A Neural Network-Based Approach to Estimate Printing Time and Cost in L-PBF Projects
Abstract
1. Introduction
2. Research Background
2.1. Machine Learning
ML in Production Techniques
- Data Collection: Gather relevant data from various sources pertinent to the AM process, such as sensor data and production logs.
- Storage: Collected data and the model’s weights must be stored securely on an available server, ensuring they are organized for easy access during model training.
- Model Training: Training an ML algorithm with adequate data. This includes selecting algorithms, model selection, training, setting, and validating model performance.
- Model Registration: After training, another critical step in streamlining the model lifecycle from development to production deployment is managing machine learning model versions, particularly if a continual learning iteration is planned within the production pipeline.
- API Gateway: The system must implement a web service and RESTful API to interact with and serve client calls.
- Continual Learning: A solution to avoid the deterioration over time of the model’s performance. This is due to the dynamic nature of the AM production environment, where the high variability in material properties and process parameters demands adaptive learning models capable of real-time adjustments.
- Monitoring: Monitoring and logging are essential for analyzing job status (such as training job failures and successes), platform health, and various metrics (including inference error rates, data drift, and training loss).
- Model Endpoint: The trained model is deployed as an endpoint, a web service tool that allows real-time predictions based on incoming requests routed through an API Gateway.
2.2. Machine Learning Applications in Design for Additive Manufacturing
3. Proposed Approach
4. Case Study
4.1. Training Results
4.2. Web-Service Platform Development
- Code: the score.py script that implements init() (model loading) and run() (prediction).
- Compute: a dedicated container instance with 8 GB RAM and 4 vCPU, provisioned from the Stock Keeping Unit (SKU) selected during deployment creation.
- Scikit-learn runtime: the framework layer installed via the Azure ML Environment image.
- Model: the serialized estimator, which resides in the container’s mounted storage and is loaded into memory at start-up.
5. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Model | When to Use | AM Applications |
---|---|---|
Support Vector Machine (SVM) | SVM is effective in solving classification problems involving datasets with numerous features, especially when using the kernel trick to handle complex, non-linear decision boundaries. It performs well on small datasets, especially when classes are separable. | Print success estimation, defect detection, process optimization, and material property analysis [21]. |
Decision Tree (DT) | DT can be useful for datasets with numerical and categorical features and can handle non-linear decision boundaries. DT performs optimally with small to medium-sized datasets and can also be used with imbalanced data. However, it is susceptible to overfitting, particularly when the tree becomes excessively deep. | Defect classification, process parameter optimization, print quality analysis, and manufacturability prediction [22]. |
Random Forest (RF) | RF excels at handling datasets with numerous features and complex non-linear interactions. | Image-based porosity classification [23]. |
K-Nearest Neighbors (KNN) | KNN does not assume any predefined distribution for the underlying data. It is non-parametric and suitable for datasets with arbitrary distributions. It works well with numerical and categorical features. It requires careful tuning and can be computationally intensive for large datasets. | Surface roughness prediction [24]. |
Naive Bayes (NB) | NB performs effectively with relatively small datasets, with good results for text classification or categorical data. The algorithm functions optimally with clean, noise-free datasets, and it can handle imbalanced data by estimating class probabilities. | Defect classification, material composition analysis, printability prediction, and anomaly detection [25]. |
Convolutional Neural Networks (CNN) | CNNs excel at automatically learning spatial hierarchies of features, making them suitable for datasets with strong local patterns or visual characteristics. They are ideal for large datasets because they can generalize well. | Quality and process control [26]. |
