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Grivel E, Berthelot B, Colin G, Legrand P, Ibanez V. Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application. ENTROPY (BASEL, SWITZERLAND) 2024; 26:332. [PMID: 38667886 PMCID: PMC11048990 DOI: 10.3390/e26040332] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2023] [Revised: 03/16/2024] [Accepted: 04/06/2024] [Indexed: 04/28/2024]
Abstract
In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.
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Affiliation(s)
- Eric Grivel
- IMS Laboratory, Bordeaux INP, Bordeaux University, UMR CNRS 5218, 33400 Talence, France
| | - Bastien Berthelot
- Thales AVS France, Campus Merignac, 75-77 Av. Marcel Dassault, 33700 Mérignac, France; (B.B.); (V.I.)
| | - Gaetan Colin
- ENSEIRB-MATMECA, Bordeaux INP, 33400 Talence, France
| | - Pierrick Legrand
- IMB Laboratory, Bordeaux University, UMR CNRS 5251, ASTRAL Team, INRIA, 33400 Talence, France;
| | - Vincent Ibanez
- Thales AVS France, Campus Merignac, 75-77 Av. Marcel Dassault, 33700 Mérignac, France; (B.B.); (V.I.)
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Rostaghi M, Khatibi MM, Ashory MR, Azami H. Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1494. [PMID: 37998186 PMCID: PMC10670069 DOI: 10.3390/e25111494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2023] [Revised: 10/14/2023] [Accepted: 10/24/2023] [Indexed: 11/25/2023]
Abstract
Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE-FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE's performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods.
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Affiliation(s)
- Mostafa Rostaghi
- Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran; (M.R.); (M.R.A.)
| | - Mohammad Mahdi Khatibi
- Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran; (M.R.); (M.R.A.)
| | - Mohammad Reza Ashory
- Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran; (M.R.); (M.R.A.)
| | - Hamed Azami
- Centre for Addiction and Mental Health, University of Toronto, Toronto, ON M6J 1H1, Canada;
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Yuan Q, Lv M, Zhou R, Liu H, Liang C, Cheng L. Use of Composite Multivariate Multiscale Permutation Fuzzy Entropy to Diagnose the Faults of Rolling Bearing. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1049. [PMID: 37509995 PMCID: PMC10377953 DOI: 10.3390/e25071049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Revised: 07/05/2023] [Accepted: 07/10/2023] [Indexed: 07/30/2023]
Abstract
The study focuses on the fault signals of rolling bearings, which are characterized by nonlinearity, periodic impact, and low signal-to-noise ratio. The advantages of entropy calculation in analyzing time series data were combined with the high calculation accuracy of Multiscale Fuzzy Entropy (MFE) and the strong noise resistance of Multiscale Permutation Entropy (MPE), a multivariate coarse-grained form was introduced, and the coarse-grained process was improved. The Composite Multivariate Multiscale Permutation Fuzzy Entropy (CMvMPFE) method was proposed to solve the problems of low accuracy, large entropy perturbation, and information loss in the calculation process of fault feature parameters. This method extracts the fault characteristics of rolling bearings more comprehensively and accurately. The CMvMPFE method was used to calculate the entropy value of the rolling bearing experimental fault data, and Support Vector Machine (SVM) was used for fault diagnosis analysis. By comparing with MPFE, the Composite Multiscale Permutation Fuzzy Entropy (CMPFE) and the Multivariate Multiscale Permutation Fuzzy Entropy (MvMPFE) methods, the results of the calculations show that the CMvMPFE method can extract rolling bearing fault characteristics more comprehensively and accurately, and it also has good robustness.
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Affiliation(s)
- Qiang Yuan
- School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China
- School of Naval Architecture and Maritime, Zhejiang Ocean University, Zhoushan 316022, China
| | - Mingchen Lv
- School of Naval Architecture and Maritime, Zhejiang Ocean University, Zhoushan 316022, China
| | - Ruiping Zhou
- School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China
| | - Hong Liu
- School of Naval Architecture and Maritime, Zhejiang Ocean University, Zhoushan 316022, China
| | - Chongkun Liang
- School of Naval Architecture and Maritime, Zhejiang Ocean University, Zhoushan 316022, China
| | - Lijiao Cheng
- School of Naval Architecture and Maritime, Zhejiang Ocean University, Zhoushan 316022, China
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Li Y, Wu J, Zhang S, Tang B, Lou Y. Variable-Step Multiscale Fuzzy Dispersion Entropy: A Novel Metric for Signal Analysis. ENTROPY (BASEL, SWITZERLAND) 2023; 25:997. [PMID: 37509944 PMCID: PMC10378684 DOI: 10.3390/e25070997] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 06/22/2023] [Accepted: 06/28/2023] [Indexed: 07/30/2023]
Abstract
Fuzzy dispersion entropy (FuzDE) is a newly proposed entropy metric, which combines the superior characteristics of fuzzy entropy (FE) and dispersion entropy (DE) in signal analysis. However, FuzDE only reflects the feature from the original signal, which ignores the hidden information on the time scale. To address this problem, we introduce variable-step multiscale processing in FuzDE and propose variable-step multiscale FuzDE (VSMFuzDE), which realizes the characterization of abundant scale information, and is not limited by the signal length like the traditional multiscale processing. The experimental results for both simulated signals show that VSMFuzDE is more robust, more sensitive to dynamic changes in the chirp signal, and has more separability for noise signals; in addition, the proposed VSMFuzDE displays the best classification performance in both real-world signal experiments compared to the other four entropy metrics, the highest recognition rates of the five gear signals and four ship-radiated noises reached 99.2% and 100%, respectively, which achieves the accurate identification of two different categories of signals.
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Affiliation(s)
- Yuxing Li
- School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
- Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi'an University of Technology, Xi'an 710048, China
| | - Junxian Wu
- School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
| | - Shuai Zhang
- School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
| | - Bingzhao Tang
- School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
| | - Yilan Lou
- School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China
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Abstract
Owing to the symmetry of the rolling bearing structure and the rotating operation mode, the rolling bearing works in a complex environment. It is very easy to be submerged by noise and misdiagnosis. For the non-stationary signal in variable speed state, this paper presents a condition monitoring method based on deep belief network (DBN) optimized by multi-order fractional Fourier transform (FRFT) and sparrow search algorithm (SSA). Firstly, the fractional Fourier transform based on curve feature segmentation is used to filter the fault vibration signal and extract the fault feature frequency. Then, the fault features are input into the SSA-DBN model for training, and the bearing fault features are classified, identified, and diagnosed. Finally, the rotating machinery fault simulator in the laboratory of Ottawa University is taken as the practical application object to verify the effectiveness of the method. The experimental results show that the proposed method has higher recognition accuracy and stronger stability.
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