An improved local maximum synchrosqueezing transform with adaptive window width for instantaneous frequency identification of time-varying structures

Abstract

Civil engineering structures usually exhibit time-varying characteristics under operational conditions due to changes in environment and loads. The identification of instantaneous frequencies (IFs) from measured responses of time-varying structures is a challenge when using the local maximum synchrosqueezing transform (LMSST) due to the difficulty in selecting the appropriate window width. In this study, an improved LMSST with adaptive window width (ALMSST) is proposed to circumvent the limitations of LMSST. The window width of ALMSST can be adaptively determined by combining the autoregressive power spectrum-based variational modal decomposition (AR-VMD) and a window width optimization algorithm. The AR-VMD is used to decompose the multi-component signal into mono-component signals. The Rényi entropy is adopted as an evaluation index in the window width optimization algorithm for selecting the optimal window width for each mono-component signal. Therefore, ALMSST can provide a highly concentrated time–frequency (TF) representation for all mono-component signals. Two simulated signals demonstrate that the ALMSST improves the accuracy of identified IFs compared with LMSST. Numerical simulation of a three-story shear building model with time-varying stiffness shows that ALMSST can accurately identify the IFs of time-varying structures under heavy noise. A cable test with linear and sinusoidal varying tension forces and a vehicle-bridge interaction (VBI) model system with different vehicle weights are investigated to verify the applicability of ALMSST to track the IFs of time-varying structures. Numerical simulation and experimental results illustrate that ALMSST performs well in identifying the IFs of time-varying structures.