PaperlayerView exact revision on arXiv

Source-linked AI summary

A Vehicle-Integrated Approach to Digital Twin Deployment for Bridges

Mehri Alamdari, Zihao Liu, Jiaji Wang, Kawabe Daigo, Chul Woo Kim

arXiv:2609.30671v1eess.SP

TL;DR

Bridge assessment commonly relies on visual inspections and permanent sensors, which can be subjective or costly to deploy widely. This project combines vehicle-based measurements with FNO models, vehicle optimisation and virtual sensing; demonstrations include response reconstruction from six channels and FNO damage identification on a benchmark beam. The work remains to be transferred from direct bridge-response demonstrations to vehicle-borne measurements and more general damage patterns.

  • Problem

    Visual inspection can miss early deterioration and permanent sensor networks are costly to deploy widely, while sparse bridge measurements leave structural responses such as displacement unrecorded.

    Source: §1 · p. 6, §2.4 · p. 25

  • Method

    The project combines FNO surrogate models, inspection-vehicle optimisation and Kalman-filter virtual sensing to predict responses, distinguish damage and reconstruct unmeasured structural responses.

    Source: §1 · p. 6, §2.1 · p. 10, §2.3.2 · p. 23

  • Results

    The FNO identifies single-region damage from direct bridge responses, vehicle optimisation found a favourable frequency-ratio range of approximately 0.3 ≤ β ≤ 0.7, and virtual sensing reconstructed displacement and velocity from six channels with errors of approximately 0.58% and 5.01%, respectively.

    Source: Summary of Algorithm Development and… · p. 3

  • Takeaways & Limitations

    The demonstrations support further development of a vehicle-driven digital twin that can enrich sparse measurements and provide rapid response prediction and damage assessment.

    Source: Summary of Algorithm Development and… · p. 3, §2.1 · p. 13

    The FNO damage demonstration uses direct bridge measurements and a single localised damage region; vehicle-borne transfer and more general truss damage patterns remain ongoing.

    Source: §2.1 · pp. 13–14

Abstract

from arXiv · show

The project A Vehicle Integrated Approach to Digital Twin Deployment for Bridges is developing a scalable framework for bridge condition assessment using vibration measurements from a sensorised inspection vehicle. It combines vehicle bridge interaction modelling, state estimation, machine learning and surrogate modelling to reduce reliance on permanent sensor networks. The Old Ada Bridge in Japan is the principal case study because it provides direct and vehicle-based field measurements across multiple experimentally introduced damage states. Progress has been made across three streams. First, forward and inverse Fourier Neural Operator (FNO) models have been demonstrated on a benchmark beam, enabling rapid response prediction and identification of damage location and severity. Second, an inspection vehicle optimisation framework has been developed to select vehicle mass and tyre suspension stiffness that maximise separation between healthy and damaged responses, integrating contact-point reconstruction, damage assessment, Kriging and particle swarm optimisation. Third, an Augmented Kalman Filter-based virtual sensing framework has been developed to estimate moving loads and reconstruct displacement, velocity and acceleration at unmeasured locations from sparse sensors. The next phase will extend and integrate these methods using the Old Ada Bridge model and field data. FNO models will be transferred to the truss structure and evaluated using intact and damaged measurements. Vehicle optimisation will be tested for transferability, while virtual sensing will be extended to the coupled vehicle bridge system to estimate road roughness, vehicle parameters, moving forces and structural responses. Ultimately, these components will form an integrated vehicle-driven digital twin for rapid simulation, response reconstruction and damage assessment under realistic conditions.

Summary of Algorithm Development and Future Actions

The project has demonstrated three complementary methods for bridge response prediction, vehicle optimisation and virtual sensing, and plans to integrate them into a vehicle-driven digital twin validated on the Old Ada Bridge. The next phase extends these methods from benchmark or numerical settings to the bridge model and field measurements.

Fourier Neural Operator

  • The FNO forward model predicts responses for unseen damage locations and severities, while its inverse model identifies the location and severity of a single damaged region from dynamic responses.The models were evaluated on a simply supported beam with a moving half-car vehicle; the next step is transfer to the Old Ada Bridge model and measurements.Source: Summary of Algorithm Development and… · p. 3
  • The FNO models will be extended to the Old Ada Bridge truss and evaluated with measured intact and damaged responses, while future work may examine multiple-member damage and physics-informed training.The planned training scenarios vary vehicle speeds, road profiles and operating conditions.Source: Summary of Algorithm Development and… · p. 3

