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Bispectrum feature extraction of gearbox faults based on nonnegative Tucker3 decomposition with 3D calculations

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Abstract

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_EDF) is investigated. The complexity of the proposed method is reduced from o(n N lgn) in 3D spaces to o(R 1 R 2 nlgn) 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_EDF 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_EDF achieves 81.66 dB against 15.17 dB by beta-divergences based on NTD(NTD_Beta) and the time-cost of NTD_EDF is only 129.3 s, which is far less than 1 747.9 s by hierarchical alternative least square based on NTD (NTD_HALS). The NTD_EDF 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.

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Authors and Affiliations

  1. School of Mechanical Engineering, Southeast University, Nanjing, 211189, China

    Haijun Wang, Feiyun Xu, Jun’ai Zhao, Minping Jia, Jianzhong Hu & Peng Huang

Authors
  1. Haijun Wang
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  2. Feiyun Xu
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  3. Jun’ai Zhao
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  4. Minping Jia
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  5. Jianzhong Hu
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  6. Peng Huang
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Corresponding author

Correspondence to Feiyun Xu.

Additional information

This project is supported by National Natural Science Foundation of China(Grant Nos. 50875048, 51175079, 51075069)

WANG Haijun, born in 1982, is currently working toward his PhD degree at School of Mechanical Engineering, Southeast University, China. He received his master degree from Guangdong University of Technology, China, in 2010. His research interests include fault diagnosis, pattern recognition and signal processing.

XU Feiyun, born in 1969, is currently a professor and a PhD candidate supervisor at School of Mechanical Engineering, Southeast University, China. He received his PhD degree from Southeast University, China, in 1996. His main research interests include artificial intelligence theory and application, intelligent measurement technology of mechanical dynamic system and time series analysis for nonlinear system identification.

ZHAO Jun’ai, born in 1980, is currently working for her PhD degree at School of Mechanical Engineering, Southeast University, China. She received her master’s degree from Nanjing Agricultural University, China, in 2007. Her current research interests include fault diagnosis and pattern recognition.

JIA Minping, born in 1960, is currently a professor and a PhD candidate supervisor at School of Mechanical Engineering, Southeast University, China. He received his PhD degree from Southeast University, China, in 1991. His main research interests include vibration analysis, fault diagnosis, nonlinear dynamic system identification, artificial intelligence theory and application.

HU Jianzhong, born in 1971, is currently an associate professor at School of Mechanical Engineering, Southeast University, China. He received his PhD from Southeast University, China, in 2003. His research interests main include artificial intelligent application in mechanical fault diagnosis and technology of numerical control.

HUANG Peng, born in 1981, is currently a lecturer at School of Mechanical Engineering, Southeast University, China. He received his PhD degree from Southeast University, China, in 2010. His research interests include signal processing and soft measurement.

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Wang, H., Xu, F., Zhao, J. et al. Bispectrum feature extraction of gearbox faults based on nonnegative Tucker3 decomposition with 3D calculations. Chin. J. Mech. Eng. 26, 1182–1193 (2013). https://doi.org/10.3901/CJME.2013.06.1182

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  • DOI: https://doi.org/10.3901/CJME.2013.06.1182

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