Advantages of cepstrum analysis in gear fault diagnosis

Cepstrum analysis plays a special role in gear fault diagnosis, especially in side band analysis.

Because the frequency spectrum of the actual gearbox vibration signal is very complex, when there are several side bands crossing each other, it is not enough to rely on the frequency refinement analysis method only, and it is often difficult to see the structure of the side band.

However, the cepstrum can clearly show the edge frequency of periodic structure in the spectrum.

If a complex frequency spectrum is regarded as a time history signal, as shown in figure (a) on the right, there are many sidebands around the meshing frequency and its harmonics. The interval frequency of the sideband is the fault frequency. The higher the harmonic order of the fault frequency is, the smaller the amplitude value is, the average envelope of the harmonic peak is close to a periodic wave.

Make another spectrum analysis (i.e. inverse Fourier transform) for the power spectrum, and convert it to a new domain, so as to show the periodic frequency structure clearly, as shown in (b) above, which is the inverse spectrum analysis method.

Cepstrum is another concentration of the energy of the periodic frequency structure component on the original spectrum, and it gives higher weight to the low amplitude component in the logarithmic conversion of power, and lower weight to the high amplitude component, so the small signal period is highlighted.

Therefore, the cepstrum can effectively identify the periodic components in the spectrum.

This is the first advantage of cepstrum analysis.

The second advantage of cepstrum analysis is that it is little affected by the signal transmission path.

The installation position of the sensor on the gearbox is different, the signal transmission way is different, and different transfer functions are formed. These transfer functions reflect different results on the output spectrum. Sometimes, the amplitude of some frequency components is very different, resulting in false grasping and missing grasping of fault feature information.

However, after the simultaneous interpreting of the signals of different transmission paths, the two inverted spectrum images have the same high frequency components, which provides a very favorable condition for gearbox fault diagnosis.

In addition, due to the simultaneous existence of amplitude modulation and frequency modulation, as well as the phase changes of the two modulation, the side frequency is unstable, which often leads to the lack of symmetrical side band on the power spectrum, which makes it difficult to identify the side band.

However, in the cepstrum, the amplitude representing the modulation level is not affected by the stability.

After the two vibration signals are modulated, even though the amplitude of the side frequency at the corresponding position on the power spectrum is quite different, the effect of the phase difference on their frequency spectrum will not be reflected in the cepstrum at all. In the cepstrum, the cepstrum peaks of the two vibration signals are completely the same.

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