PSI - Issue 79

Daniel Leidermark et al. / Procedia Structural Integrity 79 (2026) 190–197

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Fig. 3. Results from the linear augmentation method, showing a) training and b) test results, c) MAPE vs epochs, and d) verification.

materials in the linear method, but the scatter method yields a better representation of the entire stress-strain space with evenly distributed stress-strain curves. Regarding the training process of the linear augmentation method, a much lower error and better linear correlation can be seen in Figure 3 compared to the baseline. One can also see that the training goes toward a steady-state during the 10000 epochs. These better results are achieved by primarily two things, firstly more training points are present, making sure that the ANN is su ffi ciently updated during each epoch. Secondly, the process of the manual optimisation (minimum ten runs) of the network makes the training process robust, as with more training data the outcome is even more stochastic, meaning that a more favourable or non-favourable event might occur in the training-test allocation step of data. Additionally, a verification process was also added, where the 86 materials that were not sampled for augmentation was ran through the trained network. It can be seen in Figure 3d) that the MAPE is also similarly low as for the augmented state, providing an insight that the augmentation works and yields a representative image of the materials. Finally, Figure 4 shows the evaluation of the scatter augmentation method, where similar error and correlation as the linear augmentation approach are obtained. Hence, by comparing the di ff erent results one can see that the test MAPE of the baseline is a factor of 14 . 17 and the scatter method is 1 . 24 worse than the linear method, but the scatter augmentation verification is 2 . 34 times better than the linear one. This can be due to the lack of augmented data in the interval of 300 − 400 MPa for the linear method. Another aspect regarding the used augmentation techniques, is that the linear is based on an analytical function, yielding an augmented set of data that is highly linked to the adopted function. The choice of values for this function will generate augmented responses in line with used values, something that can generate unforeseen events. On the contrary, the scatter augmentation method provides a physically-based method that uses empirical statistical distribu tions of the materials, where the only varying parameter is the size of the confidence interval. Furthermore, one thing regarding the cyclic Ramberg-Osgood constitutive model, is that it is an easy and simple model that can describe the cyclic behaviour of a material. However it’s simplicity, it is of course important that the proposed data augmentation methods are robust for other, and even more complex, constitutive models. Thus, a next step would be to deploy these for more complex constitutive models.