In Table 6, again note that the method used to compute the modal scaling, Modal A, had little effect on the estimates of Modal A. Also of note in this case, is the phase angle of all Modal A terms is around ninety degrees. The sign on the phase angle and the closeness to ninety degrees (rather than zero degrees) is a function of the scaling method chosen for the modal vector. Index N Frequency (Hz) ModalA (State Vector) ModalA (Mean from cluster) real imaginary magnitude phase real imaginary magnitude phase Std. Dev. 3 19 7.406 -4.0159e+005 4.0857e+006 4.1054e+006 95.61 -4.0048e+005 4.0871e+006 4.1067e+006 95.60 1.3311e+005 2 19 8.263 -4.1063e+005 6.0755e+006 6.0893e+006 93.87 -3.7199e+005 6.0650e+006 6.0764e+006 93.51 7.2975e+005 21 14 9.465 5.1606e+006 1.3773e+007 1.4708e+007 69.46 6.6001e+006 1.4598e+007 1.6021e+007 65.67 4.9262e+006 8 19 11.253 -1.0672e+006 8.9505e+006 9.0139e+006 96.80 -2.6399e+006 1.2408e+007 1.2686e+007 102.01 1.5630e+007 35 6 12.224 -2.3579e+006 1.3038e+007 1.3250e+007 100.25 1.5347e+006 1.1077e+007 1.1183e+007 82.11 4.6407e+006 32 8 12.756 -3.7527e+005 8.6561e+006 8.6642e+006 92.48 -4.7815e+005 8.9063e+006 8.9191e+006 93.07 1.2880e+006 11 17 13.162 2.9493e+006 1.5389e+007 1.5669e+007 79.15 1.6985e+006 1.2154e+007 1.2272e+007 82.04 3.9192e+006 41 6 15.729 -1.1722e+006 9.6343e+006 9.7054e+006 96.94 -1.1850e+006 9.6038e+006 9.6766e+006 97.03 1.2406e+006 30 10 15.765 -1.2004e+006 1.0006e+007 1.0078e+007 96.84 -1.1961e+006 1.0022e+007 1.0093e+007 96.81 6.1042e+005 6 19 16.747 -1.5250e+006 1.4429e+007 1.4510e+007 96.03 -1.5462e+006 1.4422e+007 1.4504e+007 96.12 8.2761e+005 43 4 18.221 6.9955e+007 2.0003e+008 2.1191e+008 70.72 7.0403e+007 1.9977e+008 2.1181e+008 70.59 1.3292e+007 16 13 20.100 -3.4965e+005 1.9290e+007 1.9293e+007 91.04 -2.5684e+005 1.9387e+007 1.9388e+007 90.76 2.0555e+006 37 4 20.323 -1.6061e+007 7.0883e+007 7.2680e+007 102.77 -1.7005e+007 6.9200e+007 7.1258e+007 103.81 1.5557e+007 14 16 20.507 -3.8264e+005 2.2225e+007 2.2228e+007 90.99 4.2840e+006 2.3277e+007 2.3668e+007 79.57 9.5171e+006 39 5 21.236 -3.3460e+007 2.8599e+007 4.4017e+007 139.48 -3.6040e+007 2.5029e+007 4.3878e+007 145.22 1.2696e+007 31 5 21.624 3.4080e+006 1.6113e+007 1.6469e+007 78.06 2.4648e+006 1.2889e+007 1.3122e+007 79.17 3.3533e+006 25 10 22.778 -1.0823e+006 1.0448e+007 1.0504e+007 95.91 -1.0941e+006 1.0530e+007 1.0587e+007 95.93 1.1060e+006 28 10 24.247 -1.8809e+006 1.9384e+007 1.9476e+007 95.54 -1.8907e+006 1.9378e+007 1.9470e+007 95.57 5.5546e+005 9 17 25.235 -7.2001e+005 2.7462e+007 2.7471e+007 91.50 -8.3424e+005 2.6949e+007 2.6962e+007 91.77 2.2048e+006 18 14 27.824 -2.1672e+006 1.3965e+007 1.4132e+007 98.82 -2.0185e+006 1.4180e+007 1.4323e+007 98.10 3.0505e+006 23 8 28.150 -1.3309e+007 2.1013e+007 2.4873e+007 122.35 -1.1342e+007 2.1981e+007 2.4735e+007 117.29 7.1619e+006 22 9 29.492 -1.0596e+007 1.9653e+007 2.2327e+007 118.33 -1.2479e+007 2.3212e+007 2.6353e+007 118.26 1.5348e+007 TABLE 6. Bridge Example: Modal Scaling Statistics 7. Summary and Future Work This paper has presented the statistics of the estimated modal parameters that are a direct result of a new development in autonomous modal parameter estimation. The proposed method represents an important philosophical and paradigm shift in the process of identifying potentially valid modal parameters. Instead of trying to get only (statistically and numerically) well estimated modes and then adding in the marginally estimated modes from the original estimates from the consistency diagram, the autonomous MPE methodology attempts to estimate all possible modes and use the statistics of the solutions to eliminate the marginal estimates. It has also been observed that, contrary to conventional wisdom, the techniques for producing clear consistency (stabilization) diagrams are at odds with the autonomous procedure. This is in part due to the nature of the consistency diagram where frequency and damping consistency tolerances used in the consistency diagram causes somewhat inconsistent estimates to be eliminated from consideration before the vector consistency can be evaluated. The temporal-spatial nature of the CSSAMI procedure allows these helpful results to be retained by the solution procedure. One obvious extension of this work is to initiate the autonomous modal parameter estimation process using consistency diagram information from several different methods rather than just one. The inclusion of more estimates from differing algorithms may mean better consistency of estimates for some modes that are poorly estimated from a given algorithm. 399
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