High-order synchroextracting transform for characterizing signals with strong AM-FM features and its application in mechanical fault diagnosis

In this paper, a novel time–frequency analysis (TFA) technique termed High-order Synchroextracting Transform (HSET), is proposed to better characterize the changing dynamics of multi-component signals with strong AM-FM components. Synchroextracting Transform (SET) is a TFA method has been developed recently. As a post-processing technology, unlike the parameterized TFA methods that requires different demodulation operators to be designed according to different types of signals, SET can generate high-quality time–frequency representation (TFR) only on the basis of short-time Fourier transform (STFT). However, since the core of SET is based on the assumption that the signal is composed of pure harmonics, SET cannot accurately extract the time-varying characteristics of signal with strong AM-FM components. To construct a method to well characterize the time-varying laws of strong AM-FM signals, this paper uses high-order Taylor expansion to estimate the time varying laws of the signal to obtain a more accurate frequency estimation operator, which we call high-order Synchroextracting operator (HSEO), and then HSET can be constructed through Dirichlet function to generate TFR with high TF resolution. Good reconstruction quality can be achieved through the inverse transformation of HSET while signal reconstruction operation can be completed concisely. In addition, this paper applies HSET to the processing of the measured vibration signals and feature extraction of gravitational-wave (GW) signal. Compared with other advanced TFA technologies, the effectiveness and competitiveness of the proposed method can be demonstrated.