Virtual Axle Method for Bridge Weigh-in-Motion Systems Requiring No Axle Detector Wei He 1 ; Tianyang Ling 2 ; Eugene J. OBrien 3 ; and Lu Deng, Ph.D., M.ASCE 4 Abstract: Bridge weigh-in-motion (BWIM) systems provide an effective approach to identifying the axle and gross vehicle weights of vehicles as they travel over an instrumented bridge. For the majority of BWIM systems, the vehicle configuration (including axle count and axle spacing) and vehicle speed are prerequisites for identifying the axle and gross weights of vehicles. Existing nothing-on-road (NOR) BWIM systems acquire such data through dedicated sensors, namely, free-of-axle-detector (FAD) sensors, in addition to weighing sensors. These FAD sensors are usually installed on the underside of the bridge deck or girders. This study presents a novel method for identifying the axle spacing and weights of vehicles. It only requires the flexural strain signal recorded from the weighing sensors, leading to both a reduction in the installation cost and broader applications of BWIM systems. The effectiveness and accuracy of the proposed method are demonstrated through numerical simulations. Laboratory experiments based on a scaled vehicle–bridge interaction (VBI) model were also conducted for verification. The results show that the proposed method has good accuracy for axle spacing and axle weight identification. DOI: 10.1061/ (ASCE)BE.1943-5592.0001474. © 2019 American Society of Civil Engineers. Author keywords: Bridge weigh-in-motion (BWIM); Strain; Axle spacing; Vehicle weight; Overload. Introduction Accurate traffic load information is of great value for the assess- ment and maintenance of transportation infrastructure (Deng et al. 2017, 2018a). Traffic monitoring, especially of vehicle weights, is of significance for traffic management and load-limit enforcement (Jacob 2010; Richardson et al. 2014). Bridge weigh-in-motion (BWIM) is one of many technologies used today for weighing vehicles as they travel at highway speed. The concept, which was first proposed by Moses in the 1970s (Moses 1979), uses an instru- mented bridge as a scale to weigh the vehicles passing over bridges at normal speeds. Over the years, Moses’s algorithm has been the basis for many other schemes aiming to improve the accuracy and applicability of BWIM systems (Quilligan et al. 2002; Richardson et al. 2014; Sekiya et al. 2018; Yu et al. 2018; Zhao et al. 2014). State-of-the-art reviews on BWIM algorithms and their applications have been presented by Yu et al. (2016) and Lydon et al. (2016). Moses’s algorithm and its variants generally estimate the axle weights of vehicles by minimizing the Euclidean norm of the resid- ual between the actual bridge response measured from weighing sensors and the predicted bridge response based on the influence line method. The axle information (i.e., the number of axles and axle spacing) and vehicle speed are prerequisites for predicting bridge responses. Axle detectors have therefore been developed for this purpose and are needed for the majority of existing BWIM sys- tems. Conventional axle detectors identify vehicle axles using pressure-sensitive sensors installed on the upper surface of the bridge deck. This method is quite simple and has good accuracy. However, the sensors are directly exposed to the impact of wheels and are therefore not durable. In addition, the installation raises issues of safety and may cause disruption to traffic. To address this issue, nothing-on-road (NOR) BWIM systems and free-of-axle- detector (FAD) systems have been proposed (OBrien and Žnidaric ˇ 2001). In the FAD scheme, vehicle axles are detected from the local response measured by special sensors attached underneath the bridge deck. However, the FAD scheme is suitable only for specific types of bridges and is sensitive to the deck thickness, surface roughness, and vehicle transverse position (Ieng et al. 2012; Kalin 2006; OBrien and Žnidaric ˇ 2001). To overcome the disadvantages of conventional FAD methods, some researchers have attempted to use the global flexural strain in- formation acquired from the weighing sensors to identify the vehi- cle speed and axle spacing. Wall et al. (2009) obtained the vehicle velocity and axle configuration by calculating the second derivative of the bending responses of the bridge. Kalhori et al. (2017) found that vehicle axles can be identified by applying a peak analysis to the time history of flexural strains, although some axles might occa- sionally become unidentifiable. Yu et al. (2015) proposed a vehicle axle identification method using only the global strain signal from the weighing sensors based on a wavelet transformation. A shear- force-based method was recently shown to be an effective and effi- cient method for axle identification (OBrien et al. 2012), whereas Lydon et al. (2017) used bearing strain with axle detection with good success. Bao et al. (2016), based on field test results, found that vehicle weights could also be estimated from measured shear strains. In addition to these methods, a novel virtual simply- supported beam (VSSB) method was proposed by He et al. (2016), which identifies vehicle axles based on the flexural bending strains measured from four different longitudinal positions of the bridge 1 Research Assistant, College of Civil Engineering, Hunan Univ., Changsha, Hunan 410082, China. Email: hewei.hnu@gmail.com 2 Research Assistant, College of Civil Engineering, Hunan Univ., Changsha, Hunan 410082, China. Email: lingtianyang@126.com 3 Professor, School of Civil Engineering, Univ. College Dublin, Dublin D04V1W8, Ireland. ORCID: https://orcid.org/0000-0002-6867 -1009. Email: eugene.obrien@ucd.ie 4 Professor, Key Laboratory for Damage Diagnosis of Engineering Structures of Hunan Province, Hunan Univ., Changsha, Hunan 410082, China (corresponding author). Email: denglu@hnu.edu.cn Note. This manuscript was submitted on January 22, 2019; approved on May 2, 2019; published online on June 24, 2019. Discussion period open until November 24, 2019; separate discussions must be submitted for individual papers. This paper is part of the Journal of Bridge Engineering, © ASCE, ISSN 1084-0702. © ASCE 04019086-1 J. Bridge Eng. J. Bridge Eng., 2019, 24(9): 04019086 Downloaded from ascelibrary.org by HUNAN UNIVERSITY on 09/16/19. Copyright ASCE. For personal use only; all rights reserved.