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Two-dimensional composite multi-scale time–frequency reverse dispersion entropy-based fault diagnosis for rolling bearing

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Abstract

Multi-scale dispersion entropy (MDE1D) is an effective nonlinear dynamic tool to characterize the complexity of time series and has been extensively applied to mechanical fault diagnosis. However, with the increase of scale factor, the values of MDE1D often fluctuate largely, resulting in poor stability. Besides, it only extracts the complexity information from the time domain of vibration signal, while the complexity information in the frequency domain is ignored. To enhance the stability of MDE1D and extract the complexity characteristics from the time–frequency domain of vibration signal, this paper first develops a two-dimensional multi-scale reverse dispersion entropy (MRDE2D), inspired by the MDE1D and two-dimensional multi-scale dispersion entropy (MDE2D) through introducing the “distance information from white noise”. Then a two-dimensional multi-scale time–frequency reverse dispersion entropy (MTFRDE2D) combined with time–frequency analysis is proposed. After that, considering that the length of the coarse-grained sequence used in the multi-scale coarse-grained process of MTFRDE2D will become shorter and shorter with the increase of scale factor, resulting in a loss of potentially useful information, the two-dimensional composite multi-scale time–frequency reverse dispersion entropy (CMTFRDE2D) is proposed through using the composite coarse-grained process. The effectiveness and advantages of CMTFRDE2D algorithm are demonstrated by analyzing different kinds of noise signals. Following that, a new rolling bearing fault diagnosis method is proposed based on the CMTFRDE2D for feature extraction and gravitational search algorithm optimized support vector machine for mode identification. The proposed fault diagnosis method is employed on two rolling bearing test data sets and also compared with the existing MTFRDE2D,- MRDE2D,- MDE2D,- and MDE1D-based fault diagnosis methods. The analysis results reveal that the proposed fault diagnosis method can successfully extract the fault information from rolling bearing vibration signals in time–frequency domain and can accurately identify different fault locations and severities of rolling bearings with certain advantages.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. https://github.com/yyxyz/CaseWesternReserveUniversityData.

Abbreviations

ApEn1D :

Approximate entropy

SampEn1D :

Sample entropy

FE1D :

Fuzzy entropy

PE1D :

Permutation entropy

DE1D :

Dispersion Entropy

RDE1D :

Reverse dispersion entropy

MDE1D :

Multi-scale dispersion entropy

MDE2D :

Two-dimensional multi-scale dispersion entropy

MRDE2D :

Two-dimensional multi-scale reverse dispersion entropy

MTFRDE2D :

Two-dimensional multi-scale time–frequency reverse dispersion entropy

CMTFRDE2D :

Two-dimensional composite multi-scale time–frequency reverse dispersion entropy

SVM:

Support vector machine

GSA:

Gravitational search algorithm

PSO:

Particle swarm optimization

CSO:

Chicken swarm optimization

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51975004), the Natural Science Foundation of Anhui Province of China (No. 2008085QE215), and the State Key Laboratory of Mechanical Transmissions (SKLMT-MSKFKT-202107).

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Authors and Affiliations

  1. School of Mechanical Engineering, Anhui University of Technology, Maanshan, 243032, China

    Jiaqi Li, **de Zheng, Haiyang Pan & **yu Tong

  2. The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, China

    **de Zheng

  3. School of Engineering, University of British Columbia, British Columbia, Canada

    Ke Feng

  4. School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Sydney, Australia

    Qing Ni

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Correspondence to **de Zheng.

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Li, J., Zheng, J., Pan, H. et al. Two-dimensional composite multi-scale time–frequency reverse dispersion entropy-based fault diagnosis for rolling bearing. Nonlinear Dyn 111, 7525–7546 (2023). https://doi.org/10.1007/s11071-023-08250-y

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