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Uncertainty quantification of dynamic responses in the frequency domain in the context of virtual testing

par Brehm, Maik ;Deraemaeker, Arnaud
Référence Journal of sound and vibration, 342, page (303-329)
Publication Publié, 2015-04

Article révisé par les pairs

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Résumé :

For the development of innovative materials, construction types or maintenance strategies, experimental investigations are inevitable to validate theoretical approaches in praxis. Numerical simulations, embedded in a general virtual testing approach, are alternatives to expensive experimental investigations. The statistical properties of the dynamic response in the frequency domain obtained from continuously measured data are often the basis for many developments, such as the optimization of damage indicators for structural health monitoring systems or the investigation of data-based frequency response function estimates. Two straightforward numerical simulation approaches exist to derive the statistics of a response due to random excitation and measurement errors. One approach is the sample-based technique, wherein for each excitation sample a time integration solution is needed. This can be computationally very demanding if a high accuracy of the statistical properties is of interest. The other approach consists in using the relationship between the excitation and the response directly in the frequency domain, wherein a weakly stationary process is assumed. This approach is inherently related to an infinite time response, which can hardly be derived from measured data. In this paper, a novel approach is proposed that overcomes the limitation of both aforementioned methods, by providing a fast analytical probabilistic framework for uncertainty quantification to determine accurately the statistics of short time dynamic responses. It is assumed that the structural system is known and can be described by deterministic parameters. The influences of signal processing techniques, such as linear combinations, windowing, and segmentation used in Welchs method, are considered as well. The performance of the new algorithm is investigated in comparison to both previous approaches on a three degrees of freedom system. The benchmark shows that the novel approach outperforms the sample-based approach with respect to accuracy and computational effort. In comparison with the approach based on the estimator in the frequency domain, the results are more accurate in the case of short time dynamic responses. To show the interest of the technique, the novel approach is applied to the investigation of a damage indicator, which allows developing a deep insight in the effect of typical signal processing techniques on the statistics of quantities derived from response Fourier transforms.