# Entropy-Based Feature Extraction for Electromagnetic Discharges Classification in High-Voltage Power Generation

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## Abstract

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## 1. Introduction

## 2. EMI Monitoring

## 3. Description of Employed Algorithms

#### 3.1. Signal Denoising

#### 3.2. Entropy Measures

#### 3.2.1. Permutation Entropy (PE)

#### 3.2.2. Weighted Permutation Entropy (WPE)

#### 3.2.3. Sample Entropy (SE)

#### 3.2.4. Dispersion Entropy (DE)

#### 3.3. Classification Algorithms

#### 3.3.1. Support Vector Machine (SVM) and Multi-Class SVM (MCSVM)

#### 3.3.2. Random Forests (RF)

- At an initial node, randomly choose $\mathbf{P}$ feature instances from the overall instances $\mathbf{Q}$ presented to the classifier, where $\mathbf{P}$ is much smaller than $\mathbf{Q}$.
- Calculate the best split point using Information Gain defined as:$$I=H\left(\mathbf{s}\right)-\sum _{i\in \{1,2\}}\left|\frac{{\mathbf{s}}^{i}}{\mathbf{s}}\right|H\left({\mathbf{s}}^{i}\right)$$
- Using the best split point, divide the main node into daughter nodes and reduce the number of feature instances along the nodes.
- Repeat steps 1 to 3 until a maximum depth $l=5$ is reached.
- Repeat steps 1 to 4 for $K=500$ trees of the model. The more trees that are employed then the higher the achieved performance.

## 4. Experimental Set-Up

#### 4.1. EMI Signals Measurement

#### 4.2. Application of Feature Extraction and Classification

## 5. Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Example feature space representation of data instances that belong to 5 different classes (colours). (

**b**) An example decision tree classifier architecture.

**Figure 4.**Time series signals of (

**a**) Partial Discharge (PD) (

**b**) Arcing (A) (

**c**)Process Noise (PN) (

**d**) Random Noise (RN) (

**e**) Data Modulation (DM) (

**f**) Exciter (E) (

**g**) microSparking (mS).

**Figure 5.**Confusion matrix of site 1 using (

**a**) Multi-Class Support Vector Machine (MCSVM). (

**b**) Random Forest (RF). Overall classification accuracy is shown in bottom right corner.

**Figure 6.**Confusion matrix of site 2 using (

**a**) Multi-Class Support Vector Machine (MCSVM) (

**b**) Random Forest (RF). Overall classification accuracy is shown in bottom right corner.

**Figure 7.**Confusion matrix of (

**a**) site 5 (

**b**) site 7 using Random Forest (RF). Overall classification accuracy is shown in bottom right corner.

**Figure 8.**Confusion matrix of site 1 (

**a**) using Multi-Class Support Vector Machine (MCSVM) (

**b**) Random Forest (RF), site 2 (

**c**) using MCSVM (

**d**) using RF, and (

**e**) site 5 (

**f**) site 7 using RF, after denoising. Overall classification accuracy is shown in bottom right corner.

Site | Discharge Source |
---|---|

1 | PD, RN, PN |

2 | mS, DM, RN, PD, A |

3 | PD, E |

4 | PD, E |

5 | RN, DM, PD |

6 | RN, DM, E, PD, mS |

7 | PN, E, PD |

8 | PD, E |

9 | PN, E, PD |

10 | PD, E |

**Table 2.**Classification accuracy (rounded) results using Multi-Class Support Vector Machine (MCSVM) and Random Forest (RF).

Site | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Accuracy % | MCSVM | 91 | 75 | 91 | 100 | 96 | 99 | 100 | 99 | 100 | 100 |

RF | 89 | 79 | 92 | 100 | 97 | 98 | 72 | 100 | 99 | 100 |

Before Denoising | |||||
---|---|---|---|---|---|

Site | 1 | 2 | 5 | 7 | |

Accuracy % | 91/89 | 75/79 | 96/97 | 100/72 | |

Precision | 0.91/0.90 | 0.72/0.84 | 0.96/0.97 | 1/0.85 | |

Recall | 0.91/0.89 | 0.76/0.79 | 0.97/0.96 | 1/0.72 | |

F-measure | 0.91/0.90 | 0.74/0.81 | 0.96/0.96 | 1/0.78 | |

After denoising | |||||

Accuracy % | 95/98 | 90/84 | 100/100 | 100/100 | |

Precision | 0.96/0.98 | 0.85/0.87 | 1/1 | 1/1 | |

Recall | 0.98/0.98 | 0.90/0.84 | 1/1 | 1/1 | |

F-measure | 0.97/0.98 | 0.87/0.85 | 1/1 | 1/1 |

**Table 4.**Average classification performance measures for all sites before and after denoising using MCSVM/RF.

Before Denoising | Accuracy % | Precision | Recall | F-Measure |
---|---|---|---|---|

77/73 | 0.83/0.77 | 0.77/0.73 | 0.78/0.72 | |

After denoising | ||||

91/66 | 0.91/0.79 | 0.91/0.66 | 0.91/0.65 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Mitiche, I.; Morison, G.; Nesbitt, A.; Stewart, B.G.; Boreham, P. Entropy-Based Feature Extraction for Electromagnetic Discharges Classification in High-Voltage Power Generation. *Entropy* **2018**, *20*, 549.
https://doi.org/10.3390/e20080549

**AMA Style**

Mitiche I, Morison G, Nesbitt A, Stewart BG, Boreham P. Entropy-Based Feature Extraction for Electromagnetic Discharges Classification in High-Voltage Power Generation. *Entropy*. 2018; 20(8):549.
https://doi.org/10.3390/e20080549

**Chicago/Turabian Style**

Mitiche, Imene, Gordon Morison, Alan Nesbitt, Brian G. Stewart, and Philip Boreham. 2018. "Entropy-Based Feature Extraction for Electromagnetic Discharges Classification in High-Voltage Power Generation" *Entropy* 20, no. 8: 549.
https://doi.org/10.3390/e20080549