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• The proposed SAP method can estimate multi-scale motions of large-scale structures. • The spatial Laplacian of phase and amplitude value degradation index are proposed. • The full-field motion of the Tsing Ma Bridge is estimated using one camera at a 600–1000 m distance. Full-field motion with a high spatial resolution can reflect the health state of long-span bridges. Traditional structural health monitoring (SHM) systems measure the structural displacement at sparse points only. Despite the development of various methods for obtaining high-resolution responses, they fail to estimate the multi-scale motions of real long-span bridges. A novel full-field motion estimation method is proposed to directly measure the entire structural responses using one digital camera. In this approach, multi-scale motions of different components under unknown excitations are encoded in a complex pyramid. The parameters of the complex pyramid are determined by the localization index to record robust local phases at each measurement point. Two indices, namely, the spatial Laplacian of the phase and the amplitude value degradation index, are designed to adaptively estimate multi-scale displacements contained in the complex pyramid. The proposed method estimates the full-field displacements of a steel frame accurately in an experimental test. Moreover, the full-field displacement of the 1377-m long main span Tsing Ma Bridge is estimated using only one shot. Results suggest that the displacement estimated by the proposed method matches well with the GPS data and further visualizes the bridge mode shapes with a high resolution. [ABSTRACT FROM AUTHOR]

Framework of the proposed hierarchical Bayesian FEMU method. [Display omitted] • Effects of operational loads are considered in the hierarchical Bayesian FEMU. • Temperature-stiffness relationship and vehicle load estimation are established. • A two-step MCMC sampling and RSM are proposed to accelerate updating process. • Validated on a long-span arch bridge using two-year monitoring data. • An indicator is defined to assess structural states under operational loads. Excluding the variations of structural dynamic characteristics due to operational loads in finite element model updating (FEMU) is essential for response prediction and structural condition assessment. However, existing FEMU techniques for long-span bridges usually directly use modal parameters in the objective function without considering the effects of various operational loads, resulting in high variations of the updated model. To this end, this paper proposes a hierarchical Bayesian FEMU framework considering the effects of operational loads, including temperature and traffic loads. A linear temperature-elastic modulus relationship and a vehicle load estimation method based on weigh-in-motion (WIM) data are established to quantitatively consider the operational loads' effects on structural dynamic properties. In addition, the identified natural frequencies and measured expansion joint displacements are incorporated into the objective function to update structural static and dynamic properties simultaneously. A two-step Markov Chain Monte Carlo (MCMC) sampling method and a response surface surrogate model are proposed to accelerate the updating process. The proposed method is validated on a long-span arch bridge using two-year monitoring data. The updated model is then used to predict the structural static and dynamic responses by taking into account of operational loads, parameter uncertainties, and modelling errors, and the measured responses generally fall within the predicted 95% confidence interval. Finally, a structural state indicator, which has considered the effects of operational loads on structural properties, is defined to assess the structural condition and successfully detect the pavement replacement process on the bridge. [ABSTRACT FROM AUTHOR]

Tuned mass damper inerter (TMDI) has become a popular choice for vibration control in flexible structures, including long-span bridges, due to its superior performance compared to traditional tuned mass dampers (TMDs), such as improved control effect and smaller static displacement. However, the control effect of TMDI is heavily reliant on the spanning distance of inerter, which typically generates a significant internal additional moment due to the force imbalance, limiting the practical application of TMDI on flexible structures. For this reason, a novel lever-arm TMDI (LTMDI) is proposed in this study, to suppress the vibrations of long-span bridges. The non-dimensional governing equations of the bridge-LTMDI system are established in modal coordinates, and the closed-form solutions of the optimum frequency and damping ratios of LTMDI are derived based on the classical fixed-point theory. Parametric studies are conducted to investigate the influences of the fulcrum position, modal shape ratio, mass ratio, inertance ratio and asymmetric mode on the control effectiveness. Moreover, for comparison, the control effectiveness of LTMDI is further compared to those of the TMD and TMDI. Finally, a long-span bridge is selected as an example to demonstrate the effectiveness of LTMDI in reducing vortex-induced vibration (VIV). The results show that the LTMDI has superior control effect and space feasibility as compared to the TMD and TMDI in both frequency and time domains. The derived analytical formulas can accurately determine the optimal parameters, providing a simple yet efficient guideline for the application of LTMDI in flexible structures. [ABSTRACT FROM AUTHOR]

