PSI - Issue 79

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

193

a)

b)

ˆ σ a MPa

ˆ σ a MPa

σ a MPa

σ a MPa

c)

MAPE%

Epochs

Fig. 2. Results from the baseline method, showing a) training and b) test results, and c) MRE vs epochs.

5. Evaluation and discussion

Training for the three di ff erent approaches was performed using the previously described ANN. Note that all hyperparameters were kept constant between the methods, as the aim lies in training data generation and not e ffi ciency regarding the used ANN. In all the processes, minimisation of the mean absolute percentage error (MAPE) is sought, and the Pearson’s correlation coe ffi cient ( r ) as close to unity as possible. These are defined as

n i = 1

100 n

| x i − ˆ x i | x i

MAPE =

(6)

n x i ˆ x i − x i ˆ x i

(7)

n x 2 i

2

r =

− ( ˆ x i )

− ( x i )

n ˆ x 2 i

2

with x being true values and ˆ x predicted values and n is the amount of data. Thus, minimisation was obtained by manual optimisation by running the training process a minimum of ten times and taking the best trained ANN for evaluation. Starting with the baseline method, i.e. training against all available materials in Table A1, the results from the training can be seen in Figure 2. One thing standing out is that the training could have continued further, as a steady decrease in MAPE with respect to epochs can still been seen in Figure 2c). However, a constant number of epochs have been evaluated in this paper, to minimise discrepancies between the methods. When it comes to the scarce material responses, the ten sampled and augmented materials, the following results were obtained. Both augmentation methods generates a varied, yet however, narrow band surround each sampled material stress-strain response, cf. Figure 1, with a slightly larger band in the scatter augmentation method. Looking on the range of the obtained maximum versus minimum stress amplitude present in the three approaches, the baseline has 687 . 8 MPa, linear 707 . 8 MPa and scatter 801 . 2 MPa. These increases are, of course, results of defined perturbations, something that can be changed to find more consensus with the experimental data. Nonetheless, this also shows that the augmented stress-strain responses are expanding the training data outside the experimental test interval, which can be suitable in some sense. Also, the stress-strain curves in Figure 1 are closely distributed surrounding the sampled