Optimal frequency band selection is a critical step of envelope analysis for bearing fault diagnosis. In order to select the most informative band, it is necessary to define a criterion for frequency band evaluation. Kurtosis is one of such criteria, and the frequency band with largest spectral kurtosis is usually regarded as the optimal one. However, it is experimentally and mathematically proved in the past year that spectral kurtosis is sensitive to outliers in a signal. Recently, spectral L2/L1 norm is formally defined for characterizing fault transients in the squared envelope of the signal, and it is also found that spectral L2/L1 norm is actually the square root of spectral kurtosis. Thus, spectral L2/L1 norm still suffers from the drawback of spectral kurtosis. In this paper, however, we utilize this drawback and calculate L2/L1 norms of frequency bands defined by the harmonics of bearing characteristic frequency in the squared envelope spectrum. Since the new calculation is closely related to harmonics of bearing characteristic frequency, it is named as harmonic L2/L1 norm in the paper. Harmonic L2/L1 norm is then employed to evaluate frequency bands obtained from a 1/3-binary tree of filter banks. After the optimal band selection, the filtered signal is used to calculate the squared envelope spectrum. The proposed method is compared with the fast kurtogram method in two case studies, which indicate that the proposed method is more effective, especially in the presence of strong non-Gaussian noise. INDEX TERMS Bearing diagnosis, kurtogram, optimal band selection, squared envelope spectrum, sparsity index.

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An improved multi-sensor data fusion algorithm based on Dempster-Shafer evidence theory and a criterion of the object evaluation are presented in this paper. The algorithm and the criterion investigate the monitor data of the indoor air that is the research object, and evaluate the quality grade of the indoor air. Experiment shows that the improved multisensor data fusion algorithm based on the Dempster-Shafer reasoning and the resulting evaluations are correct and solve the uncertainty problem which is produced in the multi-sensor information process.