ML-Assisted Pattern Recognition for UTS Estimation in FDM PLA Specimens

2.1. Specimen Fabrication & Parameters

A dataset was generated from 31 PLA specimens fabricated via FDM. Four key process parameters were varied to create the feature set for the ML models:

• Infill Percentage: Density of the internal structure.
• Layer Height: Thickness of each deposited layer.
• Print Speed: Nozzle travel speed during deposition.
• Extrusion Temperature: Temperature of the molten filament.

The UTS of each specimen was measured experimentally and then categorized into classes (e.g., "High" or "Low" UTS) to formulate a supervised classification problem.

2.2. Machine Learning Algorithms

Four distinct supervised classification algorithms were implemented and compared:

1. Logistic Classification: A linear model for binary classification.
2. Gradient Boosting Classification: An ensemble technique that builds sequential trees to correct errors.
3. Decision Tree: A non-parametric model that splits data based on feature values.
4. K-Nearest Neighbor (KNN): An instance-based learning algorithm that classifies a point based on the majority class of its 'k' nearest neighbors in the feature space.

Model performance was evaluated using metrics like F1 Score and Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC).

3.1. Algorithm Performance Comparison

The experimental results provided a clear hierarchy of model effectiveness for this specific task:

While the Decision Tree matched KNN's F1 score, the AUC metric revealed KNN's superior ability to distinguish between UTS classes across all classification thresholds.

3.2. K-Nearest Neighbor Superiority

The KNN algorithm emerged as the most favorable model. Its success can be attributed to the nature of the dataset and problem:

• Local Similarity: UTS is likely determined by complex, non-linear interactions between parameters. KNN's local approximation captures these patterns without assuming a global functional form, unlike linear models (Logistic Regression).
• Robustness to Small Datasets: With only 31 data points, simpler, non-parametric models like KNN and Decision Trees are less prone to overfitting compared to complex ensemble methods like Gradient Boosting, which may require more data to generalize effectively.
• Interpretability vs. Performance: While a Decision Tree offers clear rule-based interpretation, its performance (AUC) was slightly inferior to KNN, suggesting KNN's distance-based reasoning was more aligned with the underlying data geometry for this property prediction task.

Chart Description (Implied): A bar chart would effectively visualize the F1 scores (all at 0.71 for KNN and DT) and a separate bar chart or table would highlight the key differentiator: the AUC scores, with KNN's bar significantly higher (0.79) than the others, clearly demonstrating its superior discriminative power.

4.1. Mathematical Formulation

The core of the KNN algorithm for classification can be formalized. Given a new input feature vector $\mathbf{x}_{\text{new}}$ (comprising infill %, layer height, etc.), its class $C$ is determined by:

1. Distance Calculation: Compute the distance (e.g., Euclidean) between $\mathbf{x}_{\text{new}}$ and all training vectors $\mathbf{x}_i$ in the dataset:

   $d_i = ||\mathbf{x}_{\text{new}} - \mathbf{x}_i||_2$

2. Neighbor Identification: Identify the $k$ training samples with the smallest distances $d_i$.
3. Majority Voting: Assign the class $C$ that is most frequent among these $k$ neighbors:

   $C(\mathbf{x}_{\text{new}}) = \arg\max_{c} \sum_{i=1}^{k} I(C_i = c)$

   where $I(\cdot)$ is the indicator function, and $C_i$ is the class of the $i$-th neighbor.

The AUC metric, where KNN excelled, represents the probability that the model ranks a random positive instance higher than a random negative instance. An AUC of 0.79 indicates a 79% chance of correct ranking, signifying good discriminative ability.

4.2. Analysis Framework Example

Scenario: An engineer wants to predict if a new set of FDM parameters will yield "High" or "Low" UTS without printing.

Framework Application (Non-Code):

1. Data Representation: The new parameter set {Infill: 80%, Layer Height: 0.2mm, Speed: 60mm/s, Temp: 210°C} is formatted as a feature vector.
2. Model Query: This vector is fed into the trained KNN model ($k=5$, using Euclidean distance, standardized features).
3. Neighborhood Analysis: The model calculates distances to all 31 historical prints. It finds the 5 most similar past prints based on parameter proximity.
4. Decision & Confidence: If 4 of those 5 similar past prints had "High" UTS, the model predicts "High" for the new set. The proportion (4/5 = 80%) acts as a confidence score. The AUC score of 0.79 gives an overall trust in the model's ranking ability across all possible thresholds.
5. Action: The engineer uses this prediction to approve the parameters for a critical part or decide to adjust them before a costly print.