PSI - Issue 81

Oleh Yasniy et al. / Procedia Structural Integrity 81 (2026) 116–122

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Fig. 5 illustrates the importance assessment of input parameters N and R ol for random forest and boosted trees models. In the random forest model, the influence of parameter N dominates, while R ol has a minimal value. In contrast, boosted trees demonstrates increased sensitivity to both parameters, especially R ol , indicating the model's superior ability to detect complex relationships between variables. This result confirms the greater flexibility of boosted trees in modelling the nonlinear effects of fatigue crack growth. Analysis of the results of modelling using the random forest and boosted trees ensemble machine learning methods demonstrated their high effectiveness in predicting fatigue crack growth in structural steel. The constructed models showed high accuracy according to the MAPE metric, which was 1.12% for random forest and 3% for boosted trees. The graphs of the dependence of experimental and predicted values confirm a close correlation, with the points located near the bisector, indicating good agreement between the model and the data. A comparative analysis of the mean square error showed that boosted trees achieve the lowest error with approximately 2,550 trees, while random forest achieves stability with as few as 300 trees. The distribution of residuals indicates the advantage of random forest in terms of stability, namely, the res iduals are concentrated within ±0.5, while boosted trees has a slightly wider spread, including isolated outliers. Feature importance analysis showed that the main influencing factor is the number of loading cycles N , and the overloading factor R ol plays a secondary role. At the same time, boosted trees proved to be more sensitive to the R ol parameter, which indicates its ability to better account for the nonlinear effects of crack growth retardation after overload. a b

Fig. 5. The importance of input parameters in models a) random forest and b) boosted trees.

Therefore, both models can be considered effective for solving the problem of fatigue crack growth prediction, with random forest providing more stable results with lower error, while boosted trees better model complex patterns under variable loading conditions. The results confirm the feasibility of using ensemble learning methods in fracture mechanics problems for engineering materials. 4. Conclusions In this study, an approach to predicting fatigue crack length in QSTE340TM structural steel using ensemble machine learning methods random forest and boosted trees was proposed and implemented. The developed models were trained on experimental data covering different loading regimes: constant amplitude and single overloading with R ol =1.5 and R ol =2.0 coefficients. The ability of the models to effectively reproduce not only the standard nature of crack growth, but also the nonlinear effects of growth retardation after overload, which are difficult to describe by traditional analytical approaches, was demonstrated. The accuracy assessment of the models demonstrated the high efficiency of random forest, which achieved the lowest mean absolute relative error MAPE = 1.12% and a stable distribution of residuals in a narrow range. Method of boosted trees provided a relatively higher error MAPE = 3%, but showed better sensitivity to the overload parameter, which is critical for modelling retardation crack growth. Feature importance analysis confirmed the physical significance of the number of loading cycles parameter N , while boosted trees demonstrated the ability to more flexibly interpret the role of overloading factor R ol . Thus, both ensemble approaches were found to be suitable for modelling fatigue failure of steel structures. Random forest model is more stable and less sensitive to overtraining, which makes it effective for tasks where the need for accurate and reliable prediction prevails. Boosted trees methods, in turn, has advantages in tasks where it is important to take into account complex nonlinear behaviour of the material and the interaction between parameters.