Preface

Bridges are essential components of lifeline systems, serving as critical links between two sides of an area that are separated by natural or artificial barriers. Bridges constitute an essential part of transportation systems, including highways, railways, city rail systems, high-speed railways, and so on. They are engineering structures designed to provide passages for people, vehicles, and goods, enabling connectivity and facilitating transportation. Due to aging, overloading in traffic, and natural disasters, such as earthquakes, typhoons, and flooding, the health condition of a bridge may decline in various forms during its service life, e.g., the deterioration in materials, cracking in cross sections, loosening or breaking connection, support settlements, and scouring in column foundations.

To assess the health condition of a bridge, vibration-based monitoring methods have been widely adopted to diagnose the variation in modal properties. Conventionally, structural health monitoring has been carried out using the vibration data recorded by sensors directly deployed on the bridge, known as the direct measurement method. However, the health monitoring system, including the vibration sensors and data logger, is usually "tailored" for the particular bridge of concern, of which the setup and maintenance costs are generally high. In addition, the continuously generated "sealike" data cannot be digested in an efficient way. What is more, the lifespan of the electronic devices installed on a bridge may not be longer than that of the bridge to be monitored. For the huge number of bridges existing all over the world, there is an urgent need to develop economical and efficient methods that can be widely used in the health monitoring of most bridges.

In 2004, the vehicle scanning method (VSM) for bridge measurement was proposed by the senior (third) author and coworkers to circumvent the drawbacks of the direct measurement method. Such a method, originally known as the indirect measurement method, is featured by the fact of mobility, economy, and efficiency, in that no vibration sensors need to be mounted on the bridge and only a small number of sensors are required to be fixed on the vehicle. It was later renamed as the vehicle scanning method for bridges to make it self-explanatory. Over the past nearly two decades, research on various aspects of the VSM has boomed globally, including the identification of bridge frequencies, modal shapes, damping ratios, and damages.

This book intends to give a broad and systematic coverage of the VSM techniques for the identification of bridge modal parameters (frequencies, modal shapes, and damping ratios). In general, the book is divided into three parts: Part I (Chapters 2-6) is dedicated to the VSM techniques for bridge frequencies, Part II (Chapters 7-11) to the VSM techniques for bridge mode shapes and damping ratios, and Part III (Chapters 12-15) to the VSM techniques for various types of bridges. To help readers quickly engage in the chapters of interest, each chapter will start with some concise background information, allowing readers to directly comprehend the chapter in a manner that requires minimal cross-reference to the previous chapters. This book contains a total of 15 chapters in the order of increasing complexity. The following is a summary of the content of each chapter.

In Chapter 1, the basic concept of extracting bridge modal parameters using a moving test vehicle is briefed. It then provides a comprehensive review of the current state-of-the-art research conducted globally up to roughly 2024 on the VSM. Progress in various aspects of the VSM is presented, including the identification of bridge frequencies, mode shapes, damping ratios, damages, and surface roughness, as well as applications to railways.

In Chapter 2, a more realistic theory is presented for the vehicle-bridge interaction (VBI) system considering the vehicle damping. To eliminate the overshadowing effect of vehicle frequency on the identification of bridge frequencies from the vehicle's spectrum, the contact response is used instead, which can be calculated backwardly from the vehicle response. The transmissibility between the vehicle and contact responses is discussed. In addition, a field test is conducted to verify the theory presented.

In Chapter 3, a refined detection technique for bridge frequencies using the rocking motion of a single-axle moving vehicle is introduced. A new formula is derived for calculating the left and right contact responses of the two wheels of the single-axle test vehicle, which will be used in the spectral analysis to eliminate the vehicle's vertical and rocking frequencies. The feasibility of the refined detection method for scanning the bridge frequencies is verified by the field test.

In Chapter 4, a theory for utilizing a single-axle, two-mass scanning vehicle to extract the bridge frequencies is presented, in which the vehicle's suspension effect is taken into account. For the two-mass vehicle model, backward formulas are presented for computing the contact response considering the vehicle's suspension effect.

In Chapter 5, a shaker is added to the bridge to enhance the bridge vibration for alleviating the adverse effect of vibrations induced by pavement roughness. Closed-form solutions are derived of the vehicle-shaker-bridge system to form the theoretical framework for future application of the shaker. The simple formula derived for the shaker's dynamic amplification factor (DAF) on the vehicle and contact responses in the study can be easily used in practice.

In Chapter 6, dual-function amplifiers are proposed for use to enhance the capability of a scanning test vehicle for bridges. The DAFs of the amplifier and vehicle are presented for assessing the bridge/vehicle and vehicle/amplifier transmissibilities. Two differentially tuned amplifiers are used: one is to suppress the vehicle frequency, acting like the tuned mass damper (TMD), and the other to enlarge the amplitude of the bridge frequency of concern.

In Chapter 7, a theoretical framework for scanning the mode shapes of a bridge by a two-axle test vehicle is presented. The effect of vehicle frequencies is removed by using the contact responses, and that of pavement roughness by the residue of the front and rear contact responses of the two-axle test vehicle. Then, the contact response is processed by the variational mode decomposition (VMD) to yield the component responses and then processed by the Hilbert transform (HT) to yield the mode shapes.

In Chapter 8, a simple formula is derived for the modal damping ratio of the bridge using the correlation between the instantaneous amplitudes of the related front and rear contact responses of a two-axle scanning vehicle by the HT technique. The feasibility of the proposed damping formula is verified in the numerical study.

As a sequel to Chapter 8, a formula for determining the bridge damping ratio from two wheels of a two-axle scanning vehicle by the wavelet transform (WT) is presented in Chapter 9. This chapter improves the preceding Chapter 8 by considering the suspension effect of the two-axle vehicle, while fully utilizing the spatial correlation between the front and rear contact points in the time-space signaling.

In Chapter 10, a normalized formula for removing the damping effect in recovering the bridge mode shapes is proposed by using a moving vehicle and a stationary vehicle. 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 is used to generate a reference response at a fixed location of the bridge for removing the damping effect.

In Chapter 11, a recursive formula for removing the damping distortion effect on bridge mode shape restoration is proposed by utilizing the spatial correlation between the front and rear contact points of a two-axle vehicle. Further, the bridge mode shapes recovered by the HT- and WT-based recursive formulas are compared, to show which technique is more effective for bridge mode shape recovery.

In Chapter 12, a procedure for recovering the frequencies and mode shapes of curved bridges is introduced. Curved bridges differ from straight bridges in that they are characterized not only by the vertical but also by radial (lateral) frequencies. The procedure for recovering vertical and radial mode shapes of the curved bridge by the VMD and synchrosqueezed wavelet transform (SWT) is presented.

In Chapter 13, a unified theory for identifying the vertical and radial damping ratios of curved bridges in a form similar to straight bridges is proposed. By using the correlation between two connected scanning vehicles and the VMD-SWT technique, the damping formula for the vertical and radial damping ratios of curved bridges is established.

In Chapter 14, based on the kinematic hypothesis of rigid cross sections for thin-walled girders, a procedure for separating and detecting the vertical and torsional frequencies of thin-walled girders from vehicle's contact responses is introduced. By the WT technique, the vertical and torsional mode shapes can be recovered from the separated vertical and torsional contact responses.

In Chapter 15, a theoretical framework for...