Issue 73

R. K. Singh et alii, Fracture and Structural Integrity, 73 (2025) 74-87; DOI: 10.3221/IGF-ESIS.73.06

(c) Figure 7: Compressive strength of PMMA-HAp Composite (a) 5, (b) 15, and (c) 30% volume.

ANN method for predicting mechanical properties A total of 240 observations were synthesized to mimic realistic patterns of Elastic Modulus and Compressive Strength for varying HAp percentages ranging from 5% to 30%. These observations were split into 192 training samples (80%) and 48 testing samples (20%) to evaluate the generalizability of the predictive models. Three machine learning models - Feedforward Neural Network (FFNN), Radial Basis Neural Network (RBNN), and Support Vector Machine (SVM) - were employed to estimate Elastic Modulus and Compressive Strength . Model performance was assessed using metrics such as R², Variance Accounted For (VAF), and Root Mean Square Error (RMSE) [22, 23]. Additionally, a 5-fold cross-validation procedure was implemented for FFNN to validate its stability and consistency. Among the models as given in Tab. 2, RBNN outperformed the others, achieving an R² of 0.590 for Elastic Modulus and 0.988 for Compressive Strength on the testing dataset, with RMSE values of 4.50 GPa and 2.50 MPa, respectively. The ability of RBNN to capture non-linear relationships with high precision highlights its suitability for mechanical property estimation. FFNN, though slightly less accurate, demonstrated stable and reliable predictions, achieving R² values of 0.820 for Elastic Modulus and 0.975 for Compressive Strength on the testing dataset. The corresponding RMSE values for FFNN were 56.39 GPa and 3.00 MPa, indicating slightly higher prediction errors compared to RBNN. SVM, while computationally efficient, showed relatively lower performance, with testing R² values of 0.875 for Elastic Modulus and 0.985 for Compressive Strength. Its RMSE values of 45.71 GPa and 2.20 MPa suggest that the model effectively balances complexity and prediction accuracy. The cross validation results for FFNN revealed consistent R² values across folds, averaging 0.879 for Elastic Modulus and 0.880 for Compressive Strength, further validating its robustness and reliability for this dataset. Overall, the results indicate that RBNN is the most accurate model for predicting mechanical properties, making it ideal for high-precision applications. FFNN provides a balanced approach, offering reliable predictions with lower computational complexity. SVM, while slightly less accurate, remains a viable option for datasets with fewer features or limited non-linearities. These findings emphasize the trade-offs between model accuracy, computational requirements, and data complexity in the context of mechanical property estimation.

Testing R²

Training VAF (%)

Testing VAF (%)

Training RMSE

Testing RMSE

Property

Training R²

Elastic Modulus (RVE) Elastic Modulus (FFNN) Elastic Modulus (RBNN) Elastic Modulus (SVM) Compressive Strength (RVE) Compressive Strength (FFNN) Compressive Strength (RBNN) Compressive Strength (SVM)

0.957 0.836 0.604 0.887 0.989 0.981 0.990 0.988

0.940 0.820 0.590 0.875 0.985 0.975 0.988 0.985

95.9 93.6 83.6 95.3 98.9 98.1 99.1 99.2

94.0 92.0 82.0 93.5 98.5 97.5 98.8 98.9

33.96 36.88 37.52 34.26

46.33 56.39 46.15 45.71

4.50 4.80 3.80 2.70

2.80 3.00 2.50 2.20

Table 2: ANN method outcomes for FFNN, RBNN and SVE.

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