PSI - Issue 84

Lorenzo Principi et al. / Procedia Structural Integrity 84 (2026) 73–80

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Phase II starts with assessing Feature Importance to quantify the informativeness of each input variable using the Feature Permutation Importance (FPI) method. The mean F1-score reduction stabilizes around 100 permutations (Figure 2a). Results (Figure 2b) indicate that Obstacle Type is the most influential feature, followed by Static Scheme, Deck Material, ADT, and Number of Spans. All features positively impact model generalization, justifying their inclusion.

Total Length - / Limit Load - H

Train Set Test Set

Obstacle Type - E Static Scheme - V Deck Material - V ADT - E Number of Spans - V PGA - H ADTT - E Max Span Length - V Bridge Age Class - E Seismic Design - V Design Code Class - V Alternate Route - V

Input Feature

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

Decrease in F1-Score

(a) (b) Figure 2. (a) Trend of F1-Score decrement for increasing permutations number for CER and (b) FPI results for CER.

3.2.2. Artificial Neural Network This study employs fully connected feed-forward ANNs. A comprehensive overview of ANNs is available in Principi et al. (2025). To determine the optimal ANN, multiple configurations are evaluated (Table 6).

Table 6. Tested architectures and hyperparameters values for GS-kFCV

Topology

Optimization Algorithms Hyperparameters

27, as the input features number (after OHE) 5, as possible outcomes class number

Complexity-Penalty From 0.0e+00 to 1.0e+00, 0.1 step size

Input Layer Neurons

Output Layer Neurons Hidden Layers Number

Max iterations number From 1 to 200, unit step size

From 1 to 10, unit step size

Batch size (*)

From 2 to 64, doubling at each step

Hidden Layers Neurons From 5 to 27, unit step size

Initial learning rate (*) From 1.0e-03 to 1.0e-01, increasing by a factor of 10 at each step

Activation function

Logistic, ReLU, Hyperbolic Tangent

Optimization algorithm L-BFGS, ADAM, SGD (*) Only for ADAM and SGD algorithms 3.2.3. Model Tuning

In this Phase II step, ANN performance is systematically evaluated across all configurations listed in Table 6. The dataset is split into 80% for training and 20% for testing. Grid Search with 5-fold Cross-Validation (GS-5FCV) is employed to explore the model parameter space. 3.3.1. Optimal Model and Performance Analysis Step 1 of Phase III, Optimal Model Selection, identifies the best-performing ANN (Table 7) based on the highest mean cross-validation F1-score, computed as the average F1-score across all folds in 5-fold CV.

Table 7. Topology and hyperparameters of the optimal ANN model selected for CER through GS-5fFCV.

Topology

Optimization Algorithms Hyperparameters

Input Layer Neurons

27

Complexity-Penalty

0.40