Approach to the Quantitative Diagnosis of Rolling Bearings Based on Optimized VMD and Lempel–Ziv Complexity under Varying Conditions

The quantitative diagnosis of rolling bearings is essential to automating maintenance decisions. Over recent years, Lempel–Ziv complexity (LZC) has been widely used for the quantitative assessment of mechanical failures as one of the most valuable indicators for detecting dynamic changes in nonlinear signals. However, LZC focuses on the binary conversion of 0–1 code, which can easily lose some effective information about the time series and cannot fully mine the fault characteristics. Additionally, the immunity of LZC to noise cannot be insured, and it is difficult to quantitatively characterize the fault signal under strong background noise. To overcome these limitations, a quantitative bearing fault diagnosis method based on the optimized Variational Modal Decomposition Lempel–Ziv complexity (VMD-LZC) was developed to fully extract the vibration characteristics and to quantitatively characterize the bearing faults under variable operating conditions. First, to compensate for the deficiency that the main parameters of the variational modal decomposition (VMD) have to be selected by human experience, a genetic algorithm (GA) is used to optimize the parameters of the VMD and adaptively determine the optimal parameters [k, α] of the bearing fault signal. Furthermore, the IMF components that contain the maximum fault information are selected for signal reconstruction based on the Kurtosis theory. The Lempel–Ziv index of the reconstructed signal is calculated and then weighted and summed to obtain the Lempel–Ziv composite index. The experimental results show that the proposed method is of high application value for the quantitative assessment and classification of bearing faults in turbine rolling bearings under various operating conditions such as mild and severe crack faults and variable loads.