Chapter 7 Operational Modal Analysis with a 3D Laser Vibrometer Without External Reference Simon Marwitz and Volkmar Zabel Abstract The use of Scanning Laser Doppler Vibrometers (SLDV) is a common practice in the context with modal analysis. 3D SLDV have been used with classical experimental modal analysis for several years. In this case, three laser heads, which simultaneously point to the same location, are used and an additional input reference signal is required to combine the results of consecutive records. In operational modal analysis the input reference signal is replaced by an output reference signal, which may be obtained, for example, from an additional vibrometer or accelerometer. Alternatively, if a 3 dimensional laser vibrometer is used, one of the three laser heads can be used to provide a reference signal for the other two heads, which can then position their laserbeams independently. However, this requires an appropriate post-estimation method for the transformation of 3D local skew coordinates since the common, built-in routines of commercially available 3D SLDV perform the respective coordinate transformation directly on the simultaneously acquired time series. In the presented study a respective algorithm has been developed and applied to measured vibration data. For the modal identification the SSI cov/ref algorithm and three different merging strategies have been employed. Keywords 3D scanning laser vibrometer • 3D SLDV • Coordinate transformation • Operational modal analysis • OMA • Reference signals 7.1 Introduction Laser Doppler Vibrometers (LDV) are widely used for noncontact measurement of vibrations, mainly under laboratory conditions. They provide several advantages over accelerometers that are typically used for vibration measurements. The most prominent is probably the elimination of additional mass loading effects on the dynamic behavior of the structure under test. Scanning LDV can position the laser beam onto different points of a structure automatically and thus speed up the process of multi-point measurements significantly. However, an LDV is limited to measuring vibrations along the direction of the laser beam. 3D SLDV combine three laser scan heads, that are placed in different locations and direct their laser beams simultaneously to the same point on a test structure. Vibrations in the Cartesian spatial directions can then be computed for each point of measurement. To combine the multiple single-point measurements, an input or an output reference signal is needed. In operational modal analysis (OMA) one or more output reference signals are used. Thus, the input or excitation of the structure needs not to be known, which eliminates the demand for any loading device connected to the structure, that might influence the dynamic behavior. Over the years, several methods for the analysis of output-only measurements have been developed. Most of them are adapted from traditional input-output modal analysis. Among the most established methods are the stochastic subspace identification (SSI) modal estimation algorithms with the covariance-driven and the data-driven versions. They originate from system realization theory [5] and are used for the identification of a stochastic state-space model, from which the modal parameters can be extracted. The combination of multiple measurements based on reference signals can be performed in different ways, depending on the modal estimation algorithm that is employed. The three steps usually involved are: modal analysis, rescaling and merging the data. For the reference-based covariance-driven stochastic subspace identification there exist three such algorithms, described in [1] and [3]. They differ in the order in which the aforementioned steps are performed. S. Marwitz ( ) •V. Zabel Institute of Structural Mechanics, Faculty of Civil Engineering, Bauhaus-University Weimar, Marienstraße 15, 99421 Weimar, Germany e-mail: simon.jakob.marwitz@uni-weimar.de © The Society for Experimental Mechanics, Inc. 2016 J. De Clerck, D.S. Epp (eds.), Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-30084-9_7 75
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