Skip to main content
SpringerLink
Log in

Spline adaptive filters based on real-time over-sampling strategy for nonlinear system identification

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

Abstract

In this paper, a new spline adaptive filter (SAF) used for identifying the nonlinear systems is presented, in which a real-time over-sampling (RTOS) strategy is proposed in order to solve the performance degradation caused by the imbalanced distribution of the input data in SAF during the adaptive process. Based on the invariance property of nonlinear system, an initialization for the linear part in SAF is implemented in advance. The number of data falling into each spline interpolation interval is counted, and the historical input and output data of each interval are recorded in real-time. In each adaption loop, a new sample is generated through the existing recorded data in a certain interval according to the data distribution in all intervals, so that the distribution of input data could be relatively evened. Several numerical experiments were implemented, and the results show that the proposed RTOS strategy can significantly improve the convergence performance compared with the existing algorithms.

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
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Ljung, L.: System Identification. Wiley Encyclopedia of Electrical and Electronics Engineering, pp. 1–19. Wiley, Hoboken (1999)

    MATH  Google Scholar 

  2. Haykin, SS.: Adaptive filter theory. Pearson Education India (2005)

  3. Hannan, E.J., Deistler, M.: The Statistical Theory of Linear Systems. SIAM, Philadelphia (2012)

    Book  Google Scholar 

  4. Pintelon, R., Schoukens, J.: System Identification: A Frequency Domain Approach. Wiley, Hoboken (2012)

    Book  Google Scholar 

  5. Hu, W.: Adaptive inverse control for aeroengines. Ph.D. thesis, Nanjing University of Aeronautics and Astronautics (2004)

  6. Chang, G., Qian, N., Chen, C., Gao, J.: Precise instantaneous velocimetry and accelerometry with a stand-alone GNSS receiver based on sparse kernel learning. Measurement 159, 107803 (2020)

    Article  Google Scholar 

  7. Chang, G., Xu, T., Yao, Y., Wang, Q.: Adaptive kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of gnss triple-frequency signals. J. Geodesy 92(11), 1241–1253 (2018)

    Article  Google Scholar 

  8. Doyle III, F.J., Ogunnaike, B.A., Pearson, R.K.: Nonlinear model-based control using second-order volterra models. Automatica 31(5), 697–714 (1995)

    Article  MathSciNet  Google Scholar 

  9. Cheng, C., Peng, Z., Zhang, W., Meng, G.: Volterra-series-based nonlinear system modeling and its engineering applications: a state-of-the-art review. Mech. Syst. Signal Process. 87, 340–364 (2017)

    Article  Google Scholar 

  10. Fallahi, K., Raoufi, R., Khoshbin, H.: An application of chen system for secure chaotic communication based on extended kalman filter and multi-shift cipher algorithm. Commun. Nonlinear Sci. Numer. Simul. 13(4), 763–781 (2008)

    Article  MathSciNet  Google Scholar 

  11. Auger, F., Hilairet, M., Guerrero, J.M., Monmasson, E., Orlowska-Kowalska, T., Katsura, S.: Industrial applications of the kalman filter: a review. IEEE Trans. Ind. Electron. 60(12), 5458–5471 (2013)

    Article  Google Scholar 

  12. Comminiello, D., Scarpiniti, M., Azpicueta-Ruiz, L.A., Arenas-Garcia, J., Uncini, A.: Functional link adaptive filters for nonlinear acoustic echo cancellation. IEEE Trans. Audio Speech Lang. Process. 21(7), 1502–1512 (2013)

    Article  Google Scholar 

  13. Comminiello, D., Scarpiniti, M., Scardapane, S., Parisi, R., Uncini, A.: Improving nonlinear modeling capabilities of functional link adaptive filters. Neural Netw. 69, 51–59 (2015)

