Operations-aware structural monitoring of a 46-year-old bridge using traffic-induced vibrations and frequency-domain analysis

Abstract

This article proposes an integrated approach for structural health monitoring (SHM), as demonstrated on the 46-year-old Rayhanna Bridge that connects visual inspection data with operational dynamics and provides mitigation strategies. This approach starts with a condition survey indicating severe bearing conditions with elastomeric pads reduced in size from 74 to 48 mm. Accelerometers were installed for tri-axial data collection, and acceleration data were recorded over 3 weeks with live traffic conditions. Operational modal analysis was used to identify three stable frequencies at 2.5, 5.1, and 7.8 Hz with the highest dynamic demand in the central girder (G2). A physics-based vehicle–bridge interaction model was created with a higher order fractional beam and compliant bearings and validated against the data. The model has produced decision support tools such as resonance proximity maps, damage rate maps, and tuned mass damper (TMD) charts. The results indicate that the vehicle speeds between 12 and 19 m/s, or 43 and 68 km/h, produce a high-risk resonance band, which explains the observed amplification phenomena. A TMD designed to target the 5.1 Hz mode (mass ratio μ = 0.04, damping ζ = 0.12) has been shown to attenuate the resonant peaks by 3–5 dB. This work has created a defensible link between the degraded bearings and the asymmetric modal energy and second mode vulnerability. Finally, the process has developed operational interventions such as the development of a speed/lane management strategy for heavy vehicles, the prioritization of the central girder bearings, and TMD implementation criteria. This low-intrusion, data-driven approach has significant implications for operations-aware SHM, which will allow modest operational interventions and retrofit actions to be undertaken to extend the life of aged bridges.

Keywords

Structural health monitoring fast Fourier transform traffic-induced vibrations natural frequency accelerometers

Introduction

The knowledge of dynamic behavior of existing bridges is an essential issue in tropical zone conditions for structural health monitoring (SHM) of bridge-like structures, which are mostly occupied with traffic.^1,2 Vibration condition monitoring was presented as a block in the research for the assessment of structural integrity and decision for maintenance and diagnostics of damages.^3–5 The synthesis in this article is based on existing literature for the combined approach of using visual inspection methods, sensor monitoring methods, and frequency analysis.

Visual inspection is considered the first step in any bridge inspection and is essential for gaining immediate knowledge of qualitative conditions of structural elements of bridges, such as girders, bearings, and drainage systems.^6–9 Visual inspection is used for detecting defects in bridges; for example, corrosion, cracks, and bearing failures, as discussed in the current study. Nevertheless, its limitations in detecting internal damages and quantifying structural behavior necessitate more sophisticated methods of non-destructive testing (NDT).^10–12 The transition from visual inspection to more sophisticated methods of NDT is considered to be the basis of SHM.^13–15

The use of sensors, particularly accelerometers, is of critical importance in monitoring the dynamic behavior of a structure.^16–18 The maximum amount of deflection was observed at the mid-point of the structure, and asymmetry in loading was achieved by using the third point. This strategic placement ensures that both static and dynamic behavior can be accurately measured to identify uneven wear and damage.^19–22 The development of data acquisition systems, such as the high-precision NI 4472 module used in this study, with high sampling rates and resolutions, has been of significant importance in ensuring accurate and precise vibration data.^23,24

Another pillar of structural analysis is frequency domain analysis, mainly through fast Fourier transform (FFT). Through FFT analysis, it is possible for engineers to transform data and identify dynamic characteristics of structures such as natural frequencies and mode shapes, which are sensitive to stiffness and boundary conditions.^25–30 For bridge structures, one of the major concerns for bridge engineers is resonance. Resonance is defined as the phenomenon in which dynamic loads (e.g., due to moving vehicles) and structures have frequencies that coincide with each other. This may cause excessive vibrations in structures and may even lead to damage.^31–33 From literature, it is seen that various types of vehicles may induce different frequency ranges. For example, heavy vehicles may induce frequencies between 5 and 25 Hz, and frequencies between 15 and 25 Hz may be related to local defects in structures or road surface defects.^34–36

Recent achievements in machine learning (ML) for SHM have focused on uncertainty-based and probabilistic modeling to improve reliability in extreme circumstances.³⁷ Bayesian dynamic linear models and a hierarchical sparse Bayesian learning framework improve data forecasting and interpretation of heteroscedastic SHM data, especially in noisy and non-stationary situations.^38,39 Gaussian process models, heteroscedastic, and variational-based models improve uncertainty quantification and strain prediction in SHM applications.^40,41

