## 1 Introduction
Researchers have adopted different approaches to reduce this error [14; 15]. To the author's knowledge, only two researchers have used accelerations directly in BWIM or MFI systems [16; 17]. [PERSON] et al. [16] proposed an MFI algorithm in the time domain, which can use acceleration signals directly. However, the force response cannot be obtained from the acceleration data alone--bending moment data is also required. [PERSON] et al. [17] introduced the concept of an acceleration-based influence line and applied it to BWIM. The issue with this method is that the magnitude of vehicle acceleration can be strongly affected by the road profile, which affects the accuracy. While the accuracy of this acceleration-based BWIM method is low, the authors demonstrated that the inferred vehicle weights obtained from a large sample of passing trucks can be used to infer damage. A different approach is taken in this paper, where acceleration is used to extract vehicle axe force, which is not strongly affected by the profile. To find a method that can directly use acceleration and estimate GVW with good accuracy, an MFI algorithm is chosen. MFI has been proposed as a method of BWIM that potentially can give more accurate and more detailed results than the traditional approach [18; 19; 20]. Several forms of the MFI algorithm exist but all derive axe force histories from the equations of motion [21; 22; 23; 24; 25]. A popular approach, which is introduced by [PERSON] [26], uses the state-space form of the dynamic equations to solve this inverse problem. In the state space approach, the 2 nd order differential equation governing displacement is replaced by two 1 st order equations that are solved simultaneously to find the displacements and velocities [27]. Numerical instability is a challenge, with many examples giving ill-conditioned solutions [28]. [PERSON] et al. [28] apply Tikhonov regularization [29] to improve the conditioning of the system of equations, which significantly improves the accuracy. [PERSON] et al. [18] further develop this algorithm by regularizing the first derivative of force to make the solution smoother and more stable. [PERSON] et al. [30] validate the algorithm of [PERSON] et al. [18] using strain data measured on a bridge in service and achieve good accuracy. The majority of BWIM and MFI approaches use strain and a few use deflection or rotation, but acceleration has only recently been considered [17]. Fewresearchers have used vehicle axle force, computed by MFI from bridge deflection data, to detect damage [31; 32; 33]. They show that the bridge's local damage will significantly affect inferred force results. As the bridge becomes damaged, bridge deflections will increase and the inferred force will be overpredicted. This principle cannot be applied when acceleration is used as acceleration magnitude is affected by the road profile. In this paper, the new acceleration-based MFI (A-MFI) algorithm is applied directly to acceleration data, requiring reformulation of the underlying equations. Unlike strain data, used in previous studies, acceleration data is damage sensitive, suggesting that it has good potential to be used as part of a bridge health monitoring approach. The concept is assessed using a numerical simulation with a half-car vehicle/bridge interaction model and a finite element model of a bridge. A sensitivity study is carried out on potential sources of error such as the scan rate of measurements, imperfect velocity measurement, pre-existing vibrations, and measurement noise. The study demonstrates that acceleration-based MFI-inferred vehicle weight data is a good indicator of bridge global damage. Global damage is considered in this study, i.e., an overall loss of stiffness. This type of damage may be due to multiple small local damages or to uniform corrosion damage over time.