Governing Equation Identification of Nonlinear Single Degree-of-Freedom Oscillators With Coulomb Friction Using Explicit Stick and Slip Temporal Constraints

Saurabh Mahajan, Alice Cicirello

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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Abstract

The friction force at joints of engineering structures is usually unknown and not directly identifiable. This contribution explores a procedure for obtaining the governing equation of motion and correctly identifying the unknown Coulomb friction force of a mass-springdashpot system. In particular, a single degree-of-freedom system is investigated both numerically and experimentally. The proposed procedure extends the state-of-the-art datadriven sparse identification of nonlinear dynamics (SINDy) algorithm by developing a methodology that explicitly imposes constraints encoding knowledge of the nonsmooth dynamics experienced during stick-slip phenomena. The proposed algorithm consists of three steps: (i) data segregation of mass-motion from mass-sticking during stick-slip response; (ii) application of SINDy on the mass-motion dataset to obtain the functional form of the governing equation; and (iii) applying sticking and slipping conditions to identify the unknown system parameters. It is shown that the proposed approach yields an improved estimate of the uncertain system parameters such as stiffness, viscous damping, and magnitude of friction force (all mass normalized) for various signal-to-noise ratios compared to SINDy.

Original languageEnglish
Article number041101
Number of pages11
JournalASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
Volume9
Issue number4
DOIs
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Coulomb friction
  • discontinuous nonlinearity
  • epistemic uncertainty
  • nonlinear dynamic system identification
  • SINDy
  • stick and slip temporal constraints

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