Parameterized Instantaneous Frequency Estimation Method for Vibration Signal with Nonlinear Frequency Modulation

The vibration signal from the rotatory machinery condition monitoring under time-varying speed is usually amplitude-modulated (AM) and frequency-modulated (FM). It is important to efficiently and accurately estimate the instantaneous frequency (IF) of the vibration signal. In this paper, a novel parameterized IF estimation method is proposed. The method employs a high-order polynomial function to approximate the nonlinear IF and subsequently constructs overdetermined systems of linear equations by calculating the Fourier transform of the derivative of the signal. The IF can be estimated by using least squares estimation to solve the equations. The proposed method has high computational efficiency because it can obtain the estimation of IF over a period of time simultaneously; it differs from traditional time-frequency analysis methods that need to calculate the IF at each point in the time axis. It is demonstrated that the proposed method is not only particularly powerful for the nonlinear FM mono-component signal but also applicable to the multi-component signal constructed by multiple harmonics. The numerical simulation validates the effectiveness of the proposed method, and the experiment's results show that the method is suitable for the IF estimation of the vibration signal from the varying-speed rotor system.