Quaternion empirical Ramanujan Fourier decomposition and its application in gear fault diagnosis

Abstract

In the field of gear health monitoring, the measured signals are traditionally derived from a single sensor or a single direction. However, with the increasing complexity and size of equipment structures nowadays, a single-channel signal often falls short in providing comprehensive status information. Furthermore, fault-induced vibrations are randomly indeterminate in both location and direction, which indicates the necessity of using multi-channel signals for effective gear fault diagnosis. As a single-channel method, Ramanujan Fourier transform (RFT) has been recognized for its effectiveness in extracting periodic components from signals. However, the RFT is limited to handling single-channel signals and lacks the ability to analyze nonstationary signals. To overcome these challenges, this paper proposes a novel multi-channel signal processing method called quaternion empirical Ramanujan Fourier decomposition (QERFD), which extends the RFT to the multi-channel field using the quaternion method. By fusing multi-channel signals while preserving the advantages of RFT, the proposed QERFD method enhances fault information extraction. In addition, QERFD shows high computational efficiency. Therefore, QERFD is of great practical value for the health monitoring of complex equipment in the present industrial context of big data. To substantiate the superiority of QERFD, simulations and experiments are carried out and compared against both single-channel and multi-channel methods.