PSI - Issue 84

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

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Table 3. Statistical report for the categorical input features

Design Code Class

Alternate Routes

Load Limit

PGA Seismic Design

Static Scheme

Deck Material

Bridge Age Class

Obstacle Type

Entry

1

Arc

Hybrid

≤1945 1945 1980 ≥1980

A

Built-up area

No

A B

< 0.05 g

Yes

Yes

0.05 g - 0.10 g No

B

Natural discontinuity

2

Beams

Masonry

RC (1)

3 4 5 6

Slab

C

River

C 0.10 g - 0.15 g D 0.15 g - 0.25 g

PRC (2)

Other

Primary road Secondary road

Other

≥ 0.25 g

Railway

(1) Reinforced Concrete; (2) PrecastReinforced Concrete Table 4 shows the CER labels distribution, highlighting a strong class imbalance.

Table 4. Distribution of the CER of the bridges (L = Low, M-L = Medium-Low, M = Medium, M-H = Medium-High, H = High).

L 0

M-L

M

M-H

H

34

131

218

137

3.1.2. Data Preprocessing The second step of Phase I involves Data Preprocessing, which prepares the dataset for ANN implementation by adopting the encoding strategies defined in Principi et al. (2025). A comprehensive overview of the preprocessing procedures is provided in Table 5.

Table 5. Preprocessing strategies for input features.

Preprocessing Strategy Normalizing ad-hoc function: ( ) = 1 − 1 . 00231 − Normalizing ad-hoc function: ( ) = 1 − 1 . 25893 − Normalizing ad-hoc function: ( ) = 1 − 1 . 09648 − Normalized (≤10k, 10k - 25k, ≥25k)

Input Features Total Length Max span length Number of Spans

Encoded Values

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

ADT

(0.00; 0.50; 1.00) (0.00; 0.50; 1.00) (1,0,0,0) to (0,0,0,1) (1,0,0,0,0) to (0,0,0,0,1)

ADTT

Normalized (≤300, 300 - 700, ≥700) One-Hot-Encoding (4 possible entries) One-Hot-Encoding (5 possible entries)

Static scheme Deck material Bridge age class Design code class Obstacle type Alternate routes

Normalized Normalized

(0.00; 0.50; 1.00) (0.00; 0.50; 1.00)

One-Hot-Encoding (8 possible entries)

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

Binarized

(1 = Yes; 0 = No)

Load Limit

Normalized

(1.00; 0.75; 0.50; 0.25)

Seismic Design

Binarized

(1 = Yes; 0 = No)

PGA

Normalized

(0.00; 0.25; 0.50; 0.75; 1.00)

3.2. Phase II: Data Processing 3.2.1. Feature Importance