Tuned mass dampers (TMDs) have proven effective in suppressing structural vibration. In existing research on vortex-induced vibration (VIV) control of flexible structures, only one mode is commonly considered at the time, and only basic aerodynamic force models, which can struggle to model amplitude-dependent damping, are considered. However, flexible structures, such as multi-span bridges, exhibit multiple modes with closely spaced frequencies. Neglecting secondary modes may introduce calculation inaccuracies, as these modes can impose additional stiffness, thereby influencing the performance of TMD. This paper presents a framework to optimize the performance of multiple TMDs in the context of multi-mode VIV control for a flexible structure. A multi-span bridge is used as a case study, and the secondary modes and nonlinear aerodynamic effects are considered. The governing equations for the force-structure-MTMDs system are derived in modal coordinates using a polynomial model to model the aerodynamic force. A novel method to calculate the contribution of each mode to determine the minimum number of secondary modes to be considered is proposed. The optimal parameters of MTMDs are obtained using a global optimization method and compared with mode-by-mode design results. Robustness analysis is conducted to verify the effectiveness of the optimization framework. The results show that the polynomial model accurately predicts the amplitude after TMD installation. Secondary modes significantly affect the optimal parameters of TMDs, and the optimized results exhibit better control performance than the mode-by-mode design results. • Introduce a novel framework for optimizing multiple TMDs for flexible structures. • Consider the secondary modes of the structure and nonlinear aerodynamic effects. • Verify the applicability of TMD design using the polynomial nonlinear force model. • Develop a quantitative indicator to determine the minimum number of secondary modes. • Showcase improved performance of the optimized TMDs compared to mode-by-mode design. [ABSTRACT FROM AUTHOR]

Vibrational energy harvested from the bridge excitation due to the traffic flow or the wind load can be supplied to sensors in a Structural Health Monitoring (SHM) system and help prolong its service life, reduce chemical battery waste and enable its use in remote locations. A common approach to designing a Piezoelectric Energy Harvester (PEH) consists in tuning its fundamental frequency to some target value (e.g., the fundamental frequency of a bridge). However, such approach does not answer the question if the chosen target frequency is optimal, and does not take into account the possibility to have multiple design configurations with the same fundamental frequency. In this work, we approach the problem of a PEH design optimisation in a rigorous way, using a PEH model based on the Kirchhoff–Love plate theory and Isogeometric Analysis (IGA), coupled with the Modal Order Reduction (MOR) approach and Runge–Kutta time integration method. The model is further equipped with the Particle Swarm Optimisation (PSO) algorithm that allows finding geometry which maximises energy output from a given base acceleration signal. A comprehensive study is conducted to infer the impact of a PEH geometry on its energy harvesting performance in a real-world setting by considering field health monitoring data of a large-scale cable-stayed bridge in NSW, Australia. A shape optimisation framework is developed based on acceleration events, i.e., where the level of response exceeds a certain threshold. Designs obtained in the event-based optimisation are then clustered to propose several best candidates for continuous energy generation. This work represents the first study on PEH design optimisation for real operational conditions. [ABSTRACT FROM AUTHOR]

• A new vision-based multi-point displacement monitoring system is proposed. • A fast multi-feature matching and location method of light spot is proposed. • The camera-motion-induced error can be well compensated. • The bridge deformation evolution in the time and space dimensions are discussed. The existing vision measurement methods face a significant challenge in the multi-point displacement monitoring of large-span bridges due to the contradiction between the measurement scale and image spatial resolution. Based on a cable-stayed bridge on a kilometer scale, a new vision-based multi-point displacement monitoring system is proposed. The bridge was designed and arranged with a camera network, consisting of a series of double-head camera stations that were connected by cooperative markers. Based on the observed multi-point deflection and lateral displacement, the deformation evolution of the bridge in the two dimensions of time and space is discussed. The results show that the proposed vision-based camera network can accurately monitor the dynamic deflection and lateral displacement across the whole span of the bridge. The measurement errors induced by the camera motion can be well compensated based on the optical constraints of the proposed camera network. The feasibility of the vision method for long-span bridge monitoring has greatly improved. The proposed system can provide a new method for displacement monitoring and fine parameters for the safety evaluation of large-span bridges. [ABSTRACT FROM AUTHOR]

