In recent years, a new method of fault diagnosis, named variational mode decomposition (VMD), has been widely used in industrial production, but the decomposition accuracy of VMD is determined by two parameters, which are respectively the decomposition layer number k and the penalty factor α, if the parameters are not properly selected, there will be over-decomposition or under-decomposition. In order to find an approach to determine the parameters adaptively, a method to optimize VMD by using the immune fruit fly optimization algorithm (IFOA) is proposed in this paper. In this method, permutation entropy is used as the fitness function, firstly, the immune fruit fly optimization algorithm is used to search the combined parameters of k and α in VMD, searching for the best combination parameters of k and α by iteration, and then uses the combined parameters to perform VMD, finally, the center frequency is determined through frequency spectrum analysis. The method mentioned is applied to the fault extraction of a simulated signal and a measured signal of a wind turbine gearbox, and the fault frequency is successfully extracted. Using ensemble empirical mode decomposition (EEMD) and singular spectrum decomposition (SSD) to compare with the proposed method, which validated feasibility of the proposed method.

Under the strong noise environment, the composite fault signal of gearbox is weak, which makes it difficult to extract fault features. For this problem, based on noise-assisted method, we propose a novel method called Modified Singular Spectrum Decomposition (MSSD). Singular Spectrum Decomposition (SSD) has many advantages such as high decomposition precision and strong ability to restrain mode mixing, etc. However, the ability of SSD to extract a weak signal is not ideal, the decomposition results usually contain a lot of redundant noise and mode mixing caused by intermittency, which is also a troubling problem. In order to improve the decomposition efficiency and make up for the defects of SSD, the new method MSSD adds an adaptive and particular noise in every SSD decomposition stage for each trial, and in addition, whenever the input signal is decomposed to obtain an intrinsic module function (IMF), a unique residual is obtained. After multiple decomposition, the average value of the residual is used as input to the next stage, until the residual cannot continue to decompose, which means that the residual component has, at most, one extreme value. Finally, analyzing simulated signals to explain the advantages of MSSD compared to ensemble empirical mode decomposition (EEMD) and complete ensemble local mean decomposition with adaptive noise (CEEMDAN). In order to further prove the effectiveness of MSSD, this new method, MSSD, is applied to the fault diagnosis of an engineering gearbox test stand in an actual engineer project case. The final results show that MSSD can extract more fault feature information, and mode mixing has been improved and suffers less interference compared to SSD.