## 1 Introduction  
Bridge structures are amongst the most critical components of transport infrastructure. Similar to other structures, they deteriorate over their lifetimes due to aging, environmental conditions and traffic loading [1; 2; 3]. Structurally deficient bridges may be unsafe, and continuous monitoring of bridges is desirable in such situations. In the United States, 9.1% of the total number of bridges in 2016 were found to be structurally deficient and to require substantial investment and improvements to operate [4]. Therefore, an effective method of bridge damage detection is important to detect damage quickly when it occurs. In recent years, many methods of bridge damage detection have been proposed for road authorities to maintain an acceptable level of bridge safety [5]. These methods are classified using levels of damage identification. For example, Level I damage detection methods identify the presence of damage in the structure, Level II methods identify the location of damage, Level III methods quantify the extent of damage and Level IV methods predict the remaining service life of the structure [6]. Visual inspection is the most frequently used method, but it can be expensive, time-consuming and disruptive to traffic. [PERSON] et al. used a combination of visual inspection and non-destructive testing of materials to calculate a condition rating number (CRN) and hence develop a low-cost SHM system [7]. This concept is tested on a set of real bridges to calculate the CRN and assess the damage category of each bridge based on their visual inspection and assumed material strength properties. Although the method is simple, low-cost and fast, it is less sensitive to small changes in temperature and environmental conditions around the bridge. Direct instrumentation is an approach to structure health monitoring (SHM) in which sensors (typically accelerometers or strain transducers) are installed on the bridge. The most popular systems are based on analysing bridge natural frequencies and modes extracted from sensors installed at various locations on the bridge [8]. However, there tends to be a slight change in the bridge natural frequencies, which are used to identify bridge damage (Level I) for a significant change in the bridge condition. [PERSON] et al. proposed a bridge damage detection method (Level I) using a strain-based weigh-in-motion (WIM) system which is sensitive to damage only if the location of damage is near the sensor [9]. For that reason, arrays of distributed sensors are required to identify damage. Indirect monitoring is an alternative approach, where an instrumented vehicle crossing the bridge is used to infer information about its condition [10]. The most recent indirect monitoring systems are able to detect changes in bridge damping [10] and natural frequency [11; 12] using vehicle accelerations. [PERSON] et al. estimated mode shape squares from vehicle accelerations and proposed a new damage index of the bridge [13]. [PERSON] et al. extracted full bridge mode shapes using vehicle accelerations in segments of the bridge [14]. While the indirect SHM methods with instrumented vehicles are easy to operate and are cost effective, the damage indicators are very sensitive to the vehicle velocity, changes in road profile and environmental conditions [10]. In some of the latest SHM systems, unmanned aerial vehicles (UAVs) have measured bridge displacements and mode shapes using vision-based techniques [15]. Although the use of UAVs is convenient, low cost and can access remote parts of the bridge, the visual measurements may not yet be accurate enough for short-span bridges, where the bridge deflections in response to passing heavy vehicles are typically less than one millimetre. Another type of SHM system involves the use of machine learning algorithms that process indirect measurements from the vehicle [16] or direct bridge response measurements [17; 18] to identify structural abnormalities.