Structural health monitoring and digital twin-based diagnosis of a prestressed concrete bridge

1.1. Background

Bridges are critical components of modern transport infrastructure, and their structural integrity has a direct impact on public safety, economic activity, and regional development [1-3]. Traditionally, bridge condition assessment has relied on visual inspections and periodic manual measurements. Although these methods remain essential for identifying apparent defects, they are inherently limited in their ability to detect early-stage deterioration, subtle structural anomalies, or the long-term effects of dynamic loads [4-6]. Consequently, visual inspections alone may fail to reveal issues that could compromise the structure’s long-term performance.

The Spyckstraße Bridge, built in 1976, is a composite slab-girder structure spanning 92.19 m over three equal spans. As a nearly 50-year-old bridge, it currently faces increased traffic demands and stricter regulatory requirements compared to those considered in its original design.

An inspection conducted in 2022 identified multiple pathologies, including concrete degradation, corrosion affecting prestressing tendons, malfunctioning bearings, and pavement deterioration, leading to the proposal of several rehabilitation measures. In a later technical assessment carried out in 2024, fractures in prestressing tendons were detected because of water ingress, raising significant concerns regarding the remaining load-bearing capacity of the structure and its long-term serviceability.

To better characterize its structural behaviour under real operating conditions, a short-term non-destructive monitoring campaign was conducted to record its dynamic response. The collected data were used to calibrate a numerical model, refined iteratively until numerical and experimental modal frequencies agreed within a 3 % margin. This calibrated model provides a basis for assessing structural performance under current normative load scenarios and supporting maintenance decisions.

This work contributes by (i) integrating short-term monitoring data with Digital Twin calibration, (ii) establishing a relationship between modal parameters and tendon degradation, and (iii) demonstrating the capability of frequency-based indicators for early damage detection in prestressed bridge systems.

1.2. Review of the state of the art

Over the past few decades, Structural Health Monitoring has moved from a promising research topic to an essential component of modern structural management, especially in bridges. The motivation is clear: traditional inspection practices, primarily visual surveys and periodic non-destructive tests, are no longer sufficient to ensure the safety and long-term performance of aging infrastructure and the increasingly stricter regulatory requirements. As highlighted in the literature, most bridge assessments worldwide still rely on visual inspection, even though this approach is inherently limited by subjectivity, accessibility constraints, and the inability to detect early-stage or internal deterioration. Zinno et al. [7] note that “the great majority of in-service bridge data is still gathered by visual examination” a situation that leaves many subtle or evolving forms of damage undetected between inspection cycles.

These limitations have accelerated the adoption of continuous SHM systems, which combine sensors, data acquisition, and computational tools to monitor structural behaviour under real operating conditions. Rizzo and Enshaeian [8] emphasize that permanent monitoring shifts the paradigm from time-based to condition-based maintenance, allowing engineers to quantify damage as it happens, rather than after it has progressed.

Despite these advances, a key challenge remains the reliable interpretation of monitoring data through physics-based numerical models. In this context, finite element (FE) model updating has become a fundamental tool for aligning numerical predictions with experimental observations, particularly through the calibration of modal parameters such as natural frequencies and mode shapes.

1.3. Paper contribution

As stated previously, the progress in SHM technologies and hybrid data–model approaches, a gap remains in the practical use of short-term monitoring data for the development of reliable, calibrated numerical models capable of supporting structural assessment of aging bridges under current design standards.

To address this gap, this work presents a structured methodology for the calibration of a numerical model based on short-term SHM data, applied to the Spyckstraße Bridge. The proposed approach combines targeted dynamic monitoring, modal identification, and iterative model updating using a genetic algorithm, achieving discrepancies below 3 % between experimental and numerical eigenfrequencies.

In contrast to studies focused exclusively on dynamic identification, the calibrated model is further employed to evaluate structural performance under code-based load combinations, enabling the computation of sectional utilisation ratios and the assessment of structural safety margins.

Additionally, parametric analyses are conducted to simulate tendon deterioration scenarios, allowing the investigation of their impact on both modal properties and structural capacity.

