PSI - Issue 64

Hendrik Holzmann et al. / Procedia Structural Integrity 64 (2024) 1303–1310 Hendrik Holzmann / Structural Integrity Procedia 00 (2019) 000 – 000

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into strips as shown in Fig. 6. Consequently, a total of 6 labels are defined for localization, with 0 representing a fault outside the sandwich panel (no fault) and 1-5 representing the substructures.

Fig. 6: Classes for localization.

The data sets are randomized and divided into 80 % training data (data that the neural network has used for training) and 20 % test data (data that the neural network has not yet seen for training). Validation data are not included because the tuning of hyperparameters is done using an optimizer that prevents overfitting. The resultant simulation dataset is subjected to a feature engineering process, encompassing time and frequency domain features. This multi-domain feature extraction enhances the dataset's informativeness. For this purpose, frequency domain features are used (mean frequency, mean phase, maximum value, minimum value, curtosis, skewness and the first 30 eigenfrequencies). The feature engineering is extended by using time domain features via an inverse fast Fourier transform of the frequency domain data assuming an excitation force of 1 N and a duration of 1 s. The time domain features used are as follows: minimum value, maximum value, mean value, root mean square (RMS), variance, standard deviation, power, peak value, peak-to-peak value, crest factor, skewness, kurtosis, form factor, pulse indicator. The calculated features are then normalized, i.e. transformed to an interval from -1 to +1. This prevents individual features from having values that are orders of magnitude higher than others. Finally, a principal component analysis (PCA) is carried out to determine the main components of the feature matrices, which increases computational efficiency and decreases feature redundancy. The determined feature dataset is subsequently used to train a fully connected neural network, which is set up with an open-source library (Paszke et al.). The effectiveness is eventually demonstrated using the testing datasets. Using an optimisation tool proposed by Akiba et al. (2019), the hyperparameters of the neural network are tuned to optimize the test accuracy. Bayesian optimization is used to improve the recognition probability of the data model, which is treated as a black box model. The parameters used are hyperparameters such as the number of training epochs, the number of elements in the hidden layers, the loss factor and the learning rate. At the same time, it is easy to parallelize individual optimization steps so that a significant increase in the recognition rate is achieved within a few hours. 3. Results and discussion A high recognition rate of the training data is achieved in all the data model variants examined. For 200 samples, 100 samples without and 100 with fault, the value of the target function after optimization is 92.0 % for detection and 68.8 % for localization. For 400 samples, 200 samples without and 200 with fault, however, a value of 94.8 % and 81.3 % is already achieved for the two cases respectively. This value is not increased any further, even by enlarging the data set several times, as shown in Fig. 7.