The simulation of fluctuating wind speed fields holds paramount importance in the wind-resistant design of significant structures such as high-rise buildings, long-span bridges, and wind turbines. To address the computational challenges posed by the original spectral representation method (SRM), a novel approach has emerged. This approach, rooted in the frequency-wavenumber spectrum (FWS), offers a solution to the complexities associated with the original SRM. An enhanced non-uniform discrete technique based on the acceptance-rejection (A-R) criterion was introduced to improve the efficiency of the FWS-based SRM. Nonetheless, this technique currently faces certain constrains, including its demand for a substantial allocation of random access memory (RAM) and its inability to be seamlessly integrated with the fast Fourier transform (FFT) algorithm. Given this scenario, a notably more effective strategy for selecting representative points emerges -the frequency-dependent acceptance-rejection (A-R) scheme. This innovative scheme holds the advantage of diminishing RAM utilization, transforming wind field modeling from a supercomputers-exclusive task to one feasible on personal computers. Moreover, its seamless integration with FFT technology bolsters simulation efficiency. The provided numerical simulation instances of two-spatial dimensional fluctuating wind speed fields underscore the proficiency of this proposed frequency-dependent A-R scheme. The outcomes demonstrated the combined A-R and FFT technique's efficiency and precision, in simulating two-spatial dimensions fluctuating wind speed fields. [ABSTRACT FROM AUTHOR]

For long-term vision-based cable force monitoring, it is essential to fully consider different types of challenges, such as complex backgrounds in the field of view, illumination changes, occlusion, camera motion, and real-time realization. To address these challenges, this study proposes a vision-based, robust real-time cable force measurement method. In terms of innovation, three unique aspects were incorporated. First, to solve the difficulty of cable edge recognition caused by complex backgrounds, a linear feature detection operator called edge drawing lines was optimized by setting screening strategy based on the slope and line segments length. Second, the average of bilateral edge displacements was used as the final value to offset the displacement deviation caused by the illumination change. Third, to overcome obstacles to identifying the cable frequency caused by the camera motion, an interference frequency elimination method without reference targets or additional sensors was proposed. Furthermore, the integrated cable force calculation method was developed into a real-time measurement software. Finally, the proposed method was applied to a long-span cable-stayed bridge, where the camera was vibrated by the bridge deck or the wind significantly. The reliability of the proposed method was proved by comparing the results obtained with those achieved by accelerometers. [ABSTRACT FROM AUTHOR]

Over the past few years, longitudinal displacement has gained popularity as a means of evaluating the condition of long-span cable-supported bridge components, such as bearings. However, accurately predicting bearing displacement under varying load conditions is challenging due to the exposure of bridges to environmental and traffic loads. To address this issue, a hierarchical convolutional neural network (HCNN) model was developed in this paper for predicting bearing displacement using comprehensive loads as predictors. Structural health monitoring (SHM) systems of a cable-stayed bridge are utilized to provide one-month datasets for training and testing of the proposed method. Temperature, wind, and vehicle loads are adopted as input variables, and bearing displacement is the output. Results demonstrated the effectiveness of the proposed approach in predicting bearing displacement with an accuracy of over 95.6%, surpassing other models like traditional CNN, encoder-decoder, and U-Net in both accuracy and efficiency. Additionally, the contributions of different loads in predicting displacement are investigated, demonstrating the importance of traffic loads. Cumulative displacement can consequently be calculated for condition assessment of components such as bearings and expansion joints. A comparison with another cable-stayed bridge showed that the expansion joints in the current bridge were in satisfactory condition. Overall, the proposed approach can facilitate predictive maintenance in long-span bridges, helping to prevent premature failures. [ABSTRACT FROM AUTHOR]

