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Application of machine learning tools in road bridge weigh-in-motion systems Cover

Application of machine learning tools in road bridge weigh-in-motion systems

Open Access
|Nov 2025

Figures & Tables

Figure 1

Comparative diagram of creating an algorithm based on traditional programming and ML.
Comparative diagram of creating an algorithm based on traditional programming and ML.

Figure 2

General concept of the proposed B-WIM system structure.
General concept of the proposed B-WIM system structure.

Figure 3

The passage of a tractor-trailer with a semi-trailer over a measuring device embedded in the pavement (on the left); The response of the measuring device to the passage of the vehicle at different speeds (on the right).
The passage of a tractor-trailer with a semi-trailer over a measuring device embedded in the pavement (on the left); The response of the measuring device to the passage of the vehicle at different speeds (on the right).

Figure 4

Diagram of a typical B-WIM system.
Diagram of a typical B-WIM system.

Figure 5

Identification and tracking of vehicles based on camera image.
Identification and tracking of vehicles based on camera image.

Figure 6

Screenshots of a model mass passage from two different perspectives.
Screenshots of a model mass passage from two different perspectives.

Figure 7

Stereo triangulation from a pair of cameras.
Stereo triangulation from a pair of cameras.

Figure 8

Comparison of estimated and actual coordinates for the tracked model mass based on screenshots triangulation, along with the corresponding estimation differences.
Comparison of estimated and actual coordinates for the tracked model mass based on screenshots triangulation, along with the corresponding estimation differences.

Figure 9

Estimation error histograms for the model mass position coordinates.
Estimation error histograms for the model mass position coordinates.

Figure 10

Experiment with image (left) and signal (right) reconstruction along with representation of the general idea of the autoencoder architecture (centre).
Experiment with image (left) and signal (right) reconstruction along with representation of the general idea of the autoencoder architecture (centre).

Figure 11

(a) Stacked autoencoder architecture and (b) results of the network operation in following steps.
(a) Stacked autoencoder architecture and (b) results of the network operation in following steps.

Figure 12

(a) Denoising autoencoder architecture and (b) results of the network operation in following steps.
(a) Denoising autoencoder architecture and (b) results of the network operation in following steps.

Figure 13

Typical structure of a CNN.
Typical structure of a CNN.

Figure 14

General block diagram of the proposed system algorithm and operation.
General block diagram of the proposed system algorithm and operation.

Figure 15

Implementation and testing scheme using mock system components.
Implementation and testing scheme using mock system components.

Figure 16

Virtual bridge model.
Virtual bridge model.

Figure 17

Learning curve values for training data.
Learning curve values for training data.

Figure 18

Comparison of reconstructed signals with the original for different training phases.
Comparison of reconstructed signals with the original for different training phases.

Figure 19

The estimation error for the test population.
The estimation error for the test population.

Determined static load values at various stages of network training_

Static loads expressed as mass (t)
Mass no. 1Mass no. 2Mass no. 3
Actual value34.428.1150.23
Before training0.000.060.20
After training34.628.2349.99
Error0.57%0.410.48

General types of tasks in civil engineering being solved by ML algorithms_

Task typeDescriptionExemplary applications in civil engineeringPossible ML algorithms
RegressionUsed to predict continuous values
  • Regression models predict total construction costs based on data [3,4]

  • Application of ML models to predict the compressive strength of new modern structural materials [5]

Linear Methods:
  • Linear Regression

  • Multiple Regression

    Neural Networks:

  • Multilayer Perceptron

ClassificationUseful for assigning categories to specific observations, such as material defect classificationAutomatic defect detection and segmentation in pulsed thermography data for defect detection in materials such as steel, plexiglass, and carbon fibre-reinforced polymer [6] Probability-Based Methods:
  • Naive Bayes Classifier

    Support Vector Machines:

  • Support Vector Machines

Neural Networks:
  • Convolutional Neural Networks for images

ClusteringUsed for grouping data based on similarityFault detection in industrial devices based on the analysis of text data from service reports using Word2Vec, autoencoders and K-means clustering [7] Clustering Algorithms:
  • DBSCAN

    Neural Networks:

  • Self-Organizing Maps

Anomaly detectionUsed to identify deviations from norms, which can be critical in structural monitoring and anomaly detectionAutoencoders for anomaly detection in structural health monitoring [8] Probability-Based Methods:
  • Naive Bayes

    Support Vector Machines:

  • One-Class Support Vector Machines

    Neural Networks:

  • Autoencoders (especially denoising variants)

Data denoisingML algorithms help to eliminate noise or interference from data such as images or signals, particularly in analysing raw structural data for better interpretationGPR data cleaning: The CFFM- ESAM-Res-UNet deep network, combining contextual fusion and spatial attention modules, effectively removes noise in GPR data and enables precise subsurface imaging using reverse time migration [9,10] Neural Networks:
  • Autoencoders (especially denoising variants)

