# Associated Fault Diagnosis of Power Supply Systems Based on Graph Matching: A Knowledge and Data Fusion Approach

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## Abstract

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## 1. Introduction

- (1)
- A knowledge and data fusion approach is proposed to diagnose the associated faults of power supply systems. The anomaly monitoring and fault path tracking based on the Warshall algorithm utilize historical data to supplement the incomplete prior fault knowledge, which establishes the complete cluster of typical associated fault mode graphs and realizes the organic combination and structured storage of knowledge and data.
- (2)
- The proposed graph-matching strategy based on a deep residual contraction network achieves high precision with regard to fault diagnosis, even under the circumstances of an insufficient number of samples and missing parameters. The comparative experiments verify the depth feature extraction ability of the proposed method, as well as its high accuracy, noise resistance, and robust diagnostic capability.
- (3)
- The proposed method preliminarily realizes deep association diagnosis and path backtracking under the condition of insufficient traditional FMEA knowledge and incomplete association information and provides an effective technical approach to solve accurate online fault diagnosis under strong coupling in the power supply system.

## 2. Preliminary Overview

#### 2.1. Warshall Algorithm

**Definition 1.**

#### 2.2. Frechet Distance

**Definition 2.**

- (1)
- The mapping $\gamma $ of $F$ on the unit interval $[0,1]$ is continuous.
- (2)
- The vector $\xi $ is mapped from the unit interval to itself, i.e., $\xi :[0,1]\to [0,1]$, and the mapping relation has the following conditions: the mapping function is continuous non-degenerate and $\xi $ is full projective, at which point the function $\xi $ is said to be a reparametrized function of the unit curve $[0,1]$.
- (3)
- Let $A$ and $B$ be two continuous curves on $S$; that is, $A:\left[0,1\right]\to S,B:\left[0,1\right]\to S$. $d(x)$ is the metric function of $S$. Then, let $\alpha $ and $\beta $ be two reparametrized functions of the unit interval. Then, the Frechet distance $F(A,B)$ of the curves $A$ and $B$ is defined as:$$F(A,B)=\underset{\alpha ,\beta ,t\in [0,1]}{\mathrm{inf}}\mathrm{max}\{d(A(\alpha (t)),B(\beta (t))\},$$

#### 2.3. Deep Residual Shrinkage Network

#### 2.3.1. Convolutional Neural Networks (CNN)

#### 2.3.2. Deep Residual Network

#### 2.3.3. Deep Residual Shrinkage Network

## 3. Proposed Method

#### 3.1. Association Graph Model Based on Knowledge and Data Fusion

**Definition 3.**

#### 3.2. Enhancement of Component Associated Knowledge Based on the Warshall Algorithm

**Definition 4.**

## 4. Case Studies

#### 4.1. Construction of the Simulation Model

#### 4.2. Establishment of the Associated Fault Diagnosis Model

#### 4.3. Diagnosis Results and Analysis

#### 4.3.1. Data Introduction

#### 4.3.2. Operating Environment

#### 4.3.3. Diagnosis Results

#### 4.3.4. Validation and Comparison

- (1)
- Cluster sum of square

- (2)
- Contour coefficient

- (3)
- Calinski–Harabaz index (CH)

- (1)
- Pearson’s correlation coefficient

- (2)
- Parametric analysis based on the gray correlation analysis model

- (3)
- Mahalanobis distance

- (4)
- Cosine similarity

- (5)
- DTW (dynamic time warping algorithm)

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Example graph of phase-to-phase short-circuit fault backtracking of exciter armature winding.

**Figure 16.**Comparison of confusion matrix of two methods with different numbers of training samples.

**Figure 17.**Comparison graph of normal state-associated fault mode graph before and after missing parameters.

No. | Components | No. | Components | No. | Components | No. | Components |
---|---|---|---|---|---|---|---|

0 | Pilot exciter 1 | 17 | Main motor 2 | 34 | High variable filter 13 | 51 | 270 V regulating 4 |

1 | Pilot exciter 2 | 18 | Main motor 3 | 35 | High variable filter 14 | 52 | 28 V regulating 1 |

2 | Pilot exciter 3 | 19 | Main motor 4 | 36 | Low variation filter 11 | 53 | 28 V regulating 2 |

3 | Pilot exciter 4 | 20 | AC load 1 | 37 | Low variation filter 12 | 54 | 28 V regulating 3 |

4 | Rectifier bridge 1 | 21 | AC load 2 | 38 | Low variation filter 13 | 55 | 28 V regulating 4 |

