# Fault diagnosis of gear wavelet analysis

As a new mathematical theory and method, wavelet transform has been widely used in many fields.

In vibration signal analysis, wavelet transform is a multi-resolution time-frequency analysis method, which has many advantages and provides a valuable tool for non-stationary signal analysis. In practical application, binary discrete wavelet transform is often used. From the perspective of multi-resolution analysis, wavelet decomposition is equivalent to a band-pass filter and a low-pass filter. Each decomposition always decomposes the original signal into two sub signals, which are called approximation signal and detail signal respectively. Each part also needs to go through an interval resampling. In this way, the wavelet decomposition results of the nth layer (on scale n) can be obtained by decomposing n times.

Wavelet transform is often used in the operation state and fault diagnosis analysis of gearbox by the following three methods:

(1) Wavelet packet energy spectrum monitoring;

(2) Sideband identification;

(3) Modulus maxima and zero crossing detection of singular points.

With the development of wavelet analysis technology and the rapid development of computer capacity and computing power, people begin to apply continuous wavelet transform to fault diagnosis and analysis recently. Continuous wavelet transform can provide great convenience for the selection of Ji Xiaobo. When we know the characteristics of the components to be detected, we can choose to construct the corresponding wavelet and make continuous wavelet transform to reveal the distribution and size of these components.

Although wavelet transform is a good signal analysis tool, it still has the following two problems: (1) the result of wavelet transform analysis is not as intuitive as that of Fourier transform, which requires the analyst to have a certain theoretical basis of wavelet analysis for judgment, and is not suitable for automatic analysis and processing of the results by computer. (2) The kernel function of wavelet transform is not the only one, which needs to be selected according to the actual engineering application.

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