Bispectrum Feature Extraction of Gearbox Faults Based on Nonnegative Tucker3 Decomposition with 3D Calculations

Nonnegative Tucker3 decomposition（NTD） has attracted lots of attentions for its good performance in 3D data array analysis. However, further research is still necessary to solve the problems of overfitting and slow convergence under the anharmonic vibration circumstance occurred in the field of mechanical fault diagnosis. To decompose a large-scale tensor and extract available bispectrum feature, a method of conjugating Choi-Williams kernel function with Gauss-Newton Cartesian product based on nonnegative Tucker3 decomposition（NTD;DF） is investigated. The complexity of the proposed method is reduced from（nNlgn） in 3D spaces to 12 o（R1R2nlgn）in 1D vectors due to its low rank form of the Tucker-product convolution. Meanwhile, a simultaneously updating algorithm is given to overcome the overfitting, slow convergence and low efficiency existing in the conventional one-by-one updating algorithm. Furthermore, the technique of spectral phase analysis for quadratic coupling estimation is used to explain the feature spectrum extracted from the gearbox fault data by the proposed method in detail. The simulated and experimental results show that the sparser and more inerratic feature distribution of basis images can be obtained with core tensor by the NTD;DF method compared with the one by the other methods in bispectrum feature extraction, and a legible fault expression can also be performed by power spectral density（PSD） function. Besides, the deviations of successive relative error（DSRE） of NTD;DF achieves 81.66 dB against 15.17 dB by beta-divergences based on NTD（NTD;eta） and the time-cost of NTD;DF is only 129.3 s, which is far less than 1747.9 s by hierarchical alternative least square based on NTD（NTD;ALS）. The NTD;DF method proposed not only avoids the data overfitting and improves the computation efficiency but also can be used to extract more inerratic and sparser bispectrum features of the gearbox fault.