Recurrent Neural Network (RNN) | RNNs are designed to handle sequential data, making them suitable for datasets with critical temporal or sequential dependencies. RNNs are effective for datasets where the current input is influenced by previous states, allowing the model to capture dynamic patterns over time. | Process monitoring, fault detection over time, predictive maintenance, and real-time monitoring [27]. |
Model | When to Use | AM Applications |
---|---|---|
Linear Regression (LR) | LR works best with numerical datasets that are well-structured, clean, and free from significant outliers. The method is sensitive to extreme values and unsuitable for datasets with strong non-linear patterns. It performs well with small to moderately sized datasets. | Process parameter optimization [28]. |
Polynomial Regression (PR) | PR is particularly suitable for small to moderately sized datasets where polynomial terms of the independent variables can approximate the non-linearity. This method works best when the dataset is clean and free from outliers, as higher-degree polynomials are sensitive to noise and overfitting. | Process parameter modeling and optimization [29]. |
Support Vector Regression (SVR) | SVR excels with small to moderately sized datasets, especially when the data has many features and the relationships are non-linear. SVR can capture intricate, non-linear. SVR is sensitive to noise and outliers. | Real-time monitoring for defect detection [30]. |
Gradient Boosting Machines (GBM) | GBMs are well-suited for moderately sized datasets with diverse feature types, including numerical and categorical variables. GBR performs well even with noisy data or datasets with missing values, as the boosting mechanism reduces bias and variance. | Melt pool shape prediction with process parameters data [31]. |
Deep Neural Networks (DNN) | DNNs excel in scenarios with high-dimensional data and multiple features, especially when sufficient labeled data is available to train the network effectively. They perform best with clean, well-preprocessed datasets, as they are sensitive to noise and can overfit smaller datasets without proper regularization techniques, such as dropout or weight decay. | Print time prediction, defect severity estimation, material property, and multi-parameter optimization [32]. |
Recurrent Neural Network (RNN) | RNN is ideal for datasets with ordered structures, such as sensor data, production logs, process monitoring logs, or sequential datasets. The model requires large, clean, sequential datasets to learn effectively, as they are sensitive to noise and data quality. | Time-series prediction for print times, process monitoring and optimization, fault prediction, and tracking of material property evolution [33]. |
Hyperparameter | Value/Type |
---|---|
Hidden layers | 5 |
Neuron per hidden layer | 25, 50, 100, 50, 25 |
Activation function | ReLU |
Solver | Adam |
Maximum iteration | 1000 |
NN_1 | Train Metrics | Test Metrics |
---|---|---|
Support Volume 0° | R2: 0.9975 | R2: 0.9973 |
MSE: 0.0022 | MSE: 0.0037 | |
MAE: 0.0338 | MAE: 0.0416 | |
Support Volume 30° | R2: 0.9930 | R2: 0.9912 |
MSE: 0.0062 | MSE: 0.0125 | |
MAE: 0.0602 | MAE: 0.0704 |
NN_2 | Train Metrics | Test Metrics |
---|---|---|
NN_2_0: Printing Time 0° | R2: 0.9799 | R2: 0.9864 |
MSE: 0.0191 | MSE: 0.0163 | |
MAE: 0.0992 | MAE: 0.1036 | |
NN_2_30: Printing Time 30° | R2: 0.9865 | R2: 0. 9846 |
MSE: 0.0122 | MSE: 0.0212 | |
MAE: 0.0811 | MAE: 0.1023 |
NN_3 | Train Metrics | Test Metrics |
---|---|---|
NN_3_0: Analytical Cost 0° | R2: 0.9984 | R2: 0.9965 |
MSE: 0.0015 | MSE: 0.0044 | |
MAE: 0.0284 | MAE: 0.0457 | |
NN_3_30: Analytical Cost 30° | R2: 0.9983 | R2: 0.9937 |
MSE: 0.0015 | MSE: 0.0044 | |
MAE: 0.0295 | MAE: 0.0527 |
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Trovato, M.; Amicarelli, M.; Prist, M.; Cicconi, P. A Neural Network-Based Approach to Estimate Printing Time and Cost in L-PBF Projects. Machines 2025, 13, 550. https://doi.org/10.3390/machines13070550
Trovato M, Amicarelli M, Prist M, Cicconi P. A Neural Network-Based Approach to Estimate Printing Time and Cost in L-PBF Projects. Machines. 2025; 13(7):550. https://doi.org/10.3390/machines13070550
Chicago/Turabian StyleTrovato, Michele, Michele Amicarelli, Mariorosario Prist, and Paolo Cicconi. 2025. "A Neural Network-Based Approach to Estimate Printing Time and Cost in L-PBF Projects" Machines 13, no. 7: 550. https://doi.org/10.3390/machines13070550
APA StyleTrovato, M., Amicarelli, M., Prist, M., & Cicconi, P. (2025). A Neural Network-Based Approach to Estimate Printing Time and Cost in L-PBF Projects. Machines, 13(7), 550. https://doi.org/10.3390/machines13070550