4.4 Step 4: Construct Normalized Pole Weighted Vectors Normalize each vector to unity length with dominant real part and then construct a predefined, higher order (typically 10th order), pole weighted vector for each solution [47]. { φ}r = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ zv r {ψ}r . . . z2 r {ψ}r z1 r {ψ}r z0 r {ψ}r ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭r 4.5 Step 5: Calculate Auto-MAC of Normalized, Pole Weighted Vectors Sort the normalized pole weighted vectors created in Step 4 into frequency order based upon damped natural frequency ( ωr). Then calculate the Auto-MAC matrix for all pole weighted vectors. Figure 9. Auto-MAC Color Plot of Tenth Order Pole Weighted Vectors, No Threshold The size of the red squares in Figure 9 (and in the following Figure 10) represents the number of vectors in each cluster of poles found anywhere in the consistency diagram. 4.6 Step 6: Remove Pole Weighted Vectors Below Threshold Retain all Auto-MAC values that have a pole weighted MAC value above a threshold, 0.8 works well for most cases. All values below the threshold are set to 0.0. 373
RkJQdWJsaXNoZXIy MTMzNzEzMQ==