# Sensor and Actuator Fault Diagnosis for Robot Joint Based on Deep CNN

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## Abstract

**:**

## 1. Introduction

- (1)
- This paper gives a fused sensor and actuator fault diagnosis model, where sensor and actuator fault could be expressed in one formulation. Still, different faults could be distinguished, which contributes to our study.
- (2)
- This paper proposes a DCNN fault diagnosis method. There are several convolution blocks in the architecture, and the depth of each kernel on different blocks varies, which helps to extract features from the time domain of input data.
- (3)
- Experiments with different neural network fault diagnosis methods, such as SVM, ANN, CNN, LTMN, are conducted and compared with DCNN to give a comparison.

## 2. Basic Structure of DCNN

#### 2.1. Convolution Layer

#### 2.2. Batch Normalization

#### 2.3. Activation Layers

#### 2.4. Pooling Layer

#### 2.5. Dropout Layer

#### 2.6. Fully Connected Layer

#### 2.7. Loss Function

_{1}, $\widehat{y}$

_{2},…, $\widehat{y}$

_{n}) is obtained. When the Softmax function is used, the outputs of the neural network meet the desired probability distribution. The calculation of the loss function is shown in Figure 7.

## 3. Sensor and Actuator Fault Diagnosis Framework Using DCNN

#### 3.1. Data Fusion

_{a}is the bias term and its value is positively correlated with the degree of actuator damage. The actuator faults with different combinations of ρ and f

_{a}are listed in Table 1.

_{1}is the state variable x multiplied by the coefficient matrix E. Thus, the robot sensor fault can be directly expressed by the output equation, as follows.

_{b}is the bias term and is positively correlated with the degree of sensor damage. The sensor faults with different combinations of λ and f

_{b}are listed in Table 2.

#### 3.2. Training of Model and Diagnosis

## 4. Experiment and Analysis

#### 4.1. Data Sets Enhancement

_{1}points is needed for single training. Assuming that the length of the data obtained is N, then the network could be trained by N/N

_{1}times according to the above method. In order to expand the coefficient of utilization for data, the start point of the second data set is h backwards compared to the first one, and the rest is roughly the same. The difference of samples before and after the data set enhancement method is used is shown in the following equation.

#### 4.2. Hyper Parameters of DCNN

_{2}regularization method is used in this paper. Regularization is to introduce the model complexity index into the loss function and suppress the noise in the training data set by weighting the parameters in the neural network. The expression of the loss function is as follows.

^{(1)},x

^{(2)},…,x

^{(m)}}. to denote it, and set corresponding goals ${y}^{(i)}$.

#### 4.3. Simulation and Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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ρ | f_{a} | Fault Type |
---|---|---|

1 | Not zero | Constant deviation fault |

0 < ρ < 1 | 0 | Constant gain fault |

0 | Not zero | Actuator stuck |

0 | 0 | Actuator broken |

λ | f_{b} | Fault Type |
---|---|---|

1 | Not zero | Constant deviation fault |

0 < λ < 1 | 0 | Constant gain fault |

0 | Not zero | sensor stuck |

0 | 0 | sensor broken |

Label | Fault Description |
---|---|

F1 | Constant deviation fault of the actuator |

F2 | Constant gain fault of the actuator |

F3 | Actuator stuck |

F4 | Actuator broken |

F5 | Constant deviation fault for both sensor and actuator |

F6 | Constant deviation fault of the sensor |

F7 | Constant gain fault of the sensor |

F8 | Sensor stuck |

F9 | Sensor broken |

F10 | Sensor and actuator are normal |

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Pan, J.; Qu, L.; Peng, K.
Sensor and Actuator Fault Diagnosis for Robot Joint Based on Deep CNN. *Entropy* **2021**, *23*, 751.
https://doi.org/10.3390/e23060751

**AMA Style**

Pan J, Qu L, Peng K.
Sensor and Actuator Fault Diagnosis for Robot Joint Based on Deep CNN. *Entropy*. 2021; 23(6):751.
https://doi.org/10.3390/e23060751

**Chicago/Turabian Style**

Pan, Jinghui, Lili Qu, and Kaixiang Peng.
2021. "Sensor and Actuator Fault Diagnosis for Robot Joint Based on Deep CNN" *Entropy* 23, no. 6: 751.
https://doi.org/10.3390/e23060751