The effectiveness of vehicle weight estimations from bridge weigh-in-motion system is studied. The measured bending moments of the instrumented bridge under a passage of vehicle are numerically simulated and are used as the input for the vehicle weight estimations. Two weight estimation methods assuming constant magnitudes and time-varying magnitudes of vehicle axle loads are investigated. The appropriate number of bridge elements and sampling frequency are considered. The effectiveness in term of the estimation accuracy is evaluated and compared under various parameters of vehicle-bridge system. The effects of vehicle speed, vehicle configuration, vehicle weight and bridge surface roughness on the accuracy of the estimated vehicle weights are intensively investigated. Based on the obtained results, vehicle speed, surface roughness level and measurement error seem to have stronger effects on the weight estimation accuracy than other parameters. In general, both methods can provide quite accurate weight estimation of the vehicle. Comparing between them, although the weight estimation method assuming constant magnitudes of axle loads is faster, the method assuming time-varying magnitudes of axle loads can provide axle load histories and exhibits more accurate weight estimations of the vehicle for almost of the considered cases.

The weights of vehicles govern the design requirements for highway infrastructure such as pavements and bridges. The traditional weigh stations are commonly used to weigh vehicles and impose fines or penalties for exceeding weight limits. They, however, take quite long time to weigh each vehicle. Moreover, their costs of system installation and maintenance are expensive. Therefore new alternative weigh system, namely, bridge weigh-in-motion (B-WIM) is developed. The bridge WIM systems deal with an existing instrumented bridge or culvert from the road network. Beside its cost advantage, the system installation and maintenance do not disturbed the traffic flow. In addition, the system is transparent to the vehicle’s drivers so that the obtained weight information is expected to be unbiased. In general, B-WIM system monitors the deflection, strain, or bending moment data of the bridge during the passages of vehicles. Knowing the physical parameters of the bridge such as span length and flexural rigidity, the system can estimate the weights of passing vehicles from those bridge response data coupled with the configuration and speed information of vehicles which are obtained from another set of sensors. Based on previous researches, although many techniques have been proposed for bridge WIM to estimate the weights of vehicles, two different assumptions of vehicle loads on the bridge, which is either constant or time-varying moving loads, are often employed.

For the constant moving loads assumption, the vehicle is assumed to pass the bridge without any vertical body motion. Therefore, dynamic moving loads from vehicle exerting on the bridge can be simply replaced by constant moving loads. The weight estimation methods, in this class of assumption, determine axle weights of the vehicle by comparing the measured bridge responses with those obtained from bridge influence lines [

Similar to many load identification methods, the vertical body motion of vehicle induced by vehicle-bridge dynamic interaction is allowed. Therefore, unlike the constant loads assumption, the dynamic moving loads from vehicle exerting on the bridge are represented by time-varying loads moving on the bridge and are estimated directly from measured bridge responses. Then the axle weights of vehicle are determined from time averaging of the obtained time-varying axle loads. Many loads identification methods such as the time domain, the frequency-time domain, and the modal methods have been proposed and studied [

Most of the mentioned weight or load estimation methods have been studied to show their effectiveness and potential for real application. However, the comparison between them has not yet been established. Therefore, in this paper, the two weight estimation methods of the vehicles using the constant moving loads and time-varying moving loads assumptions are extensively considered. Based on numerical simulations, many effects of vehicle and bridge WIM system such as bridge discretization, sampling frequency, vehicle speed, bridge surface roughness, number of measuring sections, noise, axle spacing, and axle weight distribution are investigated.

A passage of vehicle on a bridge WIM system is shown in Figure

Vehicle and bridge WIM system.

The bridge structure is modeled as a simply-supported bridge and is discretized by finite elements using beam element. The standard beam element having 2 nodes with 2 degrees of freedom in vertical displacement and rotation displacement at each node as shown in Figure

Bridge finite element model and local coordinates in beam element.

The vehicle-bridge interaction model can be formulated from the equations of vehicle motion (

It should be pointed out that the vehicle-bridge system forms a coupled time-varying dynamic system, because some elements in damping and stiffness matrices of the system keep changing with time due to a traveling of the vehicle.

To solve above equations, Newmark’s

It is noted that these axle load equations take into account both static axle weights and their dynamic loads resulted from the vehicle-bridge interaction.

The concept of axle weight estimation of a passing vehicle is to minimize the error between measured and estimated bridge responses. In this paper, the measured bending moment vector

With constant magnitude of moving axle loads assumption, the dynamic interaction loads between vehicle and bridge, that is,

Model of a vehicle and bridge WIM system used for weight estimation with constant magnitude of moving loads assumption.

Consequently, the estimated bending moment vector of the bridge at

Since the estimated bending moment of the bridge,

To minimize above objective function,

The MATLAB’s optimization function

Unlike the constant magnitudes of moving axle loads assumption, the axle loads of vehicle are assumed to be time-varying. With this assumption, the dynamic interaction loads between vehicle and bridge, that is,

In this paper, the dynamic programming method with updated static component technique [

The numerical investigation of axle weight estimation of a passing vehicle on a bridge WIM system using the two previously mentioned methods is considered. The vehicle is assumed to have two axles and crosses the bridge with a constant speed. The bending moment histories of the instrumented bridge at various sections subjected to a passage of the vehicle are simulated from the vehicle-bridge interaction model as derived in (

The parameters for the vehicle and bridge WIM system are listed in Table

Parameters of vehicle and bridge WIM system.

