# Assessment of the Critical Defect in Additive Manufacturing Components through Machine Learning Algorithms

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## Abstract

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## 1. Introduction

## 2. Machine Learning and Defect Size: Algorithms

#### 2.1. Defects in AM Components

#### 2.2. Process Parameters and Defects in AM Components

- Building orientation: several experimental results have proved the influence of the building orientation on the defect size and, accordingly, on the fatigue strength. In the following, with 0° and 90° the authors refer to a building orientation with the specimen axis parallel and perpendicular to the building platform (horizontal and vertical building orientation), respectively [23,24].
- Power and scan speed: these two parameters are strongly correlated, since the energy per unit length, dependent on both input power and scan speed, controls the formation of pores or lack of fusion defects [25].
- Powder size: the powder size affects the defect formation. For example, in [28,29], it has been shown that defects tend to be larger in parts produced with smaller powder, thus affecting the fatigue response. In the following analysis, the average powder size has been considered as the input parameter for the developed ML algorithms.

_{90}, i.e., the material volume subjected to a stress amplitude above 90% of the maximum applied stress, is considered as the loaded volume. This parameter can reliably model the volume at risk of crack nucleation in components subjected to fatigue loads [4]. Indeed, considering the whole component volume can be rather conservative, since it has been shown experimentally that only the region subjected to a stress amplitude close to the maximum stress is at risk of crack nucleation [4] and, moreover, AM components are generally subjected to a non-uniform stress amplitude.

#### 2.3. Neural Networks Architecture

#### 2.3.1. NN Architecture: Probability of a Specific Defect Size (Probability ML)

_{90}. Figure 2 visualizes the input parameters and the output of the developed ML algorithms.

#### 2.3.2. NN Architecture: LEVD Distribution Parameters (LEVD ML)

#### 2.4. k-Fold Cross Validation

## 3. Experimental Validation

#### 3.1. AlSi10Mg Validation

#### 3.1.1. Probability ML Validation

_{exp}, and the ordinate axis reporting the probability estimated with the ML algorithm, P

_{est}, for k = 4 and by considering the training and the validation data.

#### 3.1.2. LEVD ML Algorithm: Validation

^{3}and 2300 mm

^{3}). Figure 11 shows the Gumbel plot of experimental data in [30] for defects measured on the fracture surfaces of specimens built in a horizontal (Figure 11a) and vertical direction (Figure 11b) and with a risk volume of 2300 mm

^{3}. These are the validation datasets for k = 2 (Figure 11a) and k = 3 (Figure 11b), and therefore have not been considered for the training. In Figure 11, the blue line is the LEVD estimated from the experimental data, whereas the green line is the ML LEVD.

#### 3.2. Ti6Al4V Validation

#### 3.2.1. Probability ML Validation

_{exp}, and the ordinate axis the ML probability, P

_{est}.

#### 3.2.2. LEVD ML Algorithm Validation

## 4. Discussion

## 5. Conclusions

- Probability ML and LEVD ML have shown a high predicting capability for both AlSi10Mg and Ti6Al4V datasets. A k-fold cross-validation scheme has been used for the validation, proving that both approaches can be reliably used for the analysis of defects in SLM components. The loss functions with respect to the fold considered for the validation were almost constant, thus confirming the good performances of both architectures.
- LEVD ML has been shown to work well even for datasets with a trend significantly different from that of the other datasets considered for the training process. On the other hand, the Probability ML algorithm tends to overestimate the probability associated with each defect, being less conservative.
- The trend in the Gumbel Plot estimated with the Probability ML algorithm can show a large scatter and, for the same process parameters, it is not ensured that larger defects are characterized by larger probabilities. This can be solved by increasing the number of training data. On the other hand, the LEVD ML “embeds” the LEVD statistical model based on the experimental evidence, thus overcoming this criticality.
- The predicting capability of both developed ML algorithms may be enhanced by adding more input factors, whose influence on the defect size population is still debated in the literature, such as heat treatment temperature, the building platform heating temperature, the powder size ranges and the SLM production system. However, the number of available datasets for the training process should be significantly increased.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**ML algorithm which provides in output the probability associated with a defect with size $\sqrt{{a}_{c}}$ (Probability ML).

