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 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 Figure 2. Alternate Consistency Diagram - Pole Weighted MAC 3.1.1 ClearConsistencyDiagrams A number of different methods can be used to generate the consistency diagram that will impact the clarity of the consistency diagram. A number of recent papers [46-47,53-54] have identified the effects of changing the consistency tolerances on the resultant consistency diagrams, yielding a clearer presentation of symbols that indicate the presence of a structural mode of vibration. These methods can be combined with the coefficient normalization and consistency tolerances to generate a very clear diagram in most cases where the measured data has a reasonable match to linear, reciprocal system assumptions, observability issues and reasonable data noise levels. These methods have been used on a wide range of data cases in the automotive and aerospace application areas with good success. The methods include: • Symbol Sizing Based Upon Normal Mode Criteria • Complete or Incomplete Vector Comparisons • Using Both Coefficient Normalization Methods • Numerator and Denominator Model Order Variation • Fixed Denominator and Numerator Order Variation • Frequency Normalization Variation 3.2 Long Dimension Vector Solution While many high order, matrix coefficient modal parameter estimation methods estimate unscaled modal vectors as part of the estimation of the poles, there is no reason to limit the length of the unscaled modal vector to the short dimension. Each short dimension vector can be used to estimate the unscaled vector for the long dimension as a part of the solution. This requires an extra solution step but, for each model order, requires very little additional computational effort. In this case, regardless of the method employed to estimate the modal frequencies, all unscaled modal vectors will be of length equal to the long dimension. No attempt to restrict the set of modal frequencies is used at this point in the procedure; all possible poles are included in this calculation. This set of unscaled vectors will include structural modal vectors and computational vectors. Sorting these vectors is left to a correlation procedure such as the modal assurance criterion (MAC) with a threshold (minimum MAC value). Note that this extra step can include the estimation of modal scaling so that scaled modal vectors and modal scaling values can be used as part of the evaluation process. 367
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