# Wavelet-Based Optimum Identification of Vehicle Axles Using Bridge Measurements
## 1 Introduction  
As of 2016, there were over 614,387 bridges in the United States, most of which were more than 50 years old, with 9.1% of these bridges being structurally deficient [1]. To maintain bridge structural integrity and safety in operation, electronic structural health monitoring (SHM) is becoming increasingly popular, complementing the traditional approach of visual inspection. For example, ref. [2] presented to use the wavelength-based technique for detecting the slope discontinuity in simple beams associated with local damage from indirect responses. Among many measures of bridge health, the influence line is popular as it removes the variability due to vehicle configuration [3; 4; 5; 6; 7]. Usually a moving multi-axle vehicle is utilized to obtain an influence line, with known axle spacing and configuration. Hence, detecting axles is necessary as part of such an SHM system. Besides the problem of 'aging', a significant increase in commercial truck volumes and overloading is another challenge for existing bridges that has raised serious concerns worldwide. Overweight trucks have been reported to contribute significantly to the degradation of existing infrastructure systems [8]. BWIM (bridge weigh-in-motion) uses an instrumented bridge as a large scale to identify the axle weights of passing vehicles. Strain transducers are mounted on the soffits of girders across the bridge width, typically along a line perpendicular to the longitudinal direction of span. Since the BWIM concept was first proposed by [PERSON] [9], many authors have tested it on different types of bridge at sites around the world and have demonstrated that it can achieve an acceptable level of accuracy in axle weights [10; 11; 12]. Recently, fiber Bragg grating (FBG) based strain transducers have emerged as accurate and robust sensors with good potential for use in BWIM systems [13]. [PERSON]. [14] proposed a new BWIM algorithm to solve the issue of the multiple presence using FBG sensors. [PERSON]. [15] developed a new BWIM system using girder rotations at the bridge abutments to measure truck weights. The girder rotations are measured by two FBG sensors. Ref. [16] presented an FBG sensor-based BWIM system to detect damage in bridges in the context of SHM. As well as finding weights, BWIM algorithms have been used to identify the silhouettes of heavy vehicles in continuous traffic, including multiple vehicle presence scenarios [17; 18; 19]. Over the past two decades, BWIM has been developed to not only enhance the effectiveness of static weight enforcement stations, also to provide axle weight data for traffic monitoring, pavement design protocols, pavement management, and transportation safety [20]. Vehicle configurations (speed, axle numbers, and axle spacing) are necessary information required to identify axle weights in any BWIM system [21]. However, field tests show that the development of axle detectors was one of the greatest challenges in conventional BWIM systems [22]. To detect vehicle axles, early BWIM systems had two axle detectors (pneumatic tubes or tape switches) on the road pavement of each lane of interest [9; 23]. These detectors had problems with durability and disruption to traffic during installation and replacement [19; 24]. To overcome these shortcomings, modern BWIM systems use axle-detection concepts called nothing-on-the-road or free-of-axle detector (FAD) that utilize sensors on the underside of the bridge [25; 26; 27]. In a FAD BWIM system, signals from two additional strain transducers (namely, FAD sensors) are collected at different positions on the bridge, to record time stamps for axles and hence to find vehicle configuration, axle spacing and speed. Unlike conventional axle detectors, FAD sensors are mounted underneath the bridge deck. Hence, there is no disruption to traffic during installation and replacement of the axle detectors and the sensors are much less susceptible to the ingress of moisture.