The structural health monitoring system (SHM) of long-span bridges inevitably produces low-quality data. It is important to evaluate the data quality and screen out normal data. Most existing studies on data anomaly detection have focused on abnormal data with abnormal waveforms in time domain. Usually there are pseudo-normal data in the SHM system, which seems normal in time domain. However, the pseudo-normal data of bridge dynamic responses may cause wrong dynamic characteristics identification. In this study, the existing data anomaly detection was further expanded to data quality evaluation, and both obvious abnormal and pseudo-normal data are evaluated. A general data quality evaluation framework for dynamic response monitoring of long-span bridge structures was proposed. The time–frequency characteristics of monitoring data were obtained by continuous wavelet transform, and the data quality was classified and evaluated by constructing and training a convolutional neural network (CNN). The proposed framework was verified by using acceleration monitoring data of a cable-stayed bridge. The results reveal that this framework solves the problem that CNN cannot detect pseudo-normal data through time-domain characteristics, and improves the accuracy of data quality evaluation by using time–frequency information of the monitoring data. The acceleration monitoring data of a suspension bridge and a single pylon cable-stayed bridge were used to demonstrate the feasibility of the cross-object application of the proposed framework. The evaluation accuracy for the acceleration data quality of the suspension bridge exceeded 96%. After the reinforced training of a small number of pseudo-normal data samples, the evaluation accuracy for the acceleration data quality of the cables of the cable-stayed bridge reached 96.8%. The framework shows a good generalization capacity and robustness in cross-object applications. [ABSTRACT FROM AUTHOR]

Operational modal analysis (OMA) of long-span road bridges from vibration measurements is a topic of interest due to its potential applications within structural health monitoring. Algorithms for the automation of OMA (AOMA) have been proposed since around 2005, relying on machine learning to automate previously manual tasks. The fundamental principles of AOMA are explained in the theory of this work, as are the functioning principles of the clustering algorithms employed by most AOMA algorithms. A performance comparison of six AOMA algorithms (Magalhaes 2009, Reynders 2012, Zhang 2014, Neu 2017, Yang 2019, Kvåle 2020) is provided using real-world data from the Hardanger suspension bridge. To the authors' best knowledge, it is the first comparison of AOMA algorithms for bridges. While Reynders 2012 is shown to be the only fully automated algorithm, Magalhaes 2009, Zhang 2014, and Kvåle 2020 are the algorithms with the highest successful detection rate. Neu 2017 and Yang 2019, however, make the least detection errors, respectively, the least false detections and the least duplicate detections. The variability amongst datasets is shown not to impact the algorithms' comparison. An outright recommendation on which algorithm to use is impossible due to the multitude of potential use cases, but Neu 2017 seems to provide the best performance compromise for the tested case. [ABSTRACT FROM AUTHOR]

• This paper proposes a statistical representation model for the structural damage identification of long-span bridges based on the correlation of probability distribution on monitored quasi-static response, and the principle of the proposed method is that the correlation of monitored quasi-static response of linear time invariant bridges is only related with structural model and parameters under the assumption that the external load distribution pattern to be identical. • The probabilistic distribution function (PDF) of vehicle load can be modeled as a function of traffic flow parameters and the PDF of vehicle weight. It is validated that the PDF of vehicle weight usually keep invariant under normal operation conditions by the monitored vehicle weight data. The invariant PDF of vehicle weight is further termed as the same vehicle load distribution pattern. • Under the same vehicle load distribution pattern, the PDFs of monitored quasi-static responses may vary with the traffic flow, the distance of PDFs of any two monitored quasi-static responses over two statistical durations is equal for undamaged structure. And the variation of distances at different sensors can be used as the indicator for structural health diagnosis in the probabilistic perspective. Structural health diagnosis is one of the most critical issues in structural health monitoring (SHM). Vibration-based methods have been extensively investigated in the last few decades in the SHM community, but they encounter the challenges of local damage insensitivity and environmental sensitivity. However, the study of structural health diagnosis based on structural quasi-static response data, which has well-defined spatial coordinates and is sensitive to the local condition of the structure, is insufficient. It is difficult to extract structural models or parameters that directly indicate structural damage owing to the coupling effect of the damage and unknown external loads in the quasi-static response data. This study proposes a method based on the correlation of the probability distribution of the quasi-static response data for damage identification, and it is proved that the variation in the structural condition can be inferred from the variation in the correlation of the probability distribution of multiple quasi-static response data. The earth mover's distance (EMD) is introduced as a quantitative indicator of the variation in the probability distribution function. The difference in the EMD (DEMD) between two monitored quasi-static responses was adopted as the damage indicator. The monitored strain on the steel box girder of a multi-tower cable-stayed bridge and the monitored cable tension of the cable-stayed bridge were employed to validate the proposed method. The results show that the proposed method successfully identifies the damage to the steel box girders and stay cables. [ABSTRACT FROM AUTHOR]

