Nonparametric Time-Varying Operational Modal Analysis

The first subproject deals with the time variations of (vibrational) mechanical structures described by the nonparametric Operational Modal Analysis (OMA) [1]. OMA is a special identification technique for estimating the modal properties (e.g. resonance frequencies, damping) of structures based on vibration data collected when the structures are under real operating conditions without having access to the excitation signals.

The main issue is that the dynamics of underlying systems may vary significantly when operating in real-life conditions. In this case, advanced modeling is needed taking into account the time-varying behavior because the unmodeled time variations might lead to instability and structural failures. Contrary to the classical identification frameworks, a further challenge with the OMA framework is that the excitation signal is not known exactly, but it is assumed to be white noise.

The problem lies in the fact that due to the high number of parameters and the underdetermined system of linear equations, the estimation procedure is not trivial [2]. Using nonparametric modeling, these equations will have very high degrees of freedom. As a consequence, time-varying systems cannot be uniquely determined from a single set of (input and) output signals – unlike in the general case of linear time invariant systems. Additional user selected properties, e.g. smoothness, will be imposed to select a unique model. The main challenge is to build accurate models which can track the varying dynamics of these systems, while using as few experiments as possible.

References

[1] W. Heylen , S. Lammens, P. Sas: Modal Analysis Theory and Testing, Katholieke Universiteit Leuven, Department Werktuigkunde, Leuven, 1997.

[2] P. Z. Csurcsia: Nonparametric identification of linear time-varying systems, PhD thesis, Brussels, Belgium, ISBN: 978-9-4619732-6-9, 2015, downloadable from http://vubirelec.be 

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