Instantaneous rotational frequency estimation and fault diagnosis for rotating machinery based on multi-component short-time Fourier transform

• A multi-component short-time Fourier transform (MSTFT) is proposed to estimate instantaneous rotation frequency (IRF). • The energies of multiple characteristic frequencies are fused at the IFR by the MSTFT. • Definitional calculation method and the fast calculation method of MSTFT are derived. • MSTFT has better performance in accuracy and adaptivity of IRF estimation. Estimating instantaneous rotational frequency (IRF) from vibration signals is crucial for diagnosing faults in rotating machinery under variable speed conditions. However, existing IRF estimation methods lack adaptivity and their accuracies depend on the time–frequency resolution and signal-to-noise ratio (SNR) of the time–frequency distribution (TFD), which reduces the efficiency and reliability of fault diagnosis. To this end, this paper presents a novel method named the multi-component short-time Fourier transform (MSTFT) to estimate the IRF. Firstly, the mechanism of generalized parametric time–frequency transform (GPTFT) is analyzed to explore the influence of different Fourier transform basis functions on the transform results. Then, the multi-component Fourier transform basis is constructed for the vibration signals generated by rotating machinery and the basic theory of MSTFT is explained. Next, two calculation methods of MSTFT are derived, including definitional calculation and fast calculation. Finally, a fault diagnosis method for the rotating machinery based on MSTFT is designed. The IF at the IRF in the MSTFT results has the maximum energy and the highest SNR, so the IRF is estimated adaptively and accurately. The fast computational method greatly improves the computational efficiency of MSTFT for wide applications. The analyses of simulation data and field-measured data verify that MSTFT has better performance in IRF estimation and fault identification.