Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis
Abstract
:1. Introduction
2. SK Based on CWD
2.1. Definition of SK
2.2. Algorithm of CWD-SK
2.3. Impact of Window Functions
3. Diagnosis Flow Based on HMM
4. Experimental Data Analysis
4.1. Experiment Platform and Data Preprocessing
4.2. Initial Fault Feature Extraction Based on CWD-SK
4.3. Selection of Window Function
4.4. Five Types of Gear Fault Characteristics Classification
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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PF | 1 | 2 | 3 |
---|---|---|---|
Kurtosis(normal) | 3.730 | 3.212 | 3.098 |
Kurtosis (slight fault) | 3.980 | 3.402 | 3.196 |
Kurtosis (moderate fault) | 4.645 | 4.320 | 4.089 |
Kurtosis (severe fault) | 4.966 | 4.781 | 4.342 |
Kurtosis(flaking) | 5.905 | 5.455 | 5.403 |
Condition | The Mean of CWD-SK |
---|---|
Normal | 1.756 |
Slight | 2.023 |
Moderate | 2.187 |
Severe | 2.019 |
Flaking | 5.746 |
Window Functions | Smoothness |
---|---|
Rectangular | 0.447 |
Hanning | 0.449 |
Hamming | 0.508 |
Blackman | 0.458 |
Fault Case | Logarithm Likelihood Probabilities of the Input Sample Model | ||||
---|---|---|---|---|---|
Recognition Result | |||||
Slight fault | −15.114 | ||||
Moderate fault | −54.124 | -55.964 | |||
Severe fault | −62.14 | −76.44 | −134.82 | ||
Flaking | −132.67 | −199.211 | −211.342 |
Recognition Model | Slight Fault | Moderate Fault | Severe Fault | Flaking | Recognition Rate | |
---|---|---|---|---|---|---|
CWD-SK | HMM | 5 | 4 | 5 | 5 | 95% |
BP | 4 | 4 | 5 | 5 | 90% | |
SK | HMM | 4 | 5 | 4 | 5 | 90% |
BP | 4 | 4 | 4 | 5 | 85% |
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Li, Y.; Song, W.; Wu, F.; Zio, E.; Zhang, Y. Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis. Symmetry 2020, 12, 285. https://doi.org/10.3390/sym12020285
Li Y, Song W, Wu F, Zio E, Zhang Y. Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis. Symmetry. 2020; 12(2):285. https://doi.org/10.3390/sym12020285
Chicago/Turabian StyleLi, Yufei, Wanqing Song, Fei Wu, Enrico Zio, and Yujin Zhang. 2020. "Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis" Symmetry 12, no. 2: 285. https://doi.org/10.3390/sym12020285
APA StyleLi, Y., Song, W., Wu, F., Zio, E., & Zhang, Y. (2020). Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis. Symmetry, 12(2), 285. https://doi.org/10.3390/sym12020285