PSI - Issue 78

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

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Table 3. Statistical report for the categorical input features

Static Scheme

Deck Material object Hybrid

Bridge Age Class

Design Code Class

Alternate Routes

Load Limit object

PGA Seismic Design

Obstacle Type

Entry

object

object ≤1945

object

object

object

object

object

1 2 3 4 5 6 7

Arc

A B C

Built-up area

No

A B

< 0.05 g

Yes

Beams

Masonry 1945-1980

Natural discontinuity

Yes

0.05 g - 0.10 g No

RC (1)

Slab

≥1980

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

Other

(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 is Data Preprocessing, which prepares the data for the ANN using encoding strategies from Principi et al. (2025). A comprehensive overview of the preprocessing strategies 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