1. Introduction
Bridges are crucial infrastructures of transportation networks that hold a huge economic and social value for nations. However, a significant portion of the global bridge network is reaching the end of its design lifespan. In the USA, more than 42% of bridges are over the age of 50 years [
1], and more than 178 million vehicles pass through structurally deficient bridges. Due to budgetary constraints [
1], logistical challenges, and a large number of deficient bridges, comprehensive repair and rehabilitation efforts for all deficient bridges may not be feasible in the immediate future. Therefore, monitoring bridge health is becoming vital for prioritizing interventions and ensuring public safety through the timely detection of damage to the bridge. Research in structural health monitoring of bridges has developed advanced technologies and methods for early detection of structural issues in the bridge. However, most of these methods and systems were developed to detect damage to superstructure elements like decks, girders, etc. [
2]. These methods often rely on the predefined bridge models with assumed support fixity conditions [
3,
4], which are most of the time highly idealized and far from the actual condition of bearings. The agencies working on repair and rehabilitation recognized joints and supports as the single biggest reason for bridge deterioration [
5,
6]. However, there is a lack of proper methods to assess the health of bridge joints and bearings.
Bearings in the bridge are crucial components that transfer the load from the superstructure to the substructure. They are designed to constrain a specific degree of freedom for the superstructure, and based on this, all the superstructure design limits, i.e., strength limits (stresses) and service limits (deflections), etc., are calculated and designed for those limits. For substructure design, only load from the constrained degree of freedom of bearings is considered. Hence, this means the design of all bridge components is made by assuming a predefined restraining behavior of bearings. However, the performance of bearings in in-service conditions was affected by multiple factors like environmental factors, rusting, and lack of lubrication in moving parts, the collection of debris (dirt, sand, and deicing salts) from leaky expansion joints, material degradation due to chemicals like deicing salts, etc. [
7,
8]. Because those bearings fail to provide movement or increase resistance for movement, restricting the desired movement of the superstructure, these cases are generally referred to as frozen bearings. Although this is considered one of the major issues to be identified and rectified during bridge maintenance by bridge management agencies, it is not widely studied in the literature. The FHWA inspection manual [
9] specifically recognizes frozen bearing as one of the major types of damage, along with cracking, corrosion, overloading, and impact damage, that occur in any type of bridge, irrespective of the material or design of the bridge.
A frozen bearing condition in bridges, if not identified and rectified in time, can lead to serious consequences for the overall health of the bridge, potentially even causing it to collapse. Due to freezing, the bearing will not be able to allow superstructure movement for thermal expansion/contraction or traffic loading, leading to overstress of structural elements and potential cracking [
10]. In the rocker bearing, when any of the bearings has restricted movement, it is vulnerable to overturning and vertical misalignment of spans in skew bridges [
8]. In extreme cases, the horizontal forces generated due to frozen bearings can be sufficient to move or damage bridge piers and substructure components [
11]. Because of such serious implications for bridge health, frozen bearing condition assessment is considered a major task during a bridge inspection. Due to the lack of a more accurate empirical or theoretical framework, inspectors have to rely on their subjective judgment based on a visual assessment of the orientation of bearings, the presence of debris and rusts, etc. Consequently, there is a chance of false identification of the problem, as with other visual inspection methods. A data-driven model based on sensor measurements would facilitate more accurate and timely detection of frozen bearing damage and repair of such crucial components.
Currently, there are no methods to directly quantify the stiffness of in-service supports/bearings on bridges. However, a study by Locke et al. [
12] presented frozen bearing identification by estimating the stiffness of bearings using a vibration-based modal updating method. They proposed that rotational spring stiffness and the magnitude of friction at the bearing could be used to simulate frozen bearing damage in the bridge. Rotational spring stiffness was determined for this purpose using vibration-based drive-by health monitoring systems. However, for in-service conditions, the modal frequency is affected by superstructure damage or deterioration [
13,
14] and environmental conditions, such as temperature [
15]; it is difficult to pinpoint the exact magnitude of support fixity or frozen bearing condition. Moreover, implementing this method requires determining the bridge’s modal frequency and accurately simulating the entire bridge structure, which will be costly (economically and computationally). Thus, a method based on parameters influenced solely by support fixity (e.g., axial thermal expansion of the bridge) will enable a more precise prediction of bearing freezing and help reduce uncertainty in modal-based damage detection of the superstructure by accurately quantifying support fixity.
