# An Intelligent Condition Monitoring Approach for Spent Nuclear Fuel Shearing Machines Based on Noise Signals

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Wavelet Packet Transform

#### 2.2. Hidden Markov Model

#### 2.3. Artificial Neural Network

## 3. Condition Monitoring Approach for Shearing Machines

#### 3.1. Feature Extraction Method Based on WPT

#### 3.2. Hybrid HMM–ANN Model for Fault Diagnosis

#### 3.3. Training and Recognizing Process of the Hybrid HMM–ANN Model

#### 3.3.1. Training Process of the Hybrid Model

- (a)
- Initial guess of parameters. It is generally considered that the initial values of parameters $\pi $ and A have little effect while the initial value of parameters ${\mu}_{jk}$, ${\sigma}_{jk}$ and ${c}_{jk}$ have a large influence on the training result of HMMs. The initial values $\pi $ and A can be set randomly or evenly. It will be detailed in the empirical part. The initial parameters ${\mu}_{jk}^{\left(0\right)}$, ${\sigma}_{jk}^{\left(0\right)}$ and ${c}_{jk}^{\left(0\right)}$ are estimated by using the segmental k–means algorithm (see literature [40]).
- (b)
- Model revaluation. In this study, the Baum–Welch algorithm was used to reevaluate the HMM parameters. For each state of HMM, the constructed model $\lambda $ is updated based on the following revaluation equations:$$\begin{array}{l}{\widehat{\pi}}_{i}={\gamma}_{1}\left(i\right),\\ {\widehat{a}}_{ij}=\sum _{t=1}^{T-1}{\xi}_{t}(i,j)/\sum _{t=1}^{T-1}{\gamma}_{t}\left(i\right),\\ {\widehat{c}}_{jk}=\sum _{t=1}^{T}{\gamma}_{t}(j,k)/\sum _{t=1}^{T}\sum _{k=1}^{M}{\gamma}_{t}(j,k),\\ {\widehat{\mu}}_{jk}=\sum _{t=1}^{T}{\gamma}_{t}(j,k)\xb7{o}_{t}/\sum _{t=1}^{T}{\gamma}_{t}(j,k),\\ {\widehat{\sigma}}_{jk}=\sum _{t=1}^{T}{\gamma}_{t}(j,k)\xb7{({o}_{t}-{\mu}_{jk})}^{2}/\sum _{t=1}^{T}{\gamma}_{t}(j,k),\end{array}$$
- (c)
- Model determination. The output probabilities of the samples under the new model $P\left(O\right|\lambda )$ are calculated by using the forward–backward algorithm. If the condition $P\left(O\right|{\lambda}^{(n+1)})-P\left(O\right|{\lambda}^{\left(n\right)})\le \epsilon $ is met, the model obtained in the last revaluation is considered the final model. Otherwise, return to step (b) and continue reevaluating.

- (a)
- Establishment of network. An ANN with three layers (input layer, output layer, and hidden layer) is constructed. The number of neurons in the input layer is equal to the dimension of the feature vector, and that of the output layer equals the number of health states. The number of neurons in the hidden layer is mainly determined by tests, while the following empirical equation gives a preliminary range:$$h=\sqrt{(m+n)}+a$$
- (b)
- Setting training parameters, e.g., selections of initial weight, threshold, goal, learning rate, momentum factor, maximum epochs, as well as selections of learning function, training function, and performance function. They are also selected according to their applicabilities, requirements of tasks and through tests.
- (c)
- Training of ANN. Use the samples to train ANN iteratively until the accuracy meets the goal value or the accuracy does no longer improve. Thus, the trained ANN model is obtained.

#### 3.3.2. Recognizing Process of the Hybrid Model

- (a)
- Construction of input vectors for ANN. The samples to be identified are preprocessed and feature extracted with the same method as used for training samples. Consequently, observed vectors can be obtained. Next, use the feature vectors as input to calculate the output probabilities of the samples to be identified for all trained HMMs. The input vectors of ANN are constructed with these probability values.
- (b)
- Probability prediction of samples to be identified for each health state. Using the input vectors to produce the outputs of the trained ANN model. As a result, the predicted probabilities of the samples to be identified for each health state are obtained.
- (c)
- Classification decision. Finally, considering the highest likehood, the health states of the samples to be identified are determined.

## 4. Application and Results

#### 4.1. Experimental Rig Setup and Data Collection

#### 4.1.1. Experimental Setup

#### 4.1.2. Noise Acquisition Method for Shearing Machines

#### 4.1.3. Collected Data

#### 4.2. Results and Discussions

#### 4.2.1. Feature Extraction from Noise Samples

#### 4.2.2. HMM–ANN Modeling and Fault Detection Results

#### 4.2.3. Comparative Analysis Results

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Principle and structure of a hybrid HMM–ANN model (solid line: the training process, dashed line: the recognizing process).

