Multi-Direction Bridge Model Updating Using Static and Dynamic Measurement

This research present a multi-direction bridge finite element model updating method based on the static and dynamic test. A fiber optics structural health monitoring system was installed on the bridge site and 73 fiber optic sensors captured the static and dynamic data in local-level. A portable accelerometer system was used to record the ambient loading test and 15 force-balanced accelerometers were placed along bridge center to record the bridge global behavior. The original model was built according to the construction draw. The bridge model was updating by using multi-level test data. A new multi-direction model updating approach was established to separate the model updating into several stages based on the member’s direction. In each stage, the uni-direction members were updating in local-global level. This study found the multi-direction model updating can reduce the number of objective functions and variables in each stage and bridge model updating in the uni-direction has limited influence on the other directions. It is necessary to update steel girder bridge’s finite element model in the multi-direction in order to ensure the model’s accuracy.


Introduction
Consider that the current approach to structural health monitoring can be divided into two distinct areas: (1) using the structural dynamic properties to detect structural behavior at the global level based on the dynamic parameters, and (2) using several sensors to quantify the condition of the local components of the bridge structure based on the static measurements. Both approaches have advantages and limitations. Dynamic parameters give information about the global response of structures and, therefore, are not very sensitive to local phenomena. On the other hand, static measurements, such as strains and displacements, are more sensitive to the response in their vicinity and, therefore, they better suited to determine local defects.
Model updating in global-local level will overcomes the week of only using one type of measurement and combined global-local performance will assist in evaluating the bridge behavior accurately, however, it will also enhance the number of objective functions which are the difference between the measurements and the analyzed results. In this case, more variables will be selected in order to make the objective functions coverage. A large number of objective function and variable will take longer time for mathematical operation. In order to solve this problem, a new bridge finite model updating strategy required to establish in order to control the number of functions and simplify the process of model updating.
The study results indicated, updating uni-direction member can only enhance the accuracy in this direction and it have very low influence on the accuracy of other direction members. The overall accuracy of bridge model is contributed by both longitudinal members and transversal members.

Bridge Description
The Chulitna River Bridge was built in 1970 on a 22-degree skew. It is 790-feet long with five spans of 100, 185, 220, 185, and 100 feet (Figure 1). The superstructure was a 34-foot-wide by 6¾-inch-thick cast-in-place concrete deck supported by two exterior continuous longitudinal variable depth girders and three interior stringers. The girder stringers are spaced at 7 feet on center. The interior stringers are supported by cross frames that is carried by the exterior girders.

Figure 1. Elevation and Plan View of Chultina River Bridge
In 1993, the bridge deck was widened and made of precast concrete deck panels. The increased load was accounted for by strengthening the variable depth exterior girders and converting the W21x44 interior stringers to an interior truss girder; the W21x44 stringer became the upper chord of the truss (Figure 2).

Static and Dynamic Test
The research team developed a structural health monitoring system (SHMS) that could be used to monitor Alaska bridges, instrument the bridge, calibrate the system, and load test the structure. In addition to monitoring the bridge response to traffic, the research team was to develop and calibrate a FEM that would provide a reliable bridge behavioral response to traffic AASHTO loading and special permitted vehicles. The paper provides the experimental data obtained from two different field-evaluation systems: local and global.
Localized response data are obtained through the use fiber-optic sensors such as strain gauges, displacement sensor, tilt meters, etc. at specific locations. In an attempt to understand and evaluate the response of the Chulitna River Bridge to traffic loads. The global field monitoring is an ambient acceleration study that attempts to identify natural frequencies of the structure once it is excited. Horizontal, vertical, and transverse frequencies were measured by 15 portable accelerometers distributed across the top deck of the structure.
There are various methods and sensors that may be used to evaluate the discrete locations (local-level monitoring) to evaluate long-term response of the structural elements. This may be accomplished by measuring at the discrete points, temperature, acceleration, strain, and deflection. Although there are various sensors available for measuring strains, etc., not all perform well over the long term. Thus, in this study, the researchers selected a Fiber-optic structural health monitoring system (Figure 3) for the purpose of insuring that drift would be minimized over time. Fiber optic sensors have been shown to provide stable long-term real-time monitoring for bridge structures. In this research, the Chulitna River Bridge was instrumented to evaluate the local-level behavior. There are a total of 73 sensors (strain gages, accelerometers, temperature sensors, rosettes, and tilt meters) at locations that were selected to evaluate the local-level structural health of this structure. (Figure 4) The long-term monitoring can indicate the change of local components with time.

