEEE Signal Processing Letters26.8 (2019), pp. 1232-1236. doi: 10.1109/LSP.2019.2925316
  10. E. Huang, Z. Shen, S.R. Long, M.C. Wu, H. Shin, Q. Zheng, N. Yen, C.C. Tung, and H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. A Math. Phys. Eng. Sci. 454.1971 (1998), pp. 903-995. doi:10.1098/rspa.1998.0193.
  11. Kopsinis, and S. McLaughlin, Investigation and performance enhancement of the empirical mode decomposition method based on a heuristic search optimization approach, Signal Process. IEEE Trans. Signal Proces. 56.1 (2008), pp. 1–13. doi:10.1109/TSP.2007.901155.
  12. Rilling, and P. Flandrin, Sampling effects on the empirical mode decomposition, Adv. Adapt. Data Anal. 1.01 (2009), pp. 43-59. doi:10.1142/S1793536909000023.
  13. C. Peel, T.A. McMahon, and G.G.S. Pegram, Assessing the performance of rational spline-based empirical mode decomposition using a global annual precipitation dataset, Proc. R. Soc. A Math. Phys. Eng. Sci. 465.2106 (2009), pp. 1919–1937. doi:10.1098/rspa.2008.0352.
  14. G.S. Pegram, M.C. Peel, and T.A. McMahon, Empirical mode decomposition using rational splines: an application to rainfall time series, Proc. R. Soc. A Math. Phys. Eng. Sci. 464.2094 (2008), pp. 1483–1501. doi:10.1098/rspa.2007.0311.
  15. Chen, N. Huang, S. Riemenschneider, and Y. Xu, A B-spline approach for empirical mode decompositions, Adv. Comput. Math. 24 (2006), pp. 171–195. doi:10.1007/s10444-004-7614-3.
  16. R. Qin, and Y.M. Zhong, A new envelope algorithm of Hilbert-Huang Transform, Mech. Syst. Signal Process. 20.8 (2006), pp. 1941–1952. doi:10.1016/j.ymssp.2005.07.002.
  17. Shulin, Z. Haifeng, W. Hui, and M. Rui, Application of improved EMD algorithm for the fault diagnosis of reciprocating pump valves with spring failure, 9th International Symposium on Signal Processing and Its Applications, Sharjah, United Arab Emirates, 2007, IEEE. doi:10.1109/ISSPA.2007.4555473.
  18. Li, M. Xu, Y. Wei, and W. Huang, An improvement EMD method based on the optimized rational Hermite interpolation approach and its application to gear fault diagnosis, Measurement 63 (2015), pp. 330–345. doi:10.1016/j.measurement.2014.12.021.
  19. Singh, P.K. Srivastava, R.K. Patney, S.D. Joshi, and K. Saha, Nonpolynomial spline based empirical mode decomposition, 2013 International Conference on Signal Processing and Communication, Noida, India, 2013, IEEE. doi:10.1109/ICSPCom.2013.6719829
  20. Singh, S.D. Joshi, R.K. Patney, and K. Saha, Some studies on nonpolynomial interpolation and error analysis, Appl. Math. Comput. 244 (2014), pp. 809–821. doi:10.1016/j.amc.2014.07.049.
  21. A. Bagherzadeh, and M. Sabzehparvar, A local and online sifting process for the empirical mode decomposition and its application in aircraft damage detection, Mech. Syst. Signal Process. 54-55 (2015), pp. 68–83. doi:10.1016/j.ymssp.2014.09.006.
  22. Del, J. Lemoine, O. Niang, and E. Deléchelle, Empirical mode decomposition: an analytical approach for sifting process, IEEE Signal Process. Lett. 12.11 (2012), pp. 764–767. doi:10.1109/LSP.2005.856878
  23. Wang, X. Chen, F. Qiao, Z. Wu, and N.E. Huang, on Intrinsic Mode Function, Adv. Adapt. Data Anal. 02 (2010), pp. 277–293. doi:10.1142/S1793536910000549.
  24. Meignen, and V. Perrier, A New Formulation for Empirical Mode Decomposition Based on Constrained Optimization, IEEE Signal Process. Lett. 14.12 (2007), pp. 932–935. doi:10.1109/LSP.2007.904706
  25. Jin T., Xiao M., Jiang W., Shum C.K., Ding H., Kuo C.Y., Wan J, An Adaptive Method for Nonlinear Sea Level Trend Estimation by Combining EMD and SSA, Earth Space Sci. 8.3 (2021). doi: 10.1029/2020EA001300.
  26. Broomhead, D.S., and G.P. King, Extracting qualitative dynamics from experimental data, Physica D, 20 (1986), pp. 217–236
  27. Alexandrov, A Method of Trend Extraction Using SSA, Revstat – Stat. J. 7.1 (2009), pp. 1–22.
  28. Clarke, M. J. Allen, R. P. Dibley, J. Gera, and J. Hodgkinson, Flight test of the F/A-18 active aeroelastic wing airplane. AIAA Atmospheric Flight Mechanics Conference and Exhibit, San Francisco, CA, 2005, AIAA. doi: 10.2514/6.2005-6316.
  29. Cumming, and C. Diebler, Active Aeroelastic Wing Aerodynamic Model Development and Validation for a Modified F/A-18A Airplane, AIAA Atmospheric Flight Mechanics Conference and Exhibit, San Francisco, CA , 2005, AIAA. doi:10.2514/6.2005-6312.
  30. R. Moes, G.K. Noffz, and K.W. Iliff, Results from F-18B stability and control parameter estimation flight tests at high dynamic pressures, NASA Technical Publication, NASA Dryden Flight Research Center, Edwards, CA, 2000. NASA/TP-2000-209033