Nonlinear Dynamics

, Volume 94, Issue 4, pp 2491–2509 | Cite as

A modified time domain subspace method for nonlinear identification based on nonlinear separation strategy

  • Jie Liu
  • Bing LiEmail author
  • Huihui Miao
  • Xiang Zhang
  • Meng Li
Original Paper


Nonlinear factors existing in engineering structures have drawn considerable attention, and nonlinear identification is a competent technique to understand the dynamic characteristics of nonlinear structures. Therefore, in this paper, a novel nonlinear separation subspace identification (NSSI) algorithm based on subspace algorithm and nonlinear separation strategy is proposed to conduct nonlinear parameter identification of nonlinear structures. For the proposed NSSI algorithm, the low-level excitation test is firstly conducted to obtain the transfer matrix in the linear response formula. Then, the obtained transfer matrix is used in the high-level excitation test to calculate the nonlinear response part by the proposed nonlinear separation strategy, and the subspace algorithm is utilized to identify the nonlinear parameter on the modified state-space model including only the nonlinear part. The proposed NSSI algorithm can reduce the coupling error caused by simultaneously processing both the large number part (corresponding to the linear part) and small number part (corresponding to the nonlinear part) in the traditional nonlinear subspace identification (NSI) algorithm. At last, two numerical experiments are given to validate the effectiveness of the developed novel nonlinear identification method. Furthermore, some influence factors are discussed to show the stability of the identification algorithm, and some comparisons between the proposed NSSI method and traditional NSI method are also conducted to demonstrate the advantages of the novel method.


Nonlinear identification Nonlinear subspace identification method Nonlinear separation strategy 



This work is supported financially by the National Natural Science Foundation of China (51475356).

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. 2018

Authors and Affiliations

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

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