# Neuro-Fuzzy Model Evaluation for Enhanced Prediction of Mechanical Properties in AM Specimens
## 5 Model Implementation and Performance Analysis
### ANFIS Parameter Tuning and Performance Evaluation
Figure 11 depicts surface plots that illustrate the impact of two key parameters, ROI SQ, on the RMSE for predicting three mechanical properties: maximum stress, maximum strain, and Young's modulus. The surface plots provide a visual representation of how changes in ROI and SQ influence the model's prediction error. Lower RMSE values, indicated by the darker regions on the plots, suggest improved model performance. Adjusting the ROI in subtractive clustering led to significant changes in the prediction accuracy, revealing the model's sensitivity to parameter tuning. Similarly, variations in SQ showed a notable impact on the RMSE, with optimal SQ values helping to maintain a balance between capturing details and avoiding overfitting. The plots reveal specific ranges for ROI and SQ where the RMSE is minimized, highlighting the importance of carefully fine-tuning these parameters to enhance the predictive accuracy of the ANFIS model. After examining the impact of the parameters, experiments were performed to compare grid partitioning and subtractive clustering. The initial ANFIS model exhibited an average value error of \(\pm\)1.35 MPa and an accuracy of 0.77. After applying the subtractive clustering technique, the model improved to an average error value error of \(\pm\)1.15 MPa and an accuracy of 0.83. Subtractive clustering demonstrated superior adaptability in capturing nonlinear relationships, particularly in cases with noisy data, compared to grid partitioning, which exhibited limitations in processing high-dimensional input data efficiently. As shown, the Gaussian membership function proved to be the most effective for both techniques, grid partition and subtractive clustering. The grid partition algorithm resulted in an average error of \(\pm\)2.24 MPa and an accuracy of 0.37, while subtractive clustering achieved significantly better results, with a 49% lower error and 55% higher accuracy. These findings highlight the importance of selecting both the appropriate membership function and an effective model configuration to accurately capture the inherent correlations  
Figure 11: Surface plots RMSE across different combinations of ROI and SQ between (**a**) maximum stress dataset, (**b**) maximum strain dataset and (**c**) [PERSON]’s modulus dataset. Figure 12 illustrates the predicted versus actual stress values for nine datasets, revealing key trends in the performance of the three models: initial, subtractive clustering (SC), and grid partitioning (GP). The stress value is slightly overestimated, with the GP model providing the closest prediction to the actual value. At data point 2, a significant overestimation is observed, particularly by the SC model, as the actual stress value is substantially lower. For data points 3 to 9, the predictions closely align with the actual values, especially for smaller stress magnitudes, with the GP model consistently demonstrating a reliable performance across the dataset. Overall, the models exhibit higher accuracy for moderate stress values, while larger deviations are evident in extreme cases, such as at data point 2. The initial ANFIS model for maximum strain exhibited an average error of \(\pm\)1.34 with an accuracy of 0.58, which improved to an average error of \(\pm\)0.96 and an accuracy of 0.78. This improvement reflects a 28% reduction in error and a 25% increase in accuracy as depicted in Figure 13. In this case, the best membership function was the pi-shaped function for the gird partition algorithm, while for subtractive clustering, it remained Gaussian. The two techniques employ distinct methods for handling data subsets and different categorization, so they use different membership functions as the mathematical approach of the model itself changes. Figure 13 illustrates the predicted versus actual strain values for nine data points. At data point 1, all models overestimate the strain, with the GP model providing the closest prediction to the actual value.