PSI - Issue 68

Hamidreza Rohani Raftar et al. / Procedia Structural Integrity 68 (2025) 1066–1073 Hamidreza Rohani Raftar et al./ Structural Integrity Procedia 00 (2025) 000–000

1070

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Table 1. Error comparison across machine learning models

Model Type

RMSE (Validation)

MSE (Validation)

RMSE (Test)

MSE (Test)

SVM ANN

3.2E-06

1.1E-11 1.4E-06 7.2E-13 1.2E-12 1.1E-12

2.6E-06

4.6E-12 2.1E-06 2.1E-13 3.1E-13 3.2E-13

0.002

0.001

Bagged Trees

8.5E-07 1.1E-06 1.1E-06

4.5E-07 5.5E-07 5.7E-07

Kernel

Tree

MSE: Mean Squared Error RMSE: Root Mean Squared Error ANN: Artificial Neural Network

3. Results and discussion In this study, machine learning techniques were utilized to predict the FCGR diagram, specifically focusing on crack growth rate (da/dN). The predictive model incorporated diverse input parameters, including hydrogen pressure, yield strength, tensile strength, and chemical composition of the material. Using these variables, the machine learning approach aimed to reveal the complex relationship between environmental and material factors influencing crack propagation under fatigue conditions. The prediction of da/dN was conducted using the bagged trees technique, as depicted in Fig. 3. The model's performance metrics on the validation dataset (Fig. 3 (b) indicates promising results, with an RMSE of 8.5e-7, R-squared value of 0.81, and MSE of 7.3e-13. These metrics suggest an acceptable level of accuracy in predicting crack growth rates. The regression analysis (Fig. 3 (b and c)) confirms the robustness of the predictive model, demonstrating its capability to generalize well to unseen data. During the prediction procedure, feature importance scores were computed to assess the significance of input parameters in predicting da/dN, see Fig. 3 (d). The analysis revealed specific insights into the influence of different factors. The pressure of hydrogen emerged as the most crucial parameter in predicting da/dN. Among mechanical properties, tensile strength demonstrated greater importance compared to yield strength in this specific case study. However, further investigation into these parameters across diverse materials and conditions is necessary for comprehensive insights. Regarding chemical composition, Mn and S were identified as the most negative influential factors in predicting da/dN. Although this study validates the results obtained by machine learning with experiment tests, efforts were made to validate the machine learning results using data from previous research. As shown in Fig. 3d, Mn and sulfur S negatively impact hydrogen embrittlement and accelerate fatigue crack growth. This observation is supported by the findings in [29,30] which indicate that Mn and S increase hydrogen diffusion. Additionally, [31] acknowledges this effect, recommending maximum concentrations of P and S at 0.015% and 0.01%, respectively. This underscores the importance of elements in governing fatigue crack propagation. These observations highlight the intricate interplay of material characteristics