LTBP Program's Literature Review on Weigh-In-Motion Systems

Chapter 4. B-WIM Systems

Development of B-WIM Systems

B-WIM systems use the bending deformations of a bridge caused by vehicles crossing over the structure. These deformations are typically measured using strain sensors attached to the structural members and are analyzed to estimate the GVW and axle loads of passing traffic. Two main approaches to B-WIM have been used. The first approach uses strain sensors mounted on the bridge and a separate axle detection sensor installed on the road. The second approach uses only strain sensors installed on the bridge for both axle detection and weight measurements. The second approach is the more desirable since it simplifies the overall design, installation, operation, and maintenance of the B-WIM system as compared to the first approach.

One potential advantage of B-WIM systems is that the sensors can be removed and reinstalled on a different structure. The portability of the sensors provides some flexibility regarding where the system is installed to collect traffic data that is not available with permanent WIM systems installed in the roadway. Another advantage of B-WIM systems is the potential for using the measured bridge responses for traffic data collection and for evaluating the performance of the structure itself. In many cases, the same sensors on a structure can provide data that can be used for both objectives. In other cases, additional sensors of the same type and with the same signal conditioning requirements can be added to the structure to supplement the sensors needed for traffic characterization. Some examples of such applications could include prescreening, bridge rating, remaining fatigue life evaluations, and bridge condition monitoring.^(42,43,44)

Fred Moses conducted a field test of a B-WIM system and reported 11-percent error at a 95‑percent confidence interval as compared with the GVW of calibration trucks.⁽⁶⁾ This proves the feasibility of using strain measurements for weight estimation for the first time. Snyder and Moses developed an inverse matrix solution to calculate individual axle weight based on the influence lines of bridges.⁽⁴²⁾ The influence lines for an in-service bridge require rigorous modeling of the bridge structure. O’Brien et al. made the transition from requiring an actual influence line for each bridge to only requiring a theoretical influence line for B-WIM.⁽⁴⁵⁾

Ojio and Yamada developed an approach that allowed them to avoid using influence lines for data analysis and to determine GVW using integration of strain data with adjustment factors for speed and truck type.⁽⁴⁶⁾ In a separate study, Cardini and DeWolf demonstrated the feasibility of this method in a field test on a multi-span steel girder bridge.⁽⁴⁷⁾ Advanced computing methods, such as neural network and wavelet-based analyses, have been used for truck classification and analysis of strain signals to estimate vehicle speed, axle spacing, axle weight, and GVW.^(47,48,49)

Note that the accuracy of B-WIM systems using strain sensors can be affected by the presence of multiple trucks, whether in parallel or serial configurations, and by other traffic on the bridge. The analysis of measurements collected under such circumstances would require the construction and calibration of a 3D finite element (FE) model by controlled load testing in order to evaluate the measured strains. Given the complexities of the strain measurements that can be produced by the random nature and mix of heavy truck and automobile traffic that may be crossing a bridge at any given time, the use of B-WIM systems can be overly complex and inefficient for continuously characterizing every vehicle crossing a particular bridge in the same manner as permanent WIM systems installed in roadways. The system operation and data analysis can be simplified if measurements are only recorded on a triggered basis, using threshold strains corresponding to trucks crossing the structure. Controlled load testing of the structure is usually necessary to establish the threshold values. Photographs of the actual traffic on the structure when the strain measurements are triggered can also be useful for validating the measured strain results and interpreting them in conjunction with a calibrated FE model of the structure.

Moving Force Detection in B-WIM

Moving force detection is based on minimizing the differences between measurements and the corresponding strains calculated from theoretical models. The original B-WIM algorithm developed by Moses assumes that the bending of bridge is in proportion to the product of the load magnitude and the influence line of bridge.⁽⁶⁾ The measured strain is the result of all axle forces on the bridge; therefore, it is difficult to distinguish the contribution of each axle. Accordingly, this method would provide better accuracy for calculating GVWs than axle weights. In this method, the influence of bridge and vehicle dynamics on the influence line is not considered.

Solving the minimization problem is difficult even when multiple sensor data are used. The theoretical approaches used in the B-WIM model can be divided into two categories: the FE method and the exact solution method coupled with the system identification technique. The approach using an exact solution method is generally subject to large fluctuations in the predicted force at the start and end of the time history. The method of Tikhonov regularization has been employed to provide an error-bound and smoother solution.^(50,51,52)

Many alternatives have been proposed such as the Culway WIM system and Matui’s method.^(53,54) The Culway WIM system weighs trucks using culverts that minimize the vehicle dynamics as a result of the damping effect caused by the interaction between the culvert and the surrounding soil. Rowley proposed a regularization procedure to improve the accuracy of the least square approach for identifying axle weights originally developed by Moses.⁽⁵⁵⁾ Field test results showed that the modified algorithm and the experimentally calibrated influence line could generate accurate results for axle weights.

The use of one-dimensional beam models to represent the dynamics of the bridge may not be accurate because torsional and lateral modes of vibration also contribute to the overall dynamic behavior of a bridge structure. Zhu and Law modeled a bridge deck as an orthotropic plate subject to moving forces and idealized as a group of moving forces representing each wheel load.^(56,57) The principle of modal superposition is used to solve the equilibrium equation of motion in the time domain. Quilligan et al. developed two-dimensional (2D) algorithms for orthotropic steel decks that were validated using FE models and experimental tests.⁽⁵⁸⁾ A number of researchers have developed approaches that specifically consider the dynamics of the system.^(59,60)

Gonzalez et al. solved the moving force identification problem using the FE method and first-order Tikhonov regularization on a 2D orthotropic plate bridge model.⁽⁶¹⁾ Strain measurements were simulated using a 3D vehicle and bridge interaction system. The problem was solved by performing a least squares minimization of the difference between measured and theoretical strains. In this process, it is assumed that vehicle velocity, number of axles, and axle spacing are known from axle detectors on the road, and deterioration of bridge stiffness is negligible with the passage of the vehicle.

It is desirable to develop B-WIM systems that do not require separate axle detectors on the road surface because this helps simplify the design, installation, and maintenance. For example, a commercially available B-WIM system developed within the framework of the WAVE project uses a free-of-axle-detector (FAD) or nothing-on-road (NOR) configuration. The FAD or NOR systems are prevailing types of B-WIM used in Europe. FAD and NOR configurations have been applied on different types of bridges and with sensors installed on different bridge components, including web stiffeners of steel girders and the underside of the concrete deck slabs.⁽⁴⁵⁾ The accuracy of FAD or NOR is greatly dependent on the time histories of strain signals produced by moving vehicles. A recorded strain time history can be affected by the dynamic characteristics of the structure, the structural stiffness, the axle spacing, and the vehicle speed.