# Prediction of Particle Size Distribution of Mill Products Using Artificial Neural Networks

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods-ANN Model Predicting Percentage Passing Cumulative

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the proposed ANN models for PPC predictions. (FL—Feed Load (Vol.%), RL—Rod Load (Vol.%), GT—Grinding Time (min.), SO—Sieve Opening ($\mathsf{\mu}\mathrm{m}$), and PPC—Percentage of Passing Cumulative (%)).

**Figure 3.**Correlation plots between the output and target values for training, validation, and testing. The results of the 250 µm passing are plotted as an example.

**Figure 4.**(

**a**) Changes in parameters and (

**b**) mean squared error during the model optimization processes. The results of 250 µm passing are plotted as an example.

**Figure 5.**Correlation coefficient (R) of the training, validation, and test datasets in the ANN models for six SO levels.

**Figure 6.**Comparisons between the ANN-predicted PPC (ANN) and experimental PPC (EXP). The numbers in the figure legend represent FL (Vol.%), RL (Vol.%), and GT (Min.). The feed (EXP) particle size distribution without grinding (GT = 0 min) was also added as a reference value.

ANN Model | SO: 1000 | SO: 500 | SO: 250 | SO: 125 | SO: 63 | SO: 38 | |
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Max. Iteration * | 8 | 55 | 79 | 54 | 69 | 56 | |

Correlation coefficient (R) | Training | 0.994 | 0.997 | 0.999 | 0.998 | 0.987 | 0.893 |

Validation | 0.974 | 0.999 | 0.987 | 0.996 | 0.981 | 0.901 | |

Test | 0.973 | 0.995 | 0.993 | 0.938 | 0.926 | 0.809 |

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**MDPI and ACS Style**

Otsuki, A.; Jang, H.
Prediction of Particle Size Distribution of Mill Products Using Artificial Neural Networks. *ChemEngineering* **2022**, *6*, 92.
https://doi.org/10.3390/chemengineering6060092

**AMA Style**

Otsuki A, Jang H.
Prediction of Particle Size Distribution of Mill Products Using Artificial Neural Networks. *ChemEngineering*. 2022; 6(6):92.
https://doi.org/10.3390/chemengineering6060092

**Chicago/Turabian Style**

Otsuki, Akira, and Hyongdoo Jang.
2022. "Prediction of Particle Size Distribution of Mill Products Using Artificial Neural Networks" *ChemEngineering* 6, no. 6: 92.
https://doi.org/10.3390/chemengineering6060092