Experimental Testing of a Moving Force Identification Bridge Weigh-in-Motion Algorithm

Abstract

Bridge weigh-in-motion systems are based on the measurement of strain on a bridge and the use of the measurements to estimate the static weights of passing traffic loads. Traditionally, commercial systems employ a static algorithm and use the bridge influence line to infer static axle weights. This paper describes the experimental testing of an algorithm based on moving force identification theory. In this approach the bridge is dynamically modeled using the finite element method and an eigenvalue reduction technique is employed to reduce the dimension of the system. The inverse problem of finding the applied forces from measured responses is then formulated as a least squares problem with Tikhonov regularization. The optimal regularization parameter is solved using the Lcurve method. Finally, the static axle loads, impact factors and truck frequencies are obtained from a complete time history of the identified moving forces.Keywords: Bridge, Weigh-in-motion, Force identification, Regularization, Dynamic programming, Traffic loads Moving Force Identification Bridge Weigh-in-Motion AlgorithmThe traditional static bridge weigh-in-motion (B-WIM) algorithm provides static axle weights from minimizing the sum of squares of differences between measured total bridge strain and theoretical static strain [1]. Although the deviations with respect to the static response that vehicle and bridge dynamics introduce in the measured response tend to be averaged out during the minimization process, they remain a significant source of inaccuracy [2]. This paper proposes an alternative B-WIM algorithm that calculates the time history of moving forces as they cross the bridge, based on moving force identification (MFI) theory. The MFI algorithm implemented here was developed by the authors [3][4][5], and is an extension of the one-dimensional algorithm by Law and Fang [6] to two dimensions. The mathematics behind general inverse theory is available in the literature [7][8][9][10][11]. The MFI algorithm requires a finite element (FE) mathematical model that accurately represents the static and dynamic behavior of the bridge structure. The method of dynamic programming requires that the equilibrium equation of motion be converted to a discrete time integration scheme. In this case the equilibrium equation of motion is reduced to an equation in modal coordinates defined by:where [Φ] is the modal matrix of normalized eigenvectors and n z is the number of modes to be used in the inverse analysis.[Ω] is a diagonal matrix containing the natural frequencies and ζ is the percentage damping. [L(t)] is a time varying location matrix relating the n g applied vehicle forces of the vector g(t) to the degrees of freedom, n dof , of the original FE model. Tikhonov regularization [12] is applied to provide a bound to the error and 'smoother' solutions to the ill-conditioning nature of the MFI problem [13,14]. The final part of the solution lies in the calculation of the optimal regularization parameter; the L-curve has been chosen to obtain...

On the use of bridge weigh-in-motion for overweight truck enforcement

“…Briefly, the method involves formulating the equations of motion of the bridge with the help of a finite element model. The model can be adjusted using the measured frequencies and damping ratios from bridge strain measurements (Rowley et al 2009). The number of equations required is reduced using modal superposition, ill-conditioned solutions are improved using Tikhonov regularization, and the optimal predicted axle weights to minimize the differences between the measured and the predicted strains are calculated using dynamic programming.…”

Adaptation of Cross Entropy optimisation to a dynamic Bridge WIM calibration problem

“…This gives a total of 27 measurement locations in this case. The material properties found in a previous study [40] to best model the bridge at Vransko are listed in Table 2. Figure 17 gives an example of the strain responses from the beam and slab model, for the case of the same 2-axle truck as before, travelling at a velocity of 20m/s.…”

Improved axle detection for bridge weigh-in-motion systems using fiber optic sensors

“…Therefore, it can provide a solution for the long-term monitoring of our infrastructure. The B-WIM theory has been extended under a number of research initiatives [3][4][5][6], and more recently the ''BridgeMon'' project which finished in 2014 [7]. More recently, B-WIM systems have been used in conjunction with machine learning techniques to develop damage detection methods for railway bridges [8].…”

“…More recently, B-WIM systems have been used in conjunction with machine learning techniques to develop damage detection methods for railway bridges [8]. Previous research [5] has developed theoretical models for B-WIM and demonstrated that Tikhonov Regularization can be used to improve ill-conditioned Moses equations which occur when axles are closely spaced relative to the bridge span. More recently, moving force identification (MFI) techniques have been applied to measured signals to improve the accuracy of the measured axle weights [6,9,10].…”

“…More recently, moving force identification (MFI) techniques have been applied to measured signals to improve the accuracy of the measured axle weights [6,9,10]. These techniques have been found to improve the accuracy of the systems [5]. A review of global state-of-the-art of B-WIM systems by the authors [11] was carried out to inform on the development of the next-generation B-WIM with improved accuracy.…”