Application of singular spectrum analysis to nonstationary time series in flow-induced vibrations of a circular cylinder

Abstract

In numerical simulations of flow-induced vibrations (FIV) of a circular cylinder, abundant time series data are available, including cylinder displacement and acting forces. Singular spectrum analysis (SSA) is employed to deal with nonstationary multi-component time series produced in two FIV cases with proper interpretation in physics. In the first case, the cylinder displacement time series is decomposed into two oscillatory components using SSA. The instantaneous frequencies of these two components are obtained by Hilbert transform (HT) and found to be in agreement with the wavelet transform of the cylinder displacement. In the second case, three oscillatory components are extracted from the cylinder displacement time series by SSA. The dominant component is characterized by steady oscillations at the vortex shedding frequency, which suggests a relatively steady vortex shedding process behind the rear cylinder. In contrast, the second component, which is closely associated with the alternate boundary layer separations from the front cylinder, features in the increasing amplitude with time. This implies that the unsteady flow field in the gap might be attributed to the nonstationary cylinder oscillations. This work demonstrates that SSA, in conjunction with HT, enables a comprehensive time-frequency analysis of nonstationary time series obtained in FIV.