# Prediction of Dimensional Changes of Low-Cost Metal Material Extrusion Fabricated Parts Using Machine Learning Techniques

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials and Equipment

#### 2.2. Process Workflow

#### 2.3. Dataset Preparation

#### 2.4. Prediction Algorithms

#### 2.4.1. LR

**y**=

**Xθ**+

**ε**

**y**is the vector of response variables,

**X**is the matrix of independent variables,

**θ**is the coefficient vector, and

**ε**is the vector of the error term. In this research, the CAD dimension is the response variable. The 8 independent variables are layer thickness (LT), sintering temperature (ST), ramp ratio (RR), nozzle temperature (NT), printing speed (PS) and the final length (L), width (W), and height (H). The LR algorithm will generate the

**θ**and

**ε**and the matrix of independent variables X is shown below:

**X**=

**[LT ST RR NT PS L W H]**

#### 2.4.2. LRI

**y**=

**Xθ**+

**ε**

**y**is the vector of response variables,

**X**is the matrix of independent variables,

**θ**is the coefficient vector and

**ε**is the vector of the error term. In this research, the CAD dimension is the response variable. However, the matrix of independent variables X is different, The

**X**for LRI is shown below:

**X**=

**[LT ST RR NT PS L W H LT × L LT × W LT × H ST × L ST × W ST × H**

**RR × L RR × W RR × H NT × L NT × W NT × H PS × L PS × W PS × H]**

#### 2.4.3. NN

## 3. Results and Discussions

#### 3.1. Printing Accuracy

#### 3.2. Analysis of Dimensional Variations of CAD and Sintered Samples

#### 3.2.1. Results of Prediction by LR

**CAD_L**=

**X**×

**[−0.000220 0.0649 0.0136 0.000300 −0.0321 0.647 0.118 0.0793]**+

^{T}**[−0.0231]**

**CAD_W**=

**X**×

**[−0.00733 0.0698 0.0134 −0.0364 −0.100 0.250 0.556 0.0801]**+

^{T}**[0.0260]**

**CAD_H**=

**X**×

**[−0.00146 0.0633 0.0121 −0.00729 −0.0517 0.517 0.219 0.0757]**+

^{T}**[−0.0154]**

#### 3.2.2. Results of Prediction by LRI

**CAD_L**=

**X × [−0.013 1.112 0.330 −0.613 −0.322 −2.639 14.514 1.281 0.558 −0.660 0.104 7.394**

**−28.133 0.787 −0.100 −0.386 0.119 −6.460 16.737 −1.964 2.305 −2.122 0.010]**+

^{T}**[−0.317]**

**CAD_W**=

**X × [−0.099 1.354 0.505 −0.690 0.153 −15.797 30.514 4.166 0.400 −0.451 0.165 10.959**

**−36.130 0.808 −0.108 −0.606 0.138 4.270 8.337 −4.605 0.917 −1.459 0.047]**+

^{T}**[−0.607]**

**CAD_H**=

**X × [−0.124 1.134 0.294 −0.582 −0.189 −1.156 10.964 3.391 0.773 −0.718 0.121 7.144**

**−28.264 0.822 −0.132 −0.307 0.119 −7.583 20.620 −4.016 1.923 −2.281 0.290]**+

^{T}**[−0.431]**

#### 3.2.3. Results of Prediction by NN

## 4. Error Metrics

^{2}) values and mean square error (MSE) metrics was used to test the performance of the algorithms.

^{2}is the proportion of the variance in the dependent variable that is predictable from the independent variable [40]. The equation is given below:

^{2}= 1 − RSS/TSS

^{2}s of LR and LRI are shown in Table 6. LRI has a larger R

^{2}than LR. So, the correlation of LRI is more reliable than LR.