An increasing number of modern long-span bridges have been built in complex valley terrain, and the influence of non-uniform flows on the vortex-induced vibrations (VIVs) of bridges should be considered. Therefore, this study investigated the multi-mode VIVs of long-span bridges in both the completed bridge stage and erection stage using a taut-strip model under a uniform flow and two types of non-uniform flow. The non-uniform flows were generated by adjusting spires (both their separation distance and shapes) in wind tunnel. The two non-uniform flows were represented by the linear and parabolic wind velocity flow distributions. The characteristics of the vibration responses and wake flows, mechanism of multi-mode VIVs, and aerodynamic differences between different stages and under different incoming flows were discussed. The results indicated that the occurrence of multi-mode VIVs arose from a wake frequency difference covering two or more modal frequencies owing to variations in the wind profile. The non-uniform flows disturb the regular vortices in the wake due to the variable wind velocity and higher turbulence intensity, leading to suppression of the VIV response. [ABSTRACT FROM AUTHOR]

The objective of this paper is to elucidate the general conditions of resonance and cancellation for Bernoulli-Euler beam-based bridges subject to moving train loads. Firstly, the bridge's vibration shape is approximated based on the modal superposition method and Fourier series expansion. Then, the semi-analytical solution of the bridge vibrations under moving train loads is derived. After that, the general conditions of train-induced bridge resonance and cancellation are further derived, analyzed, and classified. In particular, cancellation is divided into three classes: case 1, case 2-I, and case 2-II. It is found that the resonance condition for simply-supported bridges is applicable to arbitrary Bernoulli-Euler beam-based bridges, while the cancellation conditions are related to the cancellation classes and modal characteristics of bridges. Finally, three examples are used to validate the semi-analytical solution of bridge vibrations as well as the general conditions of resonance and cancellation, including a simply-supported bridge, a continuous-beam bridge, and a long-span extradosed cable-stayed bridge. Besides, these examples show that for simply-supported bridges, both the resonance and cancellation should be considered, while for bridges with a long-span length or low fundamental frequencies, cancellation is more significant than resonance. [ABSTRACT FROM AUTHOR]

• Dynamic characteristics of bridges subjected to vortex-induced vibration are investigated; • Farnebäck dense optical flow is used to process the vibration video; • Fluid-structure interactions during vortex-induced vibration are accommodated with Scanlan's model; • Fast Bayesian analysis is utilized to consider the uncertainties arising in system identification; • The method is verified using vortex-induced vibration motion of a long-span suspension bridge. The dynamic properties of long-span bridges with flexible and light-weight features are of critical importance in safety assessment and response prediction. The primary concern of this study was to infer the dynamic characteristics of long-span bridges subjected to vortex-induced vibration (VIV) by reasonably accommodating the fluid–structure interactions during VIV and the various uncertainties arising in the dynamic characterization of the structures due to measurement noise and modeling errors. By taking the advantage of advanced image processing techniques, the Farnebäck dense optical flow method was used to process the vibration video to extract the displacement time history. In contrast to conventional operational modal analysis (OMA) approaches, which are usually based on the white noise assumption, a new frequency-domain Bayesian method is proposed to make a statistical inference for the dynamic characteristics of the bridge based on the power spectral density of the VIV measurements and the Scanlan's empirical VIV model for bridge decks. A fast computation scheme is also proposed to achieve the posterior uncertainties of the modal frequency of the bridge, the structural damping of the bridge, and the total damping of the VIV system. The efficiency and the accuracy of the proposed algorithms have been verified with the VIV motion of a super long-span suspension bridge. Comparison with those identified using different OMA approaches in the time domain and the frequency domain is also be presented. [ABSTRACT FROM AUTHOR]

