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Modal parameters are inherent structural characteristics that are valuable for model updating, condition assessment, and early warning of bridges. Operational modal tracking technology has been a popular research topic in bridge structural health monitoring (SHM) because of its output-only advantage; that is, only the vibration responses of the bridge are necessary for modal identification. The real-time objective of bridge SHM requires operational modal tracking to be fully automated. Because the loads acting on long-span high-speed railway bridges are various, the modal identification methods should be changed according to the excitation characteristics; otherwise, the results may be incorrect. However, there is no unified framework for simultaneously tracking the modal evolution of a bridge under different excitations. In this study, modal tracking strategies based on ambient loads, train loads and immediately a train moving past the bridge were developed to identify the operational modal parameters of the bridge. In addition, a unified tracking framework was established to automatically switch among the three-stage modal-tracking strategies, which utilizes the real-time positioning of the axle loads. Furthermore, the computational efficiency of the tracking strategies and the obstacles of operational modal analysis were analyzed to provide a reference for mode-based SHM of bridges, and the essential parameters in the tracking algorithms were suggested. The three-stage modal-tracking methods were validated through long-term monitoring data of a long-span high-speed railway bridge. The results indicated that the best tracking results were generated from free-vibration data, while the modal-tracking under ambient loads had best timeliness.

The boundary conditions of the main girder are complicated for suspension bridges. And they have a significant impact on the static and dynamic response of the structure. This study proposes a model updating method based on influence lines considering boundary conditions. First, rotational and translational spring elements are used to simulate the boundary conditions of the main girder. Then, rotational spring stiffness is estimated by constructing a sensitive objective function based on the influence lines. Translational spring stiffness is estimated by constructing a sensitive objective function based on the temperature-induced displacements at both ends of the girder. To improve calculation efficiency, a Gaussian process model is used instead of the finite element model (FEM). The estimation of boundary conditions is expressed as an optimization whose main goal is to iteratively estimate the boundary conditions to minimize the objective functions. After the boundary conditions are determined, the influence lines-based model updating is carried out by using the adaptive metamodel global optimization method. To validate the proposed method, a long-span suspension bridge is taken as a case study. The results show that the boundary conditions of the main girder have been successfully estimated. The accuracy of the model updating is improved after the boundary conditions are considered. The updated FEM with accurate boundary conditions can be a benchmark model for bridge damage identification or condition assessment.

Bridge influence lines can reflect the performance status of bridge structures and are an important tool to evaluate high-speed railway bridges. Because a high-speed train can cause large dynamic response on a bridge, it is difficult to identify the static influence line of the bridge. To extract the static bridge influence lines for bridge evaluation, this paper proposes a low-pass filter design method for static influence line identification. By maximizing the difference in bridge static and dynamic energy, the relationship between the frequency domain characteristics of the bridge dynamic response and the filter parameters is established. Based on this relationship, reasonable values of the low-pass filter parameters can be determined. After filtering the dynamic response, the quasi-static response can be effectively obtained, and the bridge static influence line can be identified through the least square regularization method. Finally, a numerical example of the vehicle–bridge interaction model is used to verify the effectiveness of the proposed method. The results show that the low-pass filter designed through the proposed principle can accurately remove the dynamic effects, and its stability and robustness are good. The research results provide a reliable method for the static influence line identification of high-speed railway bridges.

This paper proposes a displacement model error-based performance warning method to detect structural anomalies in bridges. A displacement data pre-processing method based on multi-rate fusion method is proposed to modify displacement data with the same position acceleration data. A correlation model of the lateral wind speed and displacement was established to eliminate wind load effects. Then principal component analysis was used to eliminate traffic load effects. A new combined Mahalanobis-Euclidean warning index and Shewhart-CUSUM control chart are proposed. Moreover, a threshold setting method for the control chart based on the kernel density estimation technique is proposed. Three different thresholds are proposed to consider the effects of temperature, humidity, snow, rime, and icing. After the bridge warning is realized, the location index is derived from contribution analysis to indicate the location of bridge performance degradation. The results show that the proposed new warning index improves the warning rate compared with that of the two traditional warning indexes. When continuous small and medium shifts occur, the traditional control chart has a false-negative alarm, while the new combined Shewhart-CUSUM control chart can accurately realize the warning. The results of monitoring data analysis of a symmetric long-span cable-stayed bridge show that correlation modeling and principal component analysis can effectively eliminate wind and traffic effects, and the proposed new performance warning method can improve the warning rate and simultaneously monitor large shifts and small shifts, to accurately detect and locate the potential performance degradation points on a bridge.

The cables of long-span cable-stayed bridges are subjected to substantial tension during long-term service and are more susceptible to corrosion and fatigue failure than concrete structures. Most existing structural health monitoring (SHM) systems do not have monitoring equipment to directly measure cable length, and long-term monitoring of the change in cables is less involved. The displacement response of a bridge is induced by the combination of dynamic effects (wind and highways) and quasi-static effects (temperature). In this paper, the dynamic responses were eliminated by averaging the displacement data for 10 min, and the relationship between temperature and displacement was studied. Based on the monitoring data, the distribution of the thermal field for the bridge was studied and the time variability of the tower displacement was investigated. The correlation was analyzed to study the relationship between the temperature and the tower displacements, the north tower–south tower distance and the tower–girder distances. A strong linear relationship between the temperature and quasi-static responses of the displacements was observed. The thermal expansion coefficient of the effective length of cables was proposed as a quantitative index for long-term cable monitoring. The error in the cable effective length is proposed as the warning index for performance warning research. The results show that the proposed performance warning method can monitor cables and perform warnings when the cable is damaged.

Modal identification is based on modal superposition theory. For structures with proportional damping, the structural responses are recognized as real modal shapes multiplied by real modal...

This paper presents a comprehensive review of moving force identification on simply supported bridges. When a vehicle moves on a bridge deck, there is a dynamic interaction force between the vehicle and the bridge deck. This dynamic interaction force is crucial for the design and condition assessment of bridges. However, this interaction force cannot be directly measured. Therefore, the indirect measurement method based on the bridge response, namely, the moving force identification method, has become an important issue in evaluating bridge condition. This paper provides a comprehensive review of current research and development activities in bridge moving force identification. First, the development and application of moving force identification are introduced. Next, the theoretical methods of bridge moving force identification are presented. Then, the robustness and accuracy of moving time-varying force identification methods are numerically simulated and compared. Finally, the characteristics of these methods are summarized, which provides a basis for selecting the suitable identification methods under different conditions and prospects of the further development of moving force identification.