Probabilistic damage detection techniques using sparse Bayesian learning methods are also useful in identifying structural damage in a probabilistic sense, thus facilitating decision-making in structural safety and damage assessment.⁴² Reliability assessment is further enhanced in structural safety using Bayesian networks, which are useful in modeling causal dependencies and assessing risks in a probabilistic sense.⁴³ Hybrid ML methods are also useful in damage detection and prediction, as demonstrated in firefly algorithm methods that are useful in optimizing predictive models in estimating rock joint shear strength.⁴⁴ Deep learning methods are also useful in predicting various parameters in geotechnical engineering using denoising and cross-correlation methods.⁴⁵

Previous studies focused on algorithmic and local diagnostic methods without operational translation. The present study addresses this by developing a unified workflow for inspection, FFT sensing, and fractional physics to deliver decision-grade tools, speed control, tuned mass damper (TMD) tuning,and fatigue mapping, which converts SHM from a diagnostic activity to a management tool for real-world bridges.

The evaluation of the Rayhanna Bridge was carried out using a hybrid approach that integrated inspection, dynamic testing, and frequency analysis using FFT. This comprehensive method helped to identify the natural frequencies of the bridge, detect abnormalities in the structure, and develop maintenance strategies.

Methodology

The role of visual inspection and non-destructive testing

The initial step in the assessment of all types of bridges is visual inspection, which provides immediate qualitative data regarding the status of various structural components of the bridge, for example, girders, bearings, and drainage systems.^6–9 Despite the fact that it can provide data regarding obvious defects, for example, corrosion, cracks, and bearing degradation, as identified in this study, it is still unable to provide data regarding internal damage and quantify the response of the structure, which necessitates more sophisticated and advanced NDT, as shown in Figure 1.^10–12 The transition from visual inspection to more sophisticated NDT is considered as a whole system of SHM.^13–15

The use of sensors, particularly accelerometers, is vital in capturing the dynamic behavior of a structure, as depicted in Figure 2. The data obtained was represented in Table 1. Accelerometers help in measuring and detecting various types of vibrations resulting from traffic, wind, and earthquakes. They help in measuring acceleration in multiple axes.^16–18 The development of data acquisition systems, such as the high-precision NI 4472 module used in this study, with high sampling rates and resolution, is vital in achieving successful and precise vibration data acquisition.^23,24 In addition, effective noise reduction and grounding techniques must be in place for successful data acquisition.

Table 1.

Instrumentation and data collection plan.

Subsystem	Item	Quantity	Location(s)	Key specs/settings	Purpose and notes
Accelerometers	ADXL335 tri-axial	6 (2 per girder)	L/2 and L/3 (or 2L/3) on G1–G3 top flanges	±3 g range; ∼300 mV/g; noise ∼150 µg/√Hz; tri-axial	Capture vertical-dominant response with some lateral/longitudinal coupling; robust under thermal swing.
Cabling	Cat7 shielded “Blue Storm”	80 m total	Sensor runs to Data Acquisition (DAQ)	Shielded twisted pair; drain wire to common copper rod	Minimize EM pickup; consistent grounding to reduce 50/60 Hz hum.
Data Acquisition (DAQ)	NI 4472	1	Protected cabinet	24-bit; fs = 200 Hz (project); anti-alias filters; Global Positioning System (GPS) time base	High dynamic range, stable timing across weeks.
Power	Regulated DC	1	Data Acquisition (DAQ) cabinet	Ripple <10 mV; surge protection	Stable excitation to reduce drift.
Video	5-megapixel (MP) pan-tilt-zoom (PTZ) internet protocol (IP) camera	1	Mast at deck level	20× optical zoom; time-sync via Network Time Protocol (NTP); vehicle speed from video	Vehicle identification and speed estimation to relate to frequency content.
Environmental	Temp probe (deck shade)	1	Mid-span	−10 to +60°C; 0.1°C resolution	Diurnal compensation for frequency tracking.
Run schedule	Live traffic	3 weeks	18–60 km/h prevailing	∼24/7 logging; Quality Control (QC) shift daily	Capture full operational envelope including heavy-truck periods.

Frequency domain analysis and the FFT

The FFT frequency domain analysis is one of the bases of structural assessment and perception of the health of concrete bridges. In this regard, it is possible to effectively convert sensor data, for example, vibrations caused by traffic and environmental loads, from the time domain into the frequency domain and identify the dynamic characteristics of the structure, for example, natural frequencies and mode shapes, which are sensitive to damage and stiffness.^25–27

This typically involves data acquisition, as shown in Table 2, data pre-processing to remove noise and Direct Current (DC) offset, and finally, the application of the FFT algorithm, which can be supported by window functions to prevent spectral leakage.^46,47

Table 2.

Acquisition and processing parameters.