• Improved interpolation scheme with high practicality is developed to realize spectral matrix decomposition in decoupling form. • New matrix factorization with a fast global convergence is used to decouple the time-frequency spectra. • Simple decoupling and interpolation are involved to realize a small amount of Cholesky decompositions and FFTs. • Case study demonstrates the superiority of the proposed method in the simulation of fully non-stationary wind fields. The classical spectral representation method and its improved versions have been widely used to generate non-stationary wind fields. However, they are not efficient for the simulation of non-stationary wind fields with time-varying coherence (i.e., fully non-stationary wind fields) due to the extensive computational demand regarding spectral matrix decomposition or harmonic superposition. To this end, this study develops a new matrix factorization assisted interpolation method, which is composed of an improved interpolation scheme and the monotone projected Barzilai-Borwein based non-negative matrix factorization (MPBB-NMF). Specifically, an improved interpolation scheme is firstly developed to quantify the desired distribution of time-frequency interpolation nodes, and only the decomposed spectra at these nodes are calculated by Cholesky decomposition. Then, MPBB-NMF with a fast global convergence is used to decouple these spectra into products of non-negative time- and frequency-dependent functions. Finally, one-dimensional interpolation is performed for these decoupled functions, which makes it possible to accelerate the harmonic superposition using a small amount of fast Fourier transforms (FFTs). Obviously, the proposed method realizes the decomposition of spectral matrix in the decoupling form. Besides reducing of the number of Cholesky decomposition and invoking FFT, its decoupling only aims at the low dimensional matrix and the interpolation merely involves a few decoupled items. Numerical simulation on the fully non-stationary wind field of a long-span bridge demonstrates the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Wind loading is an essential aspect in the design and assessment of long-span bridges, but it is often not well-known and cannot be measured directly. Most structural health monitoring systems can easily measure structural responses at discrete locations using accelerometers. This data can be combined with reduced-order modal models in Kalman filter-based algorithms for an inverse estimation of wind loads and system states. As a further development, this work investigates the incorporation of Gaussian process latent force models (GP-LFMs), which can characterize the evolution of the wind loading. The Hardanger Bridge, a 1310 m long suspension bridge instrumented with a monitoring system for wind and vibrations, is used as a case study. It is shown how the LFMs can be enriched with physical information about the stochastic wind loads using monitoring anemometer data and aerodynamic coefficients from wind tunnel tests. It is found that the estimates of the modal wind loads and modal states obtained from a Kalman filter and Rauch–Tung–Striebel smoother are stable for acceleration output only, thus avoiding the accumulation of errors. The proposed approach demonstrates how physical or environmental data can be injected as valuable information for global monitoring strategies and virtual sensing in bridges. • Load estimation is improved by fusing latent force models with state-space models. • Latent force models can be enriched with physical information on wind loads. • Modal wind loads and responses for a long-span suspension bridge are estimated. • The method utilizes both recorded structural accelerations and wind velocity data. [ABSTRACT FROM AUTHOR]

• The short-term non-destructive field vibration test was conducted on a newly-built long-span suspension bridge. • Operational modal analysis was performed efficiently by a Fast Bayesian FFT method. • Uncertainty quantification of modal parameters was carried out. • Due to the limited number of sensors, multiple setups were designed to complete the entire measurement. • Three-dimensional coordinates of the measurement locations were determined using an electronic level. In the past few decades, many large-scale bridges have been built to meet the different needs of styles and characteristics. Large bridges usually carry heavy traffic, and some bridges work in harsh environments. All these make the condition assessment of bridges very significant. On-site vibration testing is a general way to obtain the real response of the structure. Among a variety of measurements, the ambient vibration test has become popular due to its convenient usage and better economics. Based on the vibration data, modal identification can be used to identify the modal parameters that represent the dynamic characteristics of a structure. In this study, before being opened to traffic, a short-term non-destructive field vibration test was conducted on a newly-built long-span suspension bridge. Due to the limited number of sensors, multiple setups were designed to complete the entire measurement. For the measurement locations on the bridge deck, three-dimensional coordinates were determined using an electronic level. Analysis was performed based on the fast Bayesian FFT method, which can provide theoretical estimates for the posterior uncertainty and the most probable values of modal parameters. Nine modes of the bridge deck and four modes of the bridge tower were determined. The analysis results are discussed, and the posterior coefficient of variations (COVs) and sample COVs in different setups are compared. The analysis results in a healthy state can be used to verify the finite element model built in the design stage. It can also provide a benchmark for the future SHM of the bridge and improve the decision-making during usage and maintenance. [ABSTRACT FROM AUTHOR]

