基于提升模式的非抽样小波变换及其在故障诊断中的应用

由于传统离散小波变换在分解信号时采用抽样操作，使原始信号的部分时域特征不能保留在分解结果中；另外，分解结果的平移可变，使得分解结果不能完美地描述故障的时域特征。为了克服上述缺陷，根据非抽样小波变换的原理，提出一种基于提升模式的非抽样小波变换框架。首先，通过信号变换方法去除提升小波变换的剖分环节，得到提升模式下的非抽样小波变换框架；在此基础上，建立提升模式下非抽样小波变换与抽样小波变换的预测器和更新器之间的转换关系，提出非抽样提升小波变换的分解和重构算法。采用这种非抽样小波变换从齿轮箱的振动信号中有效提取幅值调制和瞬态冲击的摩擦故障特征。

UNDECIMATED WAVELET TRANSFORM BASED ON LIFTING SCHEME AND IT'S APPLICATION IN FAULT DIAGNOSIS

Because decimation operation is applied in classical discrete wavelet transform when signals decomposed, some temporal signatures of the signals are not nicely preserved in decomposition signals. Moreover, the decomposition signals are translation variant. As motioned above, the decomposition signals can not perfectly characterize fault feature in the time domain. In order to overcome the drawbacks above, a framework of undecimated wavelet transform (UWT) via lifting scheme was proposed on the basis of the principle of UWT. Firstly, removing split step of the lifting wavelet transform by using signal transformation technique, the UWT framework based on lifting scheme was obtained. Then, by virtue of the framework, the transformation relations of predictor and updater between UMT and decimated wavelet transform were found, and an algorithm for UWT decomposition and reconstruction was developed. The proposed UWT effectively extracted the friction fault features of amplitude modulation and transient impact from vibration signal of a gearbox.