Wavelet transform based on inner product in fault diagnosis of rotating machinery: A review

• This paper reviews the developments of wavelet transform (WT) and the applications in rotating machinery fault diagnosis (RMFD).
• The essence on inner product operation of WT in RMFD is revealed by simulation and field test experiments.
• The development process of WT and the engineering applications of major developments in RMFD are summarized.
• Existent problems of wavelet transform are discussed and several important prospects are presented.

As a significant role in industrial equipment, rotating machinery fault diagnosis (RMFD) always draws lots of attention for guaranteeing product quality and improving economic benefit. But non-stationary vibration signal with a large amount of noise on abnormal condition of weak fault or compound fault in many cases would lead to this task challenging. As one of the most powerful non-stationary signal processing techniques, wavelet transform (WT) has been extensively studied and widely applied in RMFD. Numerous publications about the study and applications of WT for RMFD have been presented to academic journals, technical reports and conference proceedings. Many previous publications admit that WT can be realized by means of inner product principle of signal and wavelet base. This paper verifies the essence on inner product operation of WT by simulation and field experiments. Then the development process of WT based on inner product is concluded and the applications of major developments in RMFD are also summarized. Finally, super wavelet transform as an important prospect of WT based on inner product are presented and discussed. It is expected that this paper can offer an in-depth and comprehensive references for researchers and help them with finding out further research topics.