Moving Test Vehicle Research Articles

Novel recursive formula for removing damping distortion effect on bridge mode shape restoration using a two-axle scanning vehicle

Mode shapes recovered for bridges are often distorted by bridge damping when using the vehicle scanning method (VSM). To remedy such an effect, a novel recursive formula utilizing the spatial correlation between the front and rear contact points of a two-axle scanning vehicle is theoretically established. For a bridge subjected to a two-axle moving test vehicle, the dynamic response of the system is first derived in closed form. The vehicle-bridge contact response is used as a substitute for the vehicle response in signal processing, since it is free of the masking effect posed by vehicle frequencies. Using either the Hilbert transform (HT) or wavelet transform (WT), instantaneous amplitudes are extracted for the component response of the bridge of concern. Further, recursive formula that accounts for the spatial correlation between the two contact points is established to recover the undistorted bridge mode shapes. The following are the conclusions: (1) The distortion effect of damping on bridge mode shapes can be effectively removed by the recursive formula against various factors; (2) the WT is more effective in recovering undistorted bridge mode shapes than the HT; and (3) the proposed formula works well for restoring the mode shapes of bridges with rough pavement, by adding an accompanying truck during the vehicle scanning.

Normalized formula for removing damping effect in recovering bridge mode shapes using a moving and a stationary vehicle

Recovering bridge mode shapes using the response of a moving test vehicle has become a technique of interest. However, the mode shapes recovered tend to be distorted by bridge damping. To remove the distortion effect, a normalized formula that utilizes the responses of a moving and a stationary vehicle is devised for recovering bridge mode shapes with no prior knowledge of bridge damping ratios. Specifically, the moving test vehicle is used to recover the global modal response of the bridge throughout its span length at different instants as the vehicle moves over, and the stationary vehicle to generate a reference response at a fixed location of the bridge for removing the damping effect. In this paper, closed-form solutions are derived for the dynamic responses of the bridge and two test vehicles. The contact response is used in place of the vehicle response to alleviate the vehicle frequency's masking effect on bridge frequencies. The formula for recovering the modal mode shape is derived by normalizing the instantaneous amplitude of the Hilbert transform (HT) for the bridge from the moving test vehicle with respect to that by the stationary vehicle. The following conclusions are drawn: (1) the damping distortion effect on bridge mode shapes can be removed by the normalized formula; (2) the normalized formula is robust with regard to bridge damping, stationary vehicle location, and vehicle speed for beam-type bridges; (3) the mode shapes recovered by the present method are acceptable, even in the presence of pavement roughness, when aided by an accompanying truck.

Extracting Bridge Frequencies from The Dynamic Responses of Moving and Non-moving Vehicles

Bridges can continuously suffer from structural deterioration due to inclement environmental and operational effects, making a timely inspection necessary to ensure the reliability and functionality of bridges. Recent progress in vehicle-bridge interactions has promoted the vehicle scanning method (VSM) for bridge frequency extraction, whereby the bridge frequency is typically identified from the dynamic response of a passing vehicle to reflect the bridge's health condition. Despite numerous endeavors, the low-speed limitation of the moving test vehicle and the adverse influence of road roughness still hinder the general application of VSM. In this regard, this paper presents a novel VSM for bridge frequency extraction by integrating moving and non-moving vehicles. By introducing the novel non-moving vehicle, the bridge vibration content becomes more obvious in the dynamic response of the moving vehicle, which is beneficial to the associated indirect bridge frequency extraction. Moreover, the non-moving vehicle is nearly free from the influence of road roughness, such that the performance of VSM for bridge frequency extraction can be enhanced against noisy real-world environments. To understand the inherent mechanism of the proposed method, a vehicle-bridge coupling system with moving and non-moving vehicles is theoretically formulated, and the analytical solutions of the coupled system are derived and numerically validated. Furthermore, several case studies are presented to comprehensively investigate key factors affecting the performance of bridge frequency extraction through the proposed method. The results indicate that incorporating a non-moving vehicle can significantly increase the extractability of bridge frequencies in vehicle responses. It becomes possible to accurately identify the first four-order bridge frequencies of a simply supported bridge (rather than the first two-order bridge frequencies using a moving vehicle exclusively) from the vehicle response after introducing a non-moving vehicle. More importantly, the adverse effect of the high-speed moving test vehicle and road roughness can be significantly alleviated by the non-moving vehicle, and therefore the proposed method becomes more robust in actual applications. Besides, further insights are provided in terms of the implementation strategies of the proposed method.

