Abstract
One of the main difficulties of the operational modal analysis is to deal with underdetermined problems inwhich the number of sensors is less than the number of active modes. In the last decade, methods based on the PARAllel FACtor (PARAFAC) decomposition have attracted a lot of attention in the field of modal analysis because it has been proven that these methods can deal with underdetermined cases, as well as the presence of harmonic excitations. Moreover, in combination with kurtosis value as a harmonic indicator, this makes them more efficient in distinguishing between harmonic and structural components. However, it can lead to distorted results as it does not take into account the variation in the length of the covariance functions of the modal coordinates. Since the kurtosis values are estimated from these covariance functions, the length of the latter directly affects the kurtosis. To overcome this limit, the present study proposes to introduce the choice of the length of these functions based on their frequency and damping coefficient. This change improves the existing method by more efficient separating between harmonics and modal components. The proposed procedure is validated using numerical simulations, followed by ambient vibration measurements. © 2021 Academie des sciences, Paris and the authors.
Highlights
In recent decades, operational modal analysis (OMA) has been significantly developed, and it plays a vital role in the engineering fields
The main challenge for applying the blind source separation (BSS) techniques in OMA is when the number of measurement signals is less than that of latent sources—an underdetermined case. This problem can be encountered in many practical applications with limited measurements, for example, for complex structures or in the presence of harmonic excitations, when the measurement signals may be insufficient compared to the number of hidden sources
Unlike singular value decomposition used for matrix cases, PARAllel FACtor (PARAFAC) decomposition offers an additional advantage: it gives a unique decomposition even if its rank order is greater than the smallest dimension of the tensor
Summary
Operational modal analysis (OMA) has been significantly developed, and it plays a vital role in the engineering fields. The main challenge for applying the BSS techniques in OMA is when the number of measurement signals (or sensors) is less than that of latent sources—an underdetermined case This problem can be encountered in many practical applications with limited measurements, for example, for complex structures or in the presence of harmonic excitations, when the measurement signals may be insufficient compared to the number of hidden sources. In addition to the above-mentioned techniques, there is a direct approach for distinguishing harmonic components This method proposes to consider them as zero-damping modes, while the damping ratio of the real pole of the structural component varies between 0.1% and 2% [12]. For OMA, the length of the auto-covariance function needs to be considered when using kurtosis value as a harmonic indicator in PARAFAC decomposition-based methods.
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