14 Covariance-Driven Stochastic Subspace Identification of an End-Supported Pontoon Bridge: : : 111 1N 2 3 4 5 6 7 y x Bergsøya Aspøya Joint (a) (b) Joint 1S 2N 3N 4N 5N 6N 7N 2S 3S 4S 5S 6S 7S 1 A1 A2 A3 A4 A5 1 7 GNSS Reference GNSS W1-W3 W4-W6 7 pairs of tri-axial accelerometers 5 anemometers 1 GNSS 6 wave radars Fig. 14.2 Monitoring system. (a) Top view, including coordinate system definition. (b) Side view Table 14.1 Vital statistics of the selected recording, initiated 06:47 on December 26, 2015, with a duration of 30 min Waves Horizontal wind Accelerationa Position SWH[cm] Pontoon water level [cm] Speed [m/s] Direction [ı] Lateral [mg] Vertical [mg] Center (pontoon 4) 34.8 407 12.4 264.7 1.8 0.5 Quarter (pontoon 2) 12.3b 262.7b 1.4 0.5 The indicated wind direction corresponds to the angle of origin of the wind, where 0ı corresponds to winds along the x-axis indicated in Fig. 14.2 and increases in an clockwise manner. a g is used as acceleration unit, and refers to the gravitational constant (g D9:81m/s2). b Reported wind statistics refer to anemometer A1, positioned close to pontoon 2. See Fig. 14.2. 14.4 Operational Modal Analysis The following stability criteria were used: maximum frequency deviance of 1%, maximum damping deviance of 5%, and a minimum MAC value of 95%. The stability level was chosen as s D8 for the analyses of which all presented results are based on. By investigating the statistical properties of captured recordings, a suitable time series was identified. In particular, a recording with perpendicular winds and decent excitation levels was sought after. A recording made 06:47 on December 26, 2015, fits these requirements. Some vital statistics related to this recording are found in Table 14.1. Modal analyses were performed both with BR and CVA weighting. The resulting stabilization plots are shown in Fig. 14.3, for both cases. It is clear that the CVA weighting does help in identifying the less excited modes for the current analysis. However, it is observed to behave rather erratically, and is very sensitive to input parameters, such as the number of block rows. The agreement with an updated version of the numerical prediction model in [7] is indicated with lines in the stabilization plot from the CVA analysis. To assess the effect of the increased stability level (s D8), the stabilization plot from the analysis with CVA weighting is also shown with s D 1 in Fig. 14.4. Increased stability level results in a better readability and clarity of the stabilization plot. Table 14.2 shows the modal parameters of the CVA analysis together with modal parameters obtained from the eigenvalue solution of the numerical prediction model. The corresponding mode shape comparison is found in Fig. 14.5. Overall, a decent agreement is observed. The damping levels are not satisfactory, especially for modes 2, 4 and 5. The next sub-section indicates large variability of the damping ratios. Because the modes are closely spaced, they are prone to switch their ordering in frequency with small changes in the excitation. Furthermore, the complex, coupled and environment-dependent dynamic behavior is believed to make the appearance of the mode shapes more variable.
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