Singular Value Decomposition (SVD) has been widely applied in engineering problems, such as System Identification, Model Reduction, Vibration Control, and Sensor Placement, etc.. Understanding the evolution of SVD components helps one make appropriate decisions on such problems. To this end, this paper is intended to derive analytical formulae of the decomposition components, i.e., singular values and singular vectors, for a Hankel matrix so that the mechanisms of the decomposition can be unfolded. The derivations show how singular vectors are composed of natural frequency and damping ratio, and how singular values appear in pairs and how they are affected by modal parameters. The optimal size of a candidate Hankel matrix is also discussed for single mode case. Finally, numerical examples are given and compared with analytical results. Their excellent agreements confirm the results of this work.
展开▼