Vehicle Scanning Method for Bridges Enhanced by Dual Amplifiers

Dual-function amplifiers are proposed for the first time herein for enhancing the capability of a scanning test vehicle for bridges. To start, closed-form solutions are derived for the dynamic responses of the amplifier-vehicle-bridge system with a moving test vehicle. Then, the dynamic amplification factors of the amplifier and vehicle are presented for assessing the bridge/vehicle and vehicle/amplifier transmissibility. It was known that the spectrum of the vehicle may be hindered for extracting the bridge frequencies because of vehicle frequency and rough pavement. Two differentially tuned amplifiers are called on to tackle the problem: one (i.e., the vehicle damper) is to suppress the effect of vehicle’s frequency, acting like the tuned mass damper (TMD), and the other (i.e., the bridge amplifier) is to enlarge the amplitude of bridge frequency of concern. Based on the parametric study, it is concluded that (1) the bridge amplifier performs better than the vehicle one in extracting bridge frequencies by increasing their visibility in the spectrum; (2) the effect of vehicle’s frequency can be suppressed by tuning the vehicle damper such that it functions like a TMD of the vehicle; (3) by tuning the bridge amplifier to any of the first few bridge frequencies, the latter can be well detected even for rough pavement.

Indirect Spatial Mode Shape Identification of T-Girder Bridges Using Contact-Point Response of a Moving Test Vehicle: A Theoretical Study

Indirect bridge modal parameter identification using vehicle responses has been widely studied for two-dimensional bridge model, while rare work is devoted to the indirect identification of bridge spatial mode shape (BSMS). This paper proposes an effective procedure for BSMS identification of the widely used T-girder bridges, in which the closed-form solution is derived based on the vehicle contact-point response. The BSMS is identified using the bridge related components extracted from contact-point responses of a vehicle running at different transverse positions on the bridge. The detailed procedure for the identification of BSMS is introduced, and the feasibility of the method is analyzed numerically. To verify its applicability, the influences of some key factors in the vehicle–bridge system, such as the vehicle speed, the driving position, and the road surface roughness, on the identification results are analyzed. The effect of the bridge damage conditions on the BSMS identification is also investigated. The results show that the spatial mode shapes of T-girder bridges can be identified using the proposed method with high accuracy and efficiency.

Effect of soft-end amplification on elastically supported bridges with bearings of unequal stiffnesses scanned by moving test vehicle

Bearings are commonly inserted on bridge piers to mitigate the seismic forces transmitted upward. But they often become unequal in stiffness due to ageing, overloading, etc. This study made the first attempt to exploit the soft-end amplification (SEA) effect on scanning of frequencies of the bridges with unequal end bearings, using the novel technique of forward-backward scanning to detect the soft end of the bridge. The SEA effect was clearly interpreted by the closed-form solutions derived for the dynamic responses of the test vehicle modelled by a sprung mass moving over the elastically supported (ES) beam. Both the temporal and spectral features of the vehicle response in forward-backward scanning were analytically examined, and validated against various inequality ratios by the finite element method (FEM). It was shown that the bridge frequencies shift to lower values for bearings with lower stiffness, and that both vehicle's accelerations and bridge's frequency amplitudes are much enlarged for the vehicle moving from the softer end of the bridge. Both the down-shifting in bridge frequencies and SEA of the ES bridge are helpful to assess the overall health condition of the bridge. Besides, the contact point outperforms the vehicle in that its response allows more bridge frequencies to be identified, due to elimination of vehicle's frequency. Finally, the efficacy of the proposed technique is verified in a parametric study for factors such as surface roughness, vehicle speed and frequency, followed by a more realistic example that simultaneously considers the bridge and bearing damping, and environmental noise. The proposed technique is confirmed to be able to detect the first three frequencies and softer end of ES bridges in real conditions for vehicle speeds below 10 m/s, along with an accompanying vehicle.