For long-span cable-stayed bridges, interconnecting adjacent cables using cross-ties and connecting each cable to bridge deck become a promising solution for cable vibration mitigation, leading to hybrid cable networks. However, optimizing the system parameters and configuration for best vibration control effects is still challenging. Therefore, this study proposes an optimization method based on three important ingredients, i.e., a general and efficient numerical model of cable networks, a reasonable definition of the optimization objectives, and a multi-objective optimization method. The cable network is modeled using the component mode synthesis method with modal expansion and quasi-static correction, the optimization objectives consider both multi-mode damping effects and stiffness enhancement, and the multi-objective genetic algorithm is then employed. The proposed method is first verified by comparing with analytical methods when applying to relatively simple cable–damper systems. Subsequently, a five-cable network is studied using the method for optimal design of cross-tie and damper parameters. Furthermore, the method is applied to optimize cross-ties and dampers for the eight longest cables in the Sutong Bridge, considering different numbers, locations and anchoring conditions of the cross-ties. The results have demonstrated the effectiveness of the proposed method in dealing with real-world large-scale cable networks. It is shown that the optimization can ensure that vibrations in local modes of the cable network are dominated by cable segments with a damper installed in the span and hence are sufficiently damped. Besides, damping ratios of hybrid cable networks are shown to be sensitive to the cross-tie location and parameters while they are relatively insensitive to the damper coefficients. • A MOGA-based framework proposed for optimal design of cables with cross-ties and dampers. • Objective functions presented for optimization of configuration and cross-tie/damper parameters. • Application to an eight-cable network in a real large-span cable-stayed bridge. • Low-damping local modes of hybrid cable networks avoided through the optimization. [ABSTRACT FROM AUTHOR]

• Online unsupervised early damage-detection in a long-span bowstring bridge using train-induced responses. • The performance of AR and ARX models as feature extractors was evaluated. • Influence of temperature, noise, train type and speed are efficiently removed from the features. • A novel approach to define an adaptive confidence boundary is successfully validated. • A real-time SHM procedure was simulated to check the proposed strategy's robustness and sensitivity. This paper exploits unsupervised data-driven structural health monitoring (SHM) in order to propose a continuous online procedure for damage detection based on train-induced dynamic bridge responses, taking advantage of the large-magnitude loading for enhancing sensitivity to small-scale structural changes. While such large responses induced by trains might create more damage-sensitive information in the measured response, it also amplifies the effects on those measurements from the environment. Thus, one of the biggest contributions herein is a methodology that exploits the large bridge responses induced by train passage while rejecting the confounding influences of the environment in such a way that false positive detections are mitigated. Furthermore, this research work introduces an adaptable confidence decision threshold that further improves damage detection over time. To ensure an online continuous assessment, a hybrid combination of autoregressive exogenous input (ARX) models, principal components analysis (PCA), and clustering algorithms was sequentially applied to the monitoring data, in a moving window process. A comparison between the performance obtained from autoregressive (AR) and ARX models as feature extractors was conducted, and it was concluded that ARX models lead to increased sensitivity to damage due to their ability to capture cross information between the sensors. The PCA proved its importance and effectiveness in removing observable changes induced by variations in train speed or temperature without the need to measure them, and the clustering methods allowed for an automatic classification of the damage-sensitive features. Since it was not possible to introduce damage to the bridge, several structural conditions were simulated with a highly reliable digital twin of the Sado Bridge, tuned with experimental data acquired from a SHM system installed on site, in order to test and validate the efficiency of the proposed procedure. The strategy proved to be robust when detecting a comprehensive set of damage scenarios with a false detection incidence of 2%. Moreover, it showed sensitivity to smaller damage levels (earlier in life), even when it consists of small stiffness reductions that do not impair structural safety and are imperceptible in the original signals. [ABSTRACT FROM AUTHOR]

• An approach based on the BDLM and Markov-switching theory is presented for condition assessment of bridge expansion joints. • The EM and NR approaches are compared for estimating parameters of switching BDLM. • The temperature effect on the displacement is modeled by the superposition of harmonic components in BDLM. • The switching BDLM offers the transition probability from normal to degradation state of bridge expansion joints. Age-related deterioration and premature failure have been primary concerns for bridge expansion joints. It is essential to improve the understanding of their operational performance. The existing approaches mainly formulate the deterministic/probabilistic temperature-displacement relationship (TDR) model to assess the structural condition of bridge expansion joints. Nevertheless, it is not easy to guarantee a strong correlation between representative temperature and displacement. Rather than establishing the TDR model, this work uses the displacement response to evaluate the expansion joint condition by combining the Bayesian dynamic linear model (BDLM) with Markov-switching theory. The external temperature effect on the displacement is modeled by the superposition of harmonic components in BDLM. The expectation–maximization (EM) algorithm initialized by the subspace method is employed to optimize the initial parameters. The presented approach is validated through the simulated data, and then it is applied to the expansion joint of a long-span bridge. Results show that EM with the subspace method involves high computational accuracy and efficiency in estimating unknown parameters compared to the Newton-Raphson approach. The switching BDLM successfully identifies the degradation process of expansion joints and offers the transition probability from the normal to other states. [ABSTRACT FROM AUTHOR]

