1 Integrating Multiple Algorithms in Autonomous Modal Parameter Estimation 7 0 500 1000 1500 2000 2500 12 4356 78 10911 12 11 34 11 56 11 78 12 90 22 12 22 4322 56 22 78 32 0933 12 33 34 33 56 33 78 34 90 44 12 44 34 44 56 44 78 54 0955 12 55 34 55 56 55 78 56 90 66 12 66 34 66 56 66 78 76 0977 12 77 34 77 6577 Consistency Diagram Frequency (Hz) Model Iteration pweight = λ10 pwMAC≥0.99 pwMAC≥0.97 pwMAC≥0.94 pwMAC≥0.90 pwMAC≥0.85 pwMAC≥0.79 PTD ERA PFD RFP−Z Fig. 1.4 Extended consistency diagram—Pole weighted MAC version correlation methods (MAC) to identify consistency. A similar set of symbols, as those used in Fig. 1.3, are used to define increased levels of consistency as numerical solutions are added. Both methods work very well but the implementation of Fig. 1.4 is computationally easier and not subject to a frequency drift in the symbol path that can occur in the conventional implementation shown in Fig. 1.1. Note that the solid square symbols at the top of both consistency diagrams represent the solution found from the CSSAMI autonomous modal parameter estimation procedure applied to the information represented by each consistency diagram. Note that all of the above algorithms are using the same matrix polynomial equation normalization procedure which tends to yield clear consistency diagrams. Each consistency diagram can yield twice as many estimates of the desired modal parameters if both low and high matrix coefficient normalizations are utilized. This is also under current study. 1.4 Autonomous Modal Parameter Estimation with Extended Consistency Diagrams The CSSAMI autonomous procedure utilizes all solutions indicated by a symbol in the consistency diagram. If some symbols are not present, it means the user has decided not to view solutions identified by those symbols. This provides a way to remove solutions from the autonomous procedure that are clearly not reasonable. However, experience with the CSSAMI autonomous procedure has shown that some solutions that are often eliminated by users in an attempt to have a clear consistency diagram are often statistically consistent and useful. Figure 1.5 shows the solutions that are included in the autonomous procedure. The graphical representation on the left represents a MAC matrix involving the pole weighted vectors for all possible solutions from Fig. 1.3. The graphical
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