Multi-Direction Model Updating
In this research, an enhanced approach for updating the virtual bridge model was developed. The idea is that this model will represent the structural response when subjected to load conditions typically expected in the field. The virtual model (FEM) for this bridge will be calibrated to reduce errors in global-local evaluation so that the virtual model may more accurately be calibrated and updated and it accurately represents the behavior and condition of the structure. Combined the global and the local evaluation, it will introduce more variables to be adjusted and it will involve more objective functions to be solved. It is a challenge to make the objective functions coverage when there are a large number of variables. This section shows the multi-direction global-local model updating approach which can solve this problem and simply the model calibration for large complicated bridge structure.

Simple Accuracy Test
Before model changes were made, simple accuracy tests were performed on the bridge initial finite element model. That is, the number of elements (original mesh) was increased in an effort to evaluate the results for a newly refined mesh. This test was conducted to ensure that it would converge to provide a reasonable estimate of the structural response. The desired level of accuracy was set at 2%. Subsequently, the mesh size was reduced to half its current size to determine if the resulting displacements and forces would change significantly or if the change was small enough to be considered acceptable. Multiple locations on the bridge were checked. These locations were ones of critical interest to the project (i.e., high tension, large displacement, etc.). Nine sections were considered when checking the strains and stresses. These nine sections are located in different spans and sides of the bridge. Four longitudinal displacements on different sides of the abutments were selected for checking. We refined the mesh for the FEM to half its current size in both lines and areas. In Table 1, the error shows the difference between the initial model and the refined model. This comparison is based on three trucks that were stopped and positioned so that the front axles were 369 feet from the south abutment (Abutment 1); the three trucks were in the middle of Span 3.
The locations that are presented in Table 1 are illustrated in Figure 6. Table 1 indicates that the error between the two models is low. Ignoring the sign, the largest error is 1.04%, which is within the acceptable the level of accuracy. In general, the fine mesh used in the initial model should give sufficiently accurate results. that is, calculated lower chord stresses are higher than measured. This finding illustrates that the FEM does not properly represent the distribution of stiffness between the bridge composite stringers and the girders. In consideration of these problems, objective functions J 1 in longitudinal members were selected for study.
Modifications to the objective functions affected load distribution for the composite trusses and girders.

Model Updating in Longitudinal Direction
Initially, we identified the members that were likely to affect structural response the most. In selecting objective functions for study, we adjusted member sectional data and member geometry to better reflect the 1993 as-is bridge condition. According to the longitudinal behavior described by the initial FEM, the largest error exists in a lower chord member. Modifications showed that if the cross-sectional area in the lower chord was reduced to 0.43, the resulting error in local strain dropped below 50%. This modification resulted in a change in behavior, and the largest error between measured and calculated stresses was now in the composite truss lower flange. We then investigated the bridge response to a change in stiffness for the concrete deck. Changing the elastic modulus of the concrete deck to 3,000 ksi improved structural response, and the error between the calculated and measured stresses were reduced to 5%. However, the difference between the global experimental frequency response and calculated values causes the percent error to increase to 15%. The stiffness change went from too stiff to too flexible. In order to balance the difference in error between local and global values, the elastic modulus of the concrete deck was changed to 3,300 ksi and the stringer lower flange area was changed from 2.0 to 2.5. The change in area represents the as-is bridge condition.

