## 1 Introduction
In addition, signal processing and machine learning techniques, which do not rely on modal parameters, perform well in identifying structural damage location and degree [36; 37; 38]. A bridge dynamic response can be amplified by regulating the vehicle frequency, increasing vehicle weight or speed. Increasing vehicle weight becomes a feasible solution, when considering the negative effects of increasing vehicle speed and the inconvenience of altering vehicle stiffness. When analyzing the vehicle-bridge interaction (VBI) system, we usually assume that the effect of vehicle vibration on the bridge can be ignored because the vehicle weight is so small compared to that of the bridge. In [PERSON]'s paper [39], a new assumption is made to uncouple the equation group, which is that the vehicle acceleration magnitude is much lower than the gravitational acceleration constant. Although the vehicle mass is as high as 100% of the total bridge mass in [PERSON]'s research, the vehicle was maintained at a low speed in order to meet [PERSON]'s assumption. These two assumptions both ignore the interaction between the vehicle and bridge. However, this assumption tends to be invalid when the vehicle becomes heavier and the bridge becomes lighter or the vehicle speed becomes faster. In such cases, the frequency variation of the bridge coupled with the moving vehicle should be taken into account to avoid the identification deviations. Natural frequencies are mainly sensitive to global stiffness modifications and not so much to local ones [2]. However, the global stiffness is often influenced by variations in environmental factors or heavy vehicles crossing the bridge. That influence can be high enough to completely mask the presence of even severe damage [40]. In [PERSON]'s paper [41], a steel single-span tied-arch bridge was monitored for a year. An increase of 10 \({}^{\circ}\)C in temperature resulted in a relative decrease of about 0.2\(\sim\)0.25% for the natural frequencies of the arch modes. In the field experiment in [PERSON]'s paper [42], a decrease of 2.6% in bridge frequency was observed when a truck with mass ratio of 0.082 to the experiment bridge was parked at the midspan of the bridge. In the laboratory experiments, a decrease of 10.4% was observed when a model vehicle with mass ratio of 0.154 to the scaled bridge was parked at the midspan of the bridge. The bridge frequency also changes under daily traffic conditions. From the 24-h ambient vibration monitoring on a cable-stayed bridge, it was found that the natural frequencies of the global modes can exhibit as much as 1% variation [43]. [PERSON] et al. [44] showed that the natural frequencies of the bridge modes can exhibit variation between 1.7% and 5.5%. When heavy vehicles pass, the frequency of simply supported Nongro bridge was approximately 5.7% larger than that when light vehicles pass [45]. [PERSON] et al. [46] found that frequency shifts up to 5.4% for a short span and relatively high (vehicle to bridge) mass ratio. In addition, previous studies mainly discussed the variation rule of bridge frequency with different vehicle stiffness through theoretical analysis and laboratory test [47; 48]. The analytical solution of a bridge and vehicle frequency when the vehicle is in a different position of the bridge was given, however fail to account for the applicability of bridge frequency extraction in indirect bridge detection methods. In this paper, the equation group for the general VBI system cannot be uncoupled under the strong vehicle-bridge interaction. A strong vehicle-bridge interaction is achieved through adjusting vehicle parameters, such as a large vehicle-to-bridge mass ratio and high vehicle speed. The influence of vehicle parameters on frequency extraction from a passing vehicle is discussed in detail and the accuracy of frequency identification is demonstrated. The main parameters are made dimensionless, including vehicle speed, frequency ratio, and vehicle-to-bridge mass ratio.