Research on mapping relationship between environmental load and vibration response of bridge structure based on structural health monitoring data

With the increasing lifespan of bridges, various forms of deterioration will inevitably occur. The bridge health monitoring system enables direct monitoring of the loads (such as wind, temperature, and vehicles) experienced by the bridge during operation, as well as the corresponding vibration response of the bridge structure (including main beam deformation, tower top displacement, cable acceleration, etc.). These data provide valuable insights into the safety and durability of the bridge during its operational lifetime. However, the challenge lies in extracting meaningful information from the vast amount of collected data. This article focuses on the Fuyu Bridge as a research case and analyzes the variations in environmental factors, such as temperature, humidity, wind load, and structural vibration responses (main beam and cable), obtained from the Fuyu Bridge's structural health monitoring system. It also conducts a structural safety assessment during the operational period of the bridge. Furthermore, the research explores the relationship between environmental factors, load effects, and structural response to establish a foundation for future structural safety assessments of the Fuyu Bridge during its operational period. For instance, changes in environmental factors or load effects can be used to predict structural responses. Additionally, this study provides access to the structural health monitoring data of the Fuyu Bridge, facilitating data‐driven research for other scholars in the field.

][10] For example, the Eigongyan cross-river rail bridge in Chongqing was interrupted by a broken cable.The vortex vibration of Humen Bridge in Guangdong Province may lead to traffic interruption and even damage of some components.The Tacoma Bridge in the US has been damaged by buffeting.Therefore, it is necessary to evaluate the safety and reliability status of bridge in real time.
2][13][14][15] The vehicle weighing system is installed to obtain vehicle information and determine the vehicle load on the bridge. 16][26] For example, Lydon et al. 27 proposed a roving camera technique to capture a complete derivation of the response of a laboratory model bridge under live loading, in order to identify bridge damage.From this study, it is established that either approach could detect damage in the simulation model, providing an SHM solution that negates the requirement for complex sensor installations.Yu et al. 28 proposed the structure health hybrid monitoring method, which provides a mean for synthesizing monitoring data and finite element model to reconstruct the un-monitoring structure responses, in developing a digital twin of a cable-stayed bridge.
4][35] For example, Moon et al. 36 introduced an artificial neural network for the accurate predictions of the vertical displacements from the axial strains with the SHM data.The validation results showed that the ANN-based model can accurately predict the vertical displacements.Lan et al. 37 proposed a data-driven approach based on Optimized AdaBoost-Linear SVM to indicate the bridge damage using only raw vibration signals received from a vehicle passing over the bridge.When compared to other algorithms such as SVM and Random Forest, it improves result accuracy by 5%-16.7%.Through various methods (machine learning method and theoretical modeling method), the above research has deeply mined the potential information of data, but it lacks the linkage between data and data.In other words, after obtaining wind field data, only wind field characteristics are described, and there is a lack of research and analysis between wind field and structural response.
][40] Zhang et al. 41 investigated the transient noise induced by vehicle bridge coupling vibration by employing the hybrid finite element method and boundary element method.The precision of the proposed method is validated by comparing numerical results to the on sac measurements of a steel girder plate bridge in service.Wang et al. 42 presented a finite element model of multi-tower suspension bridge with four towers and three spans.Results show that the rigid main girder can decrease the buffeting displacements in lateral and torsional directions, while the vertical buffeting displacement significantly decreases with the increasing stiffness of middle towers.][45] It can be seen that even with an accurate load model, it is difficult to obtain structural vibration response through load-structure model.
Based on this, this article firstly obtains the environmental data, load data and structural response data of the bridge based on the structural health monitoring system, and analyzes the variation trend of each data, so as to evaluate the safety state of the bridge.In addition, the correlation between data and data, that is, the correlation between environment, load and response, and the data-driven load-structure model are established to avoid the disadvantages of simplification of traditional methods.

Bridge profile
Fuyu Bridge is located in South Erhuan Road, Wuxing District, Huzhou City.The main bridge crosses the intersection of two class III waterways, namely, the Lake-Jia-Shenshen Route and the Chang-Hu-Shenshen Route, connecting Shensu-Zhe-Anhui Expressway, Shenjia-hu Expressway and National Highway 104, as shown in Figure 1.The design of Fuyu Bridge adopts the standard of two-way six-lane first-class highway, and the navigation grade is III of inland river.The main bridge is 75 + 228 + 75 m cable-suspension bridge.The main span is on the arc vertical curve of R = 4000 m, and the longitudinal slope of the bridge deck is 2.8%.

