# Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Wavelet Time-Frequency Entropy and One-Class Support Vector Machine

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## Abstract

**:**

_{6}HVCB demonstrated the improved effectiveness of the new approach.

## 1. Introduction

## 2. S-Transform

## 3. Feature Extraction from STMM Based on Wavelet Time-Frequency Entropy

#### 3.1. Wavelet Time-Frequency Entropy

**D**be a $m\times n$ matrix constituted by ${D}_{j}(k)$. According to singular value decomposition theory, for any $m\times n$ matrix, there exist a $m\times r$ matrix

**U**, a $r\times n$ matrix

**V**and a $r\times r$ diagonal matrix $\Lambda $, which make:

**A**. The singular values are all non-negative and arranged in a non-increasing order (i.e., ${\mathsf{\lambda}}_{1}\text{\hspace{0.05em}}\ge {\mathsf{\lambda}}_{2}\text{\hspace{0.05em}}\ge \cdots \ge \text{\hspace{0.05em}}{\mathsf{\lambda}}_{r}\ge 0$). Then the WSE is defined as:

#### 3.2. Feature Vector Extraction

**Z**is used as the input vector of OCSVM and SVM classifier.

## 4. Condition and Fault Classifier Based on OCSVM and SVM

#### 4.1. One-Class Support Vector Machine

#### 4.2. Advantages of OCSVM for Condition Diagnosis

#### 4.3. An Improved PSO-Based OCSVM

- (1)
- Adjustment of the inertia weight $\mathsf{\omega}$

- (2)
- Adjustment of the acceleration coefficients ${c}_{1}$ and ${c}_{2}$

#### 4.4. Fault Diagnostic Process

## 5. Experimental Results and Analysis

#### 5.1. Data Collection and Processing

_{6}circuit breakers as the analysis object. The vibration signal acquisition system is built with a CA-YD-182A piezoelectric acceleration sensor made in Jiangsu United Electronic Technology Co., Ltd. (Yangzhou, China) and NI-9234 DAQ devices made by National Instruments (NI, Austin, TX, USA). The acceleration sensor is used for vibration signal acquisition. The DAQ device is used to record the data with 25.6 kS/s sampling rate for a time period of 150 ms during opening operation. The vibration signal acquisition system for a circuit breaker is shown in Figure 5.

**Figure 6.**(

**a**) The normal signal and its STMM contour plot; (

**b**) The signal of fault type I and its STMM contour plot; (

**c**) The signal of fault type II and its STMM contour plot; (

**d**) The signal of fault type III and its STMM contour plot.

#### 5.2. Feature Extraction and Analysis

**Figure 7.**(

**a**) WTFE feature distribution of the normal signals; (

**b**) WTFE feature distribution of the iron core jam fault signals; (

**c**) WTFE feature distribution of the base screw looseness fault signals; (

**d**) WTFE feature distribution of the lack of mechanical lubrication fault signals.

**Figure 8.**(

**a**) WSE feature distribution of the normal signals; (

**b**) WSE feature distribution of the iron core jam fault signals; (

**c**) WSE feature distribution of the base screw looseness fault signals; (

**d**) WSE feature distribution of the lack of mechanical lubrication fault signals.

#### 5.3. Classification Using OCSVM-SVM

Test Sample | Diagnosis Results | STA | CA | |||
---|---|---|---|---|---|---|

Normal State | Fault Type I | Fault Type II | Fault Type III | |||

Normal state | 18 | 0 | 0 | 2 | 90% | 90% |

Fault type I | 0 | 20 | 0 | 0 | 100% | 100% |

Fault type II | 0 | 0 | 20 | 0 | 100% | 100% |

Fault type III | 0 | 0 | 0 | 20 | 100% | 100% |

Test Sample | Diagnosis Results | STA | CA | |||
---|---|---|---|---|---|---|

Normal State | Fault Type I | Fault Type II | Fault Type III | |||

Normal state | 14 | 0 | 1 | 5 | 70% | 70% |

Fault type I | 0 | 20 | 0 | 0 | 100% | 100% |

Fault type II | 0 | 0 | 18 | 2 | 100% | 90% |

Fault type III | 2 | 0 | 1 | 17 | 90% | 85% |

Classifier | Test Sample | Diagnosis Results | STA | CA | |||
---|---|---|---|---|---|---|---|

