36 Producing Simulated Time Data for Operational Modal Analysis 341 From the eigenvalues and eigenvectors the corresponding modal parameters are obtained straightforwardly. The challenge is to distinguish between physical modes of the measured structure and spurious modes occurring from model errors, measurement noise and numerical errors. Manual selection of physical modes is commonly done by use of stabilization diagrams (sometimes referred to as consistency diagrams) which is also the approach in the present work. 36.2.2 Generation of Excitation Forces The forces exciting the N DOFs of the modal model are collected in a force matrix F constructed from a number NS of independent sources. The time sequences of the sources are collected in a source matrix S with Msamples each. The distribution of the sources on the DOFs is controlled by a distribution matrix Dand the force matrix is then constructed as follows, FM N DSM NSDNS N 2 4 j j j F1 F2 : : : FN j j j 3 5 M N D2 4 j j j S1 S2 : : : SNS j j j 3 5 M NS 2 4 j j j D1 D2 : : : DN j j j 3 5 NS N (36.1) For the case of independent excitation of all DOFs the distribution matrixDequals the identity matrix and for the dependent cases were sources are randomly mixed for each DOF, Dis created randomly from a uniform distribution within the interval 0;1Œ. Equation (36.1) can be interpreted by considering a column Dn of the distribution matrix as weighting factors of sources in a single DOF. The influence of each source is thus different in all DOFs, but the influence is constant in time controlled by the columns of D. 36.2.3 Note on Randomly Mixed and Identical Distribution The method applied for creating the dependent excitations in the present work has some implicit idealizations that should not be expected for real life cases. For instance the dependency of the excitations at two close DOFs should be stronger than the dependency between two not so close DOFs, which is not the case in the present work. However, without a realistic physical model of the spatial distribution it is impossible to implement dependency between the excitation of the individual DOFs. For this reason, in the present work the independent sources are randomly mixed in the case of dependent excitation. Another aspect of the idealization is that all sources in the present work are identical distributed, for which there seems no reason in practices. For example for a bridge the distribution of the wind load should not be expected to be the same as for the load from traffic. For a generic study as the present one, identical distributions seems like an obvious choice. 36.3 Experimental OMA Test The physical Plexiglas (PMMA) plate has been experimentally tested, see Fig. 36.2a. The plate dimensions are533 321mm and thickness 20 mm. It is similar to the so-called IES-Plate proposed in [12], however, for practical reasons, the plate thickness was chosen slightly different from the IES-Plate, by choosing 20 mm thickness, which is a standard thickness in Europe. The measurement grid consist of 35 DOFs distributed uniformly out of plane on the plate as shown in Fig. 36.2b and all DOFs are measured simultaneously. Influences by the instrumentation are neglected; te structure of interest is thus the combined Plexiglas plate including its instrumentation. For measurements the following data acquisition (DAQ) and sensor equipment were used: • 3x National Instruments 4497, 16 channel, 24bit analog inputs cards • 35x Dytran 3097A2 accelerometers, 100 mV/g, IEPE, 4.3 grams • In-house software for DAQ control, based on MATLAB DAQ-toolbox
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