# Robust Soft Sensor with Deep Kernel Learning for Quality Prediction in Rubber Mixing Processes

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## Abstract

**:**

## 1. Introduction

## 2. Ensemble Deep Correntropy Kernel Regression Method

#### 2.1. Restricted Boltzmann Machine Construction

_{1}) is trained using the parameters ${\theta}_{1}=\{{W}_{1},{b}_{1},{c}_{1}\}$ to obtain ${H}_{1}$. With a built RBM

_{1}, let ${V}_{2}={H}_{1}$, and RBM

_{2}can be trained similarly. Sequentially, the RBM

_{l}module with ${H}_{l}$ and ${V}_{l}$ is trained and finally a series of RBMs are obtained [22].

#### 2.2. Deep Correntropy Kernel Regression Model

_{i}and e

_{i}are the process output and noise for ith sample, respectively; f is the DCKR model with its parameters $\beta $, and bias b, respectively.

#### 2.3. Reliability Enhancement Using Bagging-Based Ensemble Strategy

## 3. Industrial Mooney Viscosity Prediction

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Construction of the main deep brief network (DBN) structure with multiple restricted Boltzmann machine (RBM) layers.

**Figure 2.**Main modeling flowchart of ensemble deep correntropy kernel regression (EDCKR) for soft sensing of the Mooney viscosity.

**Figure 3.**Assayed values and their prediction results of the Mooney viscosity using EDCKR, deep correntropy kernel regression (DCKR), principal component analysis and correntropy kernel regression (PCA-CKR), and correntropy kernel regression (CKR) models.

**Figure 4.**Relative root mean squares error (RRMSE) comparisons of Mooney viscosity between a single DCKR model and an EDCKR model with different candidates.

**Table 1.**Comparison of the Mooney viscosity soft-sensor models: Main characteristics and prediction results.

Mooney Viscosity Soft Sensor | Main Characteristics | RRMSE (%) | Maximum Absolute Error | |
---|---|---|---|---|

Model Structure | Feature Extraction | |||

EDCKR (proposed) | deep (multiple) | nonlinear | 4.55 | 3.28 |

DCKR (proposed) | deep | nonlinear | 5.53 | 4.16 |

PCA-CKR | shallow | linear | 7.71 | 5.86 |

CKR [32] | shallow | no | 8.10 | 5.99 |

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## Share and Cite

**MDPI and ACS Style**

Zheng, S.; Liu, K.; Xu, Y.; Chen, H.; Zhang, X.; Liu, Y.
Robust Soft Sensor with Deep Kernel Learning for Quality Prediction in Rubber Mixing Processes. *Sensors* **2020**, *20*, 695.
https://doi.org/10.3390/s20030695

**AMA Style**

Zheng S, Liu K, Xu Y, Chen H, Zhang X, Liu Y.
Robust Soft Sensor with Deep Kernel Learning for Quality Prediction in Rubber Mixing Processes. *Sensors*. 2020; 20(3):695.
https://doi.org/10.3390/s20030695

**Chicago/Turabian Style**

Zheng, Shuihua, Kaixin Liu, Yili Xu, Hao Chen, Xuelei Zhang, and Yi Liu.
2020. "Robust Soft Sensor with Deep Kernel Learning for Quality Prediction in Rubber Mixing Processes" *Sensors* 20, no. 3: 695.
https://doi.org/10.3390/s20030695