# Combined Identification of Vehicle Parameters and Road Surface Roughness Using Vehicle Responses
###### Abstract  
Highways, urban roads, and bridges are the important transportation infrastructures for the economic development of modern society. The evaluation of bridge and road quality is crucial to the maintenance and management of the bridge and road industry. Road roughness is a widely accepted indicator in the evaluation of road quality and safety, which is a major input source for vehicles. The vehicle responses-based method of identifying road roughness is efficient and convenient. However, the dynamic characteristics of the vehicle have an important impact on the interaction between the vehicle and the road. When the vehicle parameters are not yet clear, the coupling of unknown parameters and unknown road roughness results in the need for mutual iteration when the existing methods simultaneously identify vehicle parameters and road roughness. To address this issue, this study proposes an effective method for the combined identification of vehicle parameters and road roughness using vehicle responses. The test vehicle is modeled as a four-degree-of-freedom half-vehicle model. In view of the coupling effect between tire stiffness and road roughness, the unknown vehicle physical parameters, except for tire stiffness, are first included in the extended state vector. Based on the extended Kalman filter for unknown excitation (EKF-UI), unknown vehicle physical parameters and unknown forces on the axle are identified. Subsequently, based on the property that the front and rear axles of the vehicle pass through the same road roughness area at a fixed time lag, the tire stiffness is identified by combining the identified unknown forces on the axle. Finally, the road roughness is obtained using the identified vehicle parameters and unknown forces. Numerical studies with different levels of roughness, different noise levels, and different vehicle speeds have verified the accuracy of this method in identifying vehicle parameters and road roughness. vehicle parameter identification; road roughness identification; extended Kalman filter with unknown inputs; vehicle responses +
Footnote †: journal: applied sciences  
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contact measurement, non-contact measurement, and system response-based method [11]. Contact measurement includes the probe method, etc. The hand-held device moves along the surface of the road, and generates up and down displacements with the microscopic unevenness of the road surface. These displacements are converted into electrical signals to calculate the roughness parameter of the road surface. Although the cost of this method is low, it is inefficient and has the problem of interrupting traffic. Non-contact measurement, such as inertial road profilers, measures the road surface elevation by analyzing the signals reflected back from the laser. Generally, non-contact measurement is expensive, its equipment installation is complicated, which is unsuitable for common road networks that require frequent inspections [12]. Road surface roughness is the primary source of vehicle excitation [13]. The system response-based method identifies unknown road surface roughness by observing the responses of moving vehicles to the road surface. This approach is not only crucial for understanding the dynamic interaction between vehicles and roads but also has significant practical implications for both road maintenance and vehicle design. To estimate road roughness, some scholars have proposed methods to identify unknown road roughness based on vehicle response with known parameters. [PERSON] et al. [14] used a calibrated quarter-car model combined with a regularized augmented Kalman filter (AKF) to identify the roughness profile and power spectral density (PSD). [PERSON] et al.