Index Sample Size (N) Frequency (Hz) Damping (Hz) Std. Dev. (Hz) 8 16 362.552 -3.1573 0.1595 19 16 363.851 -3.5473 0.1137 10 16 557.053 -2.8957 0.0823 12 16 761.222 -5.2219 0.1085 2 17 764.187 -2.5397 0.1426 16 16 1222.979 -4.0870 0.0314 13 16 1224.054 -3.9543 0.0438 4 17 1328.036 -6.6514 0.0960 17 16 1328.803 -5.4805 0.1976 6 17 2019.257 -8.2429 0.2081 23 15 2023.803 -7.5596 0.0614 26 11 2321.877 -3.9141 0.1761 28 8 2322.334 -3.8351 0.2237 22 15 2337.894 -3.7974 0.2280 TABLE 1. C-Plate Example: Modal Frequency Statistics Table 1 gives a portion of the results and statistics associated with Figure 7. Since the methods involve a cluster of size N for each mode as part of the solution, statistical information is readily available for all modal parameters. This is discussed and detailed fully in another paper [26] and includes a discussion of the statistics for modal frequencies, modal vectors and modal scaling. 4.2 Application Example: Bridge Field Test Data The next example of the CSSAMI procedure is performed in the field on a small highway bridge. The FRF data in this case has 55 inputs and 15 responses. This data set has been particularly troublesome when analyzed by any method available and is shown as a significant implementation of the autonomous modal parameter estimation procedure. The autonomous results for this case are as good or better compared to any other solution utilized in the past, as measured by reasonable estimates of frequency and damping and dominantly normal modes. In this case, a Rational Fraction Polynomial with complex z frequency mapping (RFP-Z) method is used (similar to PLSCF and PolyMAX ® ) but, for every possible pole estimated over a model order range from 2 to 20, a complete long dimension modal vector was estimated so that sufficient spatial information is available for sorting out the consistent solutions. For this case, the following thresholds and control parameters were used: • Lowest order coefficient matrix normalization. • Pole density threshold (4 and above). • Pole weighted vector of model order 10. • Pole weighted MAC threshold (0.8 and above). • Cluster size threshold (3 and above). • Cluster identification threshold (0.8 and above). This case demonstrates that, even with clear stabilization diagram techniques, the consistency diagram can get fairly difficult to interpret. Nonetheless, in this application of the autonomous modal parameter estimation procedure, it is possible to identify the modal parameters with little trouble. 410
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