5 | Rectifier bridge 2 | 22 | AC load 3 | 39 | Low variation filter 14 | 56 | High voltage busbar 1 |

6 | Rectifier bridge 3 | 23 | AC load 4 | 40 | High variable filter 21 | 57 | High voltage busbar 2 |

7 | Rectifier bridge 4 | 24 | High voltage transformer 1 | 41 | High variable filter 22 | 58 | Low voltage busbar 1 |

8 | Main exciter 1 | 25 | High voltage transformer 2 | 42 | High variable filter 23 | 59 | Low voltage busbar 2 |

9 | Main exciter 2 | 26 | High voltage transformer 3 | 43 | High variable filter 24 | 60 | Fuel pump 1 |

10 | Main exciter 3 | 27 | High voltage transformer 4 | 44 | Low variation filter 21 | 61 | Fuel pump 2 |

11 | Main exciter 4 | 28 | Low voltage transformer 1 | 45 | Low variation filter 22 | 62 | Fuel pump 3 |

12 | Rotating rectifier 1 | 29 | Low voltage transformer 2 | 46 | Low variation filter 23 | 63 | Fuel pump 4 |

13 | Rotating rectifier 2 | 30 | Low voltage transformer 3 | 47 | Low variation filter 24 | 64 | Heater 1 |

14 | Rotating rectifier 3 | 31 | Low voltage transformer 4 | 48 | 270 V regulating 1 | 65 | Heater 2 |

15 | Rotating rectifier 4 | 32 | High variable filter 11 | 49 | 270 V regulating 2 | 66 | Heater 3 |

16 | Main motor 1 | 33 | High variable filter 12 | 50 | 270 V regulating 3 | 67 | Heater 4 |

Metric Algorithm | CSS | Contour Factor | CH |
---|---|---|---|

Pearson correlation coefficient | 3.4692 | 0.0536 | 199.5176 |

Grey correlation analysis | 11.6526 | −0.1574 | 21.9299 |

Mahalanobis distance | 5.0645 | 0.6025 | 116.6640 |

Cosine similarity | 0.5429 | 0.1715 | 2694.7450 |

Dynamic Time Warping | 0.0080 | 0.7599 | 343,059.7323 |

Frechet distance | 0.0001 | 0.9425 | 15,413,927.6165 |

No. | Model | Accuracy |
---|---|---|

1 | WeightedEnsemble_L2 | 0.7727 |

2 | RandomForestGini | 0.7386 |

3 | LightGBMXT | 0.7636 |

4 | CatBoost | 0.7636 |

5 | XGBoost | 0.7705 |

6 | LightGBMLarge | 0.7568 |

7 | NeuralNetTorch | 0.7523 |

8 | NeuralNetFastAI | 0.7545 |

9 | LightGBM | 0.7409 |

10 | KNeighborsUnif | 0.7409 |

11 | The proposed model | 0.9907 |

No. | Model | Accuracy with Graph Model | Accuracy without Graph Model |
---|---|---|---|

1 | WeightedEnsemble_L2 | 0.7727 | 0.7341 |

2 | RandomForestGini | 0.7386 | 0.7341 |

3 | KNeighborsUnif | 0.7409 | 0.7386 |

4 | SVM | 0.7334 | 0.7080 |

5 | XGBoost | 0.7705 | 0.7293 |

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**MDPI and ACS Style**

Tao, L.; Liu, H.; Zhang, J.; Su, X.; Li, S.; Hao, J.; Lu, C.; Suo, M.; Wang, C.
Associated Fault Diagnosis of Power Supply Systems Based on Graph Matching: A Knowledge and Data Fusion Approach. *Mathematics* **2022**, *10*, 4306.
https://doi.org/10.3390/math10224306

**AMA Style**

Tao L, Liu H, Zhang J, Su X, Li S, Hao J, Lu C, Suo M, Wang C.
Associated Fault Diagnosis of Power Supply Systems Based on Graph Matching: A Knowledge and Data Fusion Approach. *Mathematics*. 2022; 10(22):4306.
https://doi.org/10.3390/math10224306

**Chicago/Turabian Style**

Tao, Laifa, Haifei Liu, Jiqing Zhang, Xuanyuan Su, Shangyu Li, Jie Hao, Chen Lu, Mingliang Suo, and Chao Wang.
2022. "Associated Fault Diagnosis of Power Supply Systems Based on Graph Matching: A Knowledge and Data Fusion Approach" *Mathematics* 10, no. 22: 4306.
https://doi.org/10.3390/math10224306