Bridge | Vehicle | ||
---|---|---|---|

^{2} | |||

^{2} | |||

Figure

Typical bending moment histories of the bridge under a passage of the vehicle with a speed of 15 m/s and roughness surface of level 3.

Actual axle loads and corresponding axle weight estimations (a) using Method I and (b) using Method II.

Method I

Method II

The effects of bridge discretization and sampling frequency on the accuracy of the weight estimation methods are considered. The vehicle moving on the bridge at a constant speed of 15 m/s under various bridge discretization refinements and various sampling frequencies of bridge bending moments is simulated. Based on the obtained bridge moments at three sections, that is,

Estimation errors of axle weights for different sampling rate and number of beam elements.

Sampling | Method I | Method II | |||||||||||||

Frequency | Number of beam elements | ||||||||||||||

(Hz) | 4 | 8 | 12 | 16 | |||||||||||

front | rear | gross | front | rear | gross | front | rear | gross | front | rear | gross | front | rear | gross | |

20 | 11 | ||||||||||||||

30 | 6.8 | ||||||||||||||

40 | 7.7 | ||||||||||||||

50 | 7.3 | ||||||||||||||

100 | 7.4 | ||||||||||||||

200 | 7.4 | ||||||||||||||

300 | 7.3 | ||||||||||||||

400 | 7.2 | ||||||||||||||

500 | 7.2 | ||||||||||||||

1000 | 7.2 |

Employing Method II, it is obviously found from the table that the accuracy of axle weight estimations is not affected by discretization refinement of bridge structure if it is discretized by more than 4 elements. The table also indicates that the accuracy of axle weight estimations by the two methods is significantly influenced by sampling frequency. The weight estimation errors become larger when the sampling frequency is smaller. However, the weight estimation errors obtained from both methods are rather constant if the sampling frequency is faster than around 50 Hz. Therefore, throughout this study, the number of bridge elements is set to 8 while the sampling frequency is fixed at 500 Hz to guarantee the highest accuracy of the estimation methods. These imply that the bridge vibrations up to the

The effects of vehicle speed and bridge surface roughness on the accuracy of the weight estimation methods are investigated. The practical range of vehicle speed from 1 to 30 m/s is considered. The magnitude of bridge surface roughness,

Estimation errors of axle weights under various roughness levels and vehicle speeds for (a) front axle weight, (b) rear axle weight, and (c) gross weight.

Front axle weight

Rear axle weight

Gross weight

Since Method II provides not only the estimated axle weight of vehicle but also its dynamic axle loads, it is therefore interesting to investigate the accuracy of identified dynamic axle loads of the method. To do so, the load estimation errors of rear axle defined by norm of the load error,

The rear axle load estimation error of vehicle load under various roughness levels and vehicle speeds using Method II.

The influences of number of measuring sections and noise levels in the input signals on weight estimation accuracy resulting from the two methods are investigated. The vehicle moving at a constant speed of 15 m/s on the bridge having roughness of level 3 is simulated. Based on the obtained bridge moments at various section arrangements as in Table

Measuring point arrangement.

Number of measuring points | Location arrangement |
---|---|

1 | 1/2 |

3 | 1/4 |

5 | 1/8 |

7 | 1/8 |

9 | 1/8 |

Estimation errors of axle weights under various numbers of measuring points and noise levels for (a) front axle weight, (b) rear axle weight, and (c) gross weight.

Front axle weight

Rear axle weight

Gross weight

The effects of axle spacing and axle weight distribution of vehicle on the accuracy of weight estimation methods are investigated. The axle spacing of vehicle from 2 to 15 m and the axle weight distribution of vehicle defined by ratio of front axle weight to gross weight are varied from 20% to 80%. The vehicle having different axle spacing and axle weight distribution moving on the bridge at a constant speed of 15 m/s is simulated. The bridge surface is assumed to have the roughness of level 3. Based on the obtained bridge moments at three sections, that is,

Estimation errors of axle weights under various axle spacings and axle weight distributions for (a) front axle weight, (b) rear axle weight, and (c) gross weight.

Front axle weight

Rear axle weight

Gross weight

The CPU processing time is also investigated to compare the computing speeds of Method I and Method II. Based on numerical simulation test results, the processing times required by both methods are listed in Table

Comparison on CPU processing times from the two methods.

Method | Method I | Method II | ||||

Min | Max | Avr. | Min | Max | Avr. | |

Total processing time (s) | 1.2 | 2.6 | 1.8 | 3.6 | 10.8 | 6.5 |

The effectiveness of vehicle weight estimations from bridge weigh-in-motion system is studied. The measured bending moments of the instrumented bridge at selected sections under a passage of the vehicle are numerically simulated and are used as the input for vehicle weight estimations. Two weight estimation methods assuming constant magnitudes (Method I) and time-varying magnitudes (Method II) of vehicle axle loads are investigated. Their estimation accuracy are evaluated and compared under various parameters of vehicle-bridge system.

Based on the simulation results, the minimum number of bridge discretization of 4 and the minimum sampling frequency of 50 Hz are observed. It is also found that, among many considered parameters, the vehicle speed and surface roughness seem to have stronger effect on the accuracy of the two estimation methods than others. However, the estimation errors of the gross weight of vehicle can be controlled to be within

It is also found from the effectiveness comparison between the two estimation methods under various vehicle and bridge conditions that Method II can provide better weight estimation than Method I for almost of the considered cases. In addition, it provides dynamic axle loads of vehicle. However, it exhibits about four times slower speed of computation than Method I.

The authors are very grateful to the Chulalongkorn University for the 90th year research grant for this project.