Sensor layout
The main purposes of structural monitoring of bridges are as follows: (1) When the abnormal operation status of the bridge results in abnormal monitoring data, the monitoring system can promptly give an alarm to remind the bridge management department to handle it in a timely manner; (2) when a bridge experiences an earthquake or typhoon ship collision, the monitoring system can trace the entire process of the bridge emergency and obtain the status of the bridge after encountering a special event through data analysis, providing technical support for the bridge management department to develop response plans after the emergency; (3) during the bridge operation process, the monitoring system accumulates monitoring data on the daily operation status of the bridge.Through in-depth analysis of the monitoring data, it further grasps the bridge operation status and provides technical basis for the daily management and maintenance of the bridge management department.The overall layout of monitoring system points for Fuyu bridge can be seen as Figure 3.   of 92.6%RH occurring on June 25, 2022 and the minimum value of 25.97%RH occurring on October 10, 2022.Compared with the bridge deck, the variation of the relative humidity of the air in the steel box girder is relatively stable, with the maximum value of 75.6%RH occurring on June 13, 2022, and the minimum value of 27.81%RH occurring on August 4, 2022.The relative humidity threshold in the enclosed space of the main beam is 50%RH, and the maximum average humidity of each section of the main beam exceeds the threshold, indicating that the air humidity inside the steel box girder is relatively high.After field investigation, it is found that the dehumidifier inside the steel box girder is not working.

Wind load data analysis
The measured data from June 9, 2022 to December 9, 2022 were counted, and the wind speed variation trend chart was drawn with the characteristic values in every 10 min, as shown in Figure 7.The maximum average wind speed during this period occurred on June 24, 2022, with the maximum average wind speed of 23.26 m/s, which did not exceed the design wind speed of 27.2 m/s, without alarm.

F I G U R E 7
Changes of wind speed.The wind speed and wind frequency of each wind direction in this period are counted, and the wind roses are shown in Figure 8.It can be seen that within the statistical period, the maximum 10 min average wind speed is 12.07 m/s, in the southwest direction.From the effect distribution of bridge strike and wind speed, it can be seen that for Fuyu Bridge, the southeast wind has a significant effect on the side of the main beam.

F I G U R E 8
Wind rose chart.

Vertical displacement of main beam
The vertical displacement of main beam is one of the parameters which can directly reflect the safety state of bridge structure health monitoring system, and directly reflect the overall vertical stiffness of bridge structure.The measured data from June 9, 2022 to December 9, 2022 were analyzed with 10 min average value, and the time history of vertical displacement changes at each measuring point of the main beam was obtained, as shown in Figure 9 (taking G02-001 as an example).It can be seen that the vertical displacement of the mid-span and 1/4 section of the main span and the mid-span section of the side span change regularly and obviously with time.The fluctuation amplitude of the mid-span vertical displacement of the main span is the largest, while that of the mid-span vertical displacement of the side span is the smallest, without alarm.

Cable vibration
Based on relevant design specifications, the design cable force can be obtained.In the process of calculating the design cable force, its load is constant, and the boundary conditions are also assumed.On the contrary, measuring cable force is a dynamic value.The measurement of cable force fully considers the randomness of load and the variability of boundary conditions, and is a numerical value that reflects the true stress state of the bridge during operation.Specially, the vibration acceleration data of the stay cable and sling at 0:00 on December 9 were selected to calculate the cable force in this period according to the frequency method, and the measured cable force value in the current period was obtained, as shown in Figure 10.According to the data analysis, the relative variation between the measured cable force and the designed cable force of Fuyu Bridge is between −7.5% and 34.7%, with the largest deviation between the south and north slings.The measured cable force accounted for 43%-91% of the allowable cable force, and the measured cable force was less than the allowable cable force, indicating that the cable force of the stay cable and suspension cable of Fuyu Bridge in the routine operation period is within the normal range, and the stay cable and suspension cable are in normal working state.