Stage	Parameter	Value/choice	Rationale
Sampling	Sampling rate	200 Hz	Covers target content to ∼80 Hz with margin; aligns with NI 4472 anti-alias
Session control	Segment length	Variable (continuous)	Enables long Power Spectral Density (PSD) averages while preserving heavy-vehicle bursts
Calibration	Sensitivity	Per-unit calibration file	Converts mV → m/s^2; consistent across channels
Pre-processing	Detrend Direct Current (DC) removal	Yes (per window)	Stabilizes FFT baselines; avoids leakage
Filtering	None (broadband)	—	Preserve low-frequency modal content; rely on windowing
PSD	Welch	Hanning, 4096-pt Fast Fourier Transform (FFT), 50% overlap	Good variance–resolution trade-off for 2–10 Hz peaks
Time–frequency	Spectrogram	8 s window, 50% overlap	Tracks diurnal drift; retains truck bursts
Coherence	γ²(f)	Same windows as PSD	Apples-to-apples comparability across girders
Quality Assurance/Quality Control	Stationarity checks	Daily	Flag storms, maintenance, or wiring anomalies

FFT: fast Fourier transform.

One of the major issues of concern for bridge engineers is resonance, which is caused by the coincidence between the frequency of dynamic loads, for example, traffic, and the natural frequencies of the structure.

Field investigations

Visual inspection

The structures of the Rayhanna Bridge had been inspected based on visual inspection criteria, and it was concluded that all the items were devoid of corrosion and cracking. However, it had been established that the bearing pads had to be repaired, as they had been worn out so far that there was only little left of their original dimension, and they had lost half their dimension, probably destroyed by being subjected to pressure over ages of use, as shown in Figure 3. The dimension of the pad had been established to be 48 mm, which is smaller than the dimension of the pad at the time of construction, which was 74 mm. After the visual inspection, further NDT was conducted.

Accelerometers

These sensors detect the acceleration of the bridge structure, and this is useful in detecting any kind of vibration and responses. Accelerometers are important in monitoring the impact of traffic loads, wind, and seismic activities on the stability of the bridge.³

Accelerometers had been strategically placed in key areas of the bridge girders (L/2, L/3, and 2L/3) to detect the dynamic responses of the bridge, as shown in Figure 4. ADXL335 accelerometer is used since it is stable (durable), responds to temperature, and is tri-axial, thus making it useful in SHM. The information retrieved from this sensor is useful in simulating the behavior of the bridge and has been instrumental in all decisions regarding maintenance, upgrading, and management of the bridge.

The capacity of this bridge to bear loads has also been evaluated using a load test that simulated loads equivalent to those of traffic. The setup of this system was done with care, and a precise NI 4472 module, which is considered to be the most precise data collection device, was utilized in this data acquisition setup. Moreover, precise Blue Storm Cat7 cables that are of high specification were utilized in connecting the ADXL335 accelerator sensors to shield and provide bandwidth. In addition, noise suppression techniques such as electrical isolation, grounding using a common copper rod, and the incorporation of a voltage regulator to provide a stable source of power are utilized in this setup. This setup that incorporates precise hardware installation and noise suppression techniques is considered to ensure credible and precise data acquisition in the context of this SHM setup. The experiment took place over a period of 3 weeks, and the live traffic was tested predominantly at 18–60 km/h. It was fixed on the top of the bridge a Mini IR PTZ Speed Dome Surveillance Camera with 5MP 1080P Full HD IP Network CCTV camera having 20 × ZOOM. This camera was tethered through an Ethernet to a computer to provide stability, and the software panned, tilted, and zoomed. Photographs of the chosen cars were captured, and their speed was computed relative to the duration of travelling across the length of the bridge. The live feeds were displayed and controlled on a monitor, which was linked as indicated in Figure 5.

Results and discussion

Observed data trends

The monitoring system lasted 3 weeks, and it recorded how the bridge was responsive to real-life traffic, as shown in Figure 6. The critical values of the quantities were determined quantitatively by means of the analysis, and it was pointed out that the behavior of one side of the girders is asymmetric in its dynamics. The peak and mean acceleration of the central girder were 0.256 and 0.121 m/s², respectively, which ensured this element was primarily load bearing. This was accompanied in Table 3 by the variability in G2 (standard deviation (SD) = 0.043), with greater dispersion in loading than G1 (SD = 0.024) and G3 differences, that is, SD of ¼ 0.033. In addition, a very small minimum response of 0.023 m/s² for the girder on the (G3) implied the uneven distribution of traffic. Such values have quantitatively demonstrated structural asymmetry, and it is in such conditions that load-relief policies aimed at reducing fatigue risks should be adopted.

