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

Shahab Torkamani, Eric Butcher

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

State estimation
Parameter estimation
state estimation
Extended Kalman filters
Machine tools
Ordinary differential equations
machine tools
vibration
Kalman filters
noise measurement
differential equations
augmentation
approximation
excitation

ASJC Scopus subject areas

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

Cite this

Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay. / Torkamani, Shahab; Butcher, Eric.

In: Journal of Sound and Vibration, Vol. 332, No. 14, 08.07.2013, p. 3404-3418.

Research output: Contribution to journalArticle

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