• This study is the first to propose end-to-end pipelines for comprehensive modal identification of a bridge using moving sensors within vehicles. • Both proposed methods are successful to remove vehicle suspension effects and roughness-induced vibrations from the collected data within the vehicle cabin in order to extract bridge dynamic response. • The study indicates that the FRF-based method is able to identify the bridge with high accuracy as well as an acceptable estimation of the roughness profile. • The EEMD-based method does not need any a priori information of the vehicle, leading a practically more flexible platform. • In a numerical 2D case study, first four modes are fully identified using the proposed pipelines. MAC values are all above 0.94. Natural frequencies and damping ratios are also estimated accurately for the majority of cases. Vehicles commuting over bridge structures respond dynamically to the bridge's vibrations. An acceleration signal collected within a moving vehicle contains a trace of the bridge's structural response, but also includes other sources such as the vehicle suspension system and surface roughness-induced vibrations. This paper introduces two general methods for the bridge system identification using data exclusively collected by a network of moving vehicles. The contributions of the vehicle suspension system are removed by deconvolving the vehicle response in frequency domain. The first approach utilizes the vehicle transfer function, and the second uses ensemble empirical modal decomposition (EEMD). Next, roughness-induced vibrations are extracted through a novel application of second-order blind identification (SOBI) method. After these two processes, the resulting signal is equivalent to the readings of mobile sensors that scan the bridge's dynamic response. Structural modal identification using mobile sensor data has been recently made possible with the extended structural modal identification using expectation maximization (STRIDEX) algorithm. The processed mobile sensor data is analyzed using STRIDEX to identify the modal properties of the bridge. The performance of the methods are validated on numerical case studies of a long single-span bridge with a network of moving vehicles collecting data while in motion. The analyses consider three road surface roughness patterns. Results show that for long-span bridges with medium- to high-ongoing traffic volume, the proposed algorithms are successful in extracting pure bridge vibrations, and produce accurate and comprehensive modal properties of the bridge. The study shows that the proposed transfer function method can efficiently deconvolve the linear dynamics of a moving vehicle. EEMD method is able to extract vehicle dynamic response without a priori information about the vehicle. In addition, proposed identification methods provide secondary information about the roughness pattern and the vehicle. This study is the first proposed methodology for complete bridge modal identification, including operational natural frequencies, mode shapes and damping ratios using moving vehicles sensor data. [ABSTRACT FROM AUTHOR]

• Mechanistic insights into thermal deformation of suspension bridges are reported. • General formulas to estimate thermal deformation of suspension bridges are proposed. • Effects of various temperature variables on thermal deformation are compared. Varying ambient temperature may cause significant deformation of long-span suspension bridges. This study investigates the mechanisms of the temperature-induced mid-span deflection and tower-top horizontal displacement of suspension bridges, and formulates the general analytical solutions to the thermal responses of ground-anchored suspension bridges. The temperature-induced mid-span deflection can be determined from the superposition of deflections caused by each of the separate temperature changes of the main-span cable, side-span cables, and towers, while the tower-top horizontal displacement is a combination of the thermal effects of the side-span cables and towers. It is found that the cable temperature plays the dominant role in the mid-span deflection and tower-top horizontal displacement. Moreover, the temperature effective length is proposed and a unified formula of the temperature-induced bridge responses is obtained. The accuracy of the proposed formulas is verified through the field monitoring data of the 2132-m-long Tsing Ma Bridge at Hong Kong. The present study not only provides a simple, general, and unified analytical solution to the temperature-induced deformation of long-span suspension bridges, but also assists engineers in understanding the mechanisms of thermal behaviours of such bridges. [ABSTRACT FROM AUTHOR]