Table 3.

Statistical summary of acceleration data for three girders (G1: left girder; G2: middle girder; G3: right girder) due to passing trucks.

Girder	Mean	SD	Minimum	Maximum	95% CI of mean
Middle (G2)	0.12	0.04	0.08	0.26	0.11–0.13
Left (G1)	0.10	0.03	0.07	0.18	0.10–0.11
Right (G3)	0.10	0.03	0.02	0.20	0.09–0.11

SD: standard deviation; CI: confidence interval.

FFT model-based interpretation

While analyzing the data from an accelerometer applied to a concrete prestressed bridge exposed to traffic vibrations, the FFT is an important tool which can convert time-domain data into frequency-domain data.^48,49 The data from the FFT is important since it can provide significant information regarding the dynamic response of this 46-year-old bridge to various traffic loads. For example, large vehicles such as freight trucks can have frequencies between 7 and 23 Hz, while moderate vehicles can have frequencies above 5 Hz. Damage in certain areas or road surface problems, as indicated in this wider excitation range, especially in the higher frequency range of 15–23 Hz, may not only exacerbate structural damage but also create safety concerns. They identified a similar frequency range for large vehicles and highlighted the significant need to immediately address road damage and bridge deterioration.^50–52

The range of the frequencies excited by these trucks varies between 5 and 25 Hz, and the higher frequencies, that is, 15–25 Hz, are related to structural problems in specific areas,^53,54 which indicates the need to keep an eye on frequencies over 15 Hz to detect potential problems in older infrastructure at an early stage.^55,56 There are two main areas that need to be targeted with mitigation strategies: one is the implementation of strategies to avoid resonance, which can be achieved with the use of speed restrictions, traffic control, and TMDs, and the other one is the specific areas of degradation, which need to be improved to increase the durability of the structure, as shown in Figures 7 and 8. The importance of targeted interventions and dynamic monitoring in the safety and durability of older bridge infrastructure can be highlighted with the results obtained in this work.^57,58

It is a detailed three-dimensional (3D) FFT analysis of the vehicle-induced vibrations on the prestressed concrete bridge and the responses to the variable vehicle loading conditions, as shown in Figure 9. The time-averaged spectrum of the bridge shows the natural frequencies of the bridge, denoted by the dashed vertical lines at frequencies around 5–7 Hz, characteristic of medium span prestressed concrete bridges, and the higher-level frequency bands, with more energy generated in the entire spectrum because of heavy vehicles, represented by the filled areas under the curves. More details regarding the mathematical model are in Appendix A.

The frequencies observed are consistent with literature because the basic frequencies of prestressed concrete bridges fall within the 2–10 Hz range based on span length and structural arrangement.^50,59,60 The vibrations caused by vehicles have been studied to demonstrate that the heavy vehicles are more effectively excited at lower frequencies, with the suspension system of the vehicle (usually 1–3 Hz) and body bounce (8–12 Hz) producing distinct frequency signatures, and an amplification in response to vehicle frequencies near bridge natural frequencies.^61–64

Figure 10 condenses 3 weeks of in-service acceleration from the central girder into a time–frequency view. Five narrow and persistent ridges are present in the plot, which relate to the fundamental and higher vibration modes of the girder. The smoothness of the curve and the consistency of the signal over time reflect the stability of the structure and the quality of the signal, while the smooth curvature of the signal over time is evidence of environmental changes, which are typically related to daily temperature changes. The low and uniform noise floor confirms that the acquisition chain and noise control approach have been effective in allowing the modal content to be highlighted with high contrast.

Figure 10 confirms two important aspects of the data collected during the field investigation. The central girder is subject to the major dynamic load, as can be confirmed from Figure 10, where it is evident that the modal lines are always those with the highest content, corresponding to the higher mean and peak accelerations measured at mid-span and third points. The modal content is also within the range identified by the FFT approach as related to the Rayhanna Bridge, which confirms the reliability of the frequencies reported from windowed spectra. The gentle upward trend of the modal content over time is consistent with the sensitivity of this parameter to environmental changes and to the conditions of the supports, including those related to the degraded elastomeric bearings identified during the visual inspection.

Figure 11 is a comparison of the power spectra of the three main girders under live traffic with a consistent Welch pipeline and confidence envelopes applied. Three distinct and repeatable peaks are observed that correspond to the fundamental and higher modes of the bridge. Once again, the main girder exhibits the greatest spectral density in each peak, emphasizing its position as a dominant load case. The narrow bandwidth of each peak and tight confidence envelopes give confidence in the accuracy of modal frequencies calculated from this dataset.

