PSI - Issue 79

Henrik Petersson et al. / Procedia Structural Integrity 79 (2026) 298–305

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Fig. 1. Experimental data and prediction of fatigue life, comparison ISO model and PINN model

3. Results and Discussion

The results from the PINN solution are compared against a model established through classical regression denoted as an ISO model, as mentioned previously. The regression from the ISO solution and the PINN solution are shown in Figure 1. The figure shows how the PINN capture a similar behaviour as the ISO solution where experimental data exists. It can also be observed in Figure 1 that the PINN model goes towards the upper and lower stress limits when the PINN model are extrapolated outside of the experimental data. This is a behaviour that the ISO model cannot capture. When the error estimation is applied to the models, the results in Figure 2 are obtained, showing the upper and lower band of the 95% probability interval. Figure 2 shows how a varying probability interval has been created in the PINN model, this interval is tighter for locations where there is a high density of data points, interval becomes wider in regions with limited data. Based on how the PINN model is set up in terms of the loss function, the upper and lower probability intervals tends to go to the same values as the PINN model without increase in the scatter for the lower and upper stress limit. Of course, there should exist scatter also for the upper and lower stress limits, due to material scatter. But, due to the way the mathematics in the PINN model is formulated at the moment, the model will go to these fixed values as the fatigue life goes to zero or infinity. By comparing the probability intervals between the PINN and the ISO models, of Figure 2, it can be under stood how varied safety factors can be utilized with this new approach without increasing risks. In this Figure 2 there are locations where the PINN models probability interval becomes tighter which could be utilized to reduce the safety