System identification of lumped parameter models for weakly nonlinear systems

P. S. Heaney, O. Bilgen

Research output: Contribution to journalArticle


Experimental system identification through modal analysis is often conducted by assuming linear constitutive laws and kinematic relationships. Significant prediction errors from these identified models can occur when the amplitude dependent contribution of nonlinearities is ignored. In this paper, the impact of such nonlinearities on the parameter identification and accuracy of a linear model is shown to depend significantly on the experimental procedures. Using modal analysis techniques and focusing on vibration near the fundamental mode, a cantilevered beam is modeled as a single degree of freedom oscillator with parameters to be determined through experimental system identification. Various testing procedures are described in detail and used to demonstrate the impact of nonlinearities on the outcome of different system identification processes. The signal control methods compared are (1) open loop, (2) constant input, and (3) constant response excitation. Forcing types considered are single point and distributed. Nonlinearities in experimental response are shown for all procedures, and it is demonstrated that the observed character and degree of the nonlinearities vary depending on the testing procedure. The paper makes various recommendations for experimental system identification procedures using linear structural models, which include developing empirical models for parameter shifts due to nonlinearities and using constant response tests to minimize nonlinear effects in the measured system response. By implementing these identification methods, parameter variations can be included in the linear model to significantly reduce predicted response and parameter errors for weakly nonlinear second-order systems.

Original languageEnglish (US)
Pages (from-to)78-95
Number of pages18
JournalJournal of Sound and Vibration
StatePublished - Jun 23 2019

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


  • Lumped parameter model
  • Modal analysis
  • Nonlinear identification
  • Structural dynamics
  • System identification

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