    Article  Google Scholar 

  14. Liu, W., Principe, J.C., Haykin, S.: Kernel Adaptive Filtering: A Comprehensive Introduction, vol. 57. Wiley, Hoboken (2011)

    Google Scholar 

  15. Van Vaerenbergh, S., Santamaría, I.: A comparative study of kernel adaptive filtering algorithms. In: 2013 IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), IEEE, pp 181–186 (2013)

  16. Giri, F., Bai, E.W.: Block-Oriented Nonlinear System Identification, vol. 1. Springer, Berlin (2010)

    Book  Google Scholar 

  17. Boyd, S., Chua, L.: Fading memory and the problem of approximating nonlinear operators with volterra series. IEEE Trans. Circuits And Syst. 32(11), 1150–1161 (1985)

    Article  MathSciNet  Google Scholar 

  18. Ahmadi, M., Mojallali, H.: Identification of multiple-input single-output hammerstein models using bezier curves and bernstein polynomials. Appl. Math. Model. 35(4), 1969–1982 (2011)

    Article  MathSciNet  Google Scholar 

  19. Kibangou, A.Y., Favier, G.: Tensor analysis-based model structure determination and parameter estimation for block-oriented nonlinear systems. IEEE J. Select. Top. Signal Process. 4(3), 514–525 (2010)

    Article  Google Scholar 

  20. Tang, Y., Li, Z., Guan, X.: Identification of nonlinear system using extreme learning machine based hammerstein model. Commun. Nonlinear Sci. Numer. Simul. 19(9), 3171–3183 (2014)

    Article  MathSciNet  Google Scholar 

  21. Cui, M., Liu, H., Li, Z., Tang, Y., Guan, X.: Identification of hammerstein model using functional link artificial neural network. Neurocomputing 142, 419–428 (2014)

    Article  Google Scholar 

  22. Scarpiniti, M., Comminiello, D., Parisi, R., Uncini, A.: Nonlinear spline adaptive filtering. Sig. Process. 93(4), 772–783 (2013)

    Article  Google Scholar 

  23. Scarpiniti, M., Comminiello, D., Parisi, R., Uncini, A.: Nonlinear system identification using iir spline adaptive filters. Sig. Process. 108, 30–35 (2015)

    Article  Google Scholar 

  24. Scarpiniti, M., Comminiello, D., Parisi, R., Uncini, A.: Hammerstein uniform cubic spline adaptive filters: Learning and convergence properties. Sig. Process. 100, 112–123 (2014)

    Article  Google Scholar 

  25. Scarpiniti, M., Comminiello, D., Parisi, R., Uncini, A.: Novel cascade spline architectures for the identification of nonlinear systems. IEEE Trans. Circuits Syst. I Regul. Pap. 62(7), 1825–1835 (2015)

    Article  MathSciNet  Google Scholar 

  26. Scarpiniti, M., Comminiello, D., Scarano, G., Parisi, R., Uncini, A.: Steady-state performance of spline adaptive filters. IEEE Trans. Signal Process. 64(4), 816–828 (2016)

    Article  MathSciNet  Google Scholar 

  27. Peng, S., Wu, Z., Zhang, X., Chen, B.: Nonlinear spline adaptive filtering under maximum correntropy criterion. In: TENCON 2015–2015 IEEE Region 10 Conference, IEEE, pp 1–5 (2015)

  28. Patel, V., Comminiello, D., Scarpiniti, M., George, NV., Uncini, A.: Design of hybrid nonlinear spline adaptive filters for active noise control. In: 2016 International Joint Conference on Neural Networks (IJCNN), IEEE, pp. 3420–3425 (2016)

  29. Scardapane, S., Scarpiniti, M., Comminiello, D., Uncini, A.: Diffusion spline adaptive filtering. In: 2016 24th European Signal Processing Conference (EUSIPCO), IEEE, pp. 1498–1502 (2016)

  30. Rathod, M., Patel, V., George, N.V.: Generalized spline nonlinear adaptive filters. Expert Syst. Appl. 83, 122–130 (2017)

