Skip to main content
SpringerLink
Log in

Nonlinear hysteretic parameter identification using an attention-based long short-term memory network and principal component analysis

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

Abstract

Hysteretic models are used to describe the nonlinear memory-based relationship between the input and output of some physical systems. A long short-term memory neural network-based method is proposed to identify nonlinear hysteretic parameters. Either force or vibration response data are used as the input of the network and the nonlinear hysteresis parameters as the output. The principal component analysis technique is applied to eliminate the redundant dimensionality of the input data. The attention mechanism is utilized to enhance the generalization ability of the standard network. Three representative hysteretic models are employed to verify the effectiveness of the present method. Both numerical and experimental results demonstrate that the proposed method could yield accurate identification results in all cases, even when uncertain and limited input data are used. Compared with the sensitivity methods and heuristic algorithms, the proposed method is more computationally efficient and can obtain more accurate identification results.

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Availability of data and materials

The data that support the findings of this study are available from the first author upon reasonable request.

References

  1. Li, W.L., Chen, Y.M., Lu, Z.R., Liu, J.K., Wang, L.: Parameter identification of nonlinear structural systems through frequency response sensitivity analysis. Nonlinear Dyn. 104, 3975–3990 (2021)

    Google Scholar 

  2. Xu, Z.D., Xu, F.H., Chen, X.: Vibration suppression on a platform by using vibration and mitigation devices. Nonlinear Dyn. 83(3), 1341–1353 (2016)

    Google Scholar 

  3. Pozo, F., Acho, L., Rodriguez, A., Pujol, G.: Nonlinear modeling of hysteretic systems with double hysteretic loops using position and acceleration information. Nonlinear Dyn. 57, 1–12 (2009)

    MATH  Google Scholar 

  4. Marszalek, W.: On the action parameter and one-period loops of oscillatory memristive circuits. Nonlinear Dyn. 82, 619–628 (2015)

    Google Scholar 

  5. Yu, Y., Li, Y.C., Li, J.C.: Parameter identification of a novel strain stiffness model for magnetorheological elastomer base isolator utilizing enhanced particle swarm optimization. J. Intell. Mater. Syst. Struct. 26(18), 2446–2462 (2015)

    Google Scholar 

  6. Lu, Z.R., Yao, R.Z., Wang, L., Liu, J.K.: Identification of nonlinear hysteretic parameters by enhanced response approach. Int. J. Non-Linear Mech. 96, 1–11 (2017)

    Google Scholar 

  7. Belbas, S.A., Mayergoyz, I.D.: Optimal control of dynamical systems with Preisach hysteresis. Int. J. Non-Linear Mech. 37, 1351–1361 (2002)

    MATH  Google Scholar 

  8. Janaideh, M.A., Aljanaideh, O.: Further results on open-loop compensation of rate-dependent hysteresis in a magnetostrictive actuator with Prandtl-Ishlinskii model. Mech. Syst. Signal Process. 104, 835–850 (2018)

    Google Scholar 

  9. Kim, S.Y., Lee, C.H.: Description of asymmetric hysteretic behavior based on the Bouc-Wen model and piecewise linear strength-degradation functions. Eng. Struct. 181, 181–191 (2019)

    Google Scholar 

  10. Yar, M., Hammond, J.K.: Modelling and response of bilinear hysteretic systems. J. Eng. Mech. 113(7), 1000–1013 (1987)

    Google Scholar 

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

    Google Scholar 

  12. Yang, Y.M., Ma, F.: Constrained Kalman filter for nonlinear structural identification. J. Vib. Control. 9(12), 1343–1357 (2003)

    MATH  Google Scholar 

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

    Google Scholar 

  14. Peng, Z., Li, J.: Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures. Adv. Struct. Eng. 25(7), 1652–1669 (2022)

    Google Scholar 

  15. Tian, W., Weng, S., Xia, Y.: Model updating of nonlinear structures using substructuring method. J. Sound Vib. 521, 116719 (2022)

    Google Scholar 

  16. Tian, W., Weng, S., Xia, Y.: Kron’s substructuring method to the calculation of structural responses and response sensitivities of nonlinear systems. J. Sound Vib. 502, 116101 (2021)

    Google Scholar 

  17. Xu, Z.D., Guo, Y.F., Wang, S.A., Huang, X.H.: Optimization analysis on parameters of multi-dimensional earthquake isolation and mitigation device based on genetic algorithm. Nonlinear Dyn. 72(4), 757–765 (2013)

    Google Scholar 

  18. Kwok, N.M., Ha, Q.P., Nguyen, T.H., Li, J., Samali, B.: A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization. Sens. Actuator A Phys. 132(2), 441–451 (2006)

    Google Scholar 

  19. Charalampakis, A.E., Dimou, C.K.: Identification of Bouc-Wen hysteretic systems using particle swarm optimization. Comput Struct. 88(21–22), 1197–1205 (2010)

    Google Scholar 

  20. Yao, R.Z., Chen, Y.M., Wang, L., Lu, Z.R.: Nonlinear hysteretic parameter identification using improved artificial bee colony algorithm. Adv. Struct. Eng. 24(14), 3156–3170 (2021)

    Google Scholar 

  21. Carboni, B., Lacarbonara, W., Brewick, P.T., Masri, S.F.: Dynamical response identification of a class of nonlinear hysteretic systems. J. Intell. Mater. Syst. Struct. 29(13), 2795–2810 (2016)

    Google Scholar 

  22. Ding, Z.H., Li, J., Hao, H., Lu, Z.R.: Nonlinear hysteretic parameter identification using an improved tree-seed algorithm. Swarm Evol. Comput. 46, 69–83 (2019)