The shaded band represents the force band introduced by live traffic. The second modal peak of the bridge is on the edge of this band, indicating an important interaction during periods of heavy traffic activity. This explains the large variability of the central girder and associated amplification events evident on the spectrogram.

Figure 12 shows the degree of movement of the left and central girders along the spectrum. Three narrow peaks with coherence approaching unity are again observed at frequencies of just over two and a half, just over five, and just under eight. Once again, this is related to the natural modes of the bridge and confirms that all three girders move together. The narrowness of these peaks is again indicative of a stable and well-defined dynamic signature during live load events.

Outside this natural range, the coherence tends to zero, as would be expected if all girders are responding to inputs from the highway. The shaded region between 9 and 12 is a range in which coherence is reduced.

Figure 13 illustrates the relationship between vehicle speed and the frequencies, which are more intensely exciting. It is evident from the figure that the colored region is correlated to the intensity of the resonance risk, and it has been found that higher intensity of color indicates higher risk of resonance. The light blue color indicates the region of the second bending mode of the bridge, which has been identified to be more sensitive in the previous sections. The dashed line indicates the kinematic path, where the roughness of the road is converted to vibrations by the movement of the wheels. The crossing point of this path and the modal band indicates the region where the bridge is more sensitive to dynamic amplification.

The shaded region, indicated in red, indicates an unsafe speed range, where the risk of resonance is greater than the threshold value.

The statistics regarding acceleration, as indicated in Table 4, are calculated for the girders, quantifying the asymmetry between them. It has been found that the central girder, G2, has greater values of mean, variability, and peaks compared to G1 and G3, which is in agreement with the degradation of the bearing, identified during inspection.

Table 4.

Statistics by girder under live traffic.

Metric	G1 (left)	G2 (center)	G3 (right)
Mean acceleration (m/s²)	0.10	0.121	0.10
SD (m/s²)	0.030	0.043	0.033
Minimum (m/s²)	0.07	0.08	0.023
Maximum (m/s²)	0.18	0.256	0.20
95% CI of mean (m/s²)	0.10–0.11	0.11–0.13	0.09–0.11
Qualitative note	Lower spectral energy	Dominant dynamic demand	Lower spectral energy

CI: confidence interval.

Figure 14 is used to demonstrate the comparison between the vertical frequency response for the bridge in the area of the second bending mode of oscillation for the reference case and different settings for the TMD. The dashed line for the reference case has a high and narrow peak, indicating significant amplification for traffic frequencies corresponding to this mode of oscillation. The thick green curve represents a damper setting that is close to optimal, where the peak is reduced and the curves are flattened on both sides, which is a safer condition that is less likely to lead to unstable amplification when encountering large trucks.

Figure 15 presents a display of how the level of vibration power varies with time in the frequency range of interest for the central girder of the bridge during in-service traffic. The warm ridges that rise above the surface of this display indicate the first, second, and third modes of oscillation of the bridge. Their shapes vary smoothly over time, showing the slow daily variation that occurred during this campaign. It is thought to be related to temperature and support conditions. The sharp and narrow peaks appearing from time to time on this plot result from large trucks on the traffic route, producing a wide upper end of this plot.

Figure 16 is a visualization of the way in which the bridge vibrates across the length of the structure and between the three girders. The colors represent the relative amplitude of the mode, with warmer colors indicating a higher level of participation. The black lines are representative mode traces superposed over the surface to aid in interpreting the first few bending modes. The highest crest is over the center girder and at mid-span, with lower participation in the outer two.

Figure 17 is a mapping of the way in which the determined second mode frequency varies with increasing bearing age and temperature rising from reference condition. The trend lines both slopes downwards across both axes, indicating that increasing bearing age decreases the frequency, and increasing temperature does so further. The contour underneath the surface represents the combined influence of both parameters and suggests that a moderate level of bearing age and typical daytime temperature can drive the frequency below the baseline band indicated in cool and early morning data.

This behavior relates the visual observation of thin elastomeric pads to the slow modal drift observed in the time–frequency plots.

Figure 18 illustrates the dependence of the force imparted to the bridge upon vehicle speed and excitation frequency. The high ridge running across the surface represents the kinematic transformation of road irregularities into vibration as the wheels roll over the deck. The top of this ridge represents those combinations of speed and frequency for which the vehicle most effectively transmits force into the structure. The lower ridges at low and mid-frequencies relate to suspension bounce and wheel hop characteristics typical of heavy trucks.

In relation to the study, the map helps to clarify which speeds of traffic imparted the strongest responses to the bridge structure. As speed increases, the kinematic ridge moves across the frequency range in which the structure’s second mode is found.

