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Communication Dans Un Congrès Année : 2019

On the interest of a space-time regularization for reconstructing sparse excitation sources

Résumé

In time domain, force reconstruction problems are commonly solved from Tikhonov and LASSO regularizations. Practically, these approaches can lead to inaccurate reconstructions, if the sources to identify don't share the same space-time characteristics or the corresponding force vector doesn't exhibit the desired structure. To alleviate this potential drawback, we have recently introduced a multiplicative space-time regularization that allows exploiting one's prior knowledge of the spatial distribution of the sources as well as their time history. In this contribution, the proposed regularization strategy is compared to the multiplicative Tikhonov and LASSO regularizations through an experimental application to point out the practical interest of exploiting simultaneously both spatial and temporal prior information in terms of quality and robustness of the reconstructed excitation sources. 1. Introduction Force reconstruction problems in time domain still remain an active topic in the structural dynamics community. To solve this problem, several approaches have been developed, such as Kalman filtering [1] or adaptive filtering [2]. However, the most widespread strategy is certainly the regularization, and more particularly, the Tikhonov and LASSO regularizations. From a theoretical standpoint, Tikhonov regularization should be used when the force signal exhibits a certain continuity [3, 4] and the spatial distribution of the sources is rather smooth [5]. On the contrary, LASSO regularization should be used when the excitation signal is rather impulsive [6, 7] and the spatial distribution of the sources is sparse [8]. It results that classical strategies developed in the literature are theoretically not always well adapted to tackle both the local-ization and time reconstruction problems at the same time, except for configurations where the force vector to identify has the desired structure or the spatial distribution of sources and the nature of the excitation signals share the same space-time characteristics, such as the sparsity [9]. To the best of our knowledge, only a few methods have been developed to address this specific issue and they generally consist in solving the space-time reconstruction problem in a separated manner [10].
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hal-02103243 , version 1 (18-04-2019)

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  • HAL Id : hal-02103243 , version 1

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Mathieu Aucejo, Olivier de Smet, Jean-François Deü. On the interest of a space-time regularization for reconstructing sparse excitation sources. XIIIth Conference On Recent Advances in Structural Dynamics, Apr 2019, Lyon, France. ⟨hal-02103243⟩
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