PSI - Issue 57

Khashayar Shahrezaei et al. / Procedia Structural Integrity 57 (2024) 711–717

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K. Shahrezaei et al. / Structural Integrity Procedia 00 (2023) 000–000

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4. Results and Discussions

4.1. Global accuracy of the metamodels

The global accuracy, RMSE, and R 2 , for all the trained metamodels for each output of interest, are shown in Table 1. Data samples for training and testing procedure were generated using the LHS algorithm. The metamodels are trained and tested using the same size of data sets, i.e. 240 data samples for training and 60 data samples for testing. The tabulated performance was obtained by gradually increasing the size of the data set by 50 samples until the R 2 was larger than or approximately 0.9. Although all output of interest exhibits strong non-linearity against the model inputs, the metamodels obtained are su ffi ciently accurate for performing metamodel-based GSA sensitivity.

Table 1: Performance statistics of the developed metamodels for model output predictions.

Model Out puts

Metamodels

ANN

PCE

Kriging

RMSE R 2

NTraining / Test RMSE R 2

NTraining / Test RMSE R 2

NTraining / Test

Exx 0.0370 0.9454 240 / 60 Eyy 0.0143 0.9959 240 / 60 Ezz 0.0130 0.9971 240 / 60 Gxy 0.0278 0.9794 240 / 60 Gyz 0.0105 0.9966 240 / 60 Gxz 0.0268 0.9827 240 / 60

0.0387 0.9601 240 / 60 0.0420 0.9761 240 / 60 0.0305 0.9862 240 / 60 0.0386 0.9743 240 / 60 0.0180 0.9938 240 / 60 0.0324 0.9797 240 / 60

0.0529 0.8965 240 / 60 0.0337 0.9803 240 / 60 0.0361 0.9772 240 / 60 0.0573 0.9236 240 / 60 0.0306 0.9772 240 / 60 0.0650 0.9121 240 / 60

4.2. GSA of the experimentally extracted uncertainty profiles

A metamodel-based GSA of the RVE model using the developed framework has been performed. The experimen tally decided distribution profiles of the input parameters have been employed as input distributions for the GSA. Figure 3 shows the total Sobol’ sensitivity indices obtained using 10 6 MCS. The size of the MCS is large enough to ensure convergence. The sensitivity indices shown indicate that the void size is the most influential parameter on the material properties of the CFRP material. The aim would be to minimize void size in the case of improving fatigue properties related to material sti ff ness. This case study is a simplified approach, and the interpretation of the results will vary depending on factors such as load case, structural design, and on distribution profiles.

Exx Eyy Ezz Gxy Gyz Gxz

Exx Eyy Ezz Gxy Gyz Gxz

Exx Eyy Ezz Gxy Gyz Gxz

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Ratio

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MajorAxis

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Fig. 3: The Sobol’ sensitivity indices using experimental distributions for (a) ANN, (b) PCE, and (c) Kriging.