Figure 19 is a free form view of how a TMD system can be used to reduce vibrations at the second mode of the bridge, which is its most sensitive mode. It is shown as a function of how much mass is utilized and what level of damping is provided. It rises from a low corner where a lightly damped, lightly massed damper would have minimal impact to a plateau where enough mass and damping combine to reduce the response at the second mode. The red line is a curve of best response at each level of mass utilization, tracing out the top of this plateau. It demonstrates that substantial reduction of response is not difficult to obtain but does require proper balancing of mass and damping.

Figure 20 is a view of how the left and center girders move over time and frequency. There are large ridges at the modal frequencies of the bridge where the movement of the two girders is essentially the same. Between these ridges, there is a dip to a lesser height indicating that not all of the variations from traffic and local inputs act on both girders. The horizontal plane represents a detection threshold: when it crosses this plane, it is clear that it is a global response, and when it is well below it, it is local response.

The surface is consistent with the field results. The coherence is strong through the first, second, and third modes. It supports the frequencies determined from the spectra and spectrograms.

Table 5 is a summary of all of the model properties and their operational significance. The three main frequencies of 2.5, 5.1, and 7.8 Hz are related to damping and coherence values to distinguish global structural response from local excitation between 9 and 12 Hz. Table 5 links data with causes by showing where truck-induced energy inputs overlap with the structure’s natural response.

Table 5.

Modal identification summary from Power Spectral Density (PSD)/coherence/Operational Modal Analysis (OMA) (results).

Mode	Identified frequency (Hz)	Damping ratio (half-power, %)	Peak coherence γ² (G1–G2)	Mode description	Operational interactions
1	2.5 ± 0.05	1.5–2.0	∼0.95–1.00	Global vertical bending	Limited overlap with truck band; stable reference for trending
2	5.1 ± 0.08	1.8–2.5	∼0.95–1.00	Global bending, high mid-span amplitude	Highest operational risk; sits in heavy-vehicle band
3	7.8 ± 0.10	2.0–3.0	∼0.9–0.98	Higher bending/shear participation	Intermittent overlap with upper band bursts
9–12 Hz band	—	—	Coherence dips	Localized excitation zone	Points to surface/bearing irregularities
Diurnal drift (mode 2)	∼±1–2%	—	—	Temperature-sensitive	Warm periods increase overlap risk

Figure 21 is a way of taking the monitoring data and relating it to a risk landscape of damage in terms of fatigue and serviceability. The band of yellow in the plot shows where combinations of vehicle speed and intensity create hotspots of damage. Superimposed on this plot is a blue line representing the range of speeds associated with the second bending mode of structural response that was identified during the monitoring campaign. Where this line intersects with high traffic flow, the surface response is very steep indeed.

The map also makes sense of several observations in the field. The amplified response on the central girder occurred during the truck periods because the speeds were mostly in the range of the resonant band.

Figure 22 plots temperature and time of day against the observed movement of the bridge’s second natural frequency. The smooth curve rising and falling with the hours of the day represents the natural thermal cycle, and the color gradient on the temperature scale indicates that rising temperatures always cause the natural frequency to drop. The dashed line on the floor plots the trend of the environmental temperature, which would cause the natural frequency to rise in the morning and fall in the afternoon.

Figure 23 demonstrates the impact of effective bending stiffness as damage is spread over a characteristic length scale and as higher vibration modes are considered. The trough diagonally across this plot shows that medium length scale and mid-order modes have the largest impact on stiffness reduction. At the front left of this plot, very short length scales behave almost as local damage, and the impact is moderate except at high modes. At the back right, very long length scales spread damage so broadly that it has little impact on any single mode.

Within this context of this study, this phenomenon is consistent with why there was a significant upper side-band content in the bridge’s frequency response and why there was significant sensitivity in the second and third modes, whereas the fundamental frequency remained relatively stable. The degraded elastomeric bearings and localized surface defects provide a damage of finite length rather than a point or a field. This damage length is more efficient in coupling with those modes that are most active in the measured frequency spectrum of the central girder.

In order to prevent circular reasoning and to provide a completely quantitative validation of the vehicle–bridge interaction (VBI) problem, a strict distinction is maintained in the model evaluation process between calibration and validation datasets. In calibration (inverse update), a limited parameter set (e.g., bearing stiffness and modulus drift) is determined based on a limited dataset of the monitoring record and compared to a limited set of measured modal frequency locations and their temperature trends (2.5, 5.1, and 7.8 Hz). In contrast, validation is conducted in a completely independent fashion and is quantitatively expressed in three ways: RMS acceleration error at each of the bridge girders, comparing simulated and measured RMS acceleration levels over independent traffic excitation intervals; band-limited PSD amplitude error, computed over operationally relevant frequency bands (e.g., 2–10 Hz to capture global modes and 10–25 Hz to capture localized/high-frequency excitation), using a common Welch-based PSD computation pipeline applied to simulated and measured acceleration signals; and a time-history-based comparison of peak acceleration and short-window spectral energy content of simulated and measured responses during a limited number of heavy vehicle events (located in the camera record and thus independent of frequency content), specifically in a neighborhood of the second mode frequency.

