Instantaneous multi-frequency tracker for nonstationary vibration signal in mechanical system

Abstract

A novel instantaneous frequency (IF) tracking method for non-stationary measured signals with single-frequency, multi-frequency, and harmonic-frequency is presented in this paper. Firstly, the deficiency of the mainstream time-domain IF tracking methods, such as adaptive notch filter (ANF) and Extended Kalman Filter (EKF), etc., are analyzed. Then the relationship of the amplitude, frequency, and signal value of a periodic signal in adjacent time intervals is derived, the influence of amplitude change on IF tracking results is verified, and a new state-space model for the IF tracking of a non-stationary measured signal is constructed by using the adjacent non-stationary measured signal, signal amplitude, and frequency, and the EKF is used to update the state of the model. After that, a series of non-stationary signals whose amplitude, frequency, and phase change linearly, nonlinearly, and mutation over time are designed to verify the IF tracking performance of the proposed algorithm. From the simulation results and 1000 times Monte Carlo simulation results, the proposed algorithm has faster convergence speed, higher convergence accuracy, and better robustness, compared with mainstream time-domain frequency tracking algorithms, such as ANF and EKF. Based on the proposed single-frequency IF tracking model, a multi-frequency signal IF tracking model is constructed to track the IF of non-stationary measured signals containing multiple frequency components. The effectiveness of the proposed multi-frequency IF tracking algorithm for multi-frequency signal and harmonic signal IF tracking is verified by simulation cases. After that, some experimental cases are given to further verify the feasibility of the proposed IF tracking algorithm. From the experimental results, the effectiveness of the proposed algorithm is compared with other time-domain algorithms. In addition, the initial value of frequency is set to zero in all the processes of simulation and experiment, which effectively avoids the influence of the initial condition of frequency on the IF tracking result.