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.
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