Issue 66

A. Anjum et alii, Frattura ed Integrità Strutturale, 66 (2023) 112-126; DOI: 10.3221/IGF-ESIS.66.06

0.24

Unpatched Patched

0.20

0.16

0.04 SIF (MPa. m -1/2 ) 0.08 0.12

0.00

4 5 6 7 8 9 10111213 -0.04

Crack Length (a)

Figure 6. Comparison of patched and unpatched plates.

Model Number Model 1

Model

Model Parameters

Quadratic SVM

Kernel function-Polynomial; Kernel polynomial order-2; Solver-Sequential Minimal Optimization; Epsilon-0.005 Kernel function-Polynomial; Kernel polynomial order-3; Solver-Sequential Minimal Optimization; Epsilon-0.005 Kernel function-Rational Quadratic; Optimizer-Quasi Newton; Method – Gaussian Process Regression Kernel function-Matern 5/2; Optimizer-Quasi Newton; Method – Gaussian Process Regression Kernel function- Exponential; Optimizer-Quasi Newton; Method – Gaussian Process Regression Kernel function-Squared Exponential; Optimizer-Quasi Newton; Method – Gaussian Process Regression Table 5. Model descriptions.

Model 2

Cubic SVM

Model 3

Rational Quadratic GPR Matern 5/2 GPR

Model 4

Model 5

Exponential GPR

Model 6

Squared Exponential GPR

Finite element simulations require a mesh study to achieve accurate results. Typically, a fine mesh is preferred for accurate results. After conducting mesh sensitivity analysis, a fine mesh was chosen for this study. As a result, the FE and ML work achieved less than a 1% error, which can be safely ignored. Furthermore, the selected ML models were found to be suitable for predicting and simplifying the current problem. Therefore, this simulation demonstrates that the selected ML models can accurately predict and simplify the current problem. Fig. 7 demonstrates the performance of the GPR and SVM algorithms in predicting the SIF values. Both training and testing results using GPR and SVM algorithms are presented, and the predicted values are compared to the simulation data for the respective data sets. The results reveal that the GPR algorithm using Rational Quadratic and Squared Exponential kernel functions is effective in predicting the SIF values for these data sets, and the algorithm fits well with the simulation data. The GPR algorithm was further optimized to fit the validation samples with the simulation data, which resulted in good agreement with the FE data for the tested data. This study is noteworthy as it is the first to utilize six different regression models for the regression analysis of solid mechanics and structure problems. Additionally, this study highlights the potential of GPR for the analysis of highly linear and non-linear numeric data, as the results indicate that the SIF values are significantly dependent on the patch shear strength, which was successfully predicted by GPR for the testing points. This study demonstrates the potential of GPR for various fields where regression analysis of highly linear and non-linear numeric data is required.

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