Updating singular value decomposition for modal analysis of slow-varying non-stationary vibration structures

Abstract

This paper proposes a novel method for the modal analysis of slow-varying vibration structures based on vector autoregressive models. The basic idea of this method consists of using a short-time sliding window (STSW) to identify modal parameters for non-stationary vibrations. This method uses the recursive least-squares estimation for multivariable systems with the singular value decomposition (SVD) method to find the solutions within a segment of the data from each time window. Model identification is conducted by updating the SVD of the data matrix using the order and time from the previous computational window to monitor the modal parameters of a slow-varying system. Finally, this work was validated first by numerically simulating a system's gradual changes submitted to an exciting force and further by an experiment on a hydraulic turbine blade.