Overall, this work demonstrates that short-term SHM campaigns, when combined with rigorous model calibration techniques, can provide a practical and reliable framework for structural assessment and maintenance decision-making in aging bridge infrastructure.

Preliminary results of this study were partially presented in previous conference contributions [15, 16]. The present manuscript significantly extends those works by incorporating an improved Digital Twin calibration and extended monitoring data.

2.1. Monitoring equipment and sensor installation

Fixed instrumentation was installed to continuously record traffic effects and other structural actions. The monitoring system consisted of 26 inertial sensors (yellow block) and 12 displacement sensors (green block) strategically distributed across the bridge, following the distribution shown in Fig. 2. Beams are numbered 1 to 9 from East to West.

Sensor placement was additionally validated considering modal observability criteria and expected mode shape amplitudes.

Two displacement sensors were placed on each abutment to measure longitudinal displacements of the elastomeric bearings supporting girders 1 and 9 (Fig. 3). This configuration enables the assessment of expansion joint behaviour and the verification of displacement compatibility at the supports.

Fig. 3Location of displacement sensors on the abutments of the Spyckstraße bridge

Within the three spans, sensors were distributed identically to ensure comparable measurements. Instrumentation sections were located at midspan (L/2), one-third (L/3), and one-quarter (L/4) of the span length (Fig. 4), enabling the capture of both maximum deflections and higher-order modal contributions.

Midspan sensors were used to capture maximum deflections and dominant modal responses. Accelerometers placed on central girders recorded the highest vibration amplitudes induced by traffic loads, while sensors at L/3 and L/4 positions enabled identification of higher-frequency modes and spatial variability of the dynamic response.

Similarly, piers were instrumented with inertial and displacement sensors (Fig. 5). Inertial sensors placed at the pier head measured three-directional accelerations, tilts and local vibrations, allowing the identification of pier-specific modal characteristics and their interaction with the superstructure. Displacement sensors monitored horizontal movements between spans and relative displacements of the neoprene bearings, supporting the detection of abnormal behaviour and the evaluation of serviceability conditions.

Fig. 4Approximate location of inertial sensors in the spans of the Spyckstraße bridge

a) Section at L/2 of the span

b) Section at L/3 of the span

c) Section at L/4 of the span

Fig. 5Approximate location of inertial and displacement sensors in the Spyckstraße bridge pier

2.2. Installation diagram for mobile equipment

In addition to the fixed instrumentation, a mobile monitoring scheme was implemented to enhance spatial resolution. A total of 27 mobile inertial sensors were deployed to record traffic-induced structural response for approximately one hour in each monitored section, as illustrated in Fig. 6.

The mobile sensors were positioned across all girders and deck sections, including locations at L/2, L/3, L/4, and near supports. This approach enabled a dense spatial sampling of the structural response without increasing the permanent instrumentation complexity.

The combination of fixed and mobile measurements provides complementary datasets: fixed sensors ensure temporal continuity, while mobile sensors improve spatial coverage. This dual strategy enhances the robustness of modal identification and supports the calibration and validation of the numerical model.

Fig. 6Mobile equipment installation scheme on the Spyckstraße Bridge. Elevation and underside views

2.3. Data processing and modal identification

Recorded signals were processed using standard signal processing techniques to extract relevant dynamic information. Preprocessing included detrending, filtering, and synchronization of sensor data.

Power spectral densities (PSD) were computed using Welch’s method, and modal frequencies were identified through peak-picking procedures. Time–frequency analyses, including spectrograms, were used to evaluate the stability of modal parameters under varying traffic conditions.

The extracted modal properties were subsequently used for the calibration and validation of the numerical model, providing a consistent link between experimental observations and structural simulation.

3.1. Numerical model calibration

The objective of the calibration process is to minimise the discrepancy between the numerical model and the experimentally identified dynamic behaviour of the bridge.

The structural response is governed by the classical equation of motion Eq. (1):

where $\left[M\right]$ is the mass matrix, $\left[C\right]$ the damping matrix, $\left[K\right]$ the stiffness matrix, and $\left\{X\right\}$ the displacement vector associated with each degree of freedom [20].

