Distributed Sensor Networks for Real-Time Health Monitoring of Prestressed Concrete and Steel I-Girder Bridges

1.1 Background and problem statement

A bridge is an important structure composed of two main sections: the superstructure, which includes the deck, joints, pavement layers, drainage system, girders or beams, bearings, and barriers; and the substructure, which consists of foundations, piers, and pier tops. Bridges are built to span obstacles such as rivers, roads, and railways, and they are classified according to their supports and construction materials. Common types can include concrete, pre-stressed concrete, wood and steel bridges and structurally they are divided into two general bridges as simply supported type and continuous type bridges [1-3].

Bridges are vital in any transportation system, but also very expensive to construct and maintain. Council bridges that were built decades ago are now experiencing traffic volumes significantly higher than their designed capacity, with many operating either near or at failure. With the development of sensing and non-destructive testing techniques, more attention has been paid to the design of reliable SHM systems. On the whole, periodic examination and maintenance are very important for safety and cost saving. Optimal bridge care is based on the periodic inspection of specially trained teams that assess, in detail, the condition of individual elements and such that appropriate strengthening or repair can be made [4].

Enhancements in the capacity of existing concrete bridges, generally consist of load-carrying capacity upgrades, stress redistribution or material improvement or replacement. Selection of the method depends on several factors, including structure type, age, significance of the structure, strength gain required to restore capacity, amount of damage, availability of materials, cost and aesthetics [5].

Bridges are important elements of the transportation system of today. There are >617,000 bridges in the USA and many more millions around the world, so monitoring for continued safety and economical operation is necessary [6]. When catastrophic failures of structures such as I-35W Mississippi River Bridge (2007) and Morandi Bridge in Genoa (2018) occurred, the development of advanced SHM with prevention capability that can detect structural deterioration before failure became increasingly important [7]. Traditional visual inspections and occasional measurements are not effective in evaluating dynamic behavior under actual operation [8].

There are tremendous financial and social impacts of bridge failure. It has been estimated that over one-third of the United States' bridges need rehabilitation or replacement, which comes at a staggering cost of more than $171 billion [9]. Failure to be able to monitor ongoing degradation may cause catastrophic collapse, loss of life and public confidence. Currently inspection is limited to every 2nd year, and has no potential approach for monitoring of structural performance continuously nor the gradual degradation leading to failure [10].

The financial and social consequences of bridge failures are immense. The U.S. Federal Highway Administration estimates that more than one-third of the nation’s bridges require repair or replacement at a cost exceeding $171 billion [9]. The inability to detect ongoing degradation may lead to sudden collapse, human casualties, and loss of public confidence. Current inspection procedures, which normally occur once every two years, it is not possible to continuously monitor structural behavior and its slow evolution indicative of an imminent collapse [10].

1.2 Limitations of conventional monitoring approaches

Conventional bridge monitoring systems have several inherent limitations that reduce their effectiveness in ensuring structural safety. Visual inspections, although providing useful qualitative information, are subjective and depend heavily on inspector experience and environmental conditions. Quantitative measurements using instruments such as strain gauges and displacement transducers are typically restricted to a few points and require extensive cabling, which makes large-scale monitoring costly and complex [11, 12].

Moreover, conventional systems only measure static parameters, e.g., the maximum deflection, and stress under design load and not dynamic response that can provide early warning of damage in a structure. Changes in natural frequency, damping value and mode shape can show stiffness degradation or local damage well before there are perceptible changes in the static response. The inability to continuously assess these parameters is a critical shortfall of current SHM methodologies [13].

1.3 Evolution of sensor-based monitoring technologies

The emergence of micro-electromechanical systems (MEMS) technology revolutionized structural monitoring based on the deployment of miniaturization, low-cost sensors for problem monitoring involving multi-parameter measurement concurrently [14]. Inertial measurement units (IMUs) that were initially being developed for aircraft or automotive engineering are increasingly used in civil engineering since the acceleration as well as angular velocity can be detected at high precision, as well as temporal resolution.