    Article  Google Scholar 

  31. Yang, Y., Yang, B., Niu, M.: Spline adaptive filter with fractional-order adaptive strategy for nonlinear model identification of magnetostrictive actuator. Nonlinear Dyn. 90(3), 1647–1659 (2017)

    Article  Google Scholar 

  32. Guan, S., Li, Z.: Normalised spline adaptive filtering algorithm for nonlinear system identification. Neural Process. Lett. 46(2), 595–607 (2017)

    Article  Google Scholar 

  33. Liu, C., Zhang, Z., Tang, X.: Sign normalised spline adaptive filtering algorithms against impulsive noise. Sig. Process. 148, 234–240 (2018)

    Article  Google Scholar 

  34. Cheng, S., Wei, Y., Sheng, D., Wang, Y.: Identification for hammerstein nonlinear systems based on universal spline fractional order lms algorithm. Commun. Nonlinear Sci. Numer. Simul. 79, 104901 (2019)

    Article  MathSciNet  Google Scholar 

  35. Yang, L., Liu, J., Yan, R., Chen, X.: Spline adaptive filter with arctangent-momentum strategy for nonlinear system identification. Sig. Process. 164, 99–109 (2019)

    Article  Google Scholar 

  36. Yang, L., Liu, J., Zhao, Z., Yan, R., Chen, X.: Interval variable step-size spline adaptive filter for the identification of nonlinear block-oriented system. Nonlinear Dyn. 98(3), 1629–1643 (2019)

    Article  Google Scholar 

  37. Bussgang, JJ.: Crosscorrelation functions of amplitude-distorted gaussian signals (1952)

  38. Enqvist, M.: Linear models of nonlinear systems (2005)

  39. He, H., Ma, Y.: Imbalanced Learning: Foundations, Algorithms, and Applications. Wiley, Hoboken (2013)

    Book  Google Scholar 

  40. Krawczyk, B.: Learning from imbalanced data: open challenges and future directions. Progr. Artif. Intell. 5(4), 221–232 (2016)

    Article  Google Scholar 

  41. Thai-Nghe, N., Gantner, Z., Schmidt-Thieme, L.: Cost-sensitive learning methods for imbalanced data. In: The 2010 International joint conference on neural networks (IJCNN), IEEE, pp. 1–8 (2010)

  42. Sun, Y., Kamel, MS., Wang, Y.: Boosting for learning multiple classes with imbalanced class distribution. In: Sixth International Conference on Data Mining (ICDM’06), IEEE, pp. 592–602 (2006)

  43. Chawla, N.V., Bowyer, K.W., Hall, L.O., Kegelmeyer, W.P.: Smote: synthetic minority over-sampling technique. J. Artif. Intell. Res. 16, 321–357 (2002)

    Article  Google Scholar 

  44. Han, H., Wang, WY., Mao, BH.: Borderline-smote: a new over-sampling method in imbalanced data sets learning. In: International Conference on Intelligent Computing, Springer, Berlin. pp. 878–887 (2005)

  45. He, H., Bai, Y., Garcia, EA., Li, S.: Adasyn: Adaptive synthetic sampling approach for imbalanced learning. In: 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), IEEE, pp. 1322–1328 (2008)

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 51705396, 51835009, 51911530774).

Author information

Authors and Affiliations

  1. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710054, China

    Liangdong Yang, Jinxin Liu, Ruobin Sun, Ruqiang Yan & Xuefeng Chen

Authors
  1. Liangdong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinxin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruobin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ruqiang Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xuefeng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinxin Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, L., Liu, J., Sun, R. et al. Spline adaptive filters based on real-time over-sampling strategy for nonlinear system identification. Nonlinear Dyn 103, 657–675 (2021). https://doi.org/10.1007/s11071-020-05899-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05899-7

Keywords

Search

Navigation