Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis
Fuzzy dispersion entropy (FuzzDE) is a very recently proposed non-linear dynamical indicator, which combines the advantages of both dispersion entropy (DE) and fuzzy entropy (FuzzEn) to detect dynamic changes in a time series. However, FuzzDE only reflects the information of the original signal and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/10/544 |
| _version_ | 1827650176488046592 |
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| author | Yuxing Li Bingzhao Tang Bo Geng Shangbin Jiao |
| author_facet | Yuxing Li Bingzhao Tang Bo Geng Shangbin Jiao |
| author_sort | Yuxing Li |
| collection | DOAJ |
| description | Fuzzy dispersion entropy (FuzzDE) is a very recently proposed non-linear dynamical indicator, which combines the advantages of both dispersion entropy (DE) and fuzzy entropy (FuzzEn) to detect dynamic changes in a time series. However, FuzzDE only reflects the information of the original signal and is not very sensitive to dynamic changes. To address these drawbacks, we introduce fractional order calculation on the basis of FuzzDE, propose <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>, and use it as a feature for the signal analysis and fault diagnosis of bearings. In addition, we also introduce other fractional order entropies, including fractional order DE (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>DE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>), fractional order permutation entropy (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>PE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>) and fractional order fluctuation-based DE (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>), and propose a mixed features extraction diagnosis method. Both simulated as well as real-world experimental results demonstrate that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula> at different fractional orders is more sensitive to changes in the dynamics of the time series, and the proposed mixed features bearing fault diagnosis method achieves 100% recognition rate at just triple features, among which, the mixed feature combinations with the highest recognition rates all have <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula> also appears most frequently. |
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| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:11:42Z |
| publishDate | 2022-09-01 |
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| series | Fractal and Fractional |
| spelling | doaj.art-7bb49b4d81464ae7bd821beeae469e6a2023-11-24T00:11:17ZengMDPI AGFractal and Fractional2504-31102022-09-0161054410.3390/fractalfract6100544Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault DiagnosisYuxing Li0Bingzhao Tang1Bo Geng2Shangbin Jiao3School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, ChinaFuzzy dispersion entropy (FuzzDE) is a very recently proposed non-linear dynamical indicator, which combines the advantages of both dispersion entropy (DE) and fuzzy entropy (FuzzEn) to detect dynamic changes in a time series. However, FuzzDE only reflects the information of the original signal and is not very sensitive to dynamic changes. To address these drawbacks, we introduce fractional order calculation on the basis of FuzzDE, propose <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>, and use it as a feature for the signal analysis and fault diagnosis of bearings. In addition, we also introduce other fractional order entropies, including fractional order DE (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>DE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>), fractional order permutation entropy (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>PE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>) and fractional order fluctuation-based DE (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>), and propose a mixed features extraction diagnosis method. Both simulated as well as real-world experimental results demonstrate that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula> at different fractional orders is more sensitive to changes in the dynamics of the time series, and the proposed mixed features bearing fault diagnosis method achieves 100% recognition rate at just triple features, among which, the mixed feature combinations with the highest recognition rates all have <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>FuzzDE</mi></mrow><mi>α</mi></msub></mrow></semantics></math></inline-formula> also appears most frequently.https://www.mdpi.com/2504-3110/6/10/544fuzzy dispersion entropyfractional orderfeature extractionbearing fault diagnosis |
| spellingShingle | Yuxing Li Bingzhao Tang Bo Geng Shangbin Jiao Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis Fractal and Fractional fuzzy dispersion entropy fractional order feature extraction bearing fault diagnosis |
| title | Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis |
| title_full | Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis |
| title_fullStr | Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis |
| title_full_unstemmed | Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis |
| title_short | Fractional Order Fuzzy Dispersion Entropy and Its Application in Bearing Fault Diagnosis |
| title_sort | fractional order fuzzy dispersion entropy and its application in bearing fault diagnosis |
| topic | fuzzy dispersion entropy fractional order feature extraction bearing fault diagnosis |
| url | https://www.mdpi.com/2504-3110/6/10/544 |
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