Among these devices, the MPU6050, a six-axis IMU integrating a three-axis accelerometer and a three-axis gyroscope, represents a major advancement in affordable sensing technology. With configurable ranges of ±2 g to ±16 g for acceleration and ±250 °/s to ±2000 °/s for angular velocity, combined with 16-bit analog-to-digital conversion and digital motion processing, it provides the specifications required for reliable and comprehensive structural health monitoring (SHM) applications [15].

1.4 Theoretical basis of bridge dynamic response

Characterization of the bridge response involves consideration of the interaction between static and dynamic properties that influence the behavior of the structure. Classical mechanics and vibration theories are the theoretical background for processing sensor data and detecting physical damage states [16].

1.4.1 Static parameters

• Displacement Response: The linear of displacement is the first indication of form-strain in a structure under load. based on the elastic beam theory, this load-deflection relationship is a function of material properties, geometry and boundary conditions [17].
• Stress Distribution: Significance of stress patterns in the material usage and safety features. In prestressed concrete (PSC) bridges, compressive prestress forces are induced to cancel tensile stress under allowable conditions [18]. On the other hand, steel bridges can accept both tensile and compressive load in their elastic stage.
• Serviceability Criteria: The service limits control the factors of human comfort and structural integrity by specifying the maximum permissible deformations depending on span length and type of bridge [19].

1.4.2 Dynamic parameters

• Natural frequency: The un-damped vibration of the bridge is characterized by its natural frequency that is associated with the stiffness and mass of the model structure. Variations in material stiffness may occur due to material damage or degradation and will alter the vibrational response of a structure (thus rendering frequency-analysis useful as a diagnostic tool [20].
• Damping: It is the ability of a system to dissipate energy through a material, hysteresis, friction at a joint or aerodynamic effects. It has a significant influence on both the amplitude and period of oscillation [21].
• Modal shapes: Are a description, with respect to vibration modes in the system and are affected by changes of parse supports, connections or properties of members [22].

1.4.3 Vibration analysis theory

• Amplitude characterization: Vibration amplitude measures the size of the cyclic motion and is indicative of structural response levels under dynamic loading. The amplitude analysis provides the designer with estimates on the state of serviceability and arising possible resonance effects [23].
• Frequency domain analysis: It is possible to perform the spectral analysis of dynamic signals to extract the frequency intermodal component of structural vibrations, and detect the preferred characteristic mode of response and also possible changes in the characteristics of structures with time [24].

1.5 Wireless sensor network architecture

Contemporary SHM systems have a tendency to use wireless sensor networks (WSNs) for being reductive of spatial limitations of wired networks of wires, along with complexities in the type of sensors being used for monitoring [25]. The ESP32 microcontroller platform with built-in WiFi and Bluetooth (240 MHz dual-core processing and many input/output selection possibilities) is the perfect candidate for such a distributed monitoring network [26].

The message queuing telemetry transport (MQTT) protocol supports efficient, low-overhead communication from sensors to a central control, while providing support for standard Quality of Service levels and message persistence. Such an architecture provides real-time data delivery as well as ensuring against system failure due to adverse networking conditions [27].

1.6 Research objectives and scope

The objective of this research is to fill this gap by developing and validating an innovative distributed sensor network for real-time bridge structural condition assessment. Specific objectives include:

1. An inexpensive monitoring system with MPU6050 sensors and ESP32 microcontrollers;
2. Use of advanced signal processing for reliable estimation of structure parameters through sensor information;
3. Dynamic behavior comparison of various (PSC and steel) structures;
4. Comparison of natural frequencies and mode shapes for different types of systems (PSC and steel);
5. Development of monitoring guidelines and threshold definitions for automated alert triggering.

To achieve these objectives, the study integrates both hardware development and signal processing with comparative field testing in a coherent model. UStocks16: The networked MPU6050–ESP32 chain allows for synchronous detection of vibration, and by adopting digital filtering and double-integrating algorithms we can process raw sensor data into displacement and frequency values. This technical implementation intuitively connects each research goal to a quantifiable performance measure and, therefore, the design idea, as well as experimental validation are completed in one framework of SHM.