**Figure 3.**ML algorithm which provides in output the location and the scale parameters of the LEVD of $\sqrt{{a}_{c}}$ for a given set of process parameters and risk-volume.

**Figure 6.**k-fold cross-validation: loss function with respect to the k-fold considered for the validation.

**Figure 8.**Validation of the investigated Probability ML algorithm: (

**a**) Gumbel plot for the validation dataset for k = 4; (

**b**) P-P plot for k = 4 by considering the training and the validation data.

**Figure 9.**k-fold cross-validation for the LEVD ML: loss function with respect to the k-fold considered for the validation.

**Figure 11.**Analysis of the capability of ML LEVD of predicting size effect: (

**a**) Gumbel plot for k = 2, showing the validation fold obtained through tests on horizontal specimens with a risk volume of 2300 mm

^{3}. (

**b**) Gumbel plot for k = 3, showing the validation fold obtained through tests on vertical specimens with a risk volume of 2300 mm

^{3}.

**Figure 12.**Ti6Al4V datasets considered for training and validating the developed ML algorithms on a Gumbel plot.

**Figure 13.**k-fold cross validation of the Probability ML algorithm: loss function with respect to the fold considered for the validation.

**Figure 14.**Gumbel plot for the k = 1 fold considered for the validation; (

**a**) validation dataset; (

**b**) training data.

**Figure 15.**Validation of the investigated Probability ML algorithm: (

**a**) Gumbel plot for the validation dataset for k = 3; (

**b**) P–P plot for k = 3 by considering the training and the validation data.

**Figure 16.**k-fold cross-validation: loss function with respect to the k-fold considered for the validation.

**Figure 17.**Gumbel plot for k = 1 considered for the validation; (

**a**) validation fold; (

**b**) training fold.

**Table 1.**Range of process parameters for the datasets on AlSi10Mg considered for the validation of the developed ML algorithms.

Orientation | Power | Speed | Hatch Distance | Layer Thickness | Average Powder Size | Risk Volume |
---|---|---|---|---|---|---|

[W] | [mm/s] | [$\mathsf{\mu}\mathrm{m}]$ | [$\mathsf{\mu}\mathrm{m}]$ | [$\mathsf{\mu}\mathrm{m}$] | [mm^{3}] | |

[0, 90] | [220, 380] | [600, 1650] | [130, 190] | [30, 60] | [30, 41.5] | [250, 2300] |

**Table 2.**Range of process parameters for the datasets on Ti6Al4V considered for the validation of the developed ML algorithms.

Orientation | Power | Speed | Hatch Distance | Layer Thickness | Average Powder Size | Risk Volume |
---|---|---|---|---|---|---|

[W] | [mm/s] | [$\mathsf{\mu}\mathrm{m}]$ | [$\mathsf{\mu}\mathrm{m}]$ | [$\mathsf{\mu}\mathrm{m}$] | [mm^{3}] | |

[0, 90] | [175, 400] | [150, 1400] | [120, 140] | [30, 60] | [34, 45] | [84, 1204] |

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**MDPI and ACS Style**

Tridello, A.; Ciampaglia, A.; Berto, F.; Paolino, D.S.
Assessment of the Critical Defect in Additive Manufacturing Components through Machine Learning Algorithms. *Appl. Sci.* **2023**, *13*, 4294.
https://doi.org/10.3390/app13074294

**AMA Style**

Tridello A, Ciampaglia A, Berto F, Paolino DS.
Assessment of the Critical Defect in Additive Manufacturing Components through Machine Learning Algorithms. *Applied Sciences*. 2023; 13(7):4294.
https://doi.org/10.3390/app13074294

**Chicago/Turabian Style**

Tridello, Andrea, Alberto Ciampaglia, Filippo Berto, and Davide Salvatore Paolino.
2023. "Assessment of the Critical Defect in Additive Manufacturing Components through Machine Learning Algorithms" *Applied Sciences* 13, no. 7: 4294.
https://doi.org/10.3390/app13074294