PSI - Issue 68

Tea Marohnić et al. / Procedia Structural Integrity 68 (2025) 84 – 90 T. Marohnić and R. Basan / Structural Integrity Procedia 00 (2025) 000–000

89

6

the predicted and experimental values for all data points, and from the upper right diagram in Fig. 2 it can be seen that there is one data point out of the general trend of data that impacts this criterion, and consequently the overall value of Ē for LS – HCF subgroup is low. To obtain a more specific insight into ANNs evaluation performance, it is useful to compare their performance to performance of commonly used empirical methods. Table 2 presents comparison of values of the aforementioned criteria among empirical methods and ANNs for all materials and all fatigue lives (ALLS – ALLF), while in Table 3 values for low strength, high-cycle fatigue (LS – HCF) are presented. Table 2. Values of evaluation criteria E f ( s =3), ( E a ) total , ( E a ) Dset and Ē determined for low-alloy steels, all strengths, all fatigue lives. LOW-ALLOY STEELS ALL STRENGTHS, ALL FATIGUE LIVES (ALLS – ALLF) Modified Universal Slopes Method Uniform Material Law Hardness Method Artificial Neural Networks

E f ( s = 3)

0.915

0.898

0.926

0.881

( E a ) total

0.850

0.805

0.953

0.730

( E a ) Dset

0.748

0.707

0.752

0.743

0.838

0.803

0.877

0.785

Ē

Table 3. Values of evaluation criteria E f ( s =3), ( E a ) total , ( E a ) Dset and Ē determined for low-alloy steels, low strengths, high cycle fatigue. LOW-ALLOY STEELS LOW STRENGTH, HIGH CYCLE FATIGUE (LS – HCF) Modified Universal Slopes Method Uniform Material Law Hardness Method Artificial Neural Networks

E f ( s = 3)

0.913

0.87

0.957

0.870

( E a ) total

0.399

0.300

0.441

-0.089

( E a ) Dset

0.239

0.308

0.375

0.536

0.517

0.493

0.591

0.439

Ē

From Table 2 it can be seen that ANNs perform somewhat lower than other methods, when it comes to all strengths and all fatigue lives. When comparing values for low strength, high-cycle fatigue (LS – HCF) it can be seen that although the value of ( E a ) total for ANNs method is extremely low, even other methods show low values of the same criteria. However, if the ( E a ) Dset , which represents the goodness of fit between the predicted and experimental values for individual datasets, is observed, it can be seen that ANNs significantly outperform other methods. 7. Discussion and conclusions Thorough evaluation provided insights on the applicability of developed ANNs for estimation of fatigue behavior of low-alloy steels regarding their strength and different fatigue regimes. Particular attention was given to materials dataset that was used so that the ANNs performance evaluation and ability to generalize (perform well on unseen data) could be assessed. Although evaluation data was obtained with the same testing conditions and within the same data distribution as training data, it was established that ANNs are particularly sensitive to odd combination of inputs, that resulting in lower values of the evaluation criteria. Evaluation methodology used enabled the direct comparison with performance of empirical methods, and can be further used to compare results to previously published studies such as Park and Song (1995) or Basan and Marohnić (2024).