PSI - Issue 78

Lorenzo Principi et al. / Procedia Structural Integrity 78 (2026) 1681–1688

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Phase II begins with evaluating Feature Importance to determine how informative each input feature is using the Feature Permutation Importance (FPI) algorithm. The mean F1 - score decrement stabilizes at around 100 permutations (Figure 2a, log scale). According to the results (Figure 2b), Obstacle Type emerges as the most influential, followed by Static Scheme, Deck Material, ADT, and Number of Spans. All features contribute positively to model generalization, supporting their inclusion.

(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 adopts fully connected feed - forward ANNs. A detailed overview of ANNs is provided in Principi et al. (2025). To identify the best - performing ANN, multiple configurations must be tested (Table 6).

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

Topology

Optimization Algorithms Hyperparameters

Input Layer Neurons Output Layer Neurons Hidden Layers Number Hidden Layers Neurons

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

Max iterations number From 1 to 200, unit step size

From 1 to 10, unit step size From 5 to 27, unit step size

Batch size (*)

From 2 to 64, doubling at each step

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

This step of Phase II systematically evaluates the ANN performance across all settings in Table 6. Dataset is split into 80% training and 20% testing. Grid Search with 5 - fold Cross Validation (GS - kFCV) is used to explore the model parameters space. 3.3.1. Optimal Model and Performance Analysis Step 1 of Phase III is Optimal Model Selection, which identify the best - performing ANN (Table 7) using the highest mean cross - validation F1 - score, calculated as the average F1 - score across all validation folds in 5 - fold CV.