Sensitivity analysis

In terms of controlling the model’s complexity and avoiding issues of identifiability, the work proposes the use of a structured parameter partition, such that only a limited number of model parameters directly supported by the 3-week monitoring data are calibrated. These include the degradation of the stiffness of the bearings, which can be directly inferred from the terms related to the stiffness of the left and right stiffness or the stiffness scale with the asymmetry factor, the slope of the thermal drift of the second modal frequency based on its temperature dependency, and the effective damping of the second mode, which can be directly estimated based on the bandwidth of the spectral peak and the use of the power spectral density pipeline.

The remaining model parameters are considered weakly identifiable and therefore bounded, which means they are constrained instead of being calibrated. This is because the data are primarily dominated by three modes over the short period, and therefore the fractional damping order and the nonlocal damage length scale cannot be uniquely determined, and they are constrained to reasonable ranges to ensure the problem is well posed and to avoid an ill-posed inverse problem.

A third group of inputs is fixed using literature values or engineering priors to avoid unnecessary model expansion. These are representative properties of the vehicle, such as suspension properties and axle force characteristics, and road properties such as road roughness, defined by the spectral slope. Secondary parameters that do not significantly impact the decision are also maintained at constant values, ensuring the model is at the decision grade level of complexity. Sensitivity analysis is used to determine the dependency of the modal response on each parameter. Local perturbation analysis indicates that the bearing stiffness dominates the response for the second mode, and the parameter for thermal drift is responsible for the daily variation observed in the frequency response. Other parameters, such as fractional damping order and nonlocal length scale, are included using bounded sensitivity analysis.

A global-bounded parameter sweep is then conducted to assess decision robustness. Over a range of realistic parameters, it is found that the range of high-risk vehicle speeds is relatively small, and that the TMD plateau is not significantly altered. This suggests that the proposed mitigation strategies are robust and not critically dependent on a narrow parameter range. Separate calibration and validation are also conducted to prevent circular reasoning. Calibration is conducted using a subset of monitoring data to estimate parameters that can be identified, and validation is conducted using independent monitoring days and heavy truck passages that were not used in calibration. The performance is verified on the basis of the comparison of the results of the Root Mean Square (RMS) acceleration and the calculations of the band-limited power spectral density.

Lastly, the use of bounded priority and regularization ensures physical plausibility and avoids overfitting. For cases where correlation between the parameters exists, such as the damping representation and the roughness excitation, it is not recommended that the identification can be done uniquely. Instead, the emphasis is on the decision robustness in the presence of uncertainty, and the parameters are considered in the context of the bounded ranges. Figure 24 presents the results of the sensitivity analysis. The decision robustness heatmap presents the dependency of the center of the high-risk speed band on the bearing stiffness scale and the fractional damping order, which indicates the existence of the stability zone where instabilities are not present. The 3D surface verifies smooth variation without any abrupt instabilities.

Theoretical and practical implications

This study moves SHM from signal interpretation to operations-oriented decision science for aging bridges by developing a traceable connection between inspection-based degradation of boundary conditions, long-duration output-only vibration signatures under uncontrolled traffic, and a compact mechanistic model that generates decision-grade control maps. The main theoretical contribution is that degradation of boundary conditions (bearing compliance and asymmetry) can be inferred and operationally addressed using stable modal fingerprints, screening via coherence functions, and temperature-informed frequency tracking without the need for full-scale output-only vibration testing. By using output-only modal data in conjunction with a VBI formulation, this study establishes SHM as a closed-loop framework in which monitoring detects operational vulnerability (mode-traffic overlap), modeling rationalizes mechanism (support softening and excitation efficiency), and decision maps translate mechanism into actionable interventions. The study also demonstrates that fractional/nonlocal representations can function as compact models for distributed loss mechanisms in aging prestressed concrete, provided that they are used in a decision support role with explicit parameter assumptions and uncertainty limits.

