Multivariate analysis in vibration modal parameter identification

This dissertation proposes a novel time domain method for vibration modal parameter extraction which is based on multivariate analysis. Compared with conventional time domain modal analysis methods, this method exploits statistical independence of vibration modes and aims to separate independent oscillations from each other by using only output signals. In particular, a new multivariate analysis algorithm, Smooth Orthogonal Decomposition (SOD), and current Blind Source Separation (BSS) algorithms are employed in this analysis. The dissertation starts with presentation of classical Principal Component Analysis (PCA) or Proper Orthogonal Decomposition (POD) and their engineering applications. Then the objective, mathematical formulation and properties of SOD are described in detail. SOD-based modal analysis is introduced and compared with POD-based modal analysis. A review of current time domain modal analysis methods is conducted and a uniform form of these methods which is based on generalized eigenvalue decomposition is provided. One of the contributions of this dissertation is the proposition of using BSS algorithms to extract vibration modal parameters. In particular, second order statistics based BSS algorithms, such as Algorithm for Multiple Unknown Signals Extraction (AMUSE), Second Order Blind Identification (SOBI) are used as examples. Their methodologies and mathematical formulation are compared to a well-known time domain modal analysis method, Ibrahim Time Domain (ITD) method, in order to show the similarity between the two types of problems. Numerical and experimental results from proposed methods and ITD method are provided to show their performance