Using Singular Value Decomposition to Compare Correlated Modal Vectors

A tool is needed to track several mode shape estimates from iterative or repeated (variability) testing. Modal Assurance Criterion (MAC) is a well known modal vector comparison tool, however it can compare only two modal vectors at a time. A method to compare multiple samples of modal vector is presented The approach begins with mode shape correlation and correspondence. Pseudo orthogonality is recommended to establish correspondence and facilitate mapping of the correlated mode shapes. The II t" d"" 1 mean vee or an smgu ar value decomposition" (SVD) approaches to vector avera~ing are explored. The SVD approach yields a single number Vector Space Consistency measure. A simple lumped-mass full vehicle model is used to evaluate the algorithm and study the vehicle vibration sensitivity to variations in tire, suspension, engine mount and inherent body structure stiffness. NOMENCLATURE [P] Transformation Matrix [M] Mass Matrix [] Mode Shape Matrix [$] Mode Shape Vector [\f/] Matrix of Mode Shapes Samples [A] Pole Matrix [ JH Hermitian Operator [ )+ Pseudo Inverse Operator