卷积型小波变换的实现及其在机械早期故障诊断的应用

为消除Mallat算法存在的频率折叠等固有缺陷对机械故障诊断的不利影响，本文提出采用卷积型小波变换进行机械故障诊断。基于此，本文首先推导了卷积型小波变换快速分解算法，并给出其基于滤波器组的递归分解实现方法。其次，针对滚动轴承早期故障诊断与定量识别的难题以及共振解调法与冲击脉冲法的不足，本文提出一种将卷积型小波变换与共振解调法、冲击脉冲法相结合的新方法来对滚动轴承早期故障进行诊断与定量识别，并给出了其具体实现过程。仿真实验与实例分析表明：卷积型小波变换确实消除Mallat算法的固有缺陷对机械故障诊断的不利影响，比内积型小波变换更适合于机械故障诊断，并且本文提出的新方法可以有效实现对滚动轴承早期故障的诊断与定量识别，具有一定的工程应用价值。

The Realization of Convolution Wavelet Transformation and The Application in Mechanical Incipient Fault Diagnosis

In order to avoid the influence on mechanical fault diagnosis exerted by the instinct defects in Mallat algorithm, the paper introduces the convolution type of wavelet transformation to mechanical fault diagnosis. Then, the fast decomposition algorithm of the convolution type of wavelet transformation is induced detailedly and a method based on filter banks to realize recursively the fast decomposition algorithm is given. Considering the problem of diagnosis and identification of incipient fault and the shortcomings of resonance demodulation and shock pulse method, a new method is presented which combines the convolution type of transformation with resonance demodulation and shock pulse method. The simulation and analysis of the incipient fault data shows that the convolution type of transformation is more fit for mechanical fault diagnosis, and the new method can effectively detects the incipient fault and exactly identifies weak damage of rolling bearing.