Local maximum instantaneous extraction transform based on extended autocorrelation function for bearing fault diagnosis

Extracting weak impulses from vibration signals is a tricky technique in fault diagnosis and condition monitoring of the rotating machinery. The autocorrelation function is an effective method for enhancing repetitive signals, however, the effect deteriorates as the point number of autocorrelation calculation decreases. To resolve this problem, a novel algorithm entitled extended autocorrelation function is presented. Besides, an algorithm called local maximum instantaneous extraction transform is proposed to further improve the enhancement effect, combining short-time Fourier transform, gamma transform, and local maximum sampling. Therefore, the presented algorithm is called the local maximum instantaneous extraction transform based on the extended autocorrelation function (LMIET-EACF). Firstly, we discuss the mathematical statistics theory of the autocorrelation function for realizing signal enhancement. It is illustrated that, when the number of data points involved in the calculation decreases, the amplitude variances of the noise components will increase. This is the limitation of the autocorrelation function. Secondly, an extension operation is conducted in the extended autocorrelation function to make the variance constant by keeping the number of calculation points constant. This operation can improve the enhancement effect for the fault impulses. Furtherly, the short-time Fourier transform is employed to suppress the noise. The contrast of the time–frequency distribution is improved by the gamma transform. And the local maximum sampling is employed to extract the fault impulse peaks to improve the time–frequency concentration. These operations constitute the local maximum instantaneous extraction transform. The proposed method is validated by a series of simulated signals and two public experimental signals. And a comparison is done between the LMIET-EACF and other mainstream signal enhancement algorithms. The results indicate that the proposed method performs better than several common time–frequency distributions, by quantitatively evaluating with the Rényi entropy. In addition, it can catch the fault signal in a lower signal-to-noise ratio, compared with some novel post-processing methods.