Optimized multi-synchrosqueezing transform: A precise tool for instantaneous frequency identification of non-stationary signals in time-varying structures

Engineering structures in operation are inherently time-varying structures and the resultant response signals exhibit non-stationarity. As a consequence, it is crucial to identify instantaneous modal properties of such non-stationary signals via signal processing tools. Recently, multi-synchrosqueezing transform (MSST) and its extended algorithms have offered an effective way to estimate time-dependent parameters. However, the problem of non-reassigned points is yielded, and it affects the time–frequency resolution of non-stationary signals. To address this issue, an optimized multi-synchrosqueezing transform (OMSST) algorithm is proposed. Unlike current MSST-based methods, the proposed OMSST algorithm attempts to solve the problem of non-reassigned points by merely retaining IF positions that appear most frequently within a pre-estimated range at each instance. Due to this operation, non-reassigned points are fully removed, and new refined frequency bands are yielded. A numerical example, a parameter analysis, and two experimental cases on time-varying structures are investigated to verify the effectiveness and accuracy of the proposed method. The results demonstrate that the proposed OMSST method can remove non-reassigned points entirely and its combination with the maximum modulus of time–frequency coefficients (MMTFC) method behaves better than other MSST-based approaches in terms of IF identification. In addition, the proposed OMSST showcases a good robustness on noise resistance.