## 5. Verification

## 6. Conclusions

- The three types of algorithms behave differently in predicting CAD dimensions. NN has the smallest MSE (0.00228 in length, 0.0117 in width, and 0.0000878 in height) and, hence, will be the best algorithm to predict the initial CAD dimensions.
- Since both LRI and NN have smaller MSE than LR, which means that LRI and NN are more accurate than LR, these independent parameters have internal interactions.
- After verification, the errors between the real and target dimensions are negligible; the accuracy of the prediction by NN is acceptable.
- For NN that more hidden layers can be added to develop deep model that better capture complex behavioral patterns within the data leading to better prediction accuracy. Our results support this claim since the NN gave the best results.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Samples in different status (

**a**) CAD model (

**b**) Bronze-PLA sample (

**c**) sample after sintering and polishing.

**Figure 4.**Schematic of the NN [38].

Printing Parameters | Values | ||
---|---|---|---|

Layer Thickness (mm) | 0.1 | 0.2 | 0.3 |

Nozzle Temperature (°C) | 220 | 230 | 240 |

Printing Speed (mm/s) | 10 | 15 | 20 |

Sintering Parameters | Values | ||||||||
---|---|---|---|---|---|---|---|---|---|

Layer Thickness (mm) | 0.1 | 0.2 | 0.3 | ||||||

Sintering Temperature (°C) | 870 | 875 | 880 | 885 | 890 | 895 | 900 | ||

Ramp Ratio (°C/min) | 2 | 3 | 4 |

Printing Parameters | Sintering Parameters | Sample Type | Dimensions of the Sample | ||
---|---|---|---|---|---|

Length (mm) | Width (mm) | Height (mm) | |||

0.1 mm 240 °C 10 mm/s | 0.1 mm 870 °Ca 2 °C/mm | CAD | 20 | 15 | 6 |

Non-sintered | 20.452 | 15.318 | 6.226 | ||

Sintered | 18.787 | 13.922 | 5.236 |

Number of hidden layers | 5 |

Number of neurons in each hidden layer | 128 |

Activation function at hidden layers | ReLU |

Dimensions | Length | Width | Height |
---|---|---|---|

p-value | 2.99 × 10^{−8} | 1.097 × 10^{−4} | 1.272 × 10^{−6} |

Method | R^{2} Value | ||
---|---|---|---|

Length | Width | Height | |

LR | 0.891 | 0.921 | 0.885 |

LRI | 0.989 | 0.995 | 0.999 |

Method | Mean Square Error | ||
---|---|---|---|

Length (mm) | Width (mm) | Height (mm) | |

LR | 0.269 | 0.183 | 0.0119 |

LRI | 0.118 | 0.121 | 0.00532 |

NN | 0.00228 | 0.0117 | 0.0000878 |

Printing Parameter | Sintering Parameter | ||
---|---|---|---|

Layer Thickness (mm) | 0.3 | Layer Thickness (mm) | 0.3 |

Nozzle Temperature (°C) | 220 | Sintering Temperature (°C) | 880 |

Printing Speed (mm/s) | 15 | Ramp Ratio (°C/min) | 3 |

Target Dimensions | Predicted CAD Dimensions | Final Dimensions after Sintering | |
---|---|---|---|

Length (mm) | 20 | 20.905 | 19.998 |

Width (mm) | 15 | 15.394 | 14.996 |

Height (mm) | 6 | 6.154 | 6.001 |

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**MDPI and ACS Style**

Zhang, Z.; Femi-Oyetoro, J.; Fidan, I.; Ismail, M.; Allen, M. Prediction of Dimensional Changes of Low-Cost Metal Material Extrusion Fabricated Parts Using Machine Learning Techniques. *Metals* **2021**, *11*, 690.
https://doi.org/10.3390/met11050690

**AMA Style**

Zhang Z, Femi-Oyetoro J, Fidan I, Ismail M, Allen M. Prediction of Dimensional Changes of Low-Cost Metal Material Extrusion Fabricated Parts Using Machine Learning Techniques. *Metals*. 2021; 11(5):690.
https://doi.org/10.3390/met11050690

**Chicago/Turabian Style**

Zhang, Zhicheng, James Femi-Oyetoro, Ismail Fidan, Muhammad Ismail, and Michael Allen. 2021. "Prediction of Dimensional Changes of Low-Cost Metal Material Extrusion Fabricated Parts Using Machine Learning Techniques" *Metals* 11, no. 5: 690.
https://doi.org/10.3390/met11050690