# Neuro-Fuzzy Model Evaluation for Enhanced Prediction of Mechanical Properties in AM Specimens
## 4 Methodological Framework for Enhancing ANFIS Model
### The Initial Model  
For the initial model creation, nine inputs were selected based on the FFF AM process, PLA material, and bending test: (1) infill pattern, (2) infill percentage, (3) layer thickness, (4) speed, (5) extruder temperature, (6) bed temperature, (7) position on printer bed, (8) incline against printer bed, and (9) raster angle.  
For a fair comparison between the initial and the proposed model, the same experimental data were used as in previous work [15], as presented in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Infill Pattern** & **Infill (\%)** & **Layer Thickness (mm)** & **Speed (mm/s)** & **Temperature (\({}^{\circ}\)C)** & **Bed Temperature (\({}^{\circ}\)C)** & **Position on Bed** & **Twist Angle (\({}^{\circ}\))** & **Inclination (\({}^{\circ}\))** \\ \hline
2 & 75 & 0.1 & 50 & 200 & 60 & 3 & 1 & 5 \\ \hline
3 & 100 & 0.1 & 50 & 200 & 60 & 5 & 1 & 7 \\ \hline
2 & 75 & 0.2 & 50 & 200 & 60 & 5 & 1 & 5 \\ \hline
2 & 100 & 0.2 & 50 & 200 & 60 & 1 & 1 & 5 \\ \hline
3 & 50 & 0.2 & 50 & 200 & 60 & 3 & 1 & 7 \\ \hline
2 & 50 & 0.3 & 50 & 200 & 60 & 5 & 1 & 5 \\ \hline
3 & 75 & 0.3 & 50 & 200 & 60 & 1 & 1 & 7 \\ \hline \end{tabular}
\end{table}
Table 1: Datasheet of the ANFIS bending model.  
Figure 5: Stress-strain curve of bending test (indicative). Colored lines represent the five iterations of the test and the black the average.  
Based on the collected data, an initial ANFIS model is created that is then parameterized to predict three outputs: stress, strain, and [PERSON]'s modulus. The model is then trained using a subset of the data.  
In the context of AM, ANFIS's architecture is well-suited to predict mechanical properties affected by multiple, interdependent process parameters. Specifically, experimental data from AM processes, such as temperature, infill percentage, and layer thickness, were used to train the ANFIS model, enabling it to generalize across a range of AM configurations. Similarly, in this study, the ANFIS model is employed to predict the mechanical properties of AM-fabricated parts, focusing on refining the layer thickness, printing speed, and material characteristics to achieve accurate output predictions.  
Input data is manually divided into training and checking subsets, using a predefined data percentage of 80% for training and 20% for checking. The initial model configuration includes using a subtractive clustering algorithm with the following parameters: range of influence (ROI), 0.5; squash factor (SQ), 1; accept ratio, 0.5; and reject ratio, 0.15.  
We implemented subtractive clustering to partition the input space and derive fuzzy rules for the ANFIS model. This approach calculates the potential of data points based on their proximity to others and iteratively selects cluster centers in regions of high density. Following the method outlined in [26], cluster centers were refined to minimize overlap and ensure precise rule generation. This technique was selected for its computational efficiency and ability to model nonlinear relationships effectively, as demonstrated in previous works, such as in [32].