# Neuro-Fuzzy Model Evaluation for Enhanced Prediction of Mechanical Properties in AM Specimens
## 5 Model Implementation and Performance Analysis
### Dataset Preparation and Partitioning  
In this study, the dataset is divided into two subsets: one for training and one for checking. Based on standard practices in the literature, an 80%/20% split is chosen for training and checking, respectively. The primary objective of this approach is to mimic the randomness of human selection, ensuring that both subsets represent the full range of the dataset's variability.  
To achieve representative sampling across the full dataset range, a statistical normal distribution was applied to the output data. The mean \((\mu)\) and standard deviation \((\sigma)\) of the data were calculated, and a confidence interval was established using the empirical rule, defined as \(\mu\pm 1\sigma\)[33], as depicted in Figure 7. This method resulted in the formation of two distinct groups: one comprising data points within the confidence interval (high values) and the other containing data points outside this interval (low values).  
Figure 6: Flowchart diagram of the proposed model.  
These two groups are then divided to enhance the randomness of the subset data. This division is done in such a way that both the training and checking subsets included a mix of data points from within the \(\mu\pm 1\sigma\) range and from the broader range extending beyond \(\mu\pm 3\sigma\) in a percentage of 70/30, respectively. This approach guarantees that each subset captures data representing the entire spectrum of values. The process begins with forming the training subset, followed by creating the checking subset from the remaining data. This procedure is repeated iteratively, ensuring that the initial data appear at least once in the checking subset, thus achieving a more balanced and representative sampling.  
To select the most appropriate set of values from the iterative process that preceded it, a comparison method was used. More specifically, a subtractive clustering model using ANFIS was chosen, and each set was evaluated for its performance. In this way, the evaluation is objective, as the same algorithm is used for each set of values, ensuring that effective value placement is used for training and checking data.  
Figure 8 presents scatter plots that illustrate the relationship between RMSE and R\({}^{2}\) across multiple iterations of the ANFIS model for three mechanical properties: maximum stress, maximum strain, and Young's modulus. The plots reveal an inverse relationship, where lower RMSE values are associated with higher R\({}^{2}\) values, indicating improved model performance. In these diagrams, the y-axis displays the evaluation metrics (RMSE and R\({}^{2}\)), while the x-axis represents the iterations generated from the iterative process.  
As the model is refined through iterations, the scatter plots show data points converging toward regions where R\({}^{2}\) is high and RMSE is low. This indicates that successive iterations are achieving both greater predictive accuracy (higher R\({}^{2}\)) and lower prediction error (lower RMSE). This trend suggests that the iterative refinement process is effectively adjusting the model's parameters, enhancing its reliability (consistently accurate across different datasets) and precision (with smaller deviations between predicted and actual values). Consequently, the model improves its ability to predict the mechanical properties of 3D-printed parts as the iterations progress.  
Figure 7: Normal distribution for maximum stress.