NSVR1 = √⎯ N k=2 Σ σ2 k N σ1 (5) NSVR2 = σ2 σ1 (6) 4.3 Modal Scaling Statistics If modal scaling (residue) information is available in the original vectors, it can be applied to the principal pole weighted vector such that the consistency of modal scaling (Modal A) can also be evaluated. By scaling the largest driving point response to unity, a uniform, comparable value for Modal A is chosen. Since the modal scaling parameter (Modal A) contains the physical units and hence the relative contribution of each pole/vector combination to the original data set, a means of evaluating the significance and confidence in each estimate is possible. Because the original vectors represent multiple scaled solutions and since Modal A is a single scalar complex value for each pole/vector combination, the statistical distribution of Modal A (mean and standard deviation) of the original cluster can be compared with the scaling estimated from the pole weighted (state extended) vector. The magnitude of Modal A can be used to evaluate the contribution of this vector to the total set of identified vectors. When the user believes that the identified vectors should be normal modes, the phase of the Modal A can be used to evaluate the closeness to a normal mode. 5. Typical Statistics: C-Plate Example For this example, impact data from a circular plate test article has been used. The FRF data (7x36) was processed using a Rational Fraction Polynomial algorithm with complex z frequency mapping (RFP-Z) with all data between 220 and 2450 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 phase one residues have been calculated. 0 500 1000 1500 2000 2500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Consistency Diagram Frequency (Hz) Model Iteration cluster pole & vector pole frequency conjugate non realistic 1/condition Figure 1. C-Plate Example: Consistency Diagram - All Poles Plotted 389
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