In addition, the exact quantification of support fixity level is crucial in vibration-based damage modeling and identification for bridges because the boundary conditions significantly influence the modal properties of the structure. The degree of fixity at the supports affects the stiffness distribution and structural constraints, which impact the natural frequencies, mode shapes, and modal strain energy distribution [
16,
17]. Variation of support fixity level during the service period is very likely due to factors like soil-structure interaction, bearing degradation, or unintended restraints [
17,
18]. This change in boundary conditions alters the modal characteristics, potentially masking or amplifying the effects of damage elsewhere in the structure. Inaccurate assumptions of the support fixity level lead to errors in the analytical models used for damage detection algorithms, resulting in misinterpretation of changes in modal parameters, incorrect damage localization, or severity estimation, leading to false-positive or false-negative damage detection [
16]. Therefore, a reliable support fixity estimation system and methods are urgently needed.
Wireless sensor networks (WSNs) are a group of spatially distributed sensing and communication devices that are interconnected to monitor physical and environmental conditions like temperature, strain, displacement, and vibration through wireless communication [
19]. WSNs offer a cost-effective and scalable solution for bridge health monitoring by eliminating the need for extensive cabling and enabling remote data acquisition from strategically placed sensors [
19]. The assessment of bridges using WSNs facilitates the early detection of structural anomalies through continuous monitoring. By taking timely intervention against detected damages, the safety, resilience, and lifespan of the bridge can be enhanced [
20].
The WSN can be used for frozen bearing detection due to its aforementioned strengths. The frozen bearing condition or support fixity level can be quantified in terms of the support stiffness value, which can be best determined by measuring the thermal expansion/contraction of the bridge in in-service conditions. Since the quasistatic structural response is primarily governed by temperature variations, the effects of traffic loads can be considered as noise superimposed on the thermal response [
21]. Thus, longitudinal displacement measurements using WSN with a low sampling frequency mainly contain a thermal response, based on which support stiffness can be estimated. Compared to modal updating methods based on vibration measurements, static thermal response monitoring provides direct stiffness estimates without complex modal parameter extraction, enabling efficient data collection and transmission over WSNs [
22,
23]. When there is minimal or no resistance from supports, a bridge will undergo free thermal movement. This movement is directly influenced by the thermal expansion coefficient of the bridge material and the bridge’s length. However, if there are frozen bearings or conditions where the supports offer increased fixity, the thermal movement behavior of the bridge changes significantly. Instead of experiencing simple linear expansion and contraction, the bridge will exhibit restrained thermal movements. The extent of this restrained movement is contingent upon the degree of fixity provided by the supports. Hence, the thermal response measured from bridges will essentially contain support stiffness information and can be quantified with suitable inverse calculation methods, which are known to be challenging due to uncertainties.
The recent development of machine learning algorithms can facilitate complex frozen bearing quantification. Artificial Neural Networks (ANNs) are among the simplest and most versatile machine learning tools available for predictive modeling. With their ability to learn complex nonlinear relationships from data, ANNs can predict the underlying causes or system parameters when provided with the corresponding effects or responses [
24]. However, implementing ANNs for structural health monitoring is still challenging due to the need for extensive training data and the potential for overfitting or hasty generalization to unseen scenarios [
25]. Additionally, the black-box nature of ANNs can make it difficult to interpret the underlying relationships learned by the network, which may raise concerns regarding transparency and accountability in critical infrastructure applications [
26]. Thus, the possibility of generating training by simulating real structures using their digital twins in different scenarios makes ANNs highly promising options for modeling various structural damages.