Frequency extraction for bridges with rough surface by a moving test vehicle enhanced by a shaker

The response of a test vehicle moving over bridges may be worsened by vehicle’s self frequency and pavement roughness, since they both can pollute the vehicle spectrum for bridge frequency identification. This paper is aimed at tackling the above two factors using a novel software/hardware means, i.e., by using the vehicle-bridge contact response to eliminate vehicle’s self frequency, and a shaker to enhance the bridge vibration while reducing the pavement roughness. Firstly, new closed-form solutions are derived of the vehicle-shaker-bridge system to form the theoretical framework for future application of the shaker. Then, the contact response is back calculated from the equilibrium condition of the damped vehicle. Further, the simple formula newly derived for the shaker’s dynamic amplification factor (DAF) on the vehicle and contact responses can be easily used. Based on the parametric study for the related factors, it is concluded that: (1) the shaker facilitates the vehicle scanning of frequencies for rough bridges, including the higher modes; (2) the shaker (i.e., frequency and location) can be tuned up using the DAF formula to meet the needs of various bridges; and (3) the combined use of the contact response and shaker is effective for general application.

Bridge modal identification based on successive variational mode decomposition using a moving test vehicle

Bridge modal identification using an instrumented test vehicle as a moving sensor is promising but challenging. A key factor is to extract bridge dynamic components from vehicle responses measured when the bridge is operating. A new method based on an advanced adaptive signal decomposition technique, the successive variational mode decomposition (SVMD), has been developed to estimate the bridge modal parameters from the dynamic responses of a passing test vehicle. When bridge-related dynamic components are extracted from the decomposition, the natural excitation technique and/or random-decrement technique based fitting methods are used to estimate the modal frequencies and damping ratios of the bridge. Effects of measurement noise, moving speed and vehicle properties on the decomposition are investigated numerically. The superiority of SVMD in the decomposition is verified by comparing to another adaptive decomposition technique, the singular spectrum decomposition. The results of the proposed method confirm that the bridge modal frequencies can be identified from bridge related components with high accuracy, while damping ratio is more sensitive to the random operational load. Finally, the feasibility of the proposed method for bridge monitoring using a moving test vehicle is further verified by an in-situ experimental test on a cable-stayed bridge. The components related to the bridge dynamic responses are successfully extracted from vehicle responses.

Scanning torsional-flexural frequencies of thin-walled box girders with rough surface from vehicles’ residual contact response: Theoretical study

This paper studies theoretically the retrieval of torsional-flexural frequencies of mono-symmetric thin-walled box girder bridges from vehicles’ residual contact response for the first time. To start, the three-dimensional vehicle–bridgeequations of motion including the lateral and torsional (coupled) and vertical (uncoupled) vibrations are derived for a moving test vehicle. Then, closed-form solutions for the vehicle and vehicle–bridge contact point are derived. The contact response is selected since it is free of vehicle frequency, which may overshadow the bridge frequencies in FFT spectra. The other disturbing factor is surface roughness, which will be resolved by the residue method, i.e., by using the residual response of two connected vehicles. Through the parametric study, the proposed approach is verified to be feasible. The conclusions include: (1) the contact response performs better than the vehicle response for all the scenarios considered; (2) the surface roughness effect can be virtually eliminated using the residual contact response even for damped bridges with not-so-good pavements; (3) a larger vehicle’s eccentricity from bridge’s centerline enables the torsional-flexural frequencies to be better identified; and (4) the first several flexural and torsional-flexural frequencies of the girder can always be identified for a wide variety of parameters considered.

