Skip to main content
SpringerLink
Log in

An evaluation of data-driven identification strategies for complex nonlinear dynamic systems

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The development of suitable mathematical models on the basis of dynamic measurements from dispersed structural systems that may be undergoing significant nonlinear behavior is an important and very challenging problem in the field of Applied Mechanics that has drawn the attention of numerous investigators and motivated the development of many approaches for extracting reduced-order, reduced-complexity models from such systems. However, even though numerous nonlinear system identification techniques that are focused on the class of problems encountered in the structural dynamics field have been developed over the past decades, there are no systematic studies available that rigorously compare the performance and fidelity of such methods under similar operating conditions, and when encountering challenging nonlinear phenomena (such as hysteresis) that are present in physical systems, at different scales. This paper explores a variety of data-driven identification techniques for complex nonlinear systems and provides a much needed critical comparison of the accuracy and performance of each method. The Volterra/Wiener neural network (VWNN), a more recent development in nonlinear identification, is featured and compared against several existing methods, including polynomial-based nonlinear estimators and other artificial neural network systems. A representative three degree-of-freedom structure with nonlinear restoring force elements is used as the primary means of comparison for the different methods, and a variety of nonlinear models were investigated, including bilinear hysteresis, polynomial stiffness, and Bouc–Wen hysteresis. Performance comparisons were based on the ability to estimate the acceleration responses for both training and testing simulations. The results showed that, in general, the VWNN provided better accuracy in its estimates for each model. The VWNN also performed best when evaluated for scenarios in which numerical integration is required to find velocity and displacement information from measured accelerations or sensor noise is present in the measured responses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Andronikou, A., Bekey, G.A.: Identification of hysteretic systems. In: 18th IEE Conference on Decision and Control (1984)

  2. Antoni, J.: Blind separation of vibration components: principles and demonstrations. Mech. Syst. Signal Process. 19, 1166–1180 (2005)

    Article  Google Scholar 

  3. Baber, T., Noori, M.: Random vibration of degrading, pinching systems. ASCE J. Eng. Mech. 111(8), 1010–1026 (1985)

    Article  Google Scholar 

  4. Baber, T., Noori, M.: Modeling general hysteresis behavior and random vibration application. J. Vib. Acoust. Stress Reliab. Des. 108(4), 411–420 (1986)

    Article  Google Scholar 

  5. Baber, T., Wen, Y.: Stochastic equivalent linearization for hysteretic, degrading, multistory structures. Technical Report, Civil Engeering Studies, SRS No. 471, University of Illinois, Urbana, Illinois (1979)

  6. Baber, T., Wen, Y.: Random vibration of hysteretic degrading systems. J. Eng. Mech. Div. ASCE 107, 1069–1087 (1981)

    Google Scholar 

  7. Benedettini, F., Capecchi, D., Vestroni, F.: Identification of hysteretic oscillators under earthquake loading by nonparametric models. ASCE J. Eng. Mech. 121, 606–612 (1995)

    Article  Google Scholar 

  8. Bouc, R.: Forced vibration of mechanical systems with hysteresis. In: 4th Conference on Nonlinear Oscillation, Prague, Czechoslovakia (1967)

  9. Brincker, R., Andersen, P., Zhang, L.: Modal identification from ambient responses using frequency domain decomposition. In: Proceedings of the 18th International Modal Analysis Conference (IMAC), San Antonio, TX, pp. 625–630 (2000)

  10. Caughey, T.: Random excitation of a system with bilinear hysteresis. ASME J. Appl. Mech. 27, 649–652 (1960)

    Article  MathSciNet  Google Scholar 

  11. Chassiakos, A., Masri, S., Smyth, A., Anderson, J.: Adaptive methods for identification of hysteretic structures. In: American Control Conference, ACC95, Seattle, WA (1995)

  12. Chassiakos, A., Masri, S., Smyth, A., Caughey, T.: On-line identification of hysteretic systems. ASME J. Appl. Mech. 65, 194–203 (1998)

