Rolling bearing fault diagnosis utilizing variational mode decomposition based fractal dimension estimation method

•A novel fractal dimension estimation method based on VMD is proposed.•Fractal characteristics of vibration signals are studied with the novel method.•Double-scale fractal dimensions are extracted as parameters of vibration signals.•Double-scale fractal dimensions are employed for rolling bearing fault diagnosis. A novel fractal dimension estimation method based on VMD is proposed in this paper. VMD is utilized to decompose the multi-component signal into several components. Multi-dimensional super-body volume is defined and calculated based on the decomposed components. Fractal dimension is then estimated by the least square method. Simulation results verify that fractal dimension estimation accuracy of the proposed method outperform box counting method and detrended fluctuation analysis. Furthermore, with this novel method, fractal characteristics of vibration signals form rolling bearing are studied. Achievements indicate that vibration signals are characterized by double-scale fractal features. Thus, two fractal dimensions corresponding to the small and large time scales respectively are extracted as feature parameters of vibration signals. Finally, double-scale fractal dimensions are employed for rolling bearing fault diagnosis. Classification results indicate that double-scale fractal dimensions extracted by VMD are capable of expressing fractal characteristics of vibration signals and diagnosing the rolling bearing faults.