Iterative reference-driven S-transform time-varying parameter identification for bridges under moving vehicle

Traditional bridge health monitoring is both expensive and time-consuming because of the need for installing a large quantity of sensors on the bridge. The indirect monitoring method as a feasible alternative has become popular over the last decade, as useful information can be gathered from moving vehicles installed with sensors by considering vehicle-bridge interaction. This paper describes an indirect time-varying modal parameter identification method for bridges under a moving test vehicle. A novel reference-driven S-transform is proposed for the parametric modal identification of time-varying structural systems with non-stationary characteristics based on a multisensory arrangement, comprising a fixed reference sensor installed on the bridge and another movable sensor installed on a moving test vehicle. By the phase-preservation property of S-transform and the multisensory time-frequency analysis, the proposed iterative reference-driven S-transform can be used to extract the time-varying modal parameters of the vehicle-bridge system when the vehicle moves on the bridge. Based on the coherence between measurements from the sensors mounted on the bridge and vehicle, one can track the time-varying characteristics by combining the spatial and time-frequency information obtained by the multisensory array. The efficiency of the proposed reference-driven S-transform method is validated by numerical simulations and laboratory experiments using a simply supported beam with a moving vehicle. The effects of the vehicle property, driving speed, road roughness and measurement noise are discussed. The numerical and experimental results have demonstrated that the proposed method is useful for time-varying parameter extraction with a multisensory system. This will be useful to structural condition monitoring of bridges.

Rail Diagnostics Based on Ultrasonic Guided Waves: An Overview

Rail tracks undergo massive stresses that can affect their structural integrity and produce rail breakage. The last phenomenon represents a serious concern for railway management authorities, since it may cause derailments and, consequently, losses of rolling stock material and lives. Therefore, the activities of track maintenance and inspection are of paramount importance. In recent years, the use of various technologies for monitoring rails and the detection of their defects has been investigated; however, despite the important progresses in this field, substantial research efforts are still required to achieve higher scanning speeds and improve the reliability of diagnostic procedures. It is expected that, in the near future, an important role in track maintenance and inspection will be played by the ultrasonic guided wave technology. In this manuscript, its use in rail track monitoring is investigated in detail; moreover, both of the main strategies investigated in the technical literature are taken into consideration. The first strategy consists of the installation of the monitoring instrumentation on board a moving test vehicle that scans the track below while running. The second strategy, instead, is based on distributing the instrumentation throughout the entire rail network, so that continuous monitoring in quasi-real-time can be obtained. In our analysis of the proposed solutions, the prototypes and the employed methods are described.

An effective procedure for extracting the first few bridge frequencies from a test vehicle

This study presents an effective procedure for extracting the first few bridge frequencies using the data collected by a moving test vehicle. Previously, the effectiveness of the vehicle scanning method for bridge frequencies was hampered by factors such as vehicle frequency and road surface roughness. To this end, the contact-point response of the vehicle with the bridge that is free of the vehicle frequency is adopted in the analysis. To enhance the visibility of the first few bridge frequencies for extraction, the variational mode decomposition with band-pass filter (VMD-BPF) is proposed herein. The VMD is neater and more elegant than the empirical mode decomposition (EMD) in that less decompositions are needed, while there exists no mode-coupling problem, and the BPF serves to remove the undesired roughness frequencies. To verify the feasibility of the proposed procedure, both the vehicle and contact-point responses generated either numerically or by the field test are analyzed. It is demonstrated that the VMD-BPF is an effective method for extracting the bridge frequencies using the contact-point response for the scenarios considered.