    Article  Google Scholar 

  13. Chatzi, E.N., Smyth, A.W.: The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing. Struct. Control Health Monit. 16, 99–123 (2009)

    Article  Google Scholar 

  14. Chatzi, E.N., Smyth, A.W., Masri, S.F.: Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty. Struct. Saf. 32(5), 326–337 (2010)

    Article  Google Scholar 

  15. Derkevorkian, A., Hernandez-Garcia, M., Yun, H.B., Masri, S.F., Li, P.: Nonlinear data-driven computational models for response prediction and change detection. Struct. Control Health Monit. 22(2), 273–288 (2015)

    Article  Google Scholar 

  16. Derkevorkian, A., Masri, S.F., Fujino, Y., Siringoringo, D.M.: Development and validation of nonlinear computational models of dispersed structures under strong earthquake excitation. Earthq. Eng. Struct. Dyn. 43, 1089–1105 (2014)

    Article  Google Scholar 

  17. Dominguez, A., Sedaghati, R., Stiharu, I.: A new dynamic hysteresis model for magnetorheological dampers. Smart Mater. Struct. 15, 1179–1189 (2006)

    Article  Google Scholar 

  18. Erlicher, S., Point, N.: Thermodynamic admissibility of Bouc–Wen type hysteresis models. C. R. Mec. 332, 51–57 (2004)

    Article  MATH  Google Scholar 

  19. Ewins, D.J.: Modal Testing: Theory, Practice and Application, 2nd edn. Research Studies Press LTD, Baldock (2000)

  20. Ghanem, R., Romeo, F.: Wavelet-based approach for model and parameter identification of non-linear systems. Int. J. Non-Linear Mech. 36, 835–859 (2001)

    Article  MATH  Google Scholar 

  21. Hoshiya, M., Saito, E.: Structural identification by extended Kalman filter. ASCE J. Eng. Mech. 110(12), 1757–1772 (1984)

    Article  Google Scholar 

  22. Ibrahim, S.: Efficient random decrement computation for identification of ambient responses. In: Proceedings of the 19th IMAC, Orlando, FL, pp. 678–703 (2001)

  23. Ismail, M., Ikhouane, F., Rodellar, J.: The hysteresis Bouc–Wen model, a survey. Arch. Comput. Methods Eng. 16, 161–188 (2009)

    Article  MATH  Google Scholar 

  24. Iwan, W.: A distributed-element model for hysteresis and its steady-state dynamic response. ASME J. Appl. Mech. 33, 893–900 (1966)

    Article  Google Scholar 

  25. Iwan, W., Cifuentes, A.: A model for system identification of degrading structures. Earthq. Eng. Struct. Dyn. 14, 877–890 (1986)

    Article  Google Scholar 

  26. Iwan, W., Lutes, L.: Response of the bilinear hysteretic system to stationary random excitation. J. Acoust. Soc. Am. 43, 545–552 (1968)

    Article  Google Scholar 

  27. James, G., Carne, T., Lauffer, J.: The natural excitation technique (NExT) for modal parameter extraction from operating structures. Int. J. Anal. Exp. Modal Anal. 10(4), 260–277 (1995)

    Google Scholar 

  28. Jayakumar, P., Beck, J.L.: System identification using nonlinear structural models. In: Structural Safety Evaluation Based on System Identification Approaches, pp. 82–102. Springer Fachmedien, Wiesbaden (1988)

  29. Jennings, P.: Periodic response of a general yielding structure. J. Eng. Mech. Div. ASCE 90, 131–166 (1964)

    Google Scholar 

  30. Kerschen, G., Poncelet, F., Golinval, J.C.: Physical interpretation of independent component analysis in structural dynamics. Mech. Syst. Signal Process. 21, 1561–1575 (2007)

    Article  Google Scholar 

  31. Kerschen, G., Worden, K., Vakakis, A., Golinval, J.C.: Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20, 505–592 (2006)

    Article  Google Scholar 

  32. Kosmatopoulos, E., Polycarpou, M., Christodoulou, M., Ioannou, P.: High-order neural network structures for identification of dynamical systems. IEEE Trans. Neural Netw. 6, 422–431 (1995)

