# Modeling Sensor Reliability in Fault Diagnosis Based on Evidence Theory

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## Abstract

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## 1. Introduction

## 2. Preliminaries

#### 2.1. Dempster–Shafer Evidence Theory

#### 2.2. Weighted Average Combination Method [39]

#### 2.3. Deng Entropy

#### 2.4. Fan and Zuo’s Method

## 3. The Proposed Method

#### 3.1. Static Reliability

#### 3.2. Dynamic Reliability

#### 3.3. Comprehensive Reliability of Sensor

## 4. Application

$\left(\right)open="\{"\; close="\}">{\mathbf{F}}_{\mathbf{1}}$ | $\left(\right)open="\{"\; close="\}">{\mathbf{F}}_{\mathbf{2}}$ | $\left(\right)open="\{"\; close="\}">{\mathbf{F}}_{\mathbf{2}}\mathbf{,}{\mathbf{F}}_{\mathbf{3}}$ | θ | |
---|---|---|---|---|

${E}_{1}:{m}_{1}\left(\xb7\right)$ | 0.6 | 0.1 | 0.1 | 0.2 |

${E}_{2}:{m}_{2}\left(\xb7\right)$ | 0.05 | 0.8 | 0.05 | 0.1 |

${E}_{3}:{m}_{3}\left(\xb7\right)$ | 0.7 | 0.1 | 0.1 | 0.1 |

$\left(\right)open="\{"\; close="\}">{\mathbf{F}}_{\mathbf{1}}$ | $\left(\right)open="\{"\; close="\}">{\mathbf{F}}_{\mathbf{2}}$ | $\left(\right)open="\{"\; close="\}">{\mathbf{F}}_{\mathbf{2}}\mathbf{,}{\mathbf{F}}_{\mathbf{3}}$ | θ | |
---|---|---|---|---|

D-S evidence theory | 0.4519 | 0.5048 | 0.0336 | 0.0096 |

Fan and Zuo’s method [43] | 0.8119 | 0.1096 | 0.0526 | 0.0259 |

The proposed method | 0.8948 | 0.0739 | 0.0241 | 0.0072 |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Yuan, K.; Xiao, F.; Fei, L.; Kang, B.; Deng, Y.
Modeling Sensor Reliability in Fault Diagnosis Based on Evidence Theory. *Sensors* **2016**, *16*, 113.
https://doi.org/10.3390/s16010113

**AMA Style**

Yuan K, Xiao F, Fei L, Kang B, Deng Y.
Modeling Sensor Reliability in Fault Diagnosis Based on Evidence Theory. *Sensors*. 2016; 16(1):113.
https://doi.org/10.3390/s16010113

**Chicago/Turabian Style**

Yuan, Kaijuan, Fuyuan Xiao, Liguo Fei, Bingyi Kang, and Yong Deng.
2016. "Modeling Sensor Reliability in Fault Diagnosis Based on Evidence Theory" *Sensors* 16, no. 1: 113.
https://doi.org/10.3390/s16010113