In Table 3, 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 minus 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. 8 16 362.564 3.9663e+002-5.7201e+003 5.7338e+003 -86.03 3.9574e+002-5.7195e+003 5.7332e+003 -86.04 1.3866e+002 19 16 363.860 -4.8353e+001 -4.8716e+003 4.8719e+003 -90.57 4.5311e+001 -4.9271e+003 4.9273e+003 -89.47 3.1271e+002 10 16 557.055 7.3166e+001-9.7205e+003 9.7207e+003 -89.57 8.4818e+001-9.7107e+003 9.7111e+003 -89.50 1.2295e+002 12 16 761.224 9.6911e+001-1.8433e+004 1.8434e+004 -89.70 9.5750e+001-1.8433e+004 1.8433e+004 -89.70 2.1414e+002 2 17 764.190 -3.1250e+002 -7.0511e+003 7.0580e+003 -92.54 -3.0277e+002 -7.0524e+003 7.0589e+003 -92.46 3.1198e+002 16 16 1222.980 1.1082e+003-1.7259e+004 1.7295e+004 -86.33 1.1154e+003-1.7253e+004 1.7289e+004 -86.30 5.3096e+002 13 16 1224.055 -4.6394e+003 -3.0840e+004 3.1187e+004 -98.55 -4.6441e+003 -3.0074e+004 3.0431e+004 -98.78 1.6271e+003 4 17 1328.036 -4.8959e+002 -1.5810e+004 1.5818e+004 -91.77 -4.7949e+002 -1.5803e+004 1.5810e+004 -91.74 8.5516e+002 17 16 1328.803 1.5461e+003-1.4661e+004 1.4742e+004 -83.98 1.5462e+003-1.4659e+004 1.4741e+004 -83.98 2.9335e+002 6 17 2019.269 8.1564e+002-1.3301e+004 1.3326e+004 -86.49 7.3874e+002-1.3345e+004 1.3365e+004 -86.83 6.6888e+002 23 15 2023.802 4.2669e+003-6.3248e+004 6.3392e+004 -86.14 4.1880e+003-6.3244e+004 6.3382e+004 -86.21 4.7741e+003 26 10 2321.862 1.6011e+003-2.9188e+004 2.9232e+004 -86.86 8.1739e+002-3.0454e+004 3.0465e+004 -88.46 5.2745e+003 28 8 2322.335 2.8552e+003-3.6135e+004 3.6247e+004 -85.48 1.7616e+003-3.7289e+004 3.7331e+004 -87.30 6.3617e+003 22 15 2337.895 -1.3348e+003 -5.0815e+004 5.0833e+004 -91.50 -1.3637e+003 -5.0848e+004 5.0867e+004 -91.54 2.6546e+003 TABLE 3. C-Plate Example: Modal Scaling Statistics 6. Typical Statistics: Bridge Example For this example, impact data from a civil bridge structure test (15x55) has been used. The FRF data was processed using a Z-Domain Rational Fraction Polynomial Algorithm (RFP-Z) with all data between 5 and 30 Hz included. The model order range used was 2 to 20 with a generalized residual model including all terms from (j ω)−4 to (j ω)2. Further, low order alpha coefficient normalization has been used and full length residues have been calculated to be used in the CSSAMI procedure. For the purposes of demonstration, all calculated poles (both consistent and computational) are included in the plots. As can be observed, though clearly present throughout the frequency range (Figures 6, 7 and 8) the non-realistic, computational poles, are not observed in the vicinity of the S-domain computed pole clusters (Figure 9) The effect of prefiltering (by pole density alone) the information fed into the autonomous parameter estimation algorithm is shown in Figures 7 and 8. A comparison of no filtering (Figure 7) with prefiltering (Figure 8) reveals that more potential solutions are identified when the algorithm is allowed to match parameters on the basis of both pole and vector. A review of the results also indicates that the typical procedures for achieving clear consistency diagrams may actually be detrimental to the autonomous procedure because important information which didn’t meet some arbitrary criteria was removed from consideration. 393
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