Inspection-vehicle optimisation

  • Using Wasserstein distance between healthy and damaged damage-index distributions to quantify sensing performance, the framework identified a favourable vehicle-to-bridge frequency-ratio range of approximately 0.3 ≤ β ≤ 0.7.It explored 1,500 vehicle configurations using a Kriging surrogate and particle swarm optimisation; the identified guidelines are assessed for effectiveness on a truss bridge with different modal and load-transfer characteristics.Source: Summary of Algorithm Development and… · p. 3

Virtual sensing

  • With six measured channels, virtual sensing reconstructed unmeasured-location displacement and velocity with normalised root-mean-square errors of approximately 0.58% and 5.01%, respectively.The Augmented Kalman Filter also estimates unknown moving axle loads and reconstructs displacement, velocity and acceleration responses throughout the bridge.Source: Summary of Algorithm Development and… · p. 3
  • The virtual-sensing framework will be extended to field measurements with unknown road roughness and uncertain vehicle properties, jointly estimating structural states, moving forces, road roughness and vehicle parameters.A trained FNO surrogate is planned within the recursive estimator to reduce the coupled formulation's computational cost.Source: Summary of Algorithm Development and… · p. 4

Integration of the algorithms

  • The final development stage will integrate vehicle optimisation, virtual sensing and FNO prediction into a digital twin validated against intact and damaged Old Ada Bridge field states.The optimised vehicle is intended to improve measured information, virtual sensing to reconstruct unmeasured responses, and FNO to provide rapid forward and inverse predictions.Source: Summary of Algorithm Development and… · p. 4

1 Introduction

The project aims to turn vibration data from a sensorised inspection vehicle into a scalable approach to bridge assessment, combining interaction modelling, state estimation and machine learning. It centres on the Old Ada Bridge, whose field measurements include multiple damage states, and describes project coordination and resourcing for the next development phase.

1 Introduction

  • Ageing bridges are difficult to assess at scale because visual inspections can miss early deterioration and permanent sensor networks are costly to install and maintain.The project proposes vehicle-collected vibration data and modelling methods as a scalable monitoring approach.Source: §1 · p. 6
  • The project objectives include FNO surrogates, vehicle and signal-processing optimisation, response and parameter estimation, and anomaly detection from vehicle-mounted data.The intended outcome is a transferable digital twin framework for bridge assessment, inspection planning and maintenance prioritisation.Source: §1 · p. 6

1.1 Project Team Update

  • Dr Jiaji Wang joined the team to advise on exploratory differentiable VBI models and their integration with machine learning, without changing existing responsibilities or deliverables.His participation is in-kind and he will not lead the project or serve as Chief Investigator.Source: §1.1 · p. 7

1.2 Overview of Project Meetings

  • Project meetings identified challenges including unknown vehicle parameters, sparse measurements, absent displacement data and noisy vehicle sensing, then formed mini-projects on bridge analysis, road roughness and VBI modelling.The teams planned to meet every two months to review progress and exchange findings.Source: §1.2 · pp. 7–8

1.3 Proposed Change to the Project

  • The proposed budget reallocation supports a UNSW Research Assistant to preprocess and enhance the damaged Old Ada Bridge field dataset for neural-operator development and validation, without changing project scope or milestones.The work may also require state-estimation methods such as Kalman filtering.Source: §1.3 · p. 8

1.3.1 Why Old Ada Bridge?

  • The Old Ada Bridge offers a validated model, established half-car VBI, direct and indirect sensing, and multiple real-world damage scenarios for methodological development and validation.The dataset's multiple field-captured damage states are described as rare in bridge monitoring studies.Source: §1.3.1 · pp. 8–9, Figure 2 · p. 9

2.1 Algorithm Development, Part 1: Developing surrogate models of VBI/VRI using a Fourier Neural Operator

Fourier Neural Operator surrogates address the cost of repeated vehicle–bridge simulations by predicting bridge responses and inferring damage. The beam demonstration uses bridge responses; transfer to vehicle measurements and the Old Ada Bridge remains planned.