To this end, many researchers reported that FE structural models have been used to generate training data in many of the studies [
21]. A model-free damage detection approach is proposed [
24] using ANNs trained on data gathered from simulations of train passages on the finite element model of a fictitious railway bridge. This study used a training data set from an FE simulation of two damage scenarios and a healthy bridge. The ETABS model has been utilized to generate building response data under different seismic loadings to train the ANN model to predict seismic safety parameters [
27]. An offshore jacket structure was simulated in ABAQUS to generate training data for the ANN model to extract damage-sensitive features from frequency data [
28]. Therefore, an ANN model trained on the results of FE simulations of typical highway bridges could be used to predict bearing stiffness.
This paper develops a bridge support quantification method using an ANN model based on quasi-static bridge displacement responses and temperature data using WSN. For training purposes, a steel girder-concrete deck composite highway bridge is modeled in ANSYS. Various numerical simulations of different support stiffnesses and superstructure damage scenarios were conducted using this model. The longitudinal displacement at the end of the girder was obtained for different thermal loadings (uniform temperature change and thermal gradient as per AASHTO [
4]) in the bridges. These data, with Gaussian white noise, are used to train an ANN model. Then, the trained ANN model employed to predict the support stiffness of two in-service highway bridges was predicted: one with visibly healthy elastomeric bearings and another with visibly rusted steel bearings. The field response was monitored using a real-time WSN with an ultrasonic distance sensor and digital temperature and humidity sensors. The result shows the strong potential of this method to relay relevant bridge health monitoring information regarding support to stakeholders for better infrastructure maintenance.
4. Results and Discussion
This section presents and discusses thermal response results from FE simulations, ANN model training results, thermal response from field monitoring, and predicted bearing stiffness results of monitored bridges.
4.1. Thermal Response of the Bridge
The displacement response of the composite bridge under different temperature distributions in conditions with different damage scenarios of the superstructure is studied based on the results of finite element simulation.
Figure 8a shows the longitudinal displacement of the bridge at the top and bottom flange levels for damaged and undamaged superstructures with different stiffnesses of support. This shows that the damage to the superstructure has a negligible effect on the longitudinal thermal movement of the bridge. The presence of damage marginally increases displacement at the top of the structure. However, the displacement at the bottom flange level gets marginally reduced due to damage. This constitutes a small increase in the rotation or flexural curvature of the bridge due to damage, as shown in
Figure 8b. This difference in rotation between damaged and undamaged superstructures increases slightly as support becomes stiffer. This can be attributed to the fact that longitudinal movement is dependent on the length of the superstructure and the thermal expansion coefficient. The difference in thermal movement along the depth of the superstructure is due to the fixity of the bearings.
Figure 9a supports this; as support stiffness increases, rotation increases. When the temperature of the bridge changes uniformly, the movement near the bottom fiber of the beam is restricted by support, but the effect of this restriction gets reduced along the height of the superstructure, causing almost free thermal movement near the top. This causes a flexural curvature, and hence, rotation at the end of the girder is observed. The curvature of the bridge depends upon the sectional properties and elastic modulus of the superstructure; any change in these will affect the rotation. In this case, since damage is considered in terms of section loss due to corrosion near support, rotation was affected slightly due to damage.
In
Figure 9a for K = 500 N/mm, rotation below neutral temperature (10 °C) is negative or counterclockwise, but as stiffness increases to 75,000 N/mm, this rotation becomes positive/clockwise. This demonstrates that uniform temperature change causes rotation in the opposite directions if support does not provide fixity in longitudinal movement (low support stiffness). Thus, for a bridge, the girder rotation will be zero for a given value of longitudinal stiffness of the bearing, e.g., in this case, the girder rotation will be zero for some stiffness value between 500 and 75,000 N/mm. This may be due to the difference in thermal expansion coefficients of steel and concrete (approximately 20%), causing ‘thermal bowing’ due to differential thermal expansions.
The effect of the thermal gradient on the composite bridge depends on the support stiffness and the overall temperature.
Figure 9b shows the typical rotational behavior under a vertical thermal gradient at two representative temperatures (one freezing and another expanding).
