# Combining Simulation and Machine Learning as Digital Twin for the Manufacturing of Overmolded Thermoplastic Composites

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Background of Surrogate Modeling

#### 2.2. Physics-Based Digital Twin Based on Simulation Surrogate Modeling

#### 2.3. Geometry and Simulation Model

#### 2.4. Sampling Strategy

#### 2.5. Experimental Cross Tension Tests

#### 2.6. Surrogate Modeling

## 3. Results and Discussion

#### 3.1. Evaluation of Surrogate Models for the Rib Structure

#### 3.2. Experimental Results of Cross Tension Testing

#### 3.3. Case Study of Virtual Demonstrator Structure

#### 3.3.1. Evaluation of Surrogate Models

#### 3.3.2. Transfer to a Quality Prediction System

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Cyber physical production systems (CPPS) based framework for a digital twin using Finite-Element-Method (FEM) simulation and machine learning for surrogate modeling; adapted from Thiede et al. [26].

**Figure 3.**Simulations models used: (

**a**) Tetrahedral mesh of the rib structure (

**b**) Tetrahedral mesh of the virtual demonstrator structure.

**Figure 5.**Comparison of model evaluation metrics without outliers for all investigated data-driven approaches for the rib structure: (

**a**) Error (${R}^{2}$, mean squared error (MSE), mean MAX error, mean absolute error (MAE)); (

**b**) times for training and prediction.

**Figure 7.**Comparison of ${t}_{m}$ for sample 52. (

**a**) Numerical result of full-scale simulation; (

**b**) predicted result by Random Forest; (

**c**) absolute difference; (

**d**) relative error (values with error > 1 are indicated by the color red).

**Figure 8.**Comparison of ${t}_{m}$ for sample 11. (

**a**) Numerical result of full-scale simulation; (

**b**) predicted result by Random Forest; (

**c**) absolute difference; (

**d**) relative error (values with error >1 are indicated by the color red).

**Figure 9.**Error analysis of the prediction: (

**a**) Sample 76: numerical result (all zero values for ${t}_{m}$; (

**b**) Sample 76: predicted result by Random Forest.

**Figure 10.**Correlation between experimental bond strength and computed average time period above melting temperature ${t}_{m}$ (1) at the rib interface.

**Figure 11.**Comparison of model evaluation metrics without outliers for all investigated data-driven approaches for the demonstrator structure: (

**a**) Error (${R}^{2}$, mean squared error (MSE), mean MAX error, mean absolute error (MAE)); (

**b**) times for training and prediction.

**Figure 12.**Comparison of local errors (MAX error) for all examined methods on the demonstrator geometry.

**Figure 13.**Comparison of ${t}_{m}$ for sample 52. (

**a**) Numerical result of full-scale simulation; (

**b**) predicted result by Random Forest; (

**c**) absolute difference; (

**d**) relative error (values with error > 1 are indicated by the color red).

**Figure 14.**Quality measurement for sample 52. (

**a**) Numerical result of full-scale simulation; (

**b**) predicted result by Random Forest.

**Figure 15.**Quality/Decision support for sample 31. (

**a**) Numerical result of full-scale simulation; (

**b**) predicted result by Random Forest.

Process Parameter | Min. Value | Max. Value | Distribution |
---|---|---|---|

Part insert temperature in °C | 20 | 240 | Modified Log-normal |

Mold temperature in °C | 30 | 80 | uniform |

Flow rate in cm${}^{3}$/s | 10 | 100 | uniform |

Process Parameter | Min. Value | Max. Value |
---|---|---|

Part insert temperature in °C | 50 | 160 |

Melt temperature in °C | 240 | 240 |

Mold temperature in °C | 50 | 80 |

Packing pressure in MPa | 60 | 90 |

Flow rate in cm${}^{3}$/s | 50 | 100 |

Method | Hyperparameters | Variation Range | # Steps | Best Parameters Rib Structure | Best Parameters Demonstrator |
---|---|---|---|---|---|

XGBoost | Learning rate | 0.1–1 | 10 | 0.7 | 0.4 |

# Estimators | 10–500 | 7 | 500 | 500 | |

Random Forest | Max depth | 10–70 | 4 | 50 | 70 |

Min samples leaf | 1–10 | 5 | 1 | 1 | |

# Estimators | 10–500 | 9 | 100 | 500 | |

Polyn. Regr. | Degree | 1–7 | 7 | 4 | 4 |

Grad Boost | Learning rate | 0.1–1 | 10 | 0.7 | 0.4 |

# Estimators | 10–500 | 7 | 500 | 500 | |

Decision Tree | Max depth | 1–None | 7 | None | 200 |

Min samples leaf | 1–10 | 10 | 6 | 3 | |

AdaBoost | Learning rate | 0.1–1 | 10 | 0.7 | 1 |

# Estimators | 10–100 | 7 | 30 | 100 |

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## Share and Cite

**MDPI and ACS Style**

Hürkamp, A.; Gellrich, S.; Ossowski, T.; Beuscher, J.; Thiede, S.; Herrmann, C.; Dröder, K. Combining Simulation and Machine Learning as Digital Twin for the Manufacturing of Overmolded Thermoplastic Composites. *J. Manuf. Mater. Process.* **2020**, *4*, 92.
https://doi.org/10.3390/jmmp4030092

**AMA Style**

Hürkamp A, Gellrich S, Ossowski T, Beuscher J, Thiede S, Herrmann C, Dröder K. Combining Simulation and Machine Learning as Digital Twin for the Manufacturing of Overmolded Thermoplastic Composites. *Journal of Manufacturing and Materials Processing*. 2020; 4(3):92.
https://doi.org/10.3390/jmmp4030092

**Chicago/Turabian Style**

Hürkamp, André, Sebastian Gellrich, Tim Ossowski, Jan Beuscher, Sebastian Thiede, Christoph Herrmann, and Klaus Dröder. 2020. "Combining Simulation and Machine Learning as Digital Twin for the Manufacturing of Overmolded Thermoplastic Composites" *Journal of Manufacturing and Materials Processing* 4, no. 3: 92.
https://doi.org/10.3390/jmmp4030092