Preface

Bridges constitute an essential part of transportation systems such as highways, railways, city rail systems, and high-speed railways. Regardless of their irreplaceable role in ensuring the free and safe passage of passengers and cargoes, bridges often suffer from varying degrees of damage due to degradation in stiffness of structural members, connections, supports, or material strength, caused by vehicles' overloading, weathering, or natural disasters, such as earthquakes, typhoons, or deluges. The number of bridges that have been built in the past three decades has increased tremendously. For example, in China there is a total of some 800 000 highway bridges built in this period. Many of them have been ranked among the top in the world in terms of span length, bridge type, and column height. Perhaps the most fantastic is the newly built record-breaking Hong Kong-Zhuhai-Macao Bridge system that connects Hong Kong, Zhuhai, and Macao, totaling a length of 55 km, including seabed tunnels of some 35 km. From the global picture, there is clearly an urgent need to develop efficient and mobile techniques to detect bridge damage so as to enhance the quality of maintenance and possibly rehabilitation.

To monitor the operational and/or damage conditions of bridges, vibration-based methods have been adopted for half a century or longer. Most of the methods require the installation of quite a number of sensors on the bridge for detecting the modal properties, such as frequencies, mode shapes, and damping coefficients. They were referred to as the direct approach, in that the modal properties were retrieved from the vibration data taken directly from the bridge. An enormous volume of research has been carried out along these lines using the ambient vibration, traffic vibration, forced vibration, impact vibration, etc. One drawback with the direct approach is that it usually requires numerous sensors to be installed on the bridge, along with data acquisition systems, for which the deployment and maintenance cost is generally high. Another drawback is that the vast amount of data generated, the so-called sea-like data, may not be effectively digested. It should be added that the monitoring system tailored for one bridge can hardly be transferred to another bridge and work there, a problem known as the lack of mobility.

The vehicle scanning method (VSM) for bridge measurement was proposed by the senior author and coworkers in 2004 mainly to circumvent the drawbacks of the direct approach. This method was known in the early days of development as the indirect approach. However, the term indirect approach is not self-explanatory, since it can only be explained along with the direct approach. Recently, we started to use the term vehicle scanning method for bridges instead, for its better conveyance of the meaning implied. With this technique, the vibration data collected by one or few sensors installed on the moving test vehicle are used to retrieve the modal properties of the sustaining bridge. No sensors are needed on the bridge. Compared with the direct approach, the VSM shows great potential in economy, mobility, and efficiency, although further research in software and hardware is required to enhance its robustness in field applications.

To our knowledge, this book is the first one on the subject of VSM for bridges. After some 15 years of research on the VSM, we believe it is timely, and indeed necessary, to present an in-depth coverage of the technique, at least based on the works by the senior author and coworkers. The contents of the book have been arranged such that they are reflective of the progressive advancement of the technique, which is also good for pedagogical reasons. By and large, each chapter can be comprehended by readers with little reference to the previous chapters, since a minimum amount of background information is provided in the introductory section. The following is a summary of the content in each of the 11 chapters.

In Chapter 1, a state-of-the-art review is given of the works known to the authors up to roughly 2018 on the subject of the VSM. Among these, a substantial part is the series of papers published by the senior author and coworkers. It can be seen that research has been extended from the original goal of bridge frequency extraction to a variety of applications, including damage detection, modal identification, and damping estimation of the bridges. Aside from the theoretical explorations, small-scale lab experiments and field tests have also been attempted.

In Chapter 2, the vehicle-bridge interaction (VBI) model used for extracting the bridge frequencies is introduced. For the first time, the feasibility of extracting bridge frequencies from the passing vehicle's response is theoretically investigated. For simplicity, only the first mode of vibration of the bridge is considered. From the closed-form solution derived for the passing vehicle, the key parameters involved in the VMS technique are unveiled.

Chapter 3 differs from Chapter 2 in that all the modes of vibration of the bridge are included in the formulation. The general theory presented in this chapter confirms the validity of the simplified theory presented in Chapter 2. In addition, the parameters involved in the VBI are evaluated with potential applications identified.

The first field test of the technique is presented in Chapter 4 for scanning the frequencies of vibration of a bridge in northern Taiwan. The device used is a single-axle test cart towed by a light tractor. This test confirms that the bridge frequencies can be successfully retrieved from the response recorded of the test cart during its passage over the bridge by the fast Fourier transformation (FFT).

Chapter 5 is aimed at enhancing the visibility of bridge frequencies from the vehicle's response. First, the vehicle response is processed by the empirical mode decomposition (EMD) to yield the intrinsic mode functions (IMFs). Then the IMFs are processed by the FFT to yield bridge frequencies not restricted to the first mode.

Chapter 6 deals with road roughness of the bridge, a polluting factor that may render bridge frequencies unidentifiable from the vehicle's response. Both numerical and closed-form solutions are used to physically interpret the effect of road roughness on the retrieval of bridge frequencies. Then a dual vehicle model is proposed for reducing such an effect by deducting the response of one vehicle from the other.

In Chapter 7, three filtering techniques are assessed for removing the (undesired) vehicle frequency from the vehicle's spectrum, so as to enhance the visibility of the (desired) bridge frequencies. The singular spectrum analysis with band-pass filter is demonstrated to be most effective among the three schemes.

Chapter 8 is aimed at tuning the various parameters of the test vehicle for field use. As such, a hand-drawn single-axle cart is extensively tested in the lab and in the field. The qualitative guidelines drawn from this part of study using the handy test cart serve as a useful reference for the design of practical test vehicles.

Chapter 9 presents a theoretical framework for retrieving the mode shapes of a bridge from the passing vehicle's dynamic response. By the Hilbert transform, the mode shape is recognized as the envelope of the instantaneous amplitude of the component response of the moving test vehicle. Factors that may affect such a procedure are studied.

In Chapter 10, the contact point of the vehicle with the bridge, rather than the vehicle body itself, is proposed as a better parameter for use in the VSM technique. The contact-point response, back calculated from the vehicle response, is free of the vehicle frequency that may overshadow the bridge frequencies. The relatively better performance of the contact-point response is demonstrated in the numerical simulations.

As a sequel to Chapter 10, the capability of the contact-point response for damage detection of the bridge is presented in Chapter 11. By the Hilbert transform, the instantaneous amplitude squared (IAS) calculated of the driving component of the contact-point response is demonstrated to be effective for detecting bridge damages for scenarios, including the presence of ongoing traffic.

In the Appendix, the derivation of the VBI element is given in detail based on Chang et al. (2010), a modification from Yang and Yau (1997). Also given is the procedure for assembling the VBI elements (acted upon by vehicles) and non-VBI elements (free of vehicles) for a bridge. The main reason for placing this material in the appendix rather in the main text is to not bring unnecessary intrusion to the main flow of presentation.

We are indebted to a number of friends in preparation of this book. Our work would not be complete without an acknowledgment of this debt and a particular offering of thanks by the senior author to the following:

To the late Professor William McGuire, Cornell University, for introducing him to the interesting field of structural stability and dynamics and for inspiring him to conduct researches that have eventually led to the outcome of this book.

To Professor J.D. Yau, Tamkang University, for the collaboration of research on VBI problems that partially lays the...