The calibration problem is formulated as an optimisation process in which a set of mechanical parameters is iteratively updated to minimise an objective function defined in terms of modal discrepancies. The objective function is Eq. (2), expressed as a weighted error between numerical and experimental natural frequencies:

where $w_i$ are weighting factors assigned according to modal significance.

In the calibration process, the parameters adjusted most directly include the material density $\left(\rho \right)$ and Young’s modulus $\left(E\right)$, as these govern the modal properties with greatest sensitivity [21-23]. Geometric features and boundary conditions remain fixed, as their uncertainty is comparatively low [23]. These parameters were selected based on their high sensitivity to modal properties, while geometric characteristics were kept constant due to their lower uncertainty.

Sensor data served as the primary input for the calibration. To ensure statistical robustness, Power Spectral Density functions were computed from each acceleration record using Welch’s method, with a 16-second window and 8-second overlap, yielding a frequency resolution of 0.1 Hz. The 80 % of records exhibiting the highest cross-correlation in the 0-40 Hz range were selected for calibration. This type of filtering ensures that the modal identification relies on vibration segments where the structural response is stationary and consistently captured across sensors, which is essential for obtaining stable frequency and behaviour estimates. Records with low cross-correlation typically correspond to non-stationary events, such as heavy-truck passages, braking manoeuvres or localized disturbances, that introduce transient peaks and broadband energy not representative of the underlying modal behaviour. Although these transient responses are relevant for assessing operational performance, they do not provide reliable information for frequency-based model updating and are therefore analysed separately within the serviceability and stress-response evaluation. Mean PSD curves were then obtained for each sensor, and peak-picking algorithms were applied to identify the natural frequencies associated with the different structural components. Fig. 7, Fig. 8 and Fig. 9 illustrate the PSD results for the sensors located in the north, central and south span, respectively.

Fig. 7PSD obtained in the structural elements of the north span

a) Vertical axis

b) Longitudinal axis

c) Transversal axis

Fig. 8PSD obtained in the structural elements of the central span

a) Vertical axis

b) Longitudinal axis

c) Transversal axis

Using this frequency information as a starting point, typical material properties were assigned to the FE model. An iterative genetic algorithm was then applied to calibrate the model until the difference between experimental and numerical eigenfrequencies fell below 3 %. The GA was implemented with a population of 60 individuals due to the relatively low number of studied parameters and up to 80 generations, using tournament selection, simulated binary crossover (probability 0.85) and polynomial mutation (probability 0.10). The objective function was defined as the weighted squared error between measured and numerical frequencies, prioritising the first modes. Convergence was reached when improvements fell below 10^-4, with the final solution satisfying the 3 % threshold across all identified modes. The chosen GA parameters were initially selected by comparison with similar FEM-updating studies, such as the work of Liu et al. on the Canonica Bridge [24] or the calibration strategy proposed by Rahmat Rabi et al. for steel bridge monitoring [25] and subsequently adjusted to obtain the most accurate results for the present structure.

Fig. 9PSD obtained in the structural elements of the south span

a) Vertical axis

b) Longitudinal axis

c) Transversal axis

This process enabled the refinement of key mechanical properties, including the modulus of elasticity and global density for each span and pier. Soil–structure interaction was calibrated to reproduce the near-fixed behaviour observed in the monitoring data, consistent with the bridge’s low seismicity and absence of scour-related foundation flexibility. The full sequence of calibration tasks is summarized in Fig. 10.

Fig. 10Numerical model calibration process

3.2. Model validation

The validation stage evaluates the ability of the previously calibrated Digital Twin to reproduce the real structural behaviour of the Spyckstraße Bridge under operational conditions. Following the calibration of material properties, prestressing forces, and soil-structure interaction, the model was subjected to a comprehensive verification process combining boundary condition assessment, modal validation, and comparison with experimental measurements. Validation was complemented by consistency checks in spatial response patterns and displacement levels to avoid over-reliance on frequency matching alone.