State-of-the-Art of Vehicle-Based Methods for Detecting Various Properties of Highway Bridges and Railway Tracks

The vehicle scanning method (VSM), an indirect approach for bridge measurement, has attracted intensive attention since it was proposed. By this method, a moving test vehicle is employed to detect the “mechanical” properties of the bridge, e.g. frequencies, mode shapes, damages, etc., utilizing the interaction between the two substructures. Compared with the conventional direct approach that requires quite a few sensors and data loggers to be fitted on the bridge, the advantage of the VSM is obvious: mobility, economy, and efficiency. As for railways, the broader vehicle-based techniques have long been used to detect the “geometrical” properties of the track, such as track profiles and rail conditions. Relatively little use has been made of the interaction between the moving vehicle/train and the track/bridge. This paper is a state-of-the-art report of the VSM’s applications to highway bridges and the vehicle-based techniques to railway tracks. It starts with a summary of the pioneering works by Yang and co-workers on the VSM. Then, the applications of the techniques to highway bridges and railway tracks will be separately reviewed. Conclusions will be made, along with future research directions, at the end of the paper.

Track modulus detection by vehicle scanning method

An effective technique is proposed for identifying the track modulus, i.e., the foundation stiffness of the rails, using the contact-point response of the moving test vehicle. First, for a simple beam resting on an elastic foundation under a moving sprung mass, closed-form solutions are derived for the responses of the vehicle and its contact point with the rail. It is shown that the track modulus can be well identified via the first rail frequency (RF) extracted from the contact-point response, in that (1) the first RF is most outstanding compared with the other RFs in the vehicle-generated responses; and (2) the contact-point response outperforms the vehicle response as it is free of the disturbing effects of the vehicle and driving frequencies. The proposed technique is then verified numerically along with the key parameters assessed. The main conclusions are: (1) the first RF can be easily recognized as the “cliff” of the RF “plateau” in the contact-point spectrum; (2) the track irregularity has a little effect on the identification of track modulus; (3) a moderate speed is recommended for the test vehicle for a balance between efficiency and accuracy; and (4) the efficacy of the proposed technique remains good even with the presence of track damping and irregularity. Moreover, the application of the proposed technique to detecting the damage modeled by variation in foundation stiffness is demonstrated.

Bridge damping identification by vehicle scanning method

A simple, theoretical framework is presented for identifying the damping ratios of simply supported beams using a two-axle moving test vehicle, equipped with uniformly spaced accelerometers and laser sensors. The latter are used to measure the relative displacements of the facing (moving) contact points on the beam, referred to as the scanning points. By adopting proper assumptions, closed-form solutions are derived for the responses of the beam and scanning points. In parallel, the scanning-point response is also given in discrete form for field applications. The road roughness effect is alleviated by using the residual response obtained as the difference of the responses of two consecutive scanning points. By utilizing the attenuation nature in the responses between two separate scanning points due to time lag, the damping ratio of the beam is derived in closed form using the Hilbert transformation. The framework proposed is verified by a finite element analysis with basically no assumptions. Its robustness is also tested for different ranges of parameters, including vehicle speed, vehicle damping, road roughness and environment noise.

Further Revelation on Damage Detection by IAS Computed from the Contact-Point Response of a Moving Vehicle

The instantaneous amplitude squared (IAS) of the driving component of the contact-point response of a moving test vehicle was proposed for the damage detection of the sustaining bridge. As a supplement to the properties previously presented for the IAS, this paper is aimed at unveiling the key feature of the discontinuity amplification inherent in the IAS through the double guarantee of a “square operation” in the definition and a “second derivative” in computing the contact-point response. The capability of the IAS was demonstrated with regard to the effects of the environmental noise, vehicle damping and bridge damping in the numerical simulation. It is confirmed that the IAS can be reliably used in the damage detection of bridges by a moving test vehicle.

