A Small Leak Detection Method Based on VMD Adaptive De-Noising and Ambiguity Correlation Classification Intended for Natural Gas Pipelines
Abstract
:1. Introduction
2. VMD Adaptive De-Noising Method
2.1. Variational Mode Decomposition
- (1)
- Initialize , , , and . is the Lagrange multiplier, represents components set after decomposition, and represents the center frequencies set of components after decomposition.
- (2)
- , execute the whole loop.
- (3)
- Execute innermost loop, , and are renewed according to and :
- (4)
- Renew according to for .
- (5)
- If , end the whole loop, output the modal components , otherwise, repeat steps from Equation (2) to Equation (4).
2.2. VMD-Based Noise Adaptive Removal Approach
- (1)
- For any data , calculate its PDF :
- (2)
- Calculate PDFs of the original signal and component after VMD:
- (3)
- Calculate distance () between two PDFs:
- (4)
- Choose noiseless component according to the distance:
2.3. Algorithm Simulation
3. Ambiguity Correlation Classifier
3.1. Ambiguity Correlation Theory
- (1)
- Calculate ambiguity function of signal x(t):
- (2)
- Calculate the correlation function of ambiguity function images of signals x(t) and y(t):In Equation (16), is the correlation function.
- (3)
- Calculate normalized correlation coefficient :
- (4)
- Select correlation coefficient when τ = 0 or θ = 0:
- (5)
- Calculate the ambiguity correlation coefficient :
3.2. Basic Principle of Classifier
4. Small Leak Detection Method
- (1)
- Collect experimental data by sensors and get series of U components of collected data from VMD.
- (2)
- Select noiseless components according to VMD adaptive de-noising method.
- (3)
- Reconstruct chosen noiseless components and input using the ACC.
- (4)
- Collect several groups of data for training and testing, and realize the pipeline small leak detection.
5. Experimental Results and Analysis
5.1. Experimental Apparatus and Instrumentations
5.2. Acoustic Emission Signal De-Noising
5.3. Small Leakage Detection with ACC
5.4. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Method | Simulated Signals | MSE | SNR |
---|---|---|---|
Before de-noising | 0.0463 | 13.4451 | |
VMD | After de-noising | 0.004 | 24.0253 |
EMD | After de-noising | 0.0234 | 17.5643 |
Data Group | 1# | 2# | 3# | |
---|---|---|---|---|
1 mm Leak | Non-Leak | 2 mm Leak | ||
1 mm leak | mean value | 0.4074 | 0.3664 | 0.3042 |
SD | 0.0530 | 0.0629 | 0.0969 | |
Non-leak | mean value | 0.3664 | 0.2415 | 0.3650 |
SD | 0.0629 | 0.0340 | 0.0534 | |
2 mm leak | mean value | 0.3042 | 0.3650 | 0.2789 |
SD | 0.0969 | 0.0534 | 0.0452 |
Data Group | 1# | 2# | 3# | |
---|---|---|---|---|
1 mm Leak | Non-Leak | 2 mm Leak | ||
1 mm leak | mean value | 0.7447 | 0.3134 | 0.1025 |
SD | 0.0717 | 0.1164 | 0.0969 | |
Non-leak | mean value | 0.3134 | 0.8407 | 0.0685 |
SD | 0.1164 | 0.0240 | 0.0534 | |
2 mm leak | mean value | 0.1025 | 0.0685 | 0.2253 |
SD | 0.0969 | 0.0534 | 0.0452 |
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Xiao, Q.; Li, J.; Bai, Z.; Sun, J.; Zhou, N.; Zeng, Z. A Small Leak Detection Method Based on VMD Adaptive De-Noising and Ambiguity Correlation Classification Intended for Natural Gas Pipelines. Sensors 2016, 16, 2116. https://doi.org/10.3390/s16122116
Xiao Q, Li J, Bai Z, Sun J, Zhou N, Zeng Z. A Small Leak Detection Method Based on VMD Adaptive De-Noising and Ambiguity Correlation Classification Intended for Natural Gas Pipelines. Sensors. 2016; 16(12):2116. https://doi.org/10.3390/s16122116
Chicago/Turabian StyleXiao, Qiyang, Jian Li, Zhiliang Bai, Jiedi Sun, Nan Zhou, and Zhoumo Zeng. 2016. "A Small Leak Detection Method Based on VMD Adaptive De-Noising and Ambiguity Correlation Classification Intended for Natural Gas Pipelines" Sensors 16, no. 12: 2116. https://doi.org/10.3390/s16122116
APA StyleXiao, Q., Li, J., Bai, Z., Sun, J., Zhou, N., & Zeng, Z. (2016). A Small Leak Detection Method Based on VMD Adaptive De-Noising and Ambiguity Correlation Classification Intended for Natural Gas Pipelines. Sensors, 16(12), 2116. https://doi.org/10.3390/s16122116