Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns
Distinguishing between chaotic and stochastic dynamics given an input series is a widely studied topic within the time series analysis due to high demand from the practitioners in various fields. Due to one of the fundamental properties of chaotic systems, namely, being sensitive to parameters and i...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2021-04-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0045731 |
| _version_ | 1818595311786917888 |
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| author | Zelin Zhang Mingbo Zhang Yufeng Chen Zhengtao Xiang Jinyu Xu Xiao Zhou |
| author_facet | Zelin Zhang Mingbo Zhang Yufeng Chen Zhengtao Xiang Jinyu Xu Xiao Zhou |
| author_sort | Zelin Zhang |
| collection | DOAJ |
| description | Distinguishing between chaotic and stochastic dynamics given an input series is a widely studied topic within the time series analysis due to high demand from the practitioners in various fields. Due to one of the fundamental properties of chaotic systems, namely, being sensitive to parameters and initial conditions, chaotic time series exhibit features also observed in randomly generated signals. In this paper, we introduce distance as a measure of similarity between segments based on the ordinal structure. Furthermore, we introduce a new fuzzy entropy, Fuzzy Permutation Entropy (FPE), which can be used to detect determinism in time series. FPE immunes from repeated equal values in signals to some extent, especially for chaotic series. With specific embedding dimensions, it can be employed to distinguish chaotic signals from noise. We show an example for white Gaussian noise, autoregressive moving-average, continuous or discrete chaotic time series, and test FPE’s performance with additive observational noise. We show an application of FPE on rolling bearings’ fault diagnosis. |
| first_indexed | 2024-12-16T11:14:00Z |
| format | Article |
| id | doaj.art-4d231db1bac9483898f1e259c90ef284 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-16T11:14:00Z |
| publishDate | 2021-04-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-4d231db1bac9483898f1e259c90ef2842022-12-21T22:33:39ZengAIP Publishing LLCAIP Advances2158-32262021-04-01114045122045122-1310.1063/5.0045731Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patternsZelin Zhang0Mingbo Zhang1Yufeng Chen2Zhengtao Xiang3Jinyu Xu4Xiao Zhou5School of Science, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, ChinaSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 333000, ChinaSchool of Electrical and Information Engineering, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, ChinaSchool of Electrical and Information Engineering, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, ChinaSchool of Electrical and Information Engineering, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, ChinaSchool of Science, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, ChinaDistinguishing between chaotic and stochastic dynamics given an input series is a widely studied topic within the time series analysis due to high demand from the practitioners in various fields. Due to one of the fundamental properties of chaotic systems, namely, being sensitive to parameters and initial conditions, chaotic time series exhibit features also observed in randomly generated signals. In this paper, we introduce distance as a measure of similarity between segments based on the ordinal structure. Furthermore, we introduce a new fuzzy entropy, Fuzzy Permutation Entropy (FPE), which can be used to detect determinism in time series. FPE immunes from repeated equal values in signals to some extent, especially for chaotic series. With specific embedding dimensions, it can be employed to distinguish chaotic signals from noise. We show an example for white Gaussian noise, autoregressive moving-average, continuous or discrete chaotic time series, and test FPE’s performance with additive observational noise. We show an application of FPE on rolling bearings’ fault diagnosis.http://dx.doi.org/10.1063/5.0045731 |
| spellingShingle | Zelin Zhang Mingbo Zhang Yufeng Chen Zhengtao Xiang Jinyu Xu Xiao Zhou Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns AIP Advances |
| title | Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns |
| title_full | Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns |
| title_fullStr | Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns |
| title_full_unstemmed | Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns |
| title_short | Distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns |
| title_sort | distinguishing chaotic from stochastic dynamics via the complexity of ordinal patterns |
| url | http://dx.doi.org/10.1063/5.0045731 |
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