PSI - Issue 57

Jan Schubnell et al. / Procedia Structural Integrity 57 (2024) 112–120 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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The 2DLaserNet architecture, see Figure 3 (c), uses neighboring points for feature extraction like PointNet++ (Kaleci, Turgut and Dutagaci, 2022). In contrast to the PointNet and PointNet++, 2DLaserNet considers the successive points in the feature extraction process instead of considering points individually (Kaleci, Turgut and Dutagaci, 2022). The architecture accepts an ordered 2D point set as input and provides the score for each category as output. The architecture consists of three consecutive 1D convolution layers, two of which are followed by max-pooling and three fully connected layers, see Figure 3 (c). For this work, a modified end-to-end architecture of PointNet++ and 2DLaserNet were used as a starting point. 3.2. ANN used for regression The given ANNs in section 3.1 are specifically designed for classification tasks. To the best knowledge of the authors there are no ANN available that allow a regression based on 2D- or 3D-point clouds. To adjust the given ANNs PointNet++ and 2DLasernet for regression, changes were made at the fully connected layers. By that, the ANNs were redesigned to allow for a regression with respect to the SCF instead of a classification. An additional layer was added after the last linear layer. Also, the Loss-function was changed from negative Log-Likelihood-Loss to the Mean Absolute-Error-Loss or R2-Loss. The definition of the R2-Loss function is given bellow: 2 =1− , ü > 1 with = ∑( − ( )) 2 and = ∑( − ̅) 2 (1) (2) where is the sum of the square-residuals and the total sum of the squares. The R2 score can only be calculated if two samples are available. If only one sample is available, the Mean-Absolute-Error-Loss function was applied. 3.3. Pre-processing of the data For the training of the network 2540 samples of the generated 2D-profiles and SCF data were available. 80% of the data were put into the training set and the remaining 20% were used for evaluation. During training, loss and model metrics are evaluated for the validation and training data which helps to avoid overfitting of the network. 3.4. Training of the ANNs For the training of the network the Adam optimizer and the StepLR optimizer are used. The training process spans in total 100 epochs and after each epoch the model is evaluated on the validation set. To avoid overfitting the training curves can be analyzed such that the validation error does not increase while the training error decreases.. In this case the Pointnet++ model was used and the validation loss in terms of R2 is slightly below training loss throughout the entire training history. The curves of training loss and validation loss converge towards a common value. Further training did not affect the steady state value that both curves reached after 100 epochs of training. 3.5. Performance of ANN To quantify the performance of PointNet++ and 2DLaserNet for the regression of the stress concentration factor evaluated from were compared with the stress concentration factor evaluated by these ANN models. 2 = | − ( )|, ü = 1