Nonlinear Dynamics

, Volume 98, Issue 3, pp 1629–1643 | Cite as

Interval variable step-size spline adaptive filter for the identification of nonlinear block-oriented system

  • Liangdong Yang
  • Jinxin LiuEmail author
  • Zhibin Zhao
  • Ruqiang Yan
  • Xuefeng Chen
Original paper


In order to improve the convergence speed of the nonlinear spline adaptive filter (SAF) in the identification of block-oriented systems, an interval variable step-size algorithm is proposed. Traditional SAF algorithm uses constant step size during iteration, leading to a contradiction between convergence speed and steady-state accuracy. In this paper, a new kind of variable step-size algorithm is proposed, fully considering the particularity of spline interpolation in the nonlinear part of the block-oriented model. The step size of each interpolation interval is independent from that of other intervals, and it is dominated by the correlated squared error which is evaluated by an exponential-weighted averaging (EWA) process. In this paper, the independent step size in each interpolation interval is also updated through an EWA process of the correlated error. The effects of the parameters on the convergence performance of the proposed strategy have been theoretically analyzed and verified by simulations. Finally, some numerical simulations have confirmed that the proposed interval variable step-size approach can significantly improve the convergence speed as well as reduce the steady-state error compared with the traditional SAF and the existing variable step-size SAF algorithms.


Spline adaptive filter Block-oriented model Nonlinear identification Variable step size 



This research was supported by the National Natural Science Foundation of China (Nos. 51705396, 51835009) and the Postdoctoral Science Foundation of China (No. 2018T111047).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory for Manufacturing Systems EngineeringXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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