    Article  Google Scholar 

  33. Kosmatopoulos, E., Smyth, A., Masri, S., Chassiakos, A.: Robust adaptive neural estimation of restoring forces in nonlinear structures. ASME J. Appl. Mech. 68, 880–893 (2001)

    Article  MATH  Google Scholar 

  34. Li, S., Suzuki, Y., Noori, M.: Identification of hysteretic systems with slip using bootstrap filter. Mech. Syst. Signal Process. 18, 781–795 (2004)

    Article  Google Scholar 

  35. Lin, J.W.: Adaptive identification of structural systems by training artificial neural networks. Adv. Inf. Sci. Serv. Sci. 4, 10–17 (2012)

    Google Scholar 

  36. Lin, J.W., Betti, R.: On-line identification and damage detection in non-linear structural systems using a variable forgetting factor approach. Earthq. Eng. Struct. Dyn. 33, 419–444 (2004)

    Article  Google Scholar 

  37. Lin, J.W., Wu, T.H.: Modeling and assessment of VWNN for signal processing of structural systems. Struct. Eng. Mech. 45, 53–67 (2013)

    Article  MathSciNet  Google Scholar 

  38. Loh, C., Chung, S.: A three-stage identification approach for hysteretic systems. Earthq. Eng. Struct. Dyn. 22, 129–150 (1993)

    Article  Google Scholar 

  39. Ma, F., Zhang, H., Bockstedte, A., Foliente, G., Paevere, P.: Parameter analysis of the differential model of hysteresis. ASME J. Appl. Mech. 71, 342–349 (2004)

    Article  MATH  Google Scholar 

  40. Masri, S.: Forced vibration of the damped bilinear hysteretic oscillator. J. Acoust. Soc. Am. 57, 106–113 (1975)

    Article  MATH  Google Scholar 

  41. Masri, S., Caffrey, J., Caughey, T., Smyth, A., Chassiakos, A.: A general data-based approach for developing reduced-order models of nonlinear MDOF systems. Nonlinear Dyn. 39, 95–112 (2005)

    Article  MATH  Google Scholar 

  42. Masri, S., Caughey, T.: A nonparametric identification technique for nonlinear dynamic problems. ASME J. Appl. Mech. 46, 433–447 (1979)

    Article  MATH  Google Scholar 

  43. Masri, S., Miller, R., Saud, A., Caughey, T.: Identification of nonlinear vibrating structures; part I: formulation. ASME J. Appl. Mech. 109, 918–922 (1987)

    Article  MATH  Google Scholar 

  44. Masri, S., Miller, R., Saud, A., Caughey, T.: Identification of nonlinear vibrating structures; part II: applications. ASME J. Appl. Mech. 109, 923–929 (1987)

    Article  MATH  Google Scholar 

  45. Masri, S., Miller, R., Traina, M., Caughey, T.: Development of bearing friction models from experimental measurements. J. Sound Vib. 148, 455–475 (1991)

    Article  Google Scholar 

  46. Masri, S., Tasbihgoo, F., Caffrey, J., Smyth, A., Chassiakos, A.: Data-based model-free representation of complex hysteretic MDOF systems. Struct. Control Health Monit. 13, 365–387 (2006)

    Article  MATH  Google Scholar 

  47. MATLAB and Neural Network Toolbox: Release 2014b. TheMathWorks, Inc., Natick, MA (2014)

  48. Peeters, B., De Roeck, G.: Stochastic system identification for operational modal analysis: a review. J. Dyn. Syst. Meas. Control 123, 659–667 (2001)

    Article  Google Scholar 

  49. Pei, J., Smyth, A., Kosmatopoulos, E.: Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems. J. Sound Vib. 275, 693–718 (2004)

    Article  Google Scholar 

  50. Peng, C., Iwan, W.: An identification methodology for a class of hysteretic structures. Earthq. Eng. Struct. Dyn. 21, 695–712 (1992)

    Article  Google Scholar 

  51. Pi, Y., Mickleborough, N.: Modal identification of vibrating structures using ARMA model. ASCE J. Eng. Mech. 115, 2232–2250 (1989)

