Non-linear System Identification Using the Hilbert-Huang Transform and Complex Non-linear Modal Analysis
Modal analysis is a well-established method for analysis of linear dynamic structures, but its extension to non-linear structures has proven to be much more problematic. A number of viewpoints on non-linear modal analysis as well as a range of different non-linear system identification techniques have emerged in the past, each of which tries to preserve a subset of properties of the original linear theory. The objective of this paper is to discuss how the Hilbert-Huang transform can be used for detection and characterization of non-linearity, and to present an optimization framework which combines the Hilbert-Huang transform and complex non-linear modal analysis for quantification of the selected model. It is argued that the complex non-linear modes relate to the intrinsic mode functions through the reduced order model of slow-flow dynamics. The method is demonstrated on simulated data from a system with cubic non-linearity.
KeywordsNon-linear system identification Hilbert-Huang transform Complex non-linear modal analysis Detection and characterization of non-linearity Complex non-linear modes
The authors are grateful to Rolls-Royce plc for providing the financial support for this project and for giving permission to publish this work. This work is part of a Collaborative R and T Project “SAGE 3 WP4 Nonlinear Systems” supported by the CleanSky Joint Undertaking and carried out by Rolls-Royce plc and Imperial College.
- 2.Noël, J.P., Kerschen, G.: Nonlinear system identification in structural dynamics: 10 more years of progress. Mech. Syste. Signal Process. 83, 2–35 (2017). ISSN 0888-3270, http://dx.doi.org/10.1016/j.ymssp.2016.07.020
- 9.Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (1998)Google Scholar
- 10.Yang, J.N., Lei, Y., Pan, S., Huang, N.E.: System identification of linear structures based on Hilbert-Huang spectral analysis. Part 1: normal modes. Earthq. Eng. Struct. Dyn. 32 (9), 1443–1467 (2003)Google Scholar
- 15.Ondra, V., Sever, I. A., Schwingshackl, C.W.: Non-parametric identification of asymmetric signals and characterization of a class of non-linear systems based on frequency modulation. In: ASME International Mechanical Engineering Congress and Exposition. Dynamics, Vibration, and Control, vol. 4B (2016). doi:10.1115/IMECE2016-65229 Google Scholar
- 16.Ondra, V., Sever, I.A., Schwingshackl, C.W.: A method for non-parametric identification of non-linear vibration systems with asymmetric restoring forces from a free decay response. J. Sound Vib. (2017, under review)Google Scholar
- 18.Feldman, M.: Non-linear system vibration analysis using Hilbert transform–II. Forced vibration analysis method ‘Forcevib’. Mech. Syst. Signal Process. 8 (3), 309–318 (1994)Google Scholar
- 22.Wang, Y.-H., Yeh, C.-H., Young, H.-W.V., Hu, K., Lo, M.-T.: On the computational complexity of the empirical mode decomposition algorithm. Phys. A Stat. Mech. Appl. 400, 159–167 (2014). ISSN 0378-4371, http://dx.doi.org/10.1016/j.physa.2014.01.020
- 24.Deering, R., Kaiser, J.F.: The use of a masking signal to improve empirical mode decomposition. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, vol. IV, pp. 485–488 (2005)Google Scholar
- 26.Ondra, V., Riethmueller, R., Brake, M.R.W., Schwingshackl, C.W., Polunin, P.M., Shaw, S.W.: Comparison of nonlinear system identification methods for free decay measurements with application to MEMS devices. In: Proceedings of International Modal Analysis Conference (IMAC) 2017 (2017)Google Scholar
- 28.Feldman, M.: Non-linear system vibration analysis using Hilbert transform–I. Free vibration analysis method ‘Freevib’. Mech. Syst. Signal Process. 8 (2), 119–127 (1994)Google Scholar
- 31.Arora, J.S.: Introduction to Optimum Design, 3rd edn. Academic, Boston (2012)Google Scholar