14 Roadmap for a Highly Improved Modal Test Process 169 10 100 90 80 70 60 50 40 30 20 10 20 30 40 50 60 10 20 30 Mode Mode 40 50 60 10 90 80 70 60 50 40 30 20 10 20 30 40 50 60 10 20 30 Test Mode ISPE TAM to Test Modal Coherence (Real Test Modes) ISPE Test Modal Orthogonality (NASA STD-5002 Method) ISPE TAM to Test Modal Cross-Orthogonality (NASA STD-5002 Method) Mode 40 50 60 10 90 80 70 60 50 40 30 20 10 20 30 40 50 60 70 10 20 30 Test Mode TAM Mode 40 50 60 Fig. 14.6 ISPE Conventional Mass Weighted Test-Analysis Correlation Matrices Step 3: Modal Coherence [C] =[ORTAM]−1 n [COR] , [R] =[ TEST]n −[ TAM]n [C] , [COH] =[ORTEST] − R∗R . (14.17) Extensive evaluation of the complex least squares process indicates that both the complex cross-orthogonality and coherence matrices behave in a manner that parallels the behavior of their real eigenvector counterparts. Therefore, complex modal orthogonality and test-analysis mode correlation may be separated into a “recipe” composed of two distinct sub-tasks, namely: 1. Complex mode orthogonality is perfectly satisfied by left-hand eigenvector counterparts to state-space complex eigenvectors for test and TAM eigenvector sets (following eq. 14.6b). 2. Complex mode cross-orthogonality (correlation) and complex modal coherence are defined based on the complex leastsquares process (following eqs. 14.15–14.17) Following the above “recipe”, complex mode orthogonality, cross-orthogonality, and modal coherence matrices are illustrated in Fig. 14.7. The TAM and test mode orthogonality matrices are perfect identity matrices. The cross-orthogonality matrix appears similar in form to its state-space counterpart (see Fig. 14.6), and the modal coherence matrix indicates that the majority of lower frequency (~50%) of test modes are strong linear combinations of the TAM modes. Recalling the fact that the orthogonality matrix can be “unpacked” to describe a subject system’s modal kinetic energy distribution [9], a corresponding “unpacking” of the complex state-space mode orthogonality matrix (eq. 14.6b) similarly
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