PSI - Issue 79

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

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c) Scatter

a) Baseline

b) Linear

σ a MPa

Sampled materials Artificial materials

Sampled materials Artificial materials

Available materials

ε a

ε a

ε a

Fig. 1. Ramberg-Osgood stress-strain curves from a) the baseline, b) linear augmentation and c) scatter augmentation approaches.

4. Data augmentation approaches

Now, with only ten materials from the sampling, a smart strategy is necessary to generate su ffi cient data to train the model. Two augmentation approaches are suggested: a linear one and one that is based on the inherent material parameters scatter. The fundamental idea resides in generating new artificial copies of the sampled ten materials through ”adding” small perturbed materials. Hence, the material response due to loading (stress-strain curves) are interesting, thus, the purely experimental responses in the baseline approach are displayed in Figure 1a).

4.1. Linear augmentation

In this concept, each of the three input material parameters ( E , K ′ , n ′ ) per material sampling (ten sampled materials) were multiplied by a small factor. Hence, a linear scaling through 1 . 1 to 0 . 9 was here adopted and sequenced to generate 100 equally spaced perturbations δ i , as δ i = 1 . 1 − 0 . 002 · i , ∀ i ∈ [1 : 1 : 100] (2) and a ff ects the sampled materials through the following [ E , K ′ , n ′ ] i = δ i · [ E , K ′ , n ′ ] sampling (3) This gives in total 1000 new artificial materials, and with the sampled materials 1010 materials to train the ML model with. Figure 1b) displays the generated Ramberg-Osgood stress-strain curves by employing Eq (1) for all of these materials. This approach share similarities with the above concept, but the scaling is based on empirical statistic distributions of the material parameters. First, the same latin hypercube sampled materials as above were used here as well, render ing conformity between the two augmentation methods. Then, for each material parameter of the sampled materials, the mean, standard deviation and 95% confidence interval were calculated. Based on these, 100 uniformly distributed points within each 95% confidence interval were sampled and adjusted by the mean to generate the scaling, according to where µ ξ is the mean of the respective material parameter and U ξ, i is the set of uniformly distributed points in each 95% confidence interval. Thus, 1000 artificial materials were generated by using [ E , K ′ , n ′ ] i = [ δ E , i E ,δ K ′ , i K ′ ,δ n ′ , i n ′ ] sampling (5) where i represent the same sampling point for each parameter and Eq. (1) was, again, used to generate the stress-strain curves displayed in Figure 1c). δ ξ, i = U ξ, i − µ ξ µ ξ , ξ ∈ [ E , K ′ , n ′ ] , ∀ i ∈ [1 : 1 : 100] (4) 4.2. Scatter augmentation