For low support stiffness, during the low-temperature time (see −30 °C curve in
Figure 9b), steel contracts more as compared to concrete due to ‘thermal bowing’, and the presence of a thermal gradient (high temperature on top) exacerbates this bowing by further reducing concrete contraction. Hence, it increases the negative bending/rotation (hogging). However, during the high-temperature time (see 50 °C curves in
Figure 9b), steel expands more than concrete without a thermal gradient, but the presence of a thermal gradient helps the concrete to expand more, reducing the ‘thermal bowing.’ Hence, positive bending/rotation is reduced, as shown in
Figure 9b. For high support stiffness, during the low-temperature time (see −30 °C curves), the presence of a thermal gradient reduces the positive bending/rotation (sagging). This is due to the lower contraction of the top of the superstructure, which has a higher temperature. However, during high-temperature times (see 50 °C curves in
Figure 9b), the presence of a thermal gradient increases the negative bending/rotation (hogging). This is due to the higher expansion of the top of the superstructure, which has higher temperatures. Thus, the presence of the specified thermal gradient reduces the positive bending but enhances the negative bending.
4.2. ANN Model
ANN was trained using the dataset from undamaged and damaged cases separately. The training history and model prediction accuracy of either dataset do not differ in significance. Thus, a final ANN model is trained using a combined data set of thermal responses from superstructure-damaged and undamaged bridges. Similarly, another two datasets, one response with a thermal gradient and a response without a thermal gradient, were also trained. The
R-value is a measure of the ANN’s prediction accuracy and is the correlation coefficient between the predicted value and the target value of the bearing stiffness. The
R-value for the ANN model without a temperature gradient was 0.80, and that for the model with a temperature gradient was 0.78. Since the overall model weightage and accuracy are not different, these two data sets were also combined. Hence, a final ANN model with all possible thermal response cases is trained, and training accuracy for each test, validation, and training set is presented in
Figure 10a. The training progress is shown in
Figure 10b, and the error histogram is presented in
Figure 10c.
The model achieved its optimal validation performance with a mean squared error of 3.446 (in base 10 logarithmic of kN/mm stiffness scale) or 2792.5 kN/mm of real stiffness at epoch 22. This indicates that the training data is sufficiently adequate for the model to learn and generalize well to unseen data before overfitting begins. The ANN model demonstrates strong predictive capability for support stiffness, with R-values of 0.80636 for the training set, 0.7969 for the validation set, and 0.811 for the test set, resulting in an overall R-value of 0.8057. The prediction equations, such as 0.65 × Target + 2 (ideally 1 × Target), indicate consistent and reasonably accurate estimations of the target variable. Additionally, the error histogram shows an almost normal distribution, with a mean of approximately 0 and a standard deviation of 0.52 (less than 3.5 kN/mm). These results collectively suggest that the model is robust enough to handle any thermal gradients and superstructure damages, generalizes well, and is a reliable tool for predicting support stiffness.
4.3. Field Joint Monitoring
The gap opening between the girder end and the abutment back wall is measured using an ultrasonic distance sensor through the wireless sensing system explained in the previous section. The thermal expansion/contraction is obtained by subtracting the gap opening from the reference temperature (10 °C). Due to the high noise in the sensor near the top flange, its readings are not considered in this study. The thermal displacement response of both monitored bridges is presented below.
4.3.1. Bridge 1
This bridge was tested during the summer, and the girder’s temperature varied from 14 °C in the early morning to a maximum of 27 °C at approximately 5 PM. The variation of temperature, along with corresponding thermal expansion at different sections of the girder, is shown in
Figure 11. The range of thermal movement was found to be 2.5 mm to 5.5 mm at approximately the middle of the girder and 2.5–7.4 mm (7.6 mm free linear thermal movement) at the bottom flange of the girder. This expansion behavior indicates a relatively small value of support stiffness and ‘thermal bowing’ of the bridge. This is most likely to be accurate because this bridge has an elastomeric bearing at the monitored end. The rotation due to this thermal bowing is presented in
Figure 12. This shows a rotation of approximately 0.02°–0.17° during the daily temperature fluctuation cycle.