Initial prestressing forces in the girders, deck, and piers were incorporated into the model, together with horizontal displacement restraints at span joints to account for tendon effects. All boundary conditions were first verified through visual inspection and subsequently validated against the monitoring data, confirming that the Digital Twin accurately represents the static constraints and deformation patterns observed in the structure. This ensured that the numerical model captured the correct global stiffness distribution and the interaction between spans, supports, and prestressed components.

Modal validation was performed by comparing the experimentally identified natural frequencies and mode shapes with those obtained from the calibrated finite element model. Fig. 11 and Fig. 12 illustrate the deformed shapes associated with the vertical bending and torsion around the longitudinal axis modes of each span, showing a high degree of correspondence between numerical and experimental modal patterns.

Fig. 11Deformed shapes associated with the vertical bending modes of each span in the Digital Twin of the Spyckstraße Bridge

a) Central span

b) South span

c) North span

Fig. 12Deformed shapes associated with the torsion around the longitudinal axis modes of each span in the Digital Twin of the Spyckstraße Bridge

a) Central span

b) South span

c) North span

Table 1 summarizes the measured and simulated frequencies for the main vibration modes of the north, central, and south spans, as well as the north and south piers, together with the relative errors obtained after calibration.

Across all structural components, the discrepancies between measured and numerical frequencies remained below 3 %, with most modes exhibiting errors well under 1 %.

These results demonstrate that the Digital Twin faithfully reproduces the behaviour of the whole Spyckstraße Bridge. The validated model therefore provides a reliable reference for structural assessment, anomaly detection, and scenario-based simulations, forming a robust foundation for the bridge’s ongoing structural health monitoring strategy.

5.1. Evaluation of regulatory combinations

A calibrated and validated finite element model is employed to evaluate the safety and functional performance of the Spyckstraße Bridge under multiple loading scenarios, including permanent actions such as self-weight, and variable actions due to traffic, snow, wind, temperature effects, and seismic loading, in accordance with DIN standards and the European Eurocodes.

The assessment corresponds to the structural state at the end of the monitoring period and considers eight governing load combinations defined in DIN EN 1990. This framework enables a comprehensive evaluation of the bridge response and provides insights into its long-term structural behaviour [22-30].

The general format for action effects was:

where $\gamma$ represents the partial safety factors, $G_k$ and $Q_k$ are characteristic values of permanent and variable actions, $P$ is the prestressing force and ${\mathrm{\Psi }}_0$ represents combination factors for accompanying variable actions.

Fig. 16Maximum sectional utilisation factor under tensile and compression stresses for each structural element under combination dominated by traffic loads

a) Northern span

b) Central span

c) Southern span

The advanced structural assessment focuses on the evaluation of stress distributions and sectional utilisation ratios in order to detect critical regions and potential early-stage deterioration mechanisms. It is important to note that the utilisation ratios reported, such as the 97.3 % obtained for the most unfavourable combination, correspond to Eurocode design scenarios, which are intentionally more demanding than the actual loads recorded during the short-term monitoring campaign. During the measurement period, neither the traffic spectrum nor the temperature range reached the extreme values prescribed by the standards; for instance, no heavy-traffic surges or peak summer thermal gradients were observed. By applying the full set of normative load combinations, the analysis captures low-probability but structurally relevant situations that may occur over the bridge’s service life, thereby revealing the true safety margin of the structure under design-level actions rather than under the milder conditions observed during monitoring. Under all analysed combinations, the structural components exhibit satisfactory performance, with no evidence of loss of cross-sectional capacity even in these most demanding scenarios, as illustrated in Fig. 16 and Fig. 17.

Among all analysed combinations, the highest compressive stresses were observed when extreme temperature-induced expansion and contraction acted as the leading variable action. The maximum section utilisation levels reached were 66.8 % in beam 9 of the north span, 68.6 % in beam 6 of the central span, and 81.3 % in beam 8 of the south span, all remaining safely below critical levels.

