Identification of a Vehicle-Bridge System

Apart from using the aforementioned various theoretical models of the vehicle- bridge dynamic system to predict the dynamic responses of the system, identifying the system properties from vehicular or bridge responses is another important research topic and reviewed in this section. Please note that identifications for the vehicle-bridge system are discussed theoretically only here. The applications in reality are described in section 2.2 (experimental work).

(a) Identification of modal properties of bridges

Unlike traditional methods of identifying the modal properties of bridges by using sensors to measure the dynamic responses, extracting modal properties from vehicle responses does not need the installation of sensors on bridges and could scan the modal properties of a number of bridges with high efficiency. Hence this approach has drawn much research interest in recent years.

To identify bridge frequencies from vehicle responses, Yang and Lin (2005) derived the analytical solution for the dynamic responses of both the moving sprung mass

2. Literature Review

25

and an Euler-Bernoulli beam based on the assumption that the mass ratio of mass to beam is small and the inertial effect of the mass can be ignored. The spectrum analysis of the mass response and the beam response revealed some useful information associated with the moving speed of the mass, sprung mass frequency and the beam frequencies. The possibility of identifying the bridge frequencies from the vehicular response was discussed. Yang and Chang (2009b) demonstrated the feasibility of using Empirical Mode Decomposition (EMD) technique to extract higher beam frequencies from a moving mass response. Yang and Chang (2009a) investigated the influences of the key dynamic parameters of the sprung mass-beam system on the vertical dynamic response of the moving mass. It was found that the smaller the initial mass/beam acceleration amplitude ratio in each mode is, the greater the possibility of identifying the bridge frequency in that mode from the mass response is. However, the bridge surface roughness was not considered in the above works. To overcome this drawback, Yang et al. (2012) proposed to use two connected vehicles to remove or reduce the blurring effect of road surface roughness. To enhance the visibility of bridge frequencies from the vehicular response, Yang et

al. (2013b) used the singular spectrum analysis with a band-pass filter to filter out the

vehicle frequency for identifying bridge frequencies.

While the above works focused on extracting bridge frequencies from the passing vehicles, some researchers recently began to study the feasibility of constructing the bridge mode shapes from the passing vehicles’ responses. Zhang et al. (2012) extracted the structural mode shape squares from the acceleration response of a tapping vehicle by using the Short Time Fourier Transform (STFT). Yang et al. (2014) constructed the mode shapes of a simply supported bridge from the passing vehicular responses by using Hilbert Transform (HT). Malekjafarian and OBrien (2014) identified the bridge modes from vehicular responses by using the Short Time Frequency Domain Decomposition (STFDD). The signals from the axles of two successive trailers towed by a tractor were used and external excitations were also applied to the bridge to reduce the effect of road roughness on the accuracy of identification results. Malekjafarian and OBrien (2017) believed that it was a good idea to excite a bridge by using a travelling tractor connected by two trailers and an external excitation with a frequency close to one of the bridge frequencies. The two axle responses of the second trailer were measured and a subtraction was done

2. Literature Review

26

between the two responses to reduce the effect of road surface roughness. The bridge mode shapes could be estimated from the measured axle responses by Hilbert Huang Transform (HHT).

(b) Damage detection of bridges

Damage identification of the bridge under traffic load is another interesting and important research topic and has been studied extensively. There are normally two approaches known as the indirect method (OBrien and Malekjafarian, 2016) and the

direct method (Sun et al., 2016) based on measured signals from the vehicle or the

bridge, respectively. A recent overview in this topic could be found in (Zhu and Law, 2015). Malekjafarian et al. (2015) presented another critical review on the indirect bridge monitoring using vehicular responses passing over the bridge. A very recent good discussion about the merits and limitations of using the indirect method to detect the bridge damage was given in (Hester and González, 2017). Zhang et al. (2012) proposed a damage index based on the mode shape square extracted from an instrumented tapping vehicle, which was found robust to noise. Feng and Feng (2016) proposed to use a video-based sensor to record the time history vibration of a beam traversed by moving vehicles. The first mode shape of the beam was constructed from the measured data and the curvature of the mode was then used to identify the damage of the beam.

(c) Identification of vehicle axle loads

Apart from the above large amount of work dedicated to the identification of bridge parameters, there are also some researchers identifying vehicle parameters. Karoumi

et al. (2005) studied the identification of vehicular axle loads from the measured

strain data embedded in a bridge by minimizing the difference between the measured strain and the evaluated strain which was obtained with the usage of a determined influence line. The axle positions, axle loads, speed and acceleration were evaluated. OBrien et al. (2014) identified the contact force between a moving vehicle and a bridge by using the vehicle response. The applications of this method to the identifications of the bridge’s bending stiffness and road pavements were also discussed.

2. Literature Review

27

The bridge-weight-in-motion is a significant application for identifying the vehicle axle loads from bridge responses and has attracted wide research interests. Chan and Ashebo (2006) identified the vehicle axle forces acting on a continuous beam by mounting eleven strain sensors on the beam. MS method and impulse function were used to inversely calculate the axle forces. Ding et al. (2009) evaluated the contact forces between a vehicle and a bridge with surface irregularities by using an evolutionary spectral method. The dynamic response of the vehicle-bridge system was separated into two parts: vehicle induced response and bridge surface irregularities induced response. Each part was calculated separately and then added together. Deng and Cai (2010b) used the influence surface concept to identify the vehicle axle loads travelling on a concrete slab bridge which was modelled as a 3D FE model in ANSYS program. The dynamic response of the bridge was separated into an inertial part and an interaction part. It was found that the inertial part has a significant effect on the identified results and should be excluded from the bridge response if the influence surface concept is used. As the acceleration of the bridge cannot be measured at every point in reality, the inertial part needed to be obtained from the vehicle-bridge interaction simulation.