    Article  MATH  Google Scholar 

  52. Smyth, A., Masri, S., Chassiakos, A., Caughey, T.: On-line parametric identification of MDOF nonlinear hysteretic systems. ASCE J. Eng. Mech. 125, 133–142 (1999)

    Article  Google Scholar 

  53. Smyth, A., Masri, S., Kosmatopoulos, E., Chassiakos, A., Caughey, T.: Development of adaptive modeling techniques for non-linear hysteretic systems. Int. J. Non-linear Mech. 37, 1435–1451 (2002)

    Article  MATH  Google Scholar 

  54. Smyth, A.W., Masri, S.F., Caughey, T.K., Hunter, N.F.: Surveillance of mechanical systems on the basis of vibration signature analysis. ASME J. Appl. Mech. 67, 540–551 (2000)

    Article  MATH  Google Scholar 

  55. Toussi, S., Yao, J.: Hysteretic identification of existing structures. J. Eng. Mech. Div. ASCE 109, 1189–1202 (1983)

    Article  Google Scholar 

  56. Van Overschee, P., De Moor, B.: Subspace Identification for Linear Systems: Theory-Implementation-Application. Kluwer, Dordrecht (1996)

    Book  MATH  Google Scholar 

  57. Vinogradoc, O., Pivovarov, L.: Vibrations of a system with nonlinear hysteresis. J. Sound Vib. 111, 145–152 (1986)

    Article  Google Scholar 

  58. Wen, Y.: Method for random vibration of hysteretic systems. J. Eng. Mech. Div. ASCE 102, 249–263 (1976)

    Google Scholar 

  59. Wen, Y.: Equivalent linearization for hysteretic systems under random excitation. ASME J. Appl. Mech. 47(1), 150–154 (1980)

    Article  MATH  Google Scholar 

  60. Wu, M., Smyth, A.: Real-time parameter estimation for degrading and pinching hysteretic models. Int. J. Non-linear Mech. 43, 822–833 (2008)

    Article  Google Scholar 

  61. Wu, M., Smyth, A.W.: Application of the unscented Kalman filter for real-time nonlinear structural system identification. Struct. Control Health Monit. 14, 971–990 (2007)

    Article  Google Scholar 

  62. Wu, T., Kareem, A.: Modeling hysteretic nonlinear behavior of bridge aerodynamics via cellular automata nested neural network. J. Wind Eng. Ind. Aerodyn. 99, 378–388 (2011)

  63. Yang, J., Lin, S., Huang, H., Zhou, L.: An adaptive extended Kalman filter for structural damage identification. Struct. Control Health Monit. 13(4), 849–867 (2006)

    Article  Google Scholar 

  64. Yar, M., Hammond, J.: Modeling and response of bilinear hysteretic systems. J. Eng. Mech. Div. ASCE 113, 1000–1013 (1987)

    Article  Google Scholar 

  65. Yar, M., Hammond, J.: Parameter estimation for hysteretic systems. J. Sound Vib. 117, 161–172 (1987)

    Article  Google Scholar 

  66. Zhang, H., Foliente, G., Yang, Y., Ma, F.: Parameter identification of inelastic structures under dynamic loads. Earthq. Eng. Struct. Dyn. 31(5), 1113–1130 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

The first author would like to acknowledge the support of the Viterbi Postdoctoral Fellowship from the University of Southern California. The assistance of Dr. Armen Derkevorkian in lending his expertise of artificial neural networks and generously granting permission to modify figures from his own works is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Viterbi School of Engineering, University of Southern California, Los Angeles, CA, 90089, USA

    Patrick T. Brewick & Sami F. Masri

Authors
  1. Patrick T. Brewick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sami F. Masri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Patrick T. Brewick.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Brewick, P.T., Masri, S.F. An evaluation of data-driven identification strategies for complex nonlinear dynamic systems. Nonlinear Dyn 85, 1297–1318 (2016). https://doi.org/10.1007/s11071-016-2761-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2761-x

Keywords

Search

Navigation