Application of second-order local maximum multi-synchrosqueezing transform for complex multi-modulated signals analysis

Time-frequency analysis (TFA) is an effective tool for processing non-stationary signals. Local maximum synchrosqueezing transform (LMSST) is a classic TFA method that can concentrate time-frequency (TF) energy while retaining signal reconstruction capability. The issue with LMSST lies in its inadequacy in characterizing the amplitude of non-stationary signals, and its poor performance in extracting multi-component amplitude-modulated and frequency-modulated (AM-FM) signals, resulting in divergent time-frequency energy. To address this limitation, this paper proposes a SLMMSST method to characterize the TF characteristics of non-stationary signals. The method constructs a new frequency reassignment operator by identifying local maxima in the frequency direction, using second-order instantaneous frequency (IF) estimation, performing multiple iterations and rounding. This approach resolves the problems of inaccurate amplitude extraction and energy divergence, enabling more precise assignment of TF coefficients. Simulation signal analysis demonstrates that SLMMSST can precisely extract features and perform time-frequency representation (TFR) for AM-FM signals. Experimental rotor composite fault signals demonstrate that the proposed method can accurately characterize the TF features of non-stationary signals. When the rotor is in the state of oil film whirl and mild rub-impact, AM- FM phenomena occur; when the rotor is in severe rub-impact, FM phenomena appear, which proves that intensified rub-impact has an inhibitory effect on oil film whirl. Comparisons with other advanced methods further verify the superiority of the proposed method.