Multiscale fluctuation-based symbolic dynamic entropy: a novel entropy method for fault diagnosis of rotating machinery

Abstract

Health monitoring has garnered significant and increasing attention from the research community and industrial practices thanks to its critical role in ensuring the safe operation of machinery and maintenance schedule. With regard to this, this paper introduces a novel diagnostic approach called fluctuation-based symbolic dynamic entropy (FSDE), which can enhance noise immunity and computational efficiency by utilizing fluctuation-based entropy algorithm and symbolic dynamic filtering. Moreover, the noise immunity and computational efficiency of FSDE, permutation entropy, fuzzy entropy, and sample entropy are compared by simulation signals. The simulation results show that FSDE has a more robust anti-noise performance and higher computational efficiency than the other three entropy methods. In order to extract fault features more thoroughly, multiscale analysis is applied to the entropy method, and multiscale FSDE (MFSDE) is proposed. MFSDE divides the measurement data into several scale series by coarse-grained technology, and then, FSDE is used to process each scale series separately. A series of experiments verify the effectiveness of MFSDE in fault feature extraction of fault diagnosis. Furthermore, the experimental results substantiate that MFSDE outperforms the other three currently used entropy-based approaches in terms of accuracy in classifying different health conditions of transmission systems.

Keywords

Characteristic extraction rotating machinery multiscale analysis fault diagnosis multiscale fluctuation-based symbolic dynamic entropy

Get full access to this article

View all access options for this article.

References

Wei

Wang

, et al. Intelligent fault diagnosis of rotating machinery using composite multivariate-based multi-scale symbolic dynamic entropy with multi-source monitoring data. Struct Health Monit 2023; 22: 56–77.

Yan

Yuen

, et al. An adaptive variational mode extraction method based on multi-domain and multi-objective optimization for bearing fault diagnosis. Struct Health Monit 2023; 22(4): 2708–2733.

Zhong

Shao

, et al. Multi-mode data augmentation and fault diagnosis of rotating machinery using modified ACGAN designed with new framework. Adv Eng Inform 2022; 52: 101552.

Wang

, et al. Enhanced hierarchical symbolic sample entropy: efficient tool for fault diagnosis of rotating machinery. Struct Health Monit 2023; 22: 1927–1940.

Zheng

Pan

Yang

, et al. Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis. Mech Syst Signal Process 2018; 99: 229–243.

Shannon

. A mathematical theory of communication. ACM SIGMOBILE mobile computing and communications review, 2001; 5(1): 3–55.

Pincus

. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci 1991; 88: 2297–2301.

Richman

Moorman

. Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol Heart Circ Physiol 2000; 278: H2039–H2049.

Zheng

Cheng

Yang

, et al. A rolling bearing fault diagnosis method based on multi-scale fuzzy entropy and variable predictive model-based class discrimination. Mech Mach Theory 2014; 78: 187–200.

10.

Yang

, et al. A fault diagnosis scheme for planetary gearboxes using modified multi-scale symbolic dynamic entropy and mRMR feature selection. Mech Syst Signal Process 2017; 91: 295–312.

11.

Chen

Zhuang

, et al. Measuring complexity using fuzzyen, apen, and sampen. Med Eng Phys 2009; 31: 61–68.

12.

Bandt

Pompe

. Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 2002; 88: 174102.

13.

Costa

Goldberger

Peng

. Multiscale entropy analysis of complex physiologic time series. Phys Rev Lett 2002; 89: 68102.

14.

Wang

Yao

Cai

. Rolling bearing fault diagnosis using generalized refined composite multiscale sample entropy and optimized support vector machine. Measurement 2020; 156: 107574.

15.

Guo

Wang

, et al. A new fuzzy logic classifier based on multiscale permutation entropy and its application in bearing fault diagnosis. Entropy 2019; 22: 27.

16.

Tiwari

Gupta

Kankar

. Bearing fault diagnosis based on multi-scale permutation entropy and adaptive neuro fuzzy classifier. J Vib Control 2015; 21: 461–467.

17.

Minhas

Sharma

Singh

, et al. Improvement in classification accuracy and computational speed in bearing fault diagnosis using multiscale fuzzy entropy. J Braz Soc Mech Sci 2020; 42: 1–21.

18.

Zhu

Zheng

Pan

, et al. Time-shift multiscale fuzzy entropy and laplacian support vector machine based rolling bearing fault diagnosis. Entropy 2018; 20: 602.

19.

Azami

Escudero

. Amplitude-and fluctuation-based dispersion entropy. Entropy 2018; 20: 210.

20.

Rajagopalan

Ray

. Symbolic time series analysis via wavelet-based partitioning. Signal Process 2006; 86: 3309–3320.

21.

Ray

. Symbolic dynamic analysis of complex systems for anomaly detection. Signal Process 2004; 84: 1115–1130.

22.

Beim Graben

. Estimating and improving the signal-to-noise ratio of time series by symbolic dynamics. Phys Rev E 2001; 64: 51104.

23.

Cao

Liao

, et al. Multivariate multiscale symbolic entropy analysis of human gait signals. Entropy 2017; 19: 557.

24.

Srivastava

Anderson

Freed

. A new wavelet denoising method for selecting decomposition levels and noise thresholds. IEEE Access 2016; 4: 3862–3877.

25.

Yan

Gao

. Approximate entropy as a diagnostic tool for machine health monitoring. Mech Syst Signal Process 2007; 21: 824–839.

26.

Zheng

Cheng

Yang

. Multiscale permutation entropy based rolling bearing fault diagnosis. Shock Vib 2014; 2014: 1–8.

27.

Liang

Zuo

Pandey

. Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set. Mech Mach Theory 2014; 76: 20–38.

28.

Chen

Yang

Liu

, et al. A support vector machine classifier with rough set-based feature selection for breast cancer diagnosis. Expert Syst Appl 2011; 38: 9014–9022.