2.1 Algorithm Development, Part 1: Developing surrogate models of VBI/VRI using a Fourier Neural Operator

  • The FNO evaluates a learned kernel in the frequency domain, retaining low Fourier modes for global structure while a local bypass restores high-frequency content.The learned weights act on Fourier modes rather than individual grid points.Source: §2.1 · p. 11
  • The benchmark uses a 25 m simply supported beam crossed by a two-axle half-car, with damage represented as a local flexural-stiffness reduction.Damage locations and severities are sampled, and reported results use independent test scenarios not seen in training.Source: §2.1 · pp. 11–12
  • The forward FNO reproduces midspan displacement across representative damage cases, including small damage-related perturbations, in a small fraction of finite-element solve time.The examples cover severe, moderate, and light damage.Source: §2.1 · pp. 12–13
  • The inverse FNO localises and quantifies damage across the span from bridge response, but the demonstration is limited to one idealised damage region and bridge-mounted response.Transfer to vehicle-borne measurements and more general truss damage patterns is ongoing.Source: §2.1 · p. 13
  • Vehicle-response transfer is a central next step because vehicle dynamics and road roughness can mask the bridge damage signature in vehicle-borne measurements.The proposed options are to learn from optimised, pre-processed vehicle signals or from bridge responses reconstructed by virtual sensing.Source: §2.1 · pp. 13–14

2.1.1 Complementary Neural-Operator Models Contributed by Kyoto University and the University of Hong Kong

  • The complementary TFNO predicts bridge deflection from vehicle inputs and response history, while PINO embeds vehicle–bridge equations to improve accuracy and robustness and reduce data needs.The reported data-efficiency advantage is particularly relevant to small-data field applications.Source: §2.1.1 · p. 15

2.1.2 Extension of FNO to Old Ada Bridge

  • Old Ada Bridge transfer requires extending the beam-based FNO to a more complex truss and validating a numerical model against measured modal and dynamic characteristics.The planned progression is from that model to field data, with discrete member-level damage rather than a continuous damage field.Source: §2.1.2 · p. 15, §2.1 · p. 15

2.2 Development and Validation of the Old Ada Bridge Numerical Model

A computationally efficient two-dimensional finite-element model was developed to preserve the Old Ada Bridge’s global bending behaviour while reducing the cost of repeated simulations. Bayesian updating against intact and damaged field modal data improved agreement and extended validation beyond the intact condition.

2.2 Development and Validation of the Old Ada Bridge Numerical Model

  • A simplified two-dimensional Euler–Bernoulli frame model represents the principal longitudinal truss plane and deck mass while preserving global bending behaviour for drive-by monitoring simulations.The computationally efficient representation supports repeated vehicle–bridge interaction, damage-analysis, and operator-learning activities.Source: §2.2 · p. 16, Figure 6 · p. 16
  • Bayesian TMCMC updating minimised discrepancies between measured and predicted mode shapes and natural frequencies, using nine uncertain parameters informed by sensitivity analysis.The updated parameters included elastic modulus, grouped member cross-sectional areas, and a horizontal support spring.Source: §2.2 · pp. 16–17
  • After intact-only updating, first-, second-, and third-mode frequency errors fell from 8.24%, 17.65%, and 16.65% to approximately 0.02%, 0.27%, and 0.13%, respectively.The calibrated frequencies were 2.975, 6.890, and 9.620 Hz, compared with measured values of 2.975, 6.872, and 9.608 Hz.Source: §2.2 · p. 17, Table 2 · p. 18
  • In the natural-frequency analysis, the simplified two-dimensional model developed at UNSW showed strong mode-shape agreement with the original three-dimensional numerical model [7], assessed by MAC, with all values at least 0.80.Source: §2.2 · p. 18, Figure 7 · p. 18
  • Including damaged states reduced the maximum third-mode prediction error for DMG3 from 29.96% to 2.54%.Table 3 compares measured frequencies with initial and updated model predictions across intact and damaged states.Source: §2.2 · p. 18, Table 3 · p. 19

2.3 Algorithm Development, Part 2: Inspection Vehicle Optimisation for Enhanced Drive-by Bridge Sensing

The inspection-vehicle framework combines vehicle–bridge modelling, contact-point reconstruction, road-noise suppression, damage assessment, and surrogate-based optimisation to select vehicle parameters for drive-by sensing. Its findings identify design conditions associated with damage-detection performance and guide transferability testing on the Old Ada Bridge.

