# Fault Classification Decision Fusion System Based on Combination Weights and an Improved Voting Method

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. The AHP

- The weight vector is calculated as follows:$${W}_{i}={{W}_{i}}^{\prime}/{\displaystyle \sum _{i=1}^{n}{W}_{i}{}^{\prime}},$$$${{W}_{i}}^{\prime}=\sqrt[n]{{\displaystyle \prod _{j=1}^{n}{a}_{ij}}},\text{}i=1,\cdots ,n,$$
- Calculate the largest eigenvalue ${\lambda}_{\mathrm{max}}$ of the judgment matrix:$${\lambda}_{\mathrm{max}}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\frac{{\left(A{w}_{d}\right)}_{i}}{{W}_{i}}}.$$
- The consistency check is performed as follows:$$CR=CI/RI,$$

#### 2.2. EW-TOPSIS

## 3. The Proposed Method

#### 3.1. Selection of Base Classifiers

#### 3.2. Classifier Performance Evaluation

#### 3.3. Formatting of Mathematical Components

## 4. Results

#### 4.1. TE Process

#### 4.2. Experiment

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Decision fusion system based on combination weights and the improved voting method. AHP: analytic Hierarchy Process; BP: BP neural network; EW-TOPSIS: entropy weight-technique for order performance by similarity to ideal solution; KNN: K-nearest neighbor; LDA: linear discriminant analysis.

**Figure 2.**Hierarchy of the AHP. BN: Bayesian classifier; RF: random forest; F: F-value; ACC: Accuracy; MR: Missing Rate; P: Precision.

Importance Scale | Description |
---|---|

1 | Two factors are equally important |

3 | The first factor is slightly more important than the second factor |

5 | The first factor is very important relative to the second factor |

7 | The first factor is absolutely very important compared with the second factor |

9 | The first factor is extremely important compared with the second factor |

2, 4, 6, 8 | Median between adjacent scales |

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 |

Indicators | F | ACC | MR | P | Weights |
---|---|---|---|---|---|

F | 1 | 2 | 2 | 3 | 0.4236 |

ACC | 1/2 | 1 | 1 | 2 | 0.2270 |

MR | 1/2 | 1 | 1 | 2 | 0.2270 |

P | 1/3 | 1/2 | 1/2 | 1 | 0.1223 |

Fault No. | LDA | KNN | BN | RF | SVM | BP | VOTE | IVM | CWM | ETIVM | AIVM | CWIVM |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 98 | 98.13 | 98.63 | 98.5 | 98.63 | 98.63 | 98.88 | 99.13 | 98.88 | 99.13 | 98.88 | 98.88 |

2 | 96.25 | 97.5 | 98.25 | 98 | 97.88 | 98.75 | 98.38 | 99 | 98.25 | 98.38 | 98.25 | 98.25 |

3 | 11.25 | 21.25 | 17.25 | 17.38 | 19.13 | 0 | 24.63 | 14.25 | 17.5 | 12.63 | 11.63 | 11.38 |

4 | 81.5 | 20.75 | 73.63 | 95.13 | 89.13 | 11.13 | 97.63 | 99.5 | 94.38 | 98.63 | 98.38 | 98.38 |

5 | 98.5 | 20.5 | 98.13 | 51.63 | 98.13 | 95.38 | 99.38 | 99.13 | 99.13 | 99.13 | 98.13 | 98.88 |

6 | 99.75 | 99.75 | 56.38 | 99.38 | 63.13 | 33.88 | 100 | 100 | 100 | 100 | 63.13 | 100 |

7 | 100 | 80.38 | 100 | 99.75 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

8 | 37.13 | 28.75 | 96.5 | 53.25 | 34 | 54.63 | 71.88 | 78 | 83 | 90.38 | 96.13 | 95.25 |

9 | 14.25 | 13 | 21.63 | 17.25 | 15.75 | 0 | 19.13 | 7.88 | 20.38 | 7.75 | 13.25 | 10.5 |

10 | 40.13 | 8.13 | 83.75 | 43.38 | 21.38 | 0 | 53.25 | 78.63 | 75.25 | 82 | 83.75 | 83.75 |

11 | 8.63 | 8.63 | 70.75 | 62 | 15.63 | 0 | 37.5 | 45.5 | 62.5 | 59.75 | 62.25 | 61.63 |

12 | 31.25 | 29.75 | 97.25 | 76.63 | 60.5 | 2.25 | 73.75 | 83.13 | 89 | 86.63 | 94.5 | 91.63 |

13 | 20.75 | 16.5 | 57.75 | 16.5 | 12.25 | 22.13 | 19.13 | 28.38 | 37.63 | 36.75 | 51.38 | 49.63 |

14 | 7.75 | 44.25 | 97.25 | 94 | 72.5 | 0 | 85.13 | 93.13 | 94.13 | 93.25 | 97 | 94.25 |

15 | 15 | 14.25 | 26.25 | 26 | 18.88 | 0 | 20.63 | 26.75 | 26.63 | 28.13 | 31 | 30.63 |

16 | 37.75 | 7.5 | 79.25 | 48.25 | 20.75 | 29 | 51.5 | 73.38 | 70.25 | 76.63 | 79.13 | 78.75 |

17 | 51.75 | 39.13 | 86.5 | 90.38 | 73.63 | 84.38 | 87.38 | 92.88 | 90.13 | 92.63 | 89.5 | 91.75 |

18 | 16.5 | 81.25 | 18.63 | 86.13 | 62 | 70 | 86.13 | 88.75 | 86.5 | 88.88 | 51.5 | 88.5 |

19 | 14.5 | 29.88 | 94.38 | 78.13 | 49.38 | 0 | 68 | 93.5 | 89.5 | 95.38 | 95.25 | 95.75 |

20 | 52 | 12.63 | 87.5 | 61.38 | 47.38 | 79.13 | 72.5 | 89.13 | 84.13 | 88.25 | 87.5 | 87.63 |

21 | 5.75 | 6.25 | 99.25 | 24 | 2.75 | 38 | 30 | 93.5 | 80.38 | 98.88 | 99.75 | 99.75 |

Average | 44.68 | 37.05 | 74.23 | 63.67 | 51.08 | 38.92 | 66.42 | 75.4 | 76.07 | 77.77 | 76.2 | 79.29 |

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**MDPI and ACS Style**

Zeng, F.; Li, Z.; Zhou, Z.; Du, S.
Fault Classification Decision Fusion System Based on Combination Weights and an Improved Voting Method. *Processes* **2019**, *7*, 783.
https://doi.org/10.3390/pr7110783

**AMA Style**

Zeng F, Li Z, Zhou Z, Du S.
Fault Classification Decision Fusion System Based on Combination Weights and an Improved Voting Method. *Processes*. 2019; 7(11):783.
https://doi.org/10.3390/pr7110783

**Chicago/Turabian Style**

Zeng, Fanliang, Zuxin Li, Zhe Zhou, and Shuxin Du.
2019. "Fault Classification Decision Fusion System Based on Combination Weights and an Improved Voting Method" *Processes* 7, no. 11: 783.
https://doi.org/10.3390/pr7110783