Sparse Frequency Representation Using Autocorrelation of Variational Mode Functions to Detect Compound Fault in Rotating Machines

A gearbox is a torque transmitting unit, in other words, a nonlinear dynamic system, consisting of gear pairs, bearings, and shafts. In a vibration signal, effect of gear tooth faults reflects modulations and appears as sidebands in frequency spectrum. Similarly, bearing faults exhibit modulations too. Thus, when multiple faults termed as compound faults occurring in bearing simultaneously, the sidebands in the resulting vibration signal will be difficult to investigate, due to interference, and hence, specialized techniques are required to solve such problems. An investigation considering the compound fault occurring in a rotating machine is presented in this work. A fault detection approach based on variational mode decomposition and autocorrelation is proposed in this paper for compound faults. VMD demodulates the vibration signal thereby attenuating the effect of spurious noise; however, the low-frequency component related to individual fault is unidentifiable. Therefore, autocorrelation analysis and estimation of correlation coefficient of the extracted variational mode functions (VMFs) was performed followed by the sparsity analysis using Gini Index, Hoyer Index, and \({\mathrm{l}}_{2}/{\mathrm{l}}_{1}\) norm of the most sensitive VMF to exhibit the fault. It was noted that the proposed approach attempts to solve the problem of complex oscillation characteristics, and mutual interference between multiple bearing faults. The result suggests that the proposed approach is more effective in diagnosing the compound fault.