Normal State | Fault Type I | Fault Type II | Fault Type III | ||||

SVM | Normal state | 17 | 0 | 0 | 3 | 85% | 85% |

Fault type I | 0 | 20 | 0 | 0 | 100% | 100% | |

Fault type II | 0 | 0 | 20 | 0 | 100% | 100% | |

Fault type III | 2 | 0 | 0 | 18 | 90% | 90% | |

ELM | Normal state | 18 | 0 | 0 | 2 | 90% | 90% |

Fault type I | 0 | 20 | 0 | 0 | 100% | 100% | |

Fault type II | 0 | 0 | 0 | 20 | 100% | 100% | |

Fault type III | 3 | 0 | 0 | 17 | 85% | 85% |

**Table 4.**Diagnosis results of the case of lack of training samples by using the OCSVM-SVM, SVM and ELM methods.

Classifier | Test Sample | Diagnosis Results | STA | CA | ||
---|---|---|---|---|---|---|

Normal State | Fault Type I | Fault Type II | ||||

OCSVM-SVM | Fault type III | 0 | 14 | 6 | 100% | 0 |

SVM | Fault type III | 20 | 0 | 0 | 0 | 0 |

ELM | Fault type III | 20 | 0 | 0 | 0 | 0 |

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Runde, M.; Aurud, T.; Lundgaard, L.E.; Ottesen, G.E.; Faugstad, K. Acoustic diagnosis of high voltage circuit-breakers. IEEE Trans. Power Deliv.
**1992**, 7, 1306–1315. [Google Scholar] [CrossRef] - Demjanenko, V.; Valtin, R.A.; Soumekh, M.; Haidu, H.; Antur, A.; Hess, D.P.; Soom, A.; Wright, S.E.; Tangri, M.K.; Park, S.Y. A noninvasive diagnostic instrument for power circuit breakers. IEEE Trans. Power Deliv.
**1992**, 7, 656–663. [Google Scholar] [CrossRef] - Polycarpou, A.A.; Soom, A.; Swarnakar, V.; Valtin, R.A.; Acharya, R.S.; Demjanenko, V.; Soumekh, M.; Benenson, D.M.; Porter, J.W. Event timing and shape analysis of vibration bursts from power circuit breakers. IEEE Trans. Power Deliv.
**1995**, 11, 848–857. [Google Scholar] [CrossRef] - Runde, M.; Ottesen, G.E.; Skyberg, B.; Ohlen, M. Vibration analysis for diagnostic testing of circuit-breakers. IEEE Trans. Power Deliv.
**1996**, 11, 1816–1823. [Google Scholar] [CrossRef] - CIGRE Working Group. Final Report of the Second International Enquiry on High Voltage Circuit Breaker Failures and Defects in Service; CIGRE Report No. 83; CIGRE: Paris, France, 1994. [Google Scholar]
- Gao, Z.W.; Cecati, S.; Ding, S.X. A survey of fault diagnosis and fault-tolerant techniques-Part I: Fault diagnosis with model-based and signal-based approaches. IEEE Trans. Ind. Electron.
**2015**, 62, 3757–3767. [Google Scholar] [CrossRef] - Meng, Y.P.; Jia, S.L.; Shi, Z.Q.; Rong, M.Z. The detection of the closing moments of a vacuum circuit breaker by vibration analysis. IEEE Trans. Power Deliv.
**2006**, 21, 652–658. [Google Scholar] [CrossRef] - Landry, M.; Leonard, F.; Landry, C.; Beauchemin, R. An improved vibration analysis algorithm as a diagnostic tool for detecting mechanical anomalies on power circuit breakers. IEEE Trans. Power Deliv.
**2008**, 23, 1986–1994. [Google Scholar] [CrossRef] - Lee, D.S.; Lithgow, B.J.; Morrison, R.E. New fault diagnosis of circuit breakers. IEEE Trans. Power Deliv.
**2003**, 18, 454–459. [Google Scholar] [CrossRef] - Huang, J.; Hu, X.G.; Yang, F. Support vector machine with genetic algorithm for machinery fault diagnosis of high voltage circuit breaker. Measurement
**2011**, 44, 1018–1027. [Google Scholar] [CrossRef] - Huang, J.; Hu, X.G.; Geng, X. An intelligent fault diagnosis method of high voltage circuit breaker based on improved EMD energy entropy and multi-class support vector machine. Electr. Power Syst. Res.
**2011**, 81, 400–407. [Google Scholar] [CrossRef] - Høidalen, H.K.; Runde, M. Continuous monitoring of circuit-breakers using vibration analysis. IEEE Trans. Power Deliv.
**2005**, 20, 2458–2465. [Google Scholar] [CrossRef] - Stockwell, R.G.; Mansinha, L.; Lowe, R.P. Localization of the complex spectrum: The S transform. IEEE Trans. Signal Process.
**1996**, 44, 998–1001. [Google Scholar] [CrossRef] - Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - He, Z.Y.; Chen, X.Q.; Luo, G.M. Wavelet entropy measure definition and its application for transmission line fault detection and identification. In Proceedings of the International Conference on Power System Technology, Chongqing, China, 22–26 October 2006.
- Chen, J.K.; Li, G.Q. Tsallis wavelet entropy and its application in power signal analysis. Entropy
