Parallel multi-scale entropy and it's application in rolling bearing fault diagnosis

•Frequency characteristic variation in the MSE coarse-graining procedure is analyzed.•MSE coarse-grained data can be equivalent to τ parallel series with similar properties.•A novel nonlinear dynamic method named parallel multi-scale entropy is proposed.•The parallel multi-scale entropy eliminates the aliasing effect of the original MSE.•The performance is verified by simulated bearing data and CWRU experimental data.