**Figure 11.**The time and frequency–domain diagrams of noise sample No. 1–32. (

**a**) time–domain diagram; (

**b**) frequency–domain diagram.

**Figure 14.**Feature vectors of noise signals. (

**a**) working state No. 1; (

**b**) working state N. 2; (

**c**) working state No. 3; (

**d**) working state No. 4.

**Figure 15.**Comparison of average energy of each frequency band for different health states. (

**a**) band 1; (

**b**) band 2; (

**c**) band 3; (

**d**) band 4;(

**e**) band 5; (

**f**) band 6; (

**g**) band 7; (

**h**) band 8.

Maximum Pressing Force | Maximum Shearing Force | Tool Feeding Speed | Feeding Step Distance | Section Size |
---|---|---|---|---|

165 kN | 785 kN | 0.03 m/s | 15 mm | 65 × 65 mm |

State No. | States | Sample Indices |
---|---|---|

1 | Normal (Normal state without faults) | 1–1 to 1–45 |

2 | Fault 2 (Slight tool wear) | 2–1 to 2–40 |

3 | Fault 3 (Severe tool wear) | 3–1 to 3–50 |

4 | Fault 4 (Damaged tool) | 4–1 to 4–35 |

**Table 3.**Mean of feature element values of all samples in every frequency band for every health state.

Working State No. | Mean of Feature Element Values of All Samples in Every Frequency Band | |||||||
---|---|---|---|---|---|---|---|---|

band 1 | band 2 | band 3 | band 4 | band 5 | band 6 | band 7 | band 8 | |

1 | 0.7358 | 0.1819 | 0.0107 | 0.0622 | 0.0007 | 0.0021 | 0.0043 | 0.0023 |

2 | 0.6748 | 0.1537 | 0.0196 | 0.0779 | 0.0544 | 0.0054 | 0.0095 | 0.0046 |

3 | 0.7828 | 0.1283 | 0.0161 | 0.0506 | 0.0034 | 0.0041 | 0.0088 | 0.0060 |

4 | 0.6697 | 0.2064 | 0.0199 | 0.086 | 0.001 | 0.0027 | 0.0094 | 0.0049 |

Sample Sets | Normal | Fault 2 | Fault 3 | Fault 4 | Total |
---|---|---|---|---|---|

Training | 27 | 24 | 30 | 21 | 102 |

Testing | 18 | 16 | 20 | 14 | 68 |

Training Rule | Neurons in Hidden Layer | Training Error (mse) | R |
---|---|---|---|

trainlm | 10 | 3.10 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-10}$ | 1 |

traingdx | 10 | 5.00 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ | 0.85633 |

trainrp | 10 | 4.62 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ | 0.86827 |

trainscg | 10 | 1.44 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ | 0.96095 |

trainlm | 5 | 2.26 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-3}$ | 0.99397 |

trainlm | 8 | 3.40 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$ | 0.99991 |

trainlm | 12 | 7.12 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ | 1 |

trainlm | 14 | 2.22 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-8}$ | 1 |

States | State No. | Predicted Values | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Normal | 1 | 1 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | – | – |

Fault 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | – | – | – | – |

Fault 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 4 | 3 | 3 |

Fault 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | – | – | – | – | – | – |

States | State No. | Predicted Values | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Normal | 1 | 1 | 1 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | – | – |

Fault 2 | 2 | 2 | 4 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | – | – | – | – |

Fault 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 3 | 3 | 3 | 2 | 3 | 3 |

Fault 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | – | – | – | – | – | – |

States | State No. | Predicted Values | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Normal | 1 | 4 | 3 | 3 | 4 | 4 | 4 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | – | – |

Fault 2 | 2 | 4 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 2 | – | – | – | – |

Fault 3 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 4 | 4 | 3 | 2 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 |

Fault 4 | 4 | 2 | 4 | 4 | 2 | 1 | 4 | 2 | 4 | 2 | 4 | 4 | 2 | 2 | 4 | – | – | – | – | – | – |

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## Share and Cite

**MDPI and ACS Style**

Chen, J.-H.; Zou, S.-L.
An Intelligent Condition Monitoring Approach for Spent Nuclear Fuel Shearing Machines Based on Noise Signals. *Appl. Sci.* **2018**, *8*, 838.
https://doi.org/10.3390/app8050838

**AMA Style**

Chen J-H, Zou S-L.
An Intelligent Condition Monitoring Approach for Spent Nuclear Fuel Shearing Machines Based on Noise Signals. *Applied Sciences*. 2018; 8(5):838.
https://doi.org/10.3390/app8050838

**Chicago/Turabian Style**

Chen, Jia-Hua, and Shu-Liang Zou.
2018. "An Intelligent Condition Monitoring Approach for Spent Nuclear Fuel Shearing Machines Based on Noise Signals" *Applied Sciences* 8, no. 5: 838.
https://doi.org/10.3390/app8050838