Bridge Transversal Direction Behavior
The stiffness of the cross frame and the condition of the supports determined load distribution in the transversal direction. In the investigation by HDR, Inc., five roller bearings did not fully connect with the superstructure (Figure 9), and original model removed those supports.  The load test cases conducted on September 10, 2012, three heavily loaded trucks traveling side by side crossed the bridge at low speed. The vertical movement of the five displacement sensors is shown in Figure 12 a-e. These graphs illustrate the response for an average of 50 data points over time for each of the five bearing locations.

Model Updating in Transversal Direction
Figures 13 shows for the 2012 load tests that large errors exist between measured and calculated stresses in the cross frame. At Pier 3, the largest error is -43.4% in the cross frame. At Pier 5, the largest error was -512.3%. Figure 12 indicates that bearings 1, 3, and 4 have limited movement. So the cross frame section may work as a semi-rigid support at those locations. As part of the model modifications, three spring supports were added at those locations. In order to reduce errors in the objective functions, we modified the support spring stiffness and sectional properties of the cross frame to more closely represent bridge as-is condition. Vertical spring support stiffness at  Following modification of the model, the largest error in the transversal direction decreased from -512.3% to -19.9%. Initially, five support bearings did not support the bridge (i.e., the superstructure was not in contact with the bearings). After the model was modified, we simulated the bridge response with two bearings (Bearings 2 and 4) that were not in contact with the structure. At the other three bearing locations, the superstructure is modeled with vertical springs between the bearing support and the structure. The cross frames were found to be too stiff compared with the bridge as-is condition.
After the FEM was modified to more accurately represent the transverse behavior of the bridge, a comparison between experimental and calculated stresses were made for the various load tests that were run on September 10, 2012. For example, Tables 10 and 11 show the difference in stresses between experimental and modified finite element values for the middle of the Span 3 girder flanges and the difference in stresses in the lower chord of the cross frame. These stresses are from a static load test in which three trucks side-by-side were on the bridge mid-span 3 (see Figure 15). The tables 10 and 11 show that the stiffness of the three spring supports and the cross frame had limited influence on the longitudinal distribution of load.  The FEM that resulted from modifications to better predict transverse response was evaluated for both local and global data. Using the improved model, global natural frequencies were calculated and compared with those that were measured with the portable accelerometers. Natural frequencies were calculated in three directions (vertical, longitudinal, transverse) and compared with the measured values ( objective functions. Longitudinal variables were selected and adjusted to match construction drawings so that response was within a reasonable range. The purpose was to reduce the number of objective functions and variables. In addition to verifying that calculated local strains were sufficiently accurate, we checked calculated global (vertical, longitudinal, transverse) natural frequencies against measured values. This check ensured that element and material property corrections for the model would result in convergence between measured and calculated in global-level.
In the transverse direction, the unconnected roller bearings and cross frames were selected for study. The transverse behavior was studied by evaluating load test response when two trucks were stopped at two critical cross sections. The difference between measured local strain values and calculated were evaluated and compared. The model was reviewed and modified to describe the as-is bridge condition. This process was continued until the model accurately described the behavior and the calculated values correlated well to the experimental values in multi-level.
After model modifications, both local and global values resulted in lower errors between measured and calculated. The longitudinal J 1 , transversal J 2 and multi-direction objective functions J shows in Figure 17. Model updating in longitudinal direction have limited influence on transversal member. According to the Figure  17, the longitudinal objective function enhanced 99% after updated in longitudinal direction, however, transversal objective function only increased 1%. On the other hand, updating in transversal direction can result 97% changed in transversal objective function, but only enhanced 3% in longitudinal direction. This results firmly proved that the steel girder bridge model updated in one direction have limited influence on other direction and only updating steel girder bridge in longitudinal member couldn't get accurate bridge finite element model. For local values, the largest error decreased from -512.3% to -19.9%. For global values, the largest error decreased from -10.2% to 8.9%. The modified or refined (calibrated) FEM now provides calculated values with an accuracy that is within acceptable limits for both local and global values.

Conclusion
This research established a fiber optic structural health monitoring system for the Chultina River Bridge uni-direction have every low influence on the accuracy of other directions. The overall accuracy is contributed by both longitudinal members and transversal members. It is necessary for steel girder bridge to be updated in the multi-direction.