3.1 System performance and validation

The enhanced calibration technique used for calibrating MPU6050 sensors on the Al-Faeq Hassan Bridge successfully minimized the difference between the nodes. The per-axis bias and scale factor corrections were applied along with temperature compensation and digital low-pass filtering (10 Hz accelerometer/20 Hz gyroscope), as shown in Figure 6. It may be observed that the earlier incorrect Node 3 Z-axis bias is now consistent with the remaining nodes. Summary of the final calibration parameters can be found in Table 1. The enhanced calibration process improved measurement consistency across all sensor nodes, achieving a displacement accuracy of ±0.09 mm and an angular accuracy of ±0.04°, which satisfies the required performance specifications.

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Figure 6. Accelerometer bias across sensor nodes

Table 1. Sensor calibration parameters

3.1.1 System reliability and data quality assessment

The distributed sensor network performs with high stability and robustness in the long-term monitoring (six-month) process. As illustrated in Figure 7, the system availability and the data quality provided have both been maintained at a level exceeding 98%, with relatively small differences.

• System Availability: The combined average network availability remained at 98.7%. The sources of downtime were

• Planned maintenance: 0.8%;
• Connectivity issues: 0.3%;
• Hardware failures: 0.2%.

• Data Quality: Good data collection was obtained for 99.3%, suggesting great robustness of the sensing system. There was almost no loss in the data, occurring only due to

• Communication loss: 0.4%;
• Bad readings (filtered out): 0.3%.

• Communication Performance: The network and its communication were also efficient

• Average message latency: 45 ms;
• Maximum latency at peak traffic: 127 ms;
• Message loss rate: 0.15%.

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Figure 7. System performance over 6 months

3.1.2 Comparative static performance analysis

The stress distribution and deflection control of the PSC spans under combined service loads were better than those of the steel I-girder span. As can be seen from Table 2, the pretensioning system also resulted in near-zero tensile forces at its service condition and a mild compressive force with little downward deflection compensated by the prestress camber. The steel underwent higher stress levels and deflected more than the concrete, although both were within code guidelines. These results validate that a more economical service-level response is achieved with the PSC geometry as illustrated in Figure 8.

Table 2. Static response comparison under combined loading

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Figure 8. Stress distribution comparison

3.1.3 Detailed stress distribution analysis

The PSC girder spans showed equitable stress distribution, as the individual pre-stress applied in the spans virtually nullified the tensile stresses in both the top and bottom fibres due to service loading. The maximum measured compressive stress (≈-6.0 MPa) even is about 30% of the allowable limit, which demonstrates a significant structural surplus.

By contrast, the steel I-girder span exhibited the typical bending stress profile, with a maximum tensile stress of approximately 80 MPa at the bottom fibre and a maximum compressive stress of approximately -50 MPa at the top fibre. Although these values represent only 39% and 24% utilization of the permissible tensile and compressive capacities, respectively, they remain significantly higher than those observed in the PSC span.

3.1.4 Deflection performance comparison

Deflection performance was the primary point of difference between the two types of structures. The PSC girders had a high stiffness, and the maximum vertical deflection (downwards) of the girder was about -6.0 mm, which was only 20% of the allowable limit. Cambers: This small amount of camber is essentially due to the prestressing effect that introduces an upward camber (+4 mm) and thereby eliminates the service load deflections.

In comparison, the steel I-girder span experienced much larger deflection, with maximum downward movement reaching up to approximately -70 mm. Even though still less than the code limit (about 63% of the allowable range), this could affect user comfort and enhance dynamic effects under heavy traffic loading Figure 9.

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Figure 9. Deflection profile along span

The findings of this study highlight the higher maintainability of the PSC span as opposed to the steel girder span.

3.2 Dynamic analysis results

3.2.1 Natural frequency characteristics

Mode analysis indicated distinct differences between the resonance characteristics of the two system types. It is observed that the fundamental frequency of the PSC spans is about 2.3 Hz, and similarly so for closely spaced higher modes, which occur for frequencies in the range 3.8–4.7 Hz. Across the dominant modes, the average frequency was ≈5.0 Hz due to a larger mass and damping of the system, which lowers dynamic sensitivity as shown in Table 3.

