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Application of the Nonlinear Least Squares Frequency Domain Method to the Estimation of Modal Model Parameters

100%

Iwaniec J. , Uhl T.

Machine Dynamics Problems

2003

tom Vol. 27, No. 2

37-54

The least squares method is the most popular algorithm for solving linear as well as nonlinear systems of equations. In the paper the theoretical basis of the Gauss-Newton and the Levenberg-Marquardt algorithms for solution estimation with the use of the nonlinear least squares method are presented. The discussed schemes of proceeding usually allow the user to improve the quality of the estimated solutions. The analysis of frequency data measured on a real structure with the use of the created software realizing the Gauss-Newton algorithm in the Matlab environment is presented. The comparison of the analysis results estimated by the use of the proposed software and the LSCE (least squares complex exponential) algorithm implemented in the VIOMA toolbox is also included.

On the identification of composite beam dynamics based upon experimental data

63%

Dobrzański L. A. , Honysz R. , Fassois S.

2006

tom Vol. 16, nr 1-2

114--123

Purpose: Article describes kinds and use procedures of mathematical parametric models describing dynamics of the systems based on excitation and vibration response signals. Design/methodology/approach: As a sample of identification of mathematical parametric models and estimation their parameters was a composite beam investigated under a white noise excitation force activity. Findings: Model based identification leads to finitely parameterised models described by differential equations. Research limitations/implications: Such models provide important features, in comparison with non-parametric systems: direct relationship with differential equation or physically significant modal representations used in engineering analysis, improved accuracy and frequency resolution, compactness/parsimony of representation. Practical implications: Ability to provide complete system characterisation by relatively few parameters, suitability for analysis, prediction, fault detection and control. Originality/value: Article is valuable for persons, that are interesting for identification of mathematical parametric models and vibration systems.