PSI - Issue 68

Giovanni Chianese et al. / Procedia Structural Integrity 68 (2025) 1245–1251 Chianese et al. / Structural Integrity Procedia 00 (2025) 000–000

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resulted in two matrices with dimensions of 99 x 112. The two matrices were then concatenated to be processed as a unique figure instance by the CNNs. This approach involves the use of two CNNs, one dedicated to track the crack length, and another to evaluate the aspect ratio of the crack front. The problems were set as a regression and a classification, respectively, and both received in input an image with dimensions [99 x 112 x 2]. The structure of the two networks was derived from the ConvNet, and details are reported in Table 2. The number and the dimensions of the filters in the 2-D convolutional layer were fine-tuned considering values of [16 32 64 96] for both of those factors in their combinations with a full factorial approach. The performances of the two CNNs were evaluated in terms of root mean squared error (RMSE) and accuracy, in the case of regression and classification, respectively, on a validation dataset, i.e. a set of data which is not involved in the training process. A total of 25 instances were randomly hold-out from the simulated dataset for validation, with the remaining data used for the training. The initialization of the training process and the partition of data introduce a degree of randomness, which leads to a variability in the final results. This is taken into account by repeating these validation procedure 10 times and showing an averaged result.

Table 2. Structures of the two CNNs.

Layer num.

CNN for regression of α Image input layer Dropout layer (25%)

CNN for classification of β

1 2 3 4 5 6 7 8

Image input layer

Batch normalization layer

Convolution 2-D layer (filter num.: 64, filter size: 64 x 64)

Dropout layer (25%)

Relu layer

Convolution 2-D layer (filter num.: 64, filter size: 64 x 64)

Fully connected layer

Relu layer

Regression layer

Fully connected layer

Softmax layer

Classification layer

3. Analysis and discussion of the results 3.1. Approach 1: local strain measurements with fitting functions

As stated in Subsection 2.3, different positions of SG2 on the lateral face of the specimen were considered for measuring ε 2 . However, none of the positions considered for SG2 was feasible to provide independent additional information and solve the problem. In Fig. 3, results of the simulations are plotted based on ε 1 and ε 2 , for each of the considered aspect ratio β . Curves representative of propagation with different aspect ratio lie in the same region of the plane, showing that punctual measurements were not representative of different scenarios and did not provide reliable patterns for unique solution of the problem stated in (2).

Fig. 3. Back face strain (SG1) vs. punctual strain on the lateral surface (SG2) for different values of β .