Fig. 17Maximum sectional utilisation factor under tensile and compression stresses for each structural element under combination dominated by temperature effects

a) Northern span

b) Central span

c) Southern span

Tensile stresses are of particular concern because they may lead to cracking in the concrete or indicate potential prestressing pathologies, such as tendon relaxation or early corrosion effects. The most significant tensile stresses occurred under combinations dominated by traffic loads and by temperature effects. The highest tensile stress utilisation ratios were observed in the western beams of all three spans, reaching 94.2 % in beam 9 of the north span, 97.3 % in beam 9 of the central span, and 92.5 % in beam 9 of the south span.

As of the monitoring date, the Spyckstraße Bridge shows no structural safety concerns under any of the considered critical loading scenarios, as confirmed by the calibrated and validated Digital Twin simulations. Nevertheless, beams exhibiting stress utilisation ratios above 80 % under extreme load scenarios, particularly beams 8 and 9 on the western side, should be subjected to closer monitoring and detailed inspections. This will help prevent the initiation or progression of damage mechanisms that could accelerate deterioration over time.

The spatial concentration of high utilisation ratios in the western side is consistent with the stiffness asymmetry previously identified in the sensor data analysis (Section 4).

At the time of the monitoring campaign, the bridge satisfies all ULS verification criteria under the considered load combinations.

However, elements with utilisation ratios above 0.80 should be considered critical from a durability and maintenance perspective, even if safety requirements are formally met.

5.2. Evaluation of deterioration of tendons connecting spans

Based on an expert report issued on January 2024 regarding the corrosion and even fracture of one of the tendons connecting the spans, a tailored simulation was conducted for the Spyckstraße Bridge. The aim was to enable early detection of tendon degradation at span joints that influence the global structural response of the bridge, thereby facilitating cost-effective maintenance planning.

This complementary analysis focused on the variation of the bridge’s natural frequencies under progressive loss of stiffness in the tendons that restrain horizontal movement between spans. Such degradation mechanisms, primarily corrosion, can reduce tendon stiffness and alter the bridge’s dynamic behaviour.

Several scenarios representing different levels of tendon stiffness reduction were simulated at each span joint. The evolution of the natural frequencies of the vibration modes identified during the Digital Twin calibration and validation was monitored. Results for the joint between the north and central spans showed that the tendon closest to the western side (adjacent to beams 9) is currently deteriorated. Hypothetical scenarios assuming further tendon degradation predicted a significant reduction in natural frequencies, altering the global response of the structure (Fig. 18). Such frequency shifts could be detected through routine frequency-based monitoring, even when visual inspection might fail to reveal damage.

Similarly, simulations for the tendons connecting the central and south spans revealed comparable trends. In this case, the deteriorated tendon is located near beams 4. The most affected frequencies were the first vertical bending mode ($f_1$) of the central span and both the first vertical bending ($f_1$) and first torsional ($f_2$) modes of the south span.

The magnitude of frequency variation observed in the simulations suggests that early-stage tendon degradation can be detected through routine vibration monitoring, even before visible damage appears.

Fig. 18Variation of the natural frequencies of the different vibration modes identified as a function of the number of deteriorated tendons

a) North and central joint

b) South and central joint

Complementary stress analysis under heavy traffic loading scenarios showed that the north and south beams would exceed their load-carrying capacity if four tendons became ineffective, whereas the central span would reach failure at the loss of only three tendons, regardless of whether the damage occurs at the north or south joint (Fig. 19). This demonstrates a non-linear degradation of structural capacity, with critical thresholds depending on span location. In this study, “failure” is defined as the point at which the affected section reaches a sectional utilization ratio of more than 100 %, meaning that the combined axial-flexural demand equals or exceeds the available ultimate capacity of the studied piece.

Fig. 19Percentage of sectional utilisation in tensile and compression stresses of the under combination dominated by traffic loads, as a function of the number of deteriorated tendons

a) Northern span

b) Central span

c) Southern span

This study complements the normative load-combination evaluation by providing an integrated understanding of risks associated with the progressive degradation of key bridge components. These results highlight the need for continuous monitoring of tendon performance and justify preventive interventions to mitigate the impact of such deterioration on the global bridge response. The results support the implementation of frequency-based monitoring as an effective tool for early damage detection in prestressed bridges.