Table 3. Natural frequency analysis results

Instead, the I-girder steel span exhibited a significantly lower fundamental frequency of about 0.6 Hz, which was in line with its lighter superstructure and higher flexural flexibility. But the higher modes of the steel girder governed; hence, an average natural frequency of about 6.6 Hz was achieved. Although the low first mode frequency is within acceptable limits, it may render the bridge more vulnerable to slow-moving heavy vehicles under dynamic amplification, as seen in Figure 10.

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Figure 10. Natural frequency analysis

3.2.2 Loaded vibration frequency analysis

The monitoring system measured vibration frequencies under vehicle traffic and dynamic performance of two types of structures can then be compared directly. As seen in Table 4, 3.75 Hz for the PC spans, where the loaded frequencies ranged between 3.2 Hz at the quarter span to 3.8 Hz at the three-quarter span. However, this value is much smaller than the average natural frequency of the system (4.98 Hz), showing a good ratio of frequencies r = 1.33. Such a ratio signifies unlikelihood of resonant conditions arising under typical traffic loads.

In contrast, the steel I-girder span displayed an average loaded vibration frequency of 6.42 Hz, which was substantially higher than its critical natural frequency (2.95 Hz). This results in a frequency ratio of 0.46, an unfavorable condition that suggests the potential for dynamic amplification effects. Although the system remained stable during monitoring, this outcome highlights the greater vulnerability of the steel system to resonance-related serviceability issues under repeated traffic actions.

Table 4. Dynamic vibration response under vehicle loading

3.2.3 Dynamic displacement analysis

Dynamic displacements showed significant amplitude and symmetry differences between the PSC spans and the steel I-girder span. From Table 5, it can be seen that the dynamic balance of the PSC system was relatively good with a displacement in an upward direction as large as +1.50 mm, pointing downwardly being -2.63 mm and this makes total range from above mentioned two extremes is 4.13 mm. The RMS amplitude of 1.85 mm and the peak-to-peak ratio 1:1.75 show that both the relaxation and centering profiles are relatively symmetric, which denotes a fairly well-optimized profile in terms of structural response.

The steel girder span, however, had greater amplitudes of displacement (up to -5.96 mm in downward direction and +0.66 mm upwards). This led to a full dynamic range of 6.62 mm and an RMS amplitude of 3.12 mm, far larger than that for the concrete system. The significant cross-symmetrical peak-to-peak ratio of 1:9.03 represents a distinct downward bias toward under-dynamic response, reflecting the fact that the stiffness was lower and the flexibility greater for steel Girder as presented in Figure 11.

Table 5. Dynamic displacement response comparison

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Figure 11. Dynamic displacement response of PSC VS steel

3.2.4 Acceleration and velocity response patterns

Dynamic acceleration and velocity of the two systems present significant differences. As summarized in Table 6, the PC spans suffered a greater peak vertical accelerations value (±3.7 m/s² upwards and -3.5 m/s² downwards) which motored a total acceleration range of 7.22 m/s². This suggests faster but damped motion, in agreement with the stiffness and confined properties of traffic loaded PSC vibration.

Regarding velocity response, the prestressed case also showed a greater magnitude, presenting peak positive upward +0.0517 m/s and downward -0.0600 m/s velocities resulting in a total range of 0.1117 m/s.

Table 6. Dynamic acceleration and velocity measurements

The steel I-girder span, on the other hand, showed reduced acceleration amplitudes (from 2.60 m/s²) and smaller velocity values (from 0.058 m/s). This is due to its higher ductility (as previously observed), since the structural response happens over a larger period of time with lower instantaneous accelerations but more final displacement.

3.3 Vibration analysis and frequency domain results

3.3.1 Spectral analysis results

By means of frequency-domain analysis over the acceleration response signals, a unique spectral signature for each structural system was established, and corresponding dynamic response characteristics were distinguished.

