Optimal weighted envelope spectrum with informative multi-band selection for bearing fault diagnosis

Spectral coherence theory is of practical importance for bearing fault diagnosis. However, when fault-related information is distributed across multiple spectral bands, existing methods often cannot effectively identify and integrate these informative components, which limits diagnostic performance. To address this issue, an optimal weighted envelope spectrum (OWES) is proposed. First, the expected signal to expected noise (ESEN) is constructed. By introducing local background correction and adaptive harmonic position identification, ESEN enhances the robustness of fault feature extraction to frequency deviation, amplitude variation, and spectral background fluctuation. Then, informative spectral regions are identified by thresholding the ESEN distribution along the spectral frequency axis and are merged into candidate frequency bands. A combinatorial optimization strategy is further introduced to select the candidate band subset that yields the most prominent integrated fault feature, thereby improving fault feature extraction when informative components are distributed across multiple spectral bands. Finally, the selected bands are weighted according to their information contributions and integrated to construct the OWES. The proposed method is validated using one simulated signal and three bearing experimental datasets. Compared with several advanced methods, OWES achieves clearer identification of fault characteristic frequencies and harmonics. Quantitative comparisons based on ESEN and kurtosis further demonstrate the superior performance of the proposed OWES method.