valid modes may be eliminated which may not be attractive behavior once autonomous modal parameter estimation procedures are utilized. 4. Autonomous Modal Parameter Estimation Method The autonomous modal parameter estimation method developed and presented in the following is a general method that can be used with any algorithm that fits within the UMPA structure. A complete description of the Unified Matrix Polynomial Algorithm (UMPA) thought process can be found in a number of references developed by the authors [4-8, 57] . This means that this method can be applied to both low and high order methods with low or high order base vectors. This also means that most commercial algorithms could take advantage of this procedure. Note that high order matrix coefficient polynomials normally have coefficient matrices of dimension that is based upon the short dimension of the data matrix (NS ×NS). Inthese cases, it may be useful to solve for the long dimension modal vectors or to use pole weighted modal vectors. This will extend the temporal-spatial information in the NS length base vector so that the vector will be more sensitive to change. This characteristic is what gives this autonomous method (CSSAMI) the ability to distinguish between computational and structural modal parameters. The implementation of the autonomous modal parameter estimation for this method is detailed in the following sections. 4.1 Step 1: Develop a Consistency Diagram Develop a consistency diagram using any UMPA solution method. Since this autonomous method utilizes a pole surface density plot, having a large number of iterations in the consistency diagram (due to model order, subspace iteration, starting times, equation normalization, etc.) will be potentially advantageous. The possibility of combining solutions from different consistency diagrams originating from different UMPA models is also a natural extension of this autonomous approach. 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 5. Consistency Diagram Showing All Poles The larger the number of solutions (represented by symbols) in the consistency diagram, the more computation time and memory will be required. However, restricting the number of solutions using clear stabilization (consistency) methods may be counterproductive [59]. 370
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