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In this paper, a comprehensive comparative study on several existing vehicle–bridge interaction (VBI) models is presented with the aim to provide a useful reference to the selection of vehicle and bridge models when conducting the VBI simulation. A simply-supported slab-on-girder highway bridge and the AASHTO HS20-44 vehicle are adopted in the numerical analysis. The bridge is modeled as an Euler–Bernoulli beam, grillage, plate-and-beam system and solid-element system, respectively, while the vehicle is modeled as a moving-force, moving-mass and spring-damper-mass (SDM) system, respectively. Other factors, including the road roughness and the contact condition between the vehicle tire and bridge, are also considered. The effects of different VBI models on the bridge responses are studied and the results from different models are compared in terms of their accuracy, efficiency and suitability. The results show that the accuracy of different types of bridge responses calculated varies with the number of bridge vibration modes used in the simulation. It is also found that the type of element used in the bridge model and the vehicle tire model both have a larger impact on the bridge acceleration than bridge deflection.

This paper examines the dynamics of a nonlinear semi-active suspension system using a quarter-car model moving over rough road profiles. The bifurcation analysis of the nonlinear dynamical behavior of this system is performed. Codimension-two bifurcation and homoclinic orbits can be discovered in this system. When the external force of a road profile was added to this system as a parameter with a certain range of values, a strange attractor can be found using the numerical simulation. Finally, the Lyapunov exponent is adopted to identify the onset of chaotic motion and verify the bifurcation analysis.

This paper deals with the simultaneous identification of road roughness and vehicle parameters, considering the effect of vehicle–structure interaction. The proposed technique avoids the use of bridge response data (which has practical implementation difficulties along with the high chances of corruption with environmental noises) and utilizes the vehicle response data (which is relatively easier to record). Further, vehicle calibration is not needed as the roughness is estimated simultaneously. The identification is carried out by the coupling of an unbiased minimum variance estimator with an optimization scheme. This study considers a quarter-car vehicle model and a half-car vehicle model, instrumented to measure the vehicle vibration data. The unbiased minimum variance estimator (MVE) allows a linear temporal evolution of the state variables, incorporating the roughness as an unknown input term such that the need for linearization is avoided, unlike the traditional nonlinear filters. The optimization scheme helps in choosing a set of optimal solutions for the vehicle parameters as designed in the coupled scheme. The best split of the available measurement data to be used in the two schemes (MVE and optimization scheme) is discussed. The effect of different objective functions is also studied. The proposed technique is successful in terms of simultaneously estimating the vehicle parameters, roughness profile and vehicle responses (states) accurately.

Two factors are critical to the effectiveness of the vehicle scanning method for bridge frequencies. One is the frequency of the test vehicle itself. This can be eliminated by using the vehicle–bridge contact point response calculated from the vehicle response. The other is the surface roughness of the bridge, which can be removed by using the residual response of two connected vehicles. In this paper, it is demonstrated for the first time that both vehicle’s frequency and surface roughness can be simultaneously eliminated using the contact residue of two connected vehicles. Theoretically, a formulation is presented for both the contact response and residues. In the numerical study, the contact response is demonstrated to outperform the vehicle response as more bridge frequencies can be identified, while the contact residue is verified to work well for various surface roughnesses, vehicle spacings, and bridge damping ratios. For damped bridges with rough surfaces, the contact residue enables us to extract the first three bridge frequencies.

The evaluation of road roughness plays a critical role in the life-long maintenance of the highway system. This study proposes a Kalman Filter-based scheme to evaluate the road roughness indirectly from the response of a moving adapted monitoring vehicle. Key feature of the scheme is the use of measurements from dynamic tire pressure of unsprung mass components that directly interact with roads. Combination of ideal gas law and elastic contact model results in a nonlinear relationship between the tire pressure and the contact force, in which the parameters are calibrated by the Extended Kalman Filter. Identification of vehicle’s physical parameters adopts the power spectrum method with a known-size bump test. Subsequently, the road roughness is treated as unknowns in the vehicle’s state-space equation and solved by the Discrete Kalman Filter with unknown inputs. The estimated road roughness profiles are then used to calculate the International Roughness Index and compared with that provided by the standardized laser profilometer, an outer-systematic comparison. On the other hand, available measurements are split into groups that measurements of tire pressure are used to predict the accelerations of the car body and wheels and compared with these accelerations directly measured from accelerometers, an inner-systemic comparison. Field tests are carried out on a 900m long standardized road under two scenarios of with and without the bump and four different vehicle running speeds from 20 to 50km/h. Consistence of comparison from different perspectives proves the reliability of the proposed scheme. In addition, the results unveil that the scenario with a lower running speed can offer a better estimation of road roughness.