Vibration response of main beam
The vertical and lateral mid-span vibration acceleration monitoring data of the main span at 0 o'clock (low traffic flow) and 9 o'clock in the morning (high traffic flow in morning peak) on December 1, 2022 were selected for analysis.As can  be seen from Figure 11, the vibration frequency of the main beam during morning peak is more significant than that in the early morning, and the time history diagram of typical vibration response indicates that the vibration response is normal.The monitoring data can truly reflect the vibration of the bridge.The vibration acceleration data of the vertical vibration measurement points of the main beam were counted according to the absolute maximum value and root mean square maximum value.It can be concluded that the maximum acceleration of each measurement point fluctuates within a certain range, and the maximum root mean square value does not exceed the threshold value 1000 mm/s 2 .

Correlation analysis between vertical displacement of main beam and ambient temperature
From November 1, 2022 to November 30, 2022, the characteristic values of the vertical displacement of the main beam and the ambient temperature of the bridge deck were selected for correlation analysis, and the 10 min mean value of the vertical displacement of the main beam at the south and north sections and the ambient temperature of the bridge deck were drawn, as shown in Figure 12.It can be seen that there is an obvious positive correlation between the ambient temperature of the bridge deck and the vertical displacement of the main side span beam after the removal of noise points, and the temperature of the upper arch of the side span decreases the deflection of the side span.There is an obvious negative correlation with the vertical displacement of the main span girder.The temperature increases the main span under torsion, and the temperature decreases the upper arch of the main span.The deformation of the main side span girder is coordinated, and the deformation law of the south and north side box girder is consistent.

CONCLUSIONS
Structural health monitoring systems can obtain massive amounts of data, which can be used to directly evaluate the safety status of bridges.This article establishes the correlation between environmental loads and structural responses based on the structural health monitoring data of the Fuyu Bridge, and conducts a safety state assessment of the bridge.In addition, this article also shares the monitoring data of the Fuyu Bridge for 6 months, which can provide data support for future research.Based on the monitoring data recorded by Fuyu Bridge health monitoring system from June 9, 2022 to December 9, 2022, the following conclusions are drawn: 1.During the monitoring period, the highest average ambient temperature in the middle span of the bridge deck was 43.5 • C, the lowest average ambient temperature was −1.5  ), it indicates that the air humidity inside the steel box girder is high, and the steel box girder is at risk of corrosion.After on-site inspection, it is found that the dehumidifier inside the steel box girder is not working.2. The maximum 10 min average wind speed on the bridge deck is 12.07 m/s, in the southwest direction.From the effect distribution of bridge strike and wind speed, it can be seen that the southeast wind has a significant effect on the side of the main beam.The vertical displacement of the main span changes regularly with time, and the amplitude of the vertical displacement in the main span is the largest, while the amplitude of the vertical displacement in the side span is the smallest.The minimum vertical displacement of the main beam is −148.227mm, which is located in the middle of the north main span.There is an obvious positive correlation between the ambient temperature of the bridge deck and the vertical displacement of the main side span girder, and an obvious negative correlation with the vertical displacement of the main side span girder.The deformation of the main side span girder is coordinated, and the deformation law of the south and north side box girder is consistent.3. The relative variation between the measured cable force and the designed cable force is between −7.5% and 34.7%.The biggest deviation is between the south and the north side of the cable force, but the surplus is larger than the allowable cable force.The measured cable force is less than the allowable cable force, and the ratio of the two is between 43% and 91%, indicating that the cable force of the stay cable and suspension cable of Fuyu Bridge in the routine operation period is within the normal range, and the stay cable and suspension cable are in normal working state.4. In the future research, we aim to leverage deep learning methods to thoroughly examine valuable insights hidden within vast amounts of data.Specifically, our focus will be on conducting studies related to load and response prediction, with the goal of offering early warning support for bridge safety operations and maintenance.

F I G U R E 1
Bridge bearing chart.Among them, PK section steel box girder is used in the middle span of the main beam, and concrete PK box girder with the same shape is used in the side span.The height of steel box girder is 3 m (inner outline).The full width of the box girder is 41.6 m, the length of the standard beam section is 6 m, and there are two solid diaphragms.The total length of the side span single-side prestressed concrete box girder is 76 m, among which the length of the main span beam section is 2.75 m.The appearance of the box girder is consistent with that of the steel box girder, as shown in Figure2.F I G U R E 2 Section view of main beam.(A) Cross-section of the mid-span bridge panel.(B) Side span bridge panel section.

