# A Simulation-Data-Based Machine Learning Model for Predicting Basic Parameter Settings of the Plasticizing Process in Injection Molding

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## Abstract

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## 1. Introduction

## 2. Basics

#### 2.1. The Plasticizing Process and S3 Simulation Software

#### 2.2. Artificial Neural Networks

## 3. Methods

#### 3.1. Data Generation and Preprocessing

- Which features (inputs) can be selected from the data in order to predict the desired labels?
- How can the model fulfill the requirement of good melt quality for the predictions?

- shot weight;
- melt quality—LD screw position;
- melt quality—molten material [%]; and
- plasticizing time.

#### 3.2. Model Construction

- multilayer perceptron,
- Gaussian process regression,
- support vector regression,
- polynomial regression,
- random forest, and
- gradient boosting.

- Training set: 549 samples
- Validation set: 183 samples
- Test set: 183 samples
- Layer structure: 4 –> 50 –> 50 –> 30 –> 2
- Activation function: Tanh (for all layers)
- Optimizer: Pytorch Adam
- Loss function: Pytorch MSE
- Learning rate epoch 0–600: ${10}^{-3}$
- Learning rate epoch 600–1200: ${10}^{-4}$
- Learning rate epoch 1200–1500: ${10}^{-5}$
- Weight decay: ${10}^{-4}$
- Batch size: 32
- Epochs: 1500.

#### 3.3. Experimental Evaluation of the Model

- melt value: 99% molten for each data point;
- screw Position (LD): 16, 18, 20;
- shot weight (kg): 0.02, 0.035, 0.05; and
- plasticizing time (s): 1–15.

## 4. Results

#### 4.1. Results—Multilayer Perceptron Model

#### 4.2. Results—Model vs. Experiment

#### 4.3. Conclusions and Outlook

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Fernandes, C.; Pontes, A.J.; Viana, J.C.; Nóbrega, J.M.; Gaspar-Cunha, A. Modeling of Plasticating Injection Molding—Experimental Assessment. Int. Polym. Process.
**2014**, 29, 558–569. [Google Scholar] [CrossRef] - Subramanian, M.N. The Basics of Troubleshooting in Plastics Processing; Wiley: Hoboken, NJ, USA, 2011; ISBN 978-0-470-62606-1. [Google Scholar]
- Singh, M.; Fuenmayor, E.; Hinchy, E.P.; Qiao, Y.; Murray, N.; Devine, D. Digital Twin: Origin to Future. ASI
**2021**, 4, 36. [Google Scholar] [CrossRef] - Hopmann, C.H.; Theunissen, M.; Heinisch, J. Von der Simulation in die Maschine—Objektivierte Prozesseinrichtung durch Maschinelles Lernen; VDI Wissensforum GmbH (Hrsg.); Spritzgießen: Baden-Baden, Germany, 2018; pp. 29–42. [Google Scholar] [CrossRef]
- Lee, C.; Na, J.; Park, K.; Yu, H.; Kim, J.; Choi, K.; Park, D.; Park, S.; Rho, J.; Lee, S. Development of Artificial Neural Network System to Recommend Process Conditions of Injection Molding for Various Geometries. Adv. Intell. Syst.
**2020**, 2, 2000037. [Google Scholar] [CrossRef] - Tercan, H.; Guajardo, A.; Heinisch, J.; Thiele, T.; Hopmann, C.; Meisen, T. Transfer-Learning: Bridging the Gap between Real and Simulation Data for Machine Learning in Injection Molding. Procedia CIRP
**2018**, 72, 185–190. [Google Scholar] [CrossRef] - Limper, A. Verfahrenstechnik der Thermoplastextrusion; Carl Hanser Verlag: Munich, Germany, 2012; ISBN 978-3-446-41744-1. [Google Scholar]
- Altmann, D. Advanced Process Simulation for Single-Screw Plasticizing Units in Injection Molding. Ph.D. Thesis, Johannes Kepler University, Linz, Austria, 2019. [Google Scholar]
- Janssens, J. Data Science at the Command Line: Facing the Future with Time-Tested Tools; O’Reilly and Associates: Sebastopol, CA, USA, 2014; ISBN 978-1-491-94785-2. [Google Scholar]
- Marius, P.; Balas, V.E.; Perescu-Popescu, L.; Mastorakis, N.E. Multilayer perceptron and neural networks. WSEAS Trans. Circuits Syst.
**2009**, 8, 579–588. [Google Scholar] - Bishop, C.M. Neural Networks for Pattern Recognition; Oxford University Press: New York, NY, USA, 1995; ISBN 978-0-19-853864-6. [Google Scholar]
- Rumelhart, D.; Hinton, G.; Williams, R. Learning representations by back-propagating errors. Nature
**1986**, 323, 533–536. [Google Scholar] [CrossRef] - Van Rossum, G.; Drake, F.L., Jr. Python Reference Manual; CreateSpace: Scotts Valley, CA, USA, 2009; ISBN 978-1-4414-1269-0. [Google Scholar]
- Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L.; et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library. Adv. Neural Inf. Process. Syst.
**2019**, 32, 8024–8035. Available online: http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf (accessed on 28 April 2021). - Wu, Y.; Liu, L.; Bae, J.; Chow, K.H.; Iyengar, A.; Pu, C.; Wei, W.; Yu, L.; Zhang, Q. Demystifying Learning Rate Policies for High Accuracy Training of Deep Neural Networks. arXiv
**2019**, arXiv:1908.06477. [Google Scholar]

**Figure 1.**Schematic representation of the functional zones of a plasticizing unit [7].

**Figure 2.**Forward pass of a multilayer perceptron. The red box shows the determination of the pre-activation and activation in one neuron of the hidden layer. The pre-activation is calculated by the linear sum of the product of all previous neurons ${x}_{j}$ (input layer) with their corresponding weights ${w}_{ij}$ plus a bias term ${b}_{i}$. The pre-activation ${s}_{i}$, then, serves as input to the non-linear activation function, which gives ${a}_{i}$.