**2014**, 16, 3009–3025. [Google Scholar] [CrossRef] - He, Z.Y.; Gao, S.B.; Chen, X.Q.; Zhang, J.; Bo, Z.Q.; Qian, Q.Q. Study of a new method for power system transients classification based on wavelet entropy and neural network. Int. J. Electr. Power Energy Syst.
**2011**, 33, 402–410. [Google Scholar] - Kumar, Y.; Dewal, M.L.; Anand, R.S. Epileptic seizure detection using DWT based fuzzy approximate entropy and support vector machine. Neurocomputing
**2014**, 133, 271–279. [Google Scholar] [CrossRef] - Sharma, R.; Pachori, R.B.; Acharya, U.R. An integrated index for the identification of focal electroencephalogram signals using discrete wavelet transform and entropy measures. Entropy
**2015**, 17, 5218–5240. [Google Scholar] [CrossRef] - Boškoski, P.; Juričić, Đ. Fault detection of mechanical drives under variable operating conditions based on wavelet packet Rényi entropy signatures. Mech. Syst. Signal Process.
**2012**, 31, 369–381. [Google Scholar] [CrossRef] - Dubey, R.; Samantaray, S.R. Wavelet singular entropy-based symmetrical fault-detection and out-of-step protection during power swing. IET Gener. Transm. Distrib.
**2013**, 7, 1123–1134. [Google Scholar] [CrossRef] - Wong, P.K.; Yang, Z.X.; Vong, C.M.; Zhong, J.H. Real-time fault diagnosis for gas turbine generator systems using extreme learning machine. Neurocomputing
**2014**, 128, 249–257. [Google Scholar] [CrossRef] - Yang, Z.X.; Wong, P.K.; Vong, C.M.; Zhong, J.H.; Liang, J.J. Simultaneous-fault diagnosis of gas turbine generator systems using a pairwise-coupled probabilistic classifier. Math. Probl. Eng.
**2013**, 2013. [Google Scholar] [CrossRef] - Schölkopf, B.; Platt, J.C.; Shawe-Taylor, J.; Smola, A.J.; Williamson, R.C. Estimating the support of a high-dimensional distribution. Neural Comput.
**2001**, 13, 1443–1471. [Google Scholar] [CrossRef] [PubMed] - Mahadevan, S.; Shah, S.L. Fault detection and diagnosis in process data using one-class support vector machines. J. Process Control
**2009**, 19, 1627–1639. [Google Scholar] [CrossRef] - Shin, H.J.; Eom, D.H.; Kim, S.S. One-class support vector machines—An application in machine fault detection and classification. Comput. Ind. Eng.
**2005**, 48, 395–408. [Google Scholar] [CrossRef] - Xiao, Y.C.; Wang, H.G.; Xu, W.L. Parameter selection of Gaussian kernel for one-class SVM. IEEE Trans. Cybern.
**2015**, 45, 927–939. [Google Scholar] [PubMed] - Kennedy, J.; Eberhart, R.C. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ, USA, 27 November–1 December 1995; pp. 1942–1948.
- Mishra, S.; Bhende, C.N.; Panigrahi, K.B. Detection and classification of power quality disturbances using S-transform and probabilistic neural network. IEEE Trans. Power Deliv.
**2008**, 23, 280–287. [Google Scholar] [CrossRef] - Olsson, A.E. Particle Swarm Optimization: Theory, Techniques and Applications; Nova Science Publishers: Hauppauge, NY, USA, 2011. [Google Scholar]

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**MDPI and ACS Style**

Huang, N.; Chen, H.; Zhang, S.; Cai, G.; Li, W.; Xu, D.; Fang, L.
Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Wavelet Time-Frequency Entropy and One-Class Support Vector Machine. *Entropy* **2016**, *18*, 7.
https://doi.org/10.3390/e18010007

**AMA Style**

Huang N, Chen H, Zhang S, Cai G, Li W, Xu D, Fang L.
Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Wavelet Time-Frequency Entropy and One-Class Support Vector Machine. *Entropy*. 2016; 18(1):7.
https://doi.org/10.3390/e18010007

**Chicago/Turabian Style**

Huang, Nantian, Huaijin Chen, Shuxin Zhang, Guowei Cai, Weiguo Li, Dianguo Xu, and Lihua Fang.
2016. "Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Wavelet Time-Frequency Entropy and One-Class Support Vector Machine" *Entropy* 18, no. 1: 7.
https://doi.org/10.3390/e18010007