Practically speaking, this workflow now enables owners to effectively employ low intrusion, high-impact mitigation strategies using conventional sensors and repeatable spectral analysis to derive directly implementable policies and retrofit criteria. Speaking of which, the results are particularly relevant to (1) traffic operations control, temperature-based speed and lane management for heavy vehicles to minimize re-excitation in a band around the bridge’s most sensitive modal band, (2) maintenance prioritization, bearing rehabilitation (especially in the central girder line of the bridge deck), since increasing support stiffness directly reduces dynamic asymmetry and resonance overlap, and (3) retrofit strategies, particularly for tuning regions and acceptance criteria of a TMD, such as peak PSD reduction and stabilization of modal energy/coherence. The most significant practical implication of this is that agencies can now realize a quantified reduction in vibration demand and fatigue accumulation without immediate major capital investment yet still maintain a verification mechanism by re-monitoring and comparing post-intervention spectra.

Conclusion

This article shows an unbroken and justifiable chain from condition data to operationally actionable decisions for an in-service, 46-year-old bridge. Visual inspection identified a degradation mechanism, elastomeric pads reducing from 74 to approximately 48 mm, prompting a dynamics-based assessment under live traffic conditions. Three-weeks of tri-axial accelerometry showed stable modal characteristics around 2.5, 5.1, and 7.8 Hz. The central girder (G2) showed higher dynamic demand (mean 0.121 m/s² peak 0.256 m/s² SD 0.043 m/s²), supporting the asymmetric load path suggested by support degradation. Inter-girder coherence increased to unity levels at modal peaks and troughs, and fell in the 9–12 Hz range, consistent with localized excitations caused by surface and bearing irregularities. Heavy vehicles caused significant response in the 7–23 Hz band, explaining the observed amplification during traffic conditions intersecting with the second mode.

With these results grounded in physics, we developed a fractional, nonlocal vehicle bridge model with compliant bearings, which connects what we measure to cause and control. The model reproduced the spectral peaks, models the environment’s impact on the structure (e.g., the 1–2% day-over-day shift in the second mode), and produces decision surfaces to translate monitoring into actions. For example, in the resonance proximity map, it is clear that the unsafe speeds of heavy trucks are in the range of 12–19 m/s or 43–68 km/h. Next, in the surface showing bearing aging/temperature, it is clear how the reductions in frequency accumulate and how the overlaps increase with warmer days. Finally, in the design charts showing mitigation, it is clear how the TMD, when tuned to about 5.1 Hz, with parameters such as a mass ratio of about 0.04 and a damper damping of about 0.12, reduces the peak responses by 3–5 dB or 25–35% in amplitude, and how robust this solution is to mistuning and temperature.

This process has the potential to advance practice in three significant ways. The first is that the degradation of this boundary condition is directly related to the quantified dynamics, and it is possible to separate the global and local dynamics using coherences and time–frequency analysis. The second is that this monitoring has been taken from a simple “frequency reporting” to an operation-informed SHM process, allowing for decision surfaces to be provided for speed windows, lane guidance, and retrofit requirements with clear acceptance criteria (e.g., peak PSD reduction, frequency stabilization, and coherences). The third is that this process has the potential to be easily replicated on similar bridges using standard sensors and data collection, spectral analysis, and physics-based model, allowing for policy-relevant results.

The limitations are acknowledged. They include opportunistic traffic excitation, the lack of control inputs via a shaker or drop weight, and the spatial array, which cause non-stationarity in the spectrum of the traffic inputs, restrict the resolution of higher mode shapes, and degrade the accuracy of damping estimation and inverse updating convergence due to variation in vehicle classes and road inputs. Surface condition and temperature are other sources of variability, while their effect is partially compensated for via temperature compensation of the frequency tracking, they cannot be separated from boundary condition degradation using only traffic inputs. However, these issues can be overcome via a planned program of follow-on work, including periodic re-instrumentation, denser sensor array, and better road roughness surveys, but, importantly, via planned controlled dynamic testing, such as quarterly drop weight or portable shaker testing under multiple temperature states to obtain clean frequency response data under known input conditions. This data would then provide robust baselines of vehicle response, unaffected by vehicle variation, improve parameter identifiability, reduce uncertainties in bearing stiffness estimation, and improve the validation of the VBI model and decision maps. In conclusion, the Rayhanna Bridge has demonstrated modal stability with significant second-mode sensitivity exacerbated by bearing degradation and heavy vehicle excitation. The inspection-sensing-modeling approach has identified actionable outcomes, which are central line bearing rehabilitation, enforcement of speed control to avoid 12–19 m/s during heavy vehicle excitation windows and accounting for temperature effects, and, as an option, installing a TMD tuned to 5.1 Hz. The outcomes are actionable and should reduce vibration demand, slow fatigue accumulation, and extend the bridge’s safe life with minimal operational impact.

Footnotes

Appendix A

ORCID iDs

Ali Shehadeh

Mohammed O Hussein

Akram S Mahmoud

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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