Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

Shahab Torkamani, Eric A. Butcher

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

Original languageEnglish (US)
Pages (from-to)3404-3418
Number of pages15
JournalJournal of Sound and Vibration
Volume332
Issue number14
DOIs
StatePublished - Jul 8 2013
Externally publishedYes

ASJC Scopus subject areas

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

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