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Feedforward Neural Network-Based Digital Twin for SHM of Bridges Cover

Feedforward Neural Network-Based Digital Twin for SHM of Bridges

Open Access
|Jul 2025

Figures & Tables

Figure 1.

Side view and cross-section of Soroksári bridge
Side view and cross-section of Soroksári bridge

Figure 2.

Effect of sample size on FNN performance metric: mean square error (MSE), mean absolute error (MAE) and coefficient of determination (R2)
Effect of sample size on FNN performance metric: mean square error (MSE), mean absolute error (MAE) and coefficient of determination (R2)

Figure 3.

Training and validation loss for the ANN model for; 17 locations (A), 25 locations (B), and 40 locations (C)
Training and validation loss for the ANN model for; 17 locations (A), 25 locations (B), and 40 locations (C)

Figure 4.

Predicted vs. and actual values for the FNN model for; 17 locations (A), 25 locations (B), and 40 locations (C)
Predicted vs. and actual values for the FNN model for; 17 locations (A), 25 locations (B), and 40 locations (C)

Figure 5.

Normalised metrics comparison across model versions
Normalised metrics comparison across model versions

Figure 6.

Performance vs. complexity trade-off
Performance vs. complexity trade-off

Figure 7.

Code steps for forecasting structural features
Code steps for forecasting structural features

Figure 8.

Locations for making predictions on Soroksári bridge
Locations for making predictions on Soroksári bridge

Figure 9.

Top crack width utilisations (A), bottom crack width utilisations (B) and deflection utilisations (C).
Top crack width utilisations (A), bottom crack width utilisations (B) and deflection utilisations (C).

Characteristics of the feedforward neural network

CategoryDetails
Input FeaturesDisplacement and strains on longitudinal direction.
Target OutputsCrack width data (top and bottom extreme fibres), strains (on the transverse direction), stresses (on the transverse and longitudinal directions), and displacements (on the transverse and vertical directions).
Preprocessing– Zero values replaced with non-zero means or 1e-3.– Min-Max Normalisation (range [0, 1]).
Data Split– Training: 60%– Validation: 20%– Test: 20%
Network Architecture– Input Layer: the same size as input features.– Hidden Layers:– Layer 1: 128 neurons, ReLU, L2 regularization (1e-4).– Layer 1: 64 neurons, ReLU, L2 regularization (1e-4).– Layer 2: 32 neurons, ReLU, L2 regularization (1e-4).– Output Layer: Linear activation for regression tasks.
Optimization– Optimizer: Adam.– Learning Rate: 1e-4.
Loss FunctionMean Squared Error (MSE).
MetricsMean Absolute Error (MAE).
Training Parameters– Batch Size: 32.– Epochs: 100 with Early Stopping (patience = 5).
Regularization– L2 Regularization (1e-4).– Dropout (20%) to prevent overfitting.
EvaluationFinal test performance: MSE and MAE metrics.

Selected nodes

NodeType of sensorLocation
183×Bottom of the left box girder at support 15/1
355Displacementat support 13/4
356Displacementat support 13/3
357Displacementat support 13/2
358Displacementat support 13/1
360×at support 14/3
361Displacementat support 15/4
362Displacementat support 15/3
363Displacementat support 16/4
364Displacementat support 16/3
365×at support 14/2
368×at support 15/1
369Displacementat support 16/2
370Displacementat support 16/1
375×Bottom slab of the box girder near Support 14/3
377×Bottom slab of the box girder near support 14/2
1817StrainBottom slab of the right-side box girder in the first quarter of the bridge
3851×Bottom of the transverse wall at the middle cross-section on the left-side box girder
5151StrainBottom slab of the right-side box girder in the third quarter of the bridge
7438×Middle top of the transverse wall at Pier 14
8279StrainTop slab in the right-side box girder near Pier 14 (right side)
8438StrainRight-side internal wall of the right box girder at the middle cross-section of the bridge
9280StrainTop slab of the right-side box girder at Pier 14 (left side)
9287StrainLeft-side internal wall of the right box girder at the middle cross-section of the bridge
9407StrainTop slab of the right-side box girder in the second quarter of the bridge
DOI: https://doi.org/10.2478/acee-2025-0026 | Journal eISSN: 2720-6947 | Journal ISSN: 1899-0142
Language: English
Page range: 157 - 169
Submitted on: Mar 20, 2025
Accepted on: Jun 17, 2025
Published on: Jul 3, 2025
Published by: Silesian University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Asseel AL-HIJAZEEN, Kálmán KORIS, published by Silesian University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.