In most related studies on road surface roughness, the vehicle’s wheel is often using a contact point model rather than a disk model. This results in neglecting the wheel’s size and interaction with the road. Consequently, the vehicle’s response may not be genuinely reflected, especially for the massive topic of noise, vibration, and harshness (NVH). Unlike the existing approach targeting the power spectrum, this paper proposes a new convolution method to tackle the disk effect and operates directly on the spatial domain, i.e. road surface roughness. By using a designed periphery function, it can simulate the wheel geometry passing through road surface roughness. The periphery function acts as a filter to the road surface roughness that can filter out smaller oscillations. Some examples involving roughness from ISO 8608 standards were tested. It is shown herein that the proposed method can match the theoretical result (using the geometry method (GM)) not only in the spatial domain but also in the power spectral density (PSD). Since the convolution is performed under the spatial domain, the proposed method can directly apply the disk model to any existing road surface roughness with different spectral compositions in practice. Understanding the disk effect reduces the higher frequency of the vehicle’s response depending on roughness severity, which may significantly impact the vehicle design for ride comfort, road surface roughness extraction, bridge health monitoring using the drive-by method, etc.

The study proposes a Kalman Filter Family-schemed algorithm to identify the vehicle’s parameters and evaluate the road roughness simultaneously, based on the response of an adapted monitoring vehicle. The vehicle is simplified as a three-dimensional multi-body system consisting of the unsprung mass of wheels and the sprung mass of the car body, connected by springs and dampers that represent the suspension system. Accelerometers and a gyroscope measure the accelerations or angular velocity of different positions of the vehicle during vibrations. The Kalman filter (KF) with unknown inputs enables the prediction of the car body’s accelerations from those of wheels. On the other hand, the Augmented KF can compute the accelerations of wheels based on the car body’s accelerations. Thus, an inner-systemic objective function incorporating the vehicle’s parameter is built between the predicted and measured accelerations and solved in an optimized manner with the Genetic Algorithm, so that an individual complicated impact test or bump test is avoided. The numerical examples carry out field tests on a 900m long standardized test road under two scenarios of with and without a bump. The road roughness estimated by these two KF methods from different measurements is used to calculate the International Roughness Index (IRI) and further the Riding Quality Index, which are compared with those directly provided by a standardized laser IRI profilometer. Accordance in between confirms the accuracy of the proposed algorithm under different scenarios. The analysis underlines the measurements from unsprung wheels that contact directly with the road enable a more accurate estimation of road roughness than those from the sprung car body. In addition, a vehicle speed lower than 40km/h can provide a better estimation of the road profiles.

In this study, a bridge damage identification method based on the Long Short-Term Memory (LSTM) network and the contact point response is proposed, which utilizes the time behavior of the contact point response. The contact point response serving as the input to the LSTM network is obtained by calculating the vehicle-bridge interaction motion equation. A new bridge damage indicator titled the Euclidean Distance Damage Index (EDDI) is developed based on the difference between the actual and predicted values of the contact point response. Under ideal road surface conditions, the EDDI calculated in the healthy state of the bridge remains below 0.16, while exceeding 1.0 in the damaged state. When road roughness is considered, the EDDI is calculated to be less than 0.12 in the healthy state of the bridge and higher than 0.65 in the damaged state. The results show that the EDDI is more effective in distinguishing between the damaged and the healthy states of the bridge. Meanwhile, road roughness has a negative effect on the damage sensitivity of EDDI.