The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery
Abstract
:1. Introduction
2. Optimized Multi-Scale Permutation Entropy
2.1. Time Delay Calculation Based on Mutual Information
2.2. Embedding Dimension Calculation Based on Improved Cao Method
2.2.1. Embedding Dimension Calculation
2.2.2. Threshold Adjustment using Chebyshev Distance
2.3. Procedures of OMPE Method
3. Simulation Validation
4. Experimental Validation
4.1. Experiment 1: Compound Gear Fault
4.2. Experiment 2: Compound Bearing and Unbalance Rotor Fault
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameters | Embedding Dimension | Time Delay | |||||
---|---|---|---|---|---|---|---|
Methods | BF | IRF | ORF | BF | IRF | ORF | |
FIX method | 6 | 6 | 6 | 1 | 1 | 1 | |
MI-FNN method | 4 | 4 | 4 | 3 | 2 | 2 | |
Proposed OMPE method | 6 | 9 | 5 | 3 | 2 | 2 |
Fault Type | PT | MT | CT | PC | MC | BC | NOR | BT | |
---|---|---|---|---|---|---|---|---|---|
Parameters | |||||||||
Embedding dimension | 5 | 6 | 6 | 6 | 6 | 7 | 6 | 7 | |
Time delay | 3 | 2 | 3 | 2 | 2 | 2 | 2 | 2 | |
Class label | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Bearing Type | MB ER-12K |
---|---|
Number of rolling elements | 8 |
Rolling element diameter | 0.3125 inch |
Pitch diameter | 1.318 inch |
Contact angle | 0° |
Sampling frequency | 12,800 Hz |
Rotating speed | 3000 RPM |
Fault Type | BF | CF | IRF | NOR | ORF | BFUN | CFUN | IRFUN | ORFUN | UN | |
---|---|---|---|---|---|---|---|---|---|---|---|
Parameters | |||||||||||
Embedding dimension | 6 | 6 | 6 | 5 | 6 | 6 | 6 | 6 | 6 | 7 | |
Time delay | 3 | 2 | 3 | 3 | 2 | 3 | 3 | 3 | 3 | 2 | |
Class label | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
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Wang, X.; Si, S.; Wei, Y.; Li, Y. The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery. Entropy 2019, 21, 170. https://doi.org/10.3390/e21020170
Wang X, Si S, Wei Y, Li Y. The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery. Entropy. 2019; 21(2):170. https://doi.org/10.3390/e21020170
Chicago/Turabian StyleWang, Xianzhi, Shubin Si, Yu Wei, and Yongbo Li. 2019. "The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery" Entropy 21, no. 2: 170. https://doi.org/10.3390/e21020170
APA StyleWang, X., Si, S., Wei, Y., & Li, Y. (2019). The Optimized Multi-Scale Permutation Entropy and Its Application in Compound Fault Diagnosis of Rotating Machinery. Entropy, 21(2), 170. https://doi.org/10.3390/e21020170