Dimensionality reductionUsed to reduce the number of variables in large datasets, facilitating visualization and speeding up computationMaterial analysis data reduction: Prediction of the properties of building materials (thermal, mechanical, and optical) and optimization of their production processes [11] Reduction Algorithms:
  • Principal Component Analysis, Linear Discriminant Analysis

    Neural Networks:

  • Autoencoders

Time series analysisPredicting future values based on historical dataPredict the soil liquidity index and classify the soil type based on sequences of CPTU test measurements [12] Neural Networks:
  • Recurrent Neural Networks

  • LSTM

RLParticularly useful in controlling systems requiring decision-makingConstruction site management: Application of RL in Supply Chain Management [13] Neural Networks:
  • Deep Q-Network

  • Actor-Critic Methods

Overview of ML algorithm families_

Algorithm familySelected algorithmsDescription
Linear methodsLinear RegressionIntroduced as early as the nineteenth century by Francis Galton, formalized as a statistical model by Karl Pearson at the beginning of the twentieth century
Logistic RegressionDeveloped by David Cox in the 1950s
Ridge RegressionIntroduced in the 1970s by Hoerl and Kennard
Lasso RegressionDeveloped by Robert Tibshirani in 1996
Decision trees and variantsDecision TreesDeveloped from the 1960s, formally defined in the 1980s by Leo Breiman (CART algorithm – Classification and Regression Trees)
Random ForestsIntroduced by Leo Breiman in 2001 as a combination of multiple decision trees to improve model accuracy
Support vector machinesSupport vector machinesDeveloped in the 1990s by Vladimir Vapnik and his collaborators; became popular in the second half of that decade
Probabilistic methodsNaïve Bayes ClassifierOriginates from the eighteenth century, gained importance in the 1960s as a probabilistic method for text classification
Hidden Markov ModelsDeveloped by Leonard E. Baum in the 1960s; widely used in the 1970s and 1980s for sequence analysis, e.g. in speech recognition
Dimensionality reductionPrincipal Component AnalysisIntroduced by Karl Pearson in 1901
Linear Discriminant Analysis and Quadratic Discriminant AnalysisLinear Discriminant Analysis introduced by Ronald Fisher in 1936; Quadratic Discriminant Analysis (QDA) developed later as a statistical classification method
ClusteringK-meansDeveloped by Stuart Lloyd in 1957 (published in 1982); widely used for data clustering
Density-Based Spatial Clustering of Applications with NoiseDensity-Based Spatial Clustering of Applications with Noise, introduced by Martin Ester and colleagues in 1996 as a method for grouping spatial data
Artificial neural networksFeedforward Neural NetworkEarly neural network model, developed in the 1950s, particularly by researchers such as Warren McCulloch and Walter Pitts, who proposed a theoretical model in 1943
Self-Organizing MapDeveloped by Teuvo Kohonen in the 1980s; widely used for data visualization and clustering
Radial Basis Function NetworkIntroduced by Broomhead and Lowe in the 1980s
Recurrent Neural NetworkDeveloped in the 1980s, gaining popularity in the 1990s with architectures like Long Short-Term Memory (LSTM) proposed by Hochreiter and Schmidhuber in 1997
Convolutional Neural Network (CNN)Based on convolution layers, developed by Yann LeCun in the 1980s, gaining popularity in the late 2000s
AutoencoderDeveloped in the 1980s, with significant advancements in the 2000s alongside deep learning
Generative Adversarial NetworkIntroduced by Ian Goodfellow and collaborators in 2014; popular for generating synthetic data
TransformerIntroduced by Vaswani and collaborators in 2017, revolutionized natural language processing by eliminating the need for sequential processing
Graph Neural NetworkDeveloped in the early twenty-first century, gaining popularity after 2010; used for processing data in graph form

Classification of vehicle identification algorithms in B-WIM systems_

AlgorithmTypical sensor locationResultsIntended useLiterature references
Axle configurationVelocityLongitudinal locationTransverse location
MDSIn the surface in front of the facility Short-term monitoring on low- traffic facilities for low-accuracy systems[22,24,27,28]
FADOver support points or in points that give a clear answerContinuous monitoring on medium- traffic facilities for systems with good accuracy[25,26,29]
NORMost often in the middle of the spanContinuous monitoring on medium- traffic facilities for systems with good accuracy[26,30,31,32]
DOI: https://doi.org/10.2478/sgem-2025-0020 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
Language: English
Page range: 417 - 441
Submitted on: Jan 13, 2025
Accepted on: Aug 13, 2025
Published on: Nov 19, 2025
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Aleksander Mróz, Tomasz Kamiński, Jan Bień, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.