    Google Scholar 

  23. Son, N.N., Kien, C.V., Anh, H.P.H.: Parameter identification of Bouc-Wen hysteresis model for piezoelectric actuators using hybrid adaptive differential evolution and Jaya algorithm. Eng. Appl. Artif. Intell. 87, 103317 (2020)

    Google Scholar 

  24. Brewick, P.T., Masri, S.F.: An evaluation of data-driven identification strategies for complex nonlinear dynamic systems. Nonlinear Dyn. 85, 1297–1318 (2016)

    Google Scholar 

  25. Brewick, P.T., Masri, S.F., Carboni, B., Lacarbonara, W.: Enabling reduced-order data-driven nonlinear identification and modeling through naïve elastic net regularization. Int. J. Non-Linear Mech. 94, 46–58 (2017)

    Google Scholar 

  26. Zhang, N., Shen, S.L., Zhou, A.N., Jin, Y.F.: Application of LSTM approach for modelling stress-strain behavior of soil. Appl. Soft Comput. 100, 106959 (2021)

    Google Scholar 

  27. Ding, Z.H., Li, J., Hao, H.: Structural damage identification by sparse deep belief network using uncertain and limit data. Struct. Control Health Monit. 27(5), e2522 (2020)

    Google Scholar 

  28. Yan, H.R., Qin, Y., Xiang, S., Wang, Y., Chen, H.Z.: Long-term gear life prediction based on ordered neurons LSTM neural networks. Measurement 165, 108205 (2020)

    Google Scholar 

  29. Jorges, C., Berkenbrink, C., Stumpe, B.: Prediction and reconstruction of ocean wave heights based on bathymetric data using LSTM neural networks. Ocean Eng. 232, 109046 (2021)

    Google Scholar 

  30. Shahid, F., Zameer, A., Muneeb, M.: A novel genetic LSTM model for wind power forecast. Energy 223, 120069 (2021)

    Google Scholar 

  31. Farhi, N., Kohen, E., Mamane, H., Shavitt, Y.: Prediction of wastewater treatment quality using LSTM neural network. Environ. Technol. Innov. 23, 101632 (2021)

    Google Scholar 

  32. Zhang, T., Zheng, X.Q., Liu, M.X.: Multiscale attention-based LSTM for ship motion prediction. Ocean Eng. 230, 109066 (2021)

    Google Scholar 

  33. Ding, Z.H., Li, J., Hao, H.: Simultaneous identification of structural damage and nonlinear hysteresis parameters by an evolutionary algorithm-based artificial neural network. Int. J. Non-Linear Mech. 142, 103970 (2022)

    Google Scholar 

  34. Rodriguez-Garciapina, J.L., Beltran-Perez, G., Gastillo-Mixcoatl, J., Munoz-Aguirre, S.: Application of the principal components analysis technique to optical fiber sensors for acetone detection. Opt. Laser Technol. 143, 107314 (2021)

    Google Scholar 

  35. Ouyang, Z.S., Yang, X.T., Lai, Y.Z.: Systemic financial risk early warning of financial market in China using Attention-LSTM model. N. Am. J. Econ. Finance. 56, 101383 (2021)

    Google Scholar 

  36. Pandey, R., Kumar, A., Singh, J.P., Tripathi, S.: Hybrid attention-based long short-term memory network for sarcasm identification. Appl. Soft Comput. 106, 107348 (2021)

    Google Scholar 

  37. Katsaras, C.P., Panagiotakos, T.B., Kolias, B.: Restoring capacity of bilinear hysteretic seismic isolation systems. Earthq. Eng. Struct. Dyn. 37, 557–575 (2008)

    Google Scholar 

  38. Li, Y.C., Li, J.C., Tian, T.F., Li, W.H.: A highly adjustable magnetorheological elastomer base isolator for applications of real-time adaptive control. Smart Mater. Struct. 23, 129501 (2014)

    Google Scholar 

  39. Yu, Y., Li, Y.C., Li, J.C., Gu, X.: Dynamic modelling of magnetorheological elastomer base isolator based on extreme learning machine. 24th ACMSM, Perth, 703–708 (2016)

  40. Zhang, R.Y., Chen, Z., Chen, S., Zheng, J.W., Buyukozturk, O., Hao, H.: Deep long short-term memory networks for nonlinear structural seismic response prediction. Comput. Struct. 220, 55–68 (2019)

    Google Scholar 

  41. Desimone, R., Duncan, J.: Neural mechanisms of selective visual attention. Annu. Rev. Neurosci. 18, 193–222 (1995)

    Google Scholar 

  42. Shekar, B.H., Dagnew, G.: Grid search based hyperparameter tuning and classification of microarray cancer data. ICACCP, 1–8 (2019)

  43. Monroe, R.J., Shaw, S.W.: On the transient response of forced nonlinear oscillators. Nonlinear Dyn. 67, 2609–2619 (2012)

    Google Scholar 

Download references

Funding

This work is supported by the Key Area R&D Program of Guangdong Province (Project No. 2019B111106001), the National Key R&D Program (Project No. 2019YFB1600700), and the PolyU Postdoctoral Matching Fund (Project No. W18P).

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

    Zhenghao Ding & Yong Xia

  2. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Yang Yu

  3. School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China

    Yong Xia

Authors
  1. Zhenghao Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Xia.

Ethics declarations

Conflict of interest

The author(s) claimed no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, Z., Yu, Y. & Xia, Y. Nonlinear hysteretic parameter identification using an attention-based long short-term memory network and principal component analysis. Nonlinear Dyn 111, 4559–4576 (2023). https://doi.org/10.1007/s11071-022-08095-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08095-x

Keywords

Search

Navigation