Contact-Point Response for Modal Identification of Bridges by a Moving Test Vehicle

The response of the contact point of the vehicle with the bridge, rather than the vehicle itself, is proposed for modal identification of bridges by a moving test vehicle. To begin, approximate closed-form solutions were derived for the vehicle and contact-point responses, and they were verified by finite element solutions. The contact-point acceleration is born to be free of the vehicle frequency, an annoying effect that may overshadow the bridge frequencies in case of rough surface. From the frequency response function (FRF) of the vehicle with respect to the contact point, it was shown that the contact-point response generally outperforms the vehicle response in extracting the bridge frequencies because it could identify more frequencies. In the numerical simulations, the contact-point response was compared with the vehicle response for various scenarios. It is concluded that in each case, say, for varying vehicle speeds or frequencies, for smooth or rough road surfaces, with or without existing traffic, the contact-point response outperforms the vehicle response in extracting either the frequencies or mode shapes of the bridge.

An effective means for damage detection of bridges using the contact-point response of a moving test vehicle

To further the technique of indirect measurement, the contact-point response of a moving test vehicle is adopted for the damage detection of bridges. First, the contact-point response of the vehicle moving over the bridge is derived both analytically and in central difference form (for field use). Then, the instantaneous amplitude squared (IAS) of the driving component of the contact-point response is calculated by the Hilbert transform, making use of its narrow-band feature. The IAS peaks serve as the key parameter for damage detection. In the numerical simulation, a damage (crack) is modeled by a hinge-spring unit. The feasibility of the proposed method to detect the location and severity of a damage or multi damages of the bridge is verified. Also, the effects of surface roughness, vehicle speed, measurement noise and random traffic are studied. In the presence of ongoing traffic, the damages of the bridge are identified from the repeated or invariant IAS peaks generated for different traffic flows by the same test vehicle over the bridge.

State-of-the-Art Review on Modal Identification and Damage Detection of Bridges by Moving Test Vehicles

In 2004, Yang and co-workers proposed the extraction of bridge frequencies from the dynamic response of a moving test vehicle [Y. B. Yang, C. W. Lin and J. D. Yau, Extracting bridge frequencies from the dynamic response of a passing vehicle, J. Sound Vib. 272 (2004) 471–493] and verified the technique by a field test [C. W. Lin and Y. B. Yang, Use of a passing vehicle to scan the bridge frequencies — An experimental verification, Eng. Struct. 27(13) (2005) 1865–1878]. This technique was extended to construction of mode shapes [Y. B. Yang, Y. C. Li and K. C. Chang, Constructing the mode shapes of a bridge from a passing vehicles: A theoretical study, Smart Struct. Syst. 13(5) (2014) 797–819] and damage identification of bridges. It was referred to as the indirect method for bridge measurement because no vibration sensors are needed for installation on the bridge, but it only requires one or few vibration sensors on the test vehicle. When compared with the conventional direct method that relies fully on the response of the bridge fitted with vibration sensors, the advantage of the indirect method is clear: mobility, economy, and efficiency. Over the past years, many research studies were conducted along the lines of the indirect method for bridge measurement. Significant advances have been made on various aspects of application. This paper represents a state-of-the-art review of the related research works conducted worldwide. Comments and recommendations will be made at proper places, while concluding remarks including future research directions will be presented at the end of the paper.

Wave Number-Based Technique for Detecting Slope Discontinuity in Simple Beams Using Moving Test Vehicle

The wavelength characteristic is a useful clue for locating and assessing the severity of slope discontinuity in beams. In this study, the slope discontinuity of a beam is represented by an internal hinge restrained by elastic springs, and the wavelength of the beam is calculated indirectly from the vertical response of a test vehicle during its travel over the beam. The key parameters of the problem at hand are first unveiled using an approximate, closed-form solution for the response of the vehicle moving at low speeds over the bridge. Then a two-beam element model with slope discontinuity is formulated for the vehicle–bridge interaction (VBI) system for use in numerical simulation. In the examples, the wavenumber-based response of the test vehicle is used to identify the location and severity of the discontinuity in the beam. It is demonstrated that the wavelength-based technique presented herein by using the moving test vehicle as a moving sensor system offers a promising, alternative approach for damage detection in girder type bridges.