4.3.2. Bridge 2
Thermal movement of this bridge is conducted during the winter because of the high likelihood of bearing freezing due to accumulated dirt and high corrosion on its steel bearings. The girder temperature was found to vary from 1 °C to 10 °C. The day’s temperature variation and corresponding thermal contractions are shown in
Figure 13. The bridge contracted up to 9.5 mm at the bottom flange level and up to 8.5 mm at the middle of the girder (free linear contraction of steel 11.34 mm). This shows that the bearing resistance is higher in this bridge as compared to Bridge 1. Here, the bridge is contacting 83% of free steel contraction as compared to 97% of free steel contraction in Bridge 1. Additionally, the girder end rotation varied from −0° to −0.4° (shown in
Figure 14), indicating higher thermal bending.
4.4. ANN Predicted Support Stiffness
The support stiffness corresponding to the field monitoring results for both of these bridges is predicted using the ANN model. For Bridge 1, the predicted support stiffnesses were almost uniform with a very low value (mean 9.73 kN/mm), and those for Bridge 2 were found to change with temperature with a relatively higher value (from 250 kN/mm to 1000 kN/mm).
For Bridge 1, the stiffness was uniform throughout the day, irrespective of changes in temperature.
Figure 15a shows a normal distribution of predicted stiffness with a very low standard deviation of 2.68 kN/mm. The scatter plot shown in
Figure 15b shows the temperature independence of bearing stiffness throughout the monitoring period and temperature range. The predicted results align with the visual inspection inferences from the bridge. The bearing was elastomeric, which has very low lateral stiffness, and since the bearing was relatively newer with no signs of deterioration, it was free from dust. The variance in predicted stiffness is due to the presence of noise in the measurement. The outliers near 17 °C are caused by anomalous events like ultrasonic noise from the environment or erroneous sensor readings. However, since the temperature during the monitoring period was not near freezing, there may be chances of freezing when the temperature reaches near zero.
For Bridge 2, the predicted stiffness was found to vary from 200 kN/mm to 1600 kN/mm, with a mean value of 714.1 kN/mm.
Figure 16a shows a histogram plot of predicted stiffness across the measured temperature. The predicted support stiffness has very weak normality with a very high standard deviation of 367.4 kN/mm. This lack of normality in the prediction is explained by the dependence of support stiffness on temperature, as shown in
Figure 16b. This shows an exponential increase in bearing stiffness as temperature goes below 6 °C; above this temperature, bearing stiffness is constant at approximately 300 kN/mm. The high variability prediction is higher at lower temperatures, which may be due to the time-dependent physical or chemical changes in bearings or material deposited in the moving planes near the freezing temperatures. Above 6 °C, prediction results show higher prediction precision. These results indicate that there may be a ‘Frozen bearing’ condition in the bridge. In the absence of any technique for quantifying bearing stiffness, the calculated bearing stiffness values were assessed based on the visual appearance and qualitative assessment of bearing conditions. The visual appearance of this bearing is shown in
Figure 17b. There is the deposition of dirt in the moving part of this bearing, along with heavy rusting and leaking from the expansion joint, justifying the relatively higher stiffness predicted by the ANN model.
These two case study bridges show that the ANN model trained in this study is able to predict support stiffness with reasonable accuracy, even with thermal response data measured from noisy, low-cost sensors. Thus, by integrating this ANN model with a low-cost WSN system, bearing stiffness can be predicted in real-time. The real-time alert system can be developed by defining lower and upper limits of stiffness values. Additionally, this method can be implemented along with a vibration-based damage detection system to quantify support fixity levels for higher precision in superstructure damage detection. Since this method is based on an ANN model trained on FE-simulated data, proper measurement, and quantification of the noise level in the field monitoring data need to be performed. This might turn out to be a challenging task because of the effects of traffic loadings and environmental conditions. Moreover, the computational intensiveness of the ANN model might make it difficult to integrate with a real-time monitoring system, which typically consists of low-capacity hardware components. However, advancements in sensing systems and the computational power of hardware components will help make this method more useful and robust.