2.3.1 Suppression of Road and Vehicle Effects

  • The half-car formulation reconstructs tyre–road contact-point response from axle measurements while accounting for vehicle damping.The contact-point response includes bridge displacement and road roughness; the formulation is presented as better suited to realistic vehicle–bridge interaction than approaches neglecting damping.Source: §2.3.1 · p. 21
  • Front–rear residual spectra, bridge-sensitive frequency selection, repeated-crossing averaging, and healthy-baseline normalisation suppress road and vehicle effects.The two axles encounter approximately the same road profile with a time delay, so subtraction reduces common road-induced spectral components while retaining vehicle–bridge interaction differences.Source: §2.3.1 · pp. 21–22, Figure 10 · p. 22

2.3.2 Optimisation Criterion and Principal Findings

  • The optimisation maximises the Wasserstein distance between healthy and damaged damage-index distributions, using Kriging to approximate the objective across 1,500 sampled vehicle configurations.Particle swarm optimisation then identifies the best-performing configuration; vehicle mass and tyre–suspension stiffness are the design variables.Source: §2.3.2 · pp. 23–24
  • 95% classification accuracy and Wd = 0.0782 for the optimised vehicle, versus 52% accuracy and Wd = 0.0027 at β = 1.003.The near-resonant configuration was associated with vehicle-dominated behaviour rather than useful bridge-condition information.Source: §2.3.2 · p. 24

2.3 Algorithm Development, Part 2: Inspection Vehicle Optimisation for Enhanced Drive-by Bridge Sensing

  • The framework provides a quantitative basis for adjustable vehicle mass and suspension stiffness, with sensors near both axles supporting reconstruction and residual processing.The design guidelines will be tested for transferability to the Old Ada Bridge, a more complex truss structure, and refined for field deployment if needed.Source: §2.3 · p. 19, §2.3.2 · pp. 24–25

2.3.2 Optimisation Criterion and Principal Findings

  • Favourable configurations were primarily associated with vehicle–bridge frequency ratios of approximately 0.3–0.7; configurations near β = 1 performed poorly.Within the favourable region, lighter vehicles required proportionally lower natural frequencies, while higher frequency ratios required larger vehicle–bridge mass ratios.Source: §2.3.2 · p. 24, Figure 11 · p. 25

2.4 Algorithm Development, Part 3: Virtual Sensing

Virtual sensing addresses sparse bridge measurements by combining a validated numerical model with limited observations to estimate responses at unmeasured locations. The numerical demonstration reconstructs responses from six channels, while the next phase targets joint estimation of the coupled vehicle–bridge system using field data.

2.4.1 Augmented Kalman Filter

  • The Augmented Kalman Filter jointly estimates moving loads and bridge states, with displacement and velocity at every degree of freedom providing responses at unmeasured locations.Because contact forces are unknown, the AKF augments the state with the input and models it as a random walk.Source: §2.4.1 · pp. 26–27
  • The estimator omits vehicle mass, suspension, and road profile, treating vehicle–bridge interaction as process noise to keep the recursive filter linear and fast.A trained FNO is proposed as a route to embedding the interaction within the estimator.Source: §2.4.1 · p. 27

2.4.2 Numerical Demonstration and Results

  • 0.58% normalized root-mean-square error for displacement and 5.01% error for velocity were reported at an unmeasured panel point, with full-field reconstruction from six channels.Figure 13 compares the estimated and true displacement, velocity, and acceleration responses.Source: §2.4.2 · pp. 27–28, Figure 13 · p. 28

2.4.3 Extension to Field Data and Convergence with the Surrogate Models

  • For field measurements, the planned nonlinear extension of the Universal Filter jointly estimates bridge state, road roughness, and vehicle parameters in a coupled vehicle–bridge model.The field response is described as largely governed by unknown road profile and vehicle parameters.Source: §2.4.3 · p. 29
  • The integrated digital twin links FNO surrogates for near-real-time vehicle–bridge interaction with virtual-sensing datasets for operator-learning training and validation.The project combines these components with the optimised inspection vehicle.Source: §2.4.3 · p. 29

3 Results and Impact

Project findings and planned work have been accepted for presentation at two venues, and a special session on drive-by bridge monitoring has been accepted for EVACES 2027.

Results and Impact

  • An abstract on a vehicle-integrated digital twin using FNO for drive-by bridge monitoring was accepted for presentation at ICES2026 in Brisbane.The conference is scheduled for December 2026.Source: §3 · p. 29
  • An abstract on nonlinear recursive virtual sensing under unknown road roughness and vehicle parameters was accepted for the ANSHM Workshop.It proposes joint input–state–parameter estimation and plans development and validation with the Old Ada Bridge model and field dataset.Source: §3 · p. 30
  • The EVACES 2027 Scientific Committee accepted a special session on advances in drive-by bridge monitoring and scalable bridge assessment.Project updates are also planned through professional networks, newsletters, and conference presentations, with industry and government engagement.Source: §3 · pp. 31–32

Declaration of Artificial Intelligence Use

The report acknowledges the use of artificial intelligence tools to graphically enhance its presentation.

Declaration of Artificial Intelligence Use

Loading 2609.30671v1…