Gearbox fault diagnosis based on permutation entropy optimized variational mode decomposition

Abstract: gearbox composite fault diagnosis has received extensive attention. The composite fault is that 2 or more faults occur simultaneously in the mechanical equipment. Due to the different degrees of damage of the composite fault, the complicated transmission path of the fault characteristic signal, and the interference of the background noise, the strength between the fault components is not balance. The weak fault features are usually overwhelmed by strong faults or noise and the strong faults are weakened by the high-frequency energy in the process of transmission, it is easy to be missed or misdiagnosis, especially in the case of variable speed and variable load, the coupling of composite fault features poses great challenge to the healthy and reasonable diagnosis of mechanical equipment. With the development of computer technology, some new novel adaptive noise reduction methods are proposed, including parametric decomposition methods and nonparametric decomposition methods, but they are more or less affected by noise interference and modal aliasing. Variational mode decomposition(VMD) decompose a complex signal into several different time scales, and each time scale contains a center frequency, which can overcome the modal aliasing phenomenon, variational mode decomposition is widely applied to gearbox composite fault diagnosis, and has achieved amazing results, but it needs to preset the decomposition layers k and penalty factor, and is sensitive to the background noise. In order to adaptively determine the number of decomposition layers k, this paper proposed permutation entropy optimization algorithm, which can adaptively determine the number of decomposition layers k according to the characteristics of the signal to be decomposed. In order to solve the sensitivity of VMD to noise, this paper proposed modified variational mode decomposition(MVMD) based on the idea of noise aided data analysis. The algorithm first added the opposite gauss white noise to the original signal, and then used VMD to decompose it. After repeated cycles, the noise in the original signal would offset each other, then the ensemble average is generated for each IMF（intrinsic mode function） in each cycle, and the signal was reconstructed according to the result of ensemble mean. The VMD decomposition of the reconstructed signal was taken as the final output result of MVMD. This algorithm was used to process the gear box simulation signal and the measured signal with multiple fault features respectively, and the decomposition results showed that the algorithm can not only improve the signal to noise ratio(SNR) of the signal effectively, but also successfully extract the multiple fault features of the gear box in the strong noise environment, the fault frequencies of 160 and 360 Hz were extracted respectively which correspond to the bearing outer ring frequency and the gear meshing frequency. This method provides a new idea for gearbox composite fault diagnosis, it can not only overcome the interference of strong noise, but also accurately extract fault characteristics. In the future work, the research group will introduces the intelligent algorithm into the variational mode decomposition to determine the number of layers decomposed adaptively, at the same time, the combination of variational mode decomposition and support vector machine or neural network can improve the efficiency of intelligent fault diagnosis, this is a new idea for the healthy operation of agricultural machinery.