# A Fast Wavelet-Based Bridge Condition Assessment Approach Using Only Moving Vehicle Measurements
## 1 Introduction  
As a unique structure, bridges play a vital role in road networks. With the rapid development of the world economy, bridge structures are increasingly built throughout the world and their condition is central to ensuring the required safety levels and effective operation of the traffic networks. Thus, it is essential to periodically implement bridge condition evaluations for maintaining the structural integrity of the bridges. ASCE [1] reports that there are more than 617,000 bridges in the U.S., of which over 250,000 bridges are at least 50 years old. In order to solve the huge labor-intensive problem of all bridge monitoring under visual/manual inspection, electronic monitoring of bridges has received increasing attention over the last decade, which is referred to as bridge structural health monitoring (SHM). In general, bridge SHM has four levels [2]: (1) identify the presence or absence of damage, (2) localize the damage, (3) determine the extent of the damage, and (4) assess the bridge's remaining life. For bridge SHM, many sensors are usually installed on the structure and the structural vibration responses are used as input signals for evaluating the bridge conditions [3]. In addition, this approach requires a continuous power supply, which is expensive to some extent [4]. As a result, the online SHM system is commonly applied to long-span bridges or some special/important bridge structures. It must be admitted that short-span and mid-span bridges make up a significant portion of the road network bridge inventory buthave no corresponding SHM system. Therefore, it is necessary to develop more efficient and economical bridge SHM methods for short- and medium-span bridges. The technique of 'drive-by' or vehicle scanning bridge SHM provides a promising method, namely by using the indirect measurements from a moving vehicle [2; 5; 6; 7; 8; 9]. [PERSON], et al. [10] first demonstrated the effectiveness of extracting the bridge frequencies using vehicle accelerations and proposed the potential application for bridge SHM [11]. Later, field experiments verified the effectiveness of extracting the bridge's fundamental frequency using indirect measurements [12; 13]. In comparison to conventional bridge SHM, the concept of drive-by bridge SHM shows many advantages in terms of efficiency, economy, convenience, and mobility [14]. Therefore, recently, this technology has received extensive attention and achieved great development. Most related investigations focus on extracting the bridge dynamic parameters with indirect measurements, i.e., frequencies [6; 14; 15; 16; 17; 18; 19], damping [5; 20; 21; 22], and mode shapes [8; 23; 24; 25; 26; 27; 28; 29]. The change of those modal properties is frequently used for bridge damage detection. In addition to modal properties, some damage indexes associated with the drive-by concept using signal processing methods are proposed, such as wavelet transform and Hilbert transforms [30; 31; 32; 33]. Wavelet transform is often used in bridge SHM because it analyzes signals in both frequency and time domains. One of the most critical features of wavelet transform is that it is sensitive to discontinuity in the signal. Therefore, wavelet transform can be used to indicate the damage location. [PERSON], et al. [34] applied the wavelet transform to localize the crack of an Euler-Bernoulli beam under a moving force. In this approach, both the fixed sensor (installed on the beam) and the moving sensor (installed on the moving force) are studied to detect the defect. The results show that the wavelet coefficients associated with wavelet Gaussian 4 have the highest magnitude at the exact location of the crack, and moving sensors are more efficient than fixed sensors. Later, [PERSON] and [PERSON] [35] numerically investigated to identify multi-cracks with wavelet analysis using indirect measurements from vehicle vibrations.