F I G U R E 3
SHM of bridge.The structural health monitoring system of Fuyu Bridge consists of two thermometers, which mainly monitor the ambient temperature and humidity with a sampling frequency of once every 10 min.The measurement range of air relative humidity is 0%-100%, with an accuracy of ±1.5%, and the measurement range of air temperature is −30 ∼ 70 • C, with an accuracy of ±0.3 • C, as shown in Figure3A. 1 wind speed and direction sensor is mainly used to monitor wind load.Its sampling frequency is 1 Hz, the measuring range of wind speed is 0 ∼ 40 m/s, the measuring range of wind direction is 0 ∼ 359 • , and the accuracy is ±3 • , as shown in Figure4A.Four main beam accelerometers are mainly used to monitor structural vibration.The sampling frequency is 50 Hz and the accuracy is ±0.055%, as shown in Figure4B.There are 24 cable accelerometers, mainly used to monitor cable force changes.The sampling frequency is 50 Hz and the measurement range is ±1.6 g, as shown in Figure4C.Based on the above sensors, this article analyzes the correlation between environment, load and response.In addition, the structural health monitoring system of Fuyu Bridge also includes 86 sensors such as the displacement monitoring sensor of the main tower, the vertical displacement sensor of the main beam, and the displacement sensor of the beam end.If there is any need for data analysis, readers can contact the corresponding author for requests.The data is shared at https://pan .baidu.com/s/17tlyfevYKfz7Ckh9PWvOZA (Password: 1029).F I G U R E 4Structure health monitoring system of Fuyu Bridge (A) Temperature, humidity, wind speed and direction sensor (B) Main beam accelerometer (C) Cable acceleration sensor.
temperature and humidity dataMonitoring data from June 9, 2022 to December 9, 2022 were counted with 10 min characteristic values, and the ambient temperature changes at each measuring point were shown in Figure5.It can be seen that during the statistical period, the ambient temperature of the main span of the bridge deck changed significantly.The highest average temperature was 43.5 • C on August 13, 2022, and the lowest average temperature was −1.5 • C on December 1, 2022.The ambient temperature inside the steel box girder also changed significantly, with the highest temperature of 52.22 • C occurring on July 13, 2022, and the lowest temperature of 3.76 • C occurring on December 1, 2022.The design reference temperature of the bridge is 20 • C, the maximum temperature threshold of the bridge deck environment is 45 • C, and the minimum temperature threshold is 0 • C (used to indicate the ice of the steel bridge deck).The maximum ambient temperature threshold of the steel box girder adopts the historical maximum value of 52.22 • C, and the minimum temperature threshold is 0 • C without alarm.The monitoring data from June 9, 2022 to December 9, 2022 were counted with the characteristic values every 10 min, and the changes of ambient humidity at each measuring point were shown in Figure 6.It can be seen that during the analysis period, the air relative humidity on the bridge deck changed significantly, with the maximum value F I G U R E 5 Trend chart of ambient temperature change.(A) Deck ambient temperature (B) Ambient temperature inside the box.

F I G U R E 6
Ambient humidity trend diagram.(A) Ambient humidity of bridge deck and (B) Humidity inside the box.

F I G U R E 9
Time history curve of vertical displacement of main beam.(A) Time history curve of vertical displacement of the southern main beam (B) Time history curve of vertical displacement of the north main beam.

F I G U R E 10
Cable force calculation.F I G U R E 11 Vertical acceleration in the span of the main beam.(A) Time history of vertical acceleration monitoring data of main span (0:00-1:00, December 1, 2022).(B) Time-history diagram of vertical acceleration monitoring data of main span (9:00-10:00, December1, 2022).

F G U R E 12
Time history curve of vertical displacement of main beam and ambient temperature change.
The relative humidity of the air in the steel box girder changes steadily, with the maximum value of 75.6%RH and the minimum of 27.81%RH.If the relative humidity inside the box exceeds the threshold (50%RH • C, the highest ambient temperature in the steel box girder was 52.22 • C, and the lowest ambient temperature was 3.76 • C. The relative humidity of the ambient air in the bridge deck changes obviously, with the maximum value of 92.6%RH and the minimum value of 25.97%RH.