# Classification of Partial Discharge Images Using Deep Convolutional Neural Networks

## Abstract

**:**

## 1. Introduction

## 2. Partial Discharge Phase-Resolved Acquisition

## 3. Machine Learning and Partial Discharge Image Recognition

## 4. Architecture of Deep Convolutional Neural Networks

**I**) and a typically much smaller weight matrix (called a kernel or filter

**M**) to an output matrix

**O**according to the following formula:

**M**

_{k}coefficients are unknown elements of a CNN, which will be specified by a backpropagation method during the training process. Backpropagation is a technique used for the evaluation of connections between neurons. When it receives an input, each neuron can completely and independently calculate the output value and the local gradient of the input (taking into account the output value). This phase is called a forward pass. When this phase is over, the backpropagation training phase starts. During the backpropagation, each neuron learns the gradient of its output value considering the complexity of the entire network. The neuron takes the gradient of the whole network topology and multiples it with each gradient with which it is connected.

- ■
- Convolution;
- ■
- Activation;
- ■
- Pooling;
- ■
- Classification by fully connected layers.

**W**with a mask vector

**D**. A visualization of the dropout operation is shown in Figure 4. Depending of the position of 1 and 0 in a mask vector

**D**, certain neurons are discarded in matrix

**W**(i and j refer to the position of a neuron in a layer; k is the layer number), providing a reduced topology

**W**(Figure 4b), which results in a shorter training time for each epoch.

_{D}## 5. Experimental Results

## 6. Discussion

**M**was changed between 32 and 128. The dense fully connected layers were defined with 512 or 1024 neurons and the activation function ReLu, followed by an output layer with the Softmax activation function and a number of neurons corresponding to the number of classes to be recognized. The model was trained with various batch sizes (e.g., 32–256) and numbers of epochs (10–200), and the data were split into training and validation sets (20–30%). A dropout operation of 0.2 to 0.5 after the convolution and future map layers was tested.

- TP—true positives;
- TN—true negatives;
- FP—false positives;
- FN—false negatives.

## 7. Conclusions

## Funding

## Conflicts of Interest

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**Figure 6.**Representative PD images of distinctive classes in the long-term monitoring of the aging of electrical insulation.

**Figure 7.**Exemplary set of training (

**a**) and test (

**b**) partial discharge images exhibiting distinguishable classes (start, middle, end and noise/disturbance) of electrical insulation degradation stages.

**Figure 9.**Exemplary parameters of the test convolutional neural network (CNN) architecture applied to PD images.

**Figure 10.**Exemplary recognition trial of PD monitoring stages using a convolutional neural network: (

**a**) accuracy adjustment after 30 epochs; (

**b**) after 200 epochs; (

**c**) partial discharge recognition score after 10 epochs; (

**d**) after 50 epochs. Rows in the score matrix correspond to distinguishable classes, and columns refer to the number of test sets.

**Figure 11.**Visualization of output filter banks in convolutional layers, providing an illustration of automatic feature extraction: (

**a**) first Conv2D layer; (

**b**) third Conv2D layer.

**Figure 12.**Exemplary confusion matrix for a set of 400 validation PD images subdivided into four classes (start, middle, end and noise) representing the insulation stages of electrical insulating aging monitoring. Each column of the confusion matrix refers to instances of the predicted class, while each row exhibits instances of the actual class.

Topology | Conv2D | Conv Kernel | FC NN | A [%] | F1 [%] |

CNN | 64-Mp-128-Mp | 5 × 5-5 × 5 | 1024-1024-512-4 | 99.14 | 97.41 |

CNN | 64-Mp-128-Mp | 3 × 3-3 × 3 | 1024-512-4 | 96.17 | 97.22 |

CNN | 16-Mp-32-Mp | 5 × 5-5 × 5 | 1024-512-4 | 68.54 | 65.33 |

CNN | 64-Mp-128-Mp | 5 × 5-5 × 5 | 1024-4 | 95.23 | 96.11 |

CNN | 64-Mp-128-Mp | 5 × 5-5 × 5 | 1024-512-4 | 99.21 | 98.16 |

CNN | 64-Mp-Dout(0.25)-128-Mp-Dout(0.25) | 5 × 5-5 × 5 | 1024-4 | 97.87 | 95.66 |

CNN | 64-Mp-128-Mp-256-Mp | 5 × 5-5 × 5-3 × 3 | 1024-4 | 96.33 | 94.43 |

CNN | 64-Mp-128-Mp-256-Mp | 3 × 3-3 × 3-3 × 3 | 1024-512-5 | 94.15 | 95.18 |

CNN | 64-Mp-128-Mp-256-Mp | 5 × 5-5 × 5-5 × 5 | 1024-5 | 98.28 | 97.30 |

CNN | 64-Mp-128-Mp-256-Mp | 5 × 5-5 × 5-5 × 5 | 1024-512-5 | 99.65 | 97.91 |

CNN | 64-Mp-128-Mp-256-Mp | 5 × 5-5 × 5-3 × 3 | 1024-512-5 | 94.37 | 95.67 |

CNN | 64-Mp-128-Mp-256-Mp-512-Mp | 5 × 5-5 × 5-5 × 5-5 × 5 | 1024-5 | 99.67 | 99.45 |

CNN | 32-Mp-32-Mp | 5 × 5-5 × 5 | 1024-5 | 71.55 | 67.48 |

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Florkowski, M.
Classification of Partial Discharge Images Using Deep Convolutional Neural Networks. *Energies* **2020**, *13*, 5496.
https://doi.org/10.3390/en13205496

**AMA Style**

Florkowski M.
Classification of Partial Discharge Images Using Deep Convolutional Neural Networks. *Energies*. 2020; 13(20):5496.
https://doi.org/10.3390/en13205496

**Chicago/Turabian Style**

Florkowski, Marek.
2020. "Classification of Partial Discharge Images Using Deep Convolutional Neural Networks" *Energies* 13, no. 20: 5496.
https://doi.org/10.3390/en13205496