1. PSC Spans Spectral Content:
   • Main peak: 3.75 Hz (traffic induced vibrations);
   • Secondary peaks: 2.27 Hz (fundamental) and 4.98 Hz (fundamental mode);
   • Frequency bandwidth: 0.5–12 Hz concentrated below 8 Hz;
   • Spectral purity: Narrow peaks and next to no broadband noise.
2. Steel I-Girder Span Spectral Content:
   • Main peak: 6.42 Hz (traffic induced vibrations);
   • Secondary peaks: 2.95 Hz (fundamental) and 0.56 Hz (fundamental mode);
   • Frequency bandwidth: 0.2–15 Hz with distributed energy content;
   • Spectral complexity: Multiple overlapping peaks indicate complex modal interaction.

3.3.2 Resonance risk assessment

The resonance risk assessment was conducted based on the ratio of the primary natural frequency (fn) to the dominant loaded vibration frequency (fl). This frequency ratio criterion is widely accepted for the assessment of resonance safety, and ratios higher than 1.2 are usually believed to be safe, whereas those lower than 0.8 are considered susceptible to resonance.

1. PSC Spans:
   • Frequency ratio (fn/fl): 4.98/3.75 = 1.33;
   • Risk level: Low (ratio >1.2 considered safe);
   • Recommendation: Continue normal monitoring.
2. Steel I-Girder Span:
   • Frequency ratio (fn/fl): 2.95/6.42 = 0.46;
   • Risk level: High (ratio <0.8 indicates concern);
   • Recommendation: Immediate structural enhancement required.

3.4 Comparative performance assessment

3.4.1 Overall structural performance matrix

The comparison performance assessment integrates the static, dynamic and material efficiency factors into one consolidated evaluation matrix. At 30 years, the paramount of the PSC spans in surpassing most performance metrics is demonstrated in Table 7.

• Static Stress Control: PSC was highly efficient as the stress utilization ratio was only about 20.6% of the allowable range vs. 41.5% for the steel girder.
• Deflection Performance: The concrete span used 14% of the deflection limit, in contrast with the steel one that used more than 80%, meaning virtually six times better performance for concrete.
• Dynamic stability: The PSC had a frequency ratio in the safe condition (fn > fl) revealed stable dynamic characteristics, whereas for the steel girder there were resonance issues (fn > fl).
• Vibration amplitude: Displacement amplitude of the concrete span was less by 38% than that for the steel system, indicating better serviceability.
• Frequency Response: A distinctly safe resonance ratio (1.33) was held by the concrete spans and no such safety margin was found for steel girder (0.46).
• Material Economy: Balance of material with regard to the prestress system, stress in concrete is minimized to zero, achieving durability against tensile stress; but in steel girders the limit state was elastic and a smaller safety margin.

Table 7. Comprehensive performance comparison

3.5 Statistical analysis of dynamic parameters

To improve the reliability and interpretability of the results, the measured dynamic parameters were statistically analyzed across multiple recordings under comparable traffic conditions. The calculated mean values, standard deviations, and 95% confidence interval (CI), Table 8, provide quantitative evidence of the system’s accuracy and repeatability.

The PSC span exhibited consistent vibration characteristics, with a narrow CI indicating minimal data dispersion. Conversely, the steel I-girder span showed larger variability in both frequency and displacement, confirming its higher sensitivity to dynamic amplification effects. The standard deviations below ±0.22 Hz and ±0.12 mm across all readings confirm the stability and precision of the distributed MPU6050–ESP32 sensor network.

Table 8. Statistical summary of dynamic response parameters

These findings validate that the proposed MEMS-based SHM system provides repeatable and statistically significant results under real operating conditions, ensuring its suitability for long-term field monitoring.

3.6 Economic analysis and sensitivity evaluation

The economic study used real component costs provided by local suppliers and checked with online electronics suppliers (up to the year 2025). The average cost of the market price of each module is summarized in Table 9; this shows the implementation cost of the distributed MPU6050-ESP32 system.

Table 9. Market-based cost breakdown of the distributed MPU6050–ESP32 monitoring system

To evaluate the sensitivity of the system cost with respect to the changes on the markets, the costs of hardware, personnel, and maintenance were varied by ±20%. The variation of the costs and their effects on the system costs are shown in Table 10.

Table 10. Market-based cost breakdown of the distributed MPU6050–ESP32 monitoring system