The 1/3-binary tree structure bandwidth is fixed, while the bands containing fault information sometimes do not fall equally in the fixed structure. To solve this problem, it is proposed to utilize the power spectrum to replace the Fourier spectrum, and to reconstruct the signal based on the scale space representation for the empirical wavelet decomposition. The fluctuation characteristics of the power spectrum frequency components and the energy distribution within frequency bands are taken full advantage of in this method. A new size parameter updating mechanism is employed to accelerate the signal reconstruction process. At the same time, it is thought that fault frequency is affected by the factor of slippage phenomena in order to realize a self-running diagnosis of bearing failure, and the occurring probability of the bearing fault is introduced to transform the envelope spectrum into a scalar indicator. As a result, without human intervention, the whole failure diagnosis process of the rolling bearing can be achieved by the manner of nonparametric testing. Simulation signal analysis results and experimental analysis results demonstrate the effectiveness and superiority of the proposed method.