## 1 Introduction  
Structural performance degradation is an extensively concerned issue for in-service bridges, and the inspection and evaluation is an essential and necessary work to keep bridges in good operating condition. However, a traditional bridge inspection method usually requires considerable preparatory work, such as field installation of sensors and undesirably traffic closure, which require massive time and economic costs. The disadvantages of a traditional bridge inspection method limit its wide application to highways and urban bridges. To meet the increasing maintenance requirements of these bridges, rapid detection methods and techniques are urgently needed and have received more attention in recent years [1; 2; 3; 4]. The indirect bridge detection method was first proposed by [PERSON] [5] as early as 2004 and has gained great popularity because of its low cost and low maintenance effort. Unlike the traditional bridge inspection method [6; 7; 8], this approach employed the dynamic response of a passing vehicle instead of a bridge itself. A vehicle acts as an exciter and a signal collection device simultaneously in this method. In the initial stage, researchers use the acceleration signal of a passing vehicle to extract the bridge natural frequency. The accuracy of the result was verified through a theoretical derivation [9; 10], laboratory investigation [11; 12; 13], and field tests [14; 15; 16]. With further development of this method, more bridge modal parameters were identified from vehicles' acceleration signal, such as modal shape and damping parameter [17; 18; 19]. In order to reduce vehicle response interference in the signal, the response of the contact point of the vehicle with the bridge, rather than the vehicle itself, is proposed [20]. On this basis, the effect of identifying bridge parameters using the acceleration signals of passing vehicles is further improved, especially the extraction of bridge frequency [21; 22; 23; 24]. The vehicle model is also developed from a single-degree-of-freedom (DOF) model to a single-axle vehicle model. The single-axle vehicle is modeled as a two DOF system, including both the rocking and vertical motions [25]. In bridge modal analysis, [PERSON] and [PERSON] present a novel algorithm for the estimation of bridge mode shapes using the response measured on a passing vehicle [17]. A rescaling process is proposed to construct the bridge mode shapes using the amplitude of the responses measured on two following axles. And the concept of subtraction is employed to remove the effect of the road profile in the measured responses. They also present a novel algorithm for bridge damage detection based on the mode shapes estimated from a passing vehicle [26]. Different from previous studies, a measurement system based on laser vibrometers and accelerometers is employed to measure the bridge response at moving coordinates on a passing vehicle. The bridge mode shape is estimated with a high resolution by using an improved short time frequency domain decomposition method. Moreover, a number of signal processing methods were introduced to achieve better parameter identification by reducing false-positive feedbacks extracted from the roughness of road surfaces [27; 28; 29]. A novel indirect method of extracting bridge fundamental frequency was proposed by [PERSON] [30], which aimed to eliminate the roughness influence in vehicle signals. A particle filter in combination with a random walk model is used to estimate the displacement inputs at the front and rear tires. Then the bridge's fundamental frequency can be clearly shown through the subtraction between the displacement inputs at the front and rear tires. Bridge damage identification methods can be divided into frequency-based and mode shape-based methods, depending on whether or not they rely on modal parameters [31]. They are both capable of damage detection [14; 32; 33], while only the mode shape-based methods are able to realize damage localization [19; 34; 35].