Fast Bayesian identification of a class of elastic weakly nonlinear systems using backbone curves

T. L. Hill*, P. L. Green, Andrea Cammarano, S. A. Neild

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)
358 Downloads (Pure)


This paper introduces a method for the identification of the parameters of nonlinear structures using a probabilistic Bayesian framework, employing a Markov chain Monte Carlo algorithm. This approach uses analytical models to describe the unforced, undamped dynamic responses of structures in the frequency-amplitude domain, known as the backbone curves. The analytical models describing these backbone curves are then fitted to measured responses, found using the resonant-decay method. To investigate the proposed identification method, a nonlinear two-degree-of-freedom example structure is simulated numerically and analytical expressions describing the backbone curves are found. These expressions are then used, in conjunction with the backbone curve data found through simulated experiment, to estimate the system parameters. It is shown that the use of these computationally-cheap analytical expressions allows for an extremely efficient method for modelling the dynamic behaviour, providing an identification procedure that is both fast and accurate. Furthermore, for the example structure, it is shown that the estimated parameters may be used to accurately predict the existence of dynamic behaviours that are well-away from the backbone curve data provided; specifically the existence of an isola is predicted.

Original languageEnglish
Pages (from-to)156-170
Number of pages15
JournalJournal of Sound and Vibration
Publication statusPublished - 6 Jan 2016

Bibliographical note

Date of Acceptance: 06/09/2015


  • Nonlinear system identification
  • Second-order normal form technique
  • Backbone curves
  • Bayesian inference,
  • Markov chain Monte Carlo

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