A sparse Frequency-domain Bayesian filter for broadband source identification
Résumé
In the frequency domain, broadband mechanical sources are typically identified frequency by frequency using Tikhonov-like regularization strategies. However, such an approach does not exploit the spectral characteristics of the sources to be identified, which can be detrimental to the quality of the identification, especially in the vicinity of the resonance frequencies of the structure. Based on this observation, mixed-norm regularization has been developed and applied with some success. However, this comes at the price of an increase in the computational cost, since the problem is solved for all frequencies at once. In order to reduce the computational cost of the identification procedure, while taking into account the spectral characteristics of the sources to identify, an original frequency-domain Bayesian filter is presented in this contribution. More precisely, the proposed strategy is a frequency-domain application of the Bayesian filtering theory to which Kalman filters belong. To evaluate the identification ability of the proposed approach, a numerical experiment is conducted on a simply-supported beam excited by a broadband point mechanical point force. A comparison with sparse regularization applied at each frequency independently is also proposed.
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