PSI - Issue 62

Lorenzo Principi et al. / Procedia Structural Integrity 62 (2024) 89–96 Principi L./ Structural Integrity Procedia 00 (2019) 000 – 000

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algorithms, including the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS), the stochastic gradient descent (SGD), and the Adaptive Moment Estimation (known as ADAM) are tested.

Table 3. Description of the Dataset and Preprocessing Strategies

IF

Values

Preprocessing Strategy

Encoded Values

Total length

min = 1, max = 1943 min = 1, max = 167 min = 1, max = 56 min = 0, max = 70199 min = 0, max = 4158

Ad-hoc scaling function: f(x)=1-1.00231 -x Ad-hoc scaling function: f(x)=1-1.09648 -x Ad-hoc scaling function: f(x)=1-1.25893 -x Scaled on MIT (2020) (≤10k, 10k - 25k, ≥25k) Scaled on MIT (2020) (≤300, 300 - 700, ≥700)

[0, 1) [0, 1) [0, 1)

Max span length Number of spans

ADLT ADTT

(0.33, 0.66, 1.00) (0.33, 0.66, 1.00)

Static scheme

Supported Beams, Arc, Slab, Other OHE on original data

From (1,0,0,0) to (0,0,0,1)

PRC, RC, Masonry, Composite, Other ≤1945, 1945 - 1980, ≥1980 Class A, Class B, Class C* River, Primary Road Network, Secondary Road Network, Natural Discontinuity, Railway, Built-Up Area, Ditch

From (1,0,0,0,0) to (0,0,0,0,1)

OHE on original data

Deck material

Age class Code class

OHE + MIT (2020) ( ≤1945, 1945 - 1980, ≥1980)

From (1,0,0) to (0,0,1) From (1,0,0) to (0,0,1)

OHE + MIT (2020) (A, B, C)

From (1,0,0,0,0,0,0,0) to (0,0,0,0,0,0,0,1)

Obstacle type

OHE on original data

Alternatives

Yes, No

OHE + MIT (2020) (yes, no)

(1,0) or (0,1)

Allowable Mass

60 t, ≤44 t, ≤26 t, ≤8 t, ≤3,5 t

OHE + MIT (2020) (A, B, C, D, E)

(1.00, 0.75, 0.50, 0.25, 1.00)

*Ranges and classes as intended by MIT (2020) Regarding the activations functions assigned to the neurons, the logistic Sigmoid Function, Hyperbolic Tangent, and Rectified Linear Unit (ReLU), each of them generally adopted in ML classification problems, are considered. Then, the alpha value represents the magnitude of the L2 regularization term (Cortes et al., 2012), which aims to counteract overfitting (Scikit-learn, 2019). Maximum number of iterations is also considered as hyperparameter due to its influence on model predictions. For LBFGS solver, it is intended as the limit on the number of steps the algorithm will perform to achieve convergence, (if the tolerance value is not met). For stochastic solver, i.e., SGD and ADAM, this hyperparameter represents the epoch number to pass (Scikit-learn, 2019). The two last hyperparameters are the learning rate, which controls the step size of the change during the model's update of the weights, and the size of batches, which represents the dimension of the subsets of training dataset used during the training of the algorithm. Table 4 summarizes the architectures and hyperparameters tested in this work. The selection of the best-performing combination among all possible architectures and values of hyperparameters is performed by the CV in conjunction with the k-fold technique. For the validation of the model, the dataset is partitionated into two set: 80% is used as training set, while the remaining 20% is reserved for the testing set, which is used to evaluate the performance on unseen data (James et al., 2013). Than, Grid Search (GS) is conducted on the training set to systematically test all possible combinations of the hyperparameters values (Liashchynskyi and Liashchynskyi, 2019). In conjunction, a k -fold Cross Validation (CV) is conducted in combination with GS (Stone, 1974) with the aim to validate the model ability to predict unseen data. In k -fold CV, the original dataset is divided into k partitions of the same dimension, known as folds. Out of these k set, one is left out to serve as the validation set for assessing the model on unseen data, while the remaining k - 1 subsets are adopted as the training data. The CV process is repeated k times, with each of the k subsets serving as the validation data exactly once. The results from these k iterations can then be averaged to fournish an estimation of the model performance, that serve as a basis for the selection of the best model. The value of k folds is set equal to 5, given the small dimension of the dataset. Finally, the F1-score has been used to assess the model performance given the fact that it offers a more accurate measure of the model performance in the case of imbalanced datasets. A synthetic representation of this part of the work is depicted in Fig. 1. In Table 4 is reported the testing values of parameters and hyperparameter selected according to well-established guidelines, such as those provided by Heaton (2008). The best model obtained, i.e., the one with the higher mean cross validation F1-Score, is an ANN with 3 hidden layers and 26 neurons per layer. Further details of the selected model are reported in Table 5.