| Summary: | 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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