**Figure 8.**Accuracy of the back pressure predictions on the training (samples from which the model is trained), validation (unseen samples for hyperparameter tuning during training), and test (evaluation on unseen samples after training) data sets.

**Figure 9.**Accuracy of the screw rotational speed predictions on the training (samples from which the model is trained), validation (unseen samples for hyperparameter tuning during training), and test (evaluation on unseen samples after training) data sets.

**Figure 10.**Mean error between the real and desired plasticizing times based on the predicted basic parameter settings obtained for three materials. Each scattered sample shows the mean and the standard deviation of three experiments per operating point. The mean absolute errors were 2.8%, 10.8%, and 14.5% for PEHD-MB7541, PA6-B30S, and PP-HE125MO, respectively. The ordinate shows the machine setting arrays for all experiments. An array contains the back pressures and screw rotational speeds predicted by the neural network model for specified shot weights and plasticizing times. The screw position where the material is 99% melted is described by the LD value. For example, the sample at the bottom (PP-HE125MO with the array (36, 0.18, 0.02, and 16)) shows a mean error of about 3% between the real and desired plasticizing times. The input information that the shot weight of 20 g is 99% melted at screw position LD 16 was fed into the neural network model, which predicted 36 bar back pressure and a 0.18 m/s screw rotational speed.

**Table 1.**Limits of the input parameters for the simulation. Within these limits, the data set was drawn randomly.

Back Pressure | Metering Stroke | Screw Rotational Speed | Cycle Time | |
---|---|---|---|---|

Min | 25 bar | 0.8 D | 0.2 $\frac{\mathrm{m}}{\mathrm{s}}$ | 10 s |

Max | 225 bar | 4 D | 1 $\frac{\mathrm{m}}{\mathrm{s}}$ | 60 s |

**Table 2.**Experimental configurations for 0.035 kg shot weight and 99% melt value. The first entry describes that, for a back pressure of 148.7 bar and a screw rotational speed of 0.24 m/s, 99% of 35 g of material is predicted to be melted at screw position LD 16 within a plasticizing time of 9.62 s.

Screw Position [LD] | Plasticizing Time [s] | Back Pressure [bar] | Screw Rotational Speed [$\frac{\mathbf{m}}{\mathbf{s}}$] |
---|---|---|---|

16 | 9.62 | 148.7 | 0.24 |

16 | 11.05 | 90.9 | 0.20 |

16 | 12.13 | 38.7 | 0.16 |

18 | 6.03 | 163.2 | 0.38 |

18 | 7.10 | 84.9 | 0.30 |

18 | 7.82 | 37.1 | 0.25 |

20 | 3.87 | 180.4 | 0.60 |

20 | 4.59 | 102.2 | 0.45 |

20 | 5.31 | 38.1 | 0.36 |

**Table 3.**Comparison of relevant supervised machine learning methods. The absolute prediction errors of the labels back pressure and screw rotational speed are listed for the training and test sets.

Method | Mean Error [%] | Std Error [%] | ||
---|---|---|---|---|

Train | Test | Train | Test | |

Multilayer Perceptron | 0.21 | 0.27 | 0.26 | 0.37 |

Gaussian Process Regression | 0.08 | 1.16 | 0.18 | 2.25 |

Polynomial Regression | 0.34 | 1.27 | 0.55 | 4.98 |

Support Vector Regression | 2.57 | 2.87 | 2.64 | 3.81 |

Random Forest | 8.39 | 21.42 | 14.40 | 37.18 |

Gradient Boosting | 18.44 | 24.34 | 31.44 | 43.54 |

Label | RMSE Train | RMSE Test |
---|---|---|

Back Pressure [bar] | 0.41 | 0.61 |

Screw Rotational Speed [m/s] | 0.0008 | 0.001 |

**Table 5.**Absolute errors between the real and desired plasticizing times for the predicted parameter settings. the mean and standard deviation were calculated based on all samples per material. Each maximum error was based on only one data point and gives further insights into the differences among the observations of each material.

PP-HE125MO | PEHD-MB7541 | PA6-B30S | |
---|---|---|---|

Mean | 14.4% | 2.8% | 10.8% |

Std | 10% | 2% | 6% |

Max | 34% | 8% | 18% |

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**MDPI and ACS Style**

Schmid, M.; Altmann, D.; Steinbichler, G.
A Simulation-Data-Based Machine Learning Model for Predicting Basic Parameter Settings of the Plasticizing Process in Injection Molding. *Polymers* **2021**, *13*, 2652.
https://doi.org/10.3390/polym13162652

**AMA Style**

Schmid M, Altmann D, Steinbichler G.
A Simulation-Data-Based Machine Learning Model for Predicting Basic Parameter Settings of the Plasticizing Process in Injection Molding. *Polymers*. 2021; 13(16):2652.
https://doi.org/10.3390/polym13162652

**Chicago/Turabian Style**

Schmid, Matthias, Dominik Altmann, and Georg Steinbichler.
2021. "A Simulation-Data-Based Machine Learning Model for Predicting Basic Parameter Settings of the Plasticizing Process in Injection Molding" *Polymers* 13, no. 16: 2652.
https://doi.org/10.3390/polym13162652