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Transverse synchronization of vertical displacements of all jacking-up points is an important monitoring indicator to replace bearings in assembled multigirder bridges during the jacking phase. Currently, using target paper to identify the 3D coordinates of control points reduces the complexity of monitoring operations and improves the stability of data precision. However, the existing planar target locating methods have low accuracy, inefficiency, and subjectivity, which seriously hinders the construction process of bearing replacement. Accurately obtaining the center coordinates of multiple targets from a point cloud in a short monitoring period remains a challenge. This study proposes a high-precision automated algorithm to extract target center points in low-density point clouds to quickly calculate real target center points. First, we construct a standard point cloud model of the target papers for scanning, including color and geometric features. Then, we extract the measured point cloud of the typical jacking operation phase based on the reflection intensity and size information. Next, we map the intensity values of the measured point cloud into the color channel and register the measured point cloud with its standard point cloud model using the normal vector estimation and colored ICP algorithms. Finally, we extract the center point of the measured targets. Numerical experiments and engineering test results show that the proposed method converges quickly with high precision and good robustness, which saves 91.4% of the time compared with the traditional method. In general, this research can provide effective technical support for 3D laser scanning in monitoring the operation phase of bridge jacking. [ABSTRACT FROM AUTHOR]

As the world's transport infrastructure ages, the importance of bridge condition monitoring is becoming increasingly acknowledged. Large-scale deployment of existing inspection and monitoring techniques is infeasible due to cost and logistical challenges. The concept of using sensors located within vehicles for low cost 'drive-by' monitoring has become the focus of much attention in recent years. This paper presents a new data-driven approach for drive-by bridge monitoring. Machine learning techniques are leveraged to allow the influence of vehicle speed to be considered and the Operating Deflection Shape Ratio (ODSR) is presented as an alternative damage-sensitive feature to the commonly used frequency spectrum. Extensive laboratory experiments demonstrate that the method is capable of detecting midspan cracking and seized bearings. A statistical classification approach is adopted to classify damage indicators as either 'damaged' or 'healthy'. Classification accuracy is seen to vary between 65-96% and is similar whether using the frequency spectrum or ODSR. Based on the results of the laboratory testing, it is expected that this approach could be implemented on a large scale to act as an early warning tool for infrastructure owners to identify bridges presenting signs of distress or deterioration. [ABSTRACT FROM AUTHOR]

Constructional material deterioration and member damage can cause changes in the dynamic characteristics of bridge structures, and such changes can be tracked in the responses of passing vehicles via the vehicle-bridge interaction (VBI). Though data-driven methods have shown promising results in damage inspection for drive-by methods, there is still much room for improvement in their performance. Given this background, this paper proposes a novel time-domain signal processing algorithm for the raw vehicle acceleration data of data-driven drive-by inspection methods. To achieve the best data processing performance, an optimizing strategy is designed to automatically search for the optimal parameters, tuning the algorithm. The proposed method intentionally overcomes the difficulties in the application of drive-by methods, such as measurement noise, speed variance, and enormous data volumes. Meanwhile, the use of this method can greatly improve the accuracy and efficiency of Machine Learning (ML) models in vehicle-based damage detection. It consists of a filtering process to denoise the data, a pooling process to reduce data redundancy, and an optimizing procedure to maximize algorithm performance. A dataset is obtained to validate the proposed algorithm through laboratory experiments with a scale truck model and a steel beam. The results show that, compared to using raw data, the present algorithm can increase the average accuracy by 12.2–15.0%, and the average efficiency by 35.7–96.7% for different damaged cases and ML models. Additionally, the functions of filtering and pooling operations, the influence of window function parameters, as well as the performance of different sensor locations, are also investigated in the paper. The goal is to present a signal processing algorithm for data-driven drive-by inspection methods to improve their detection performance of bridge damage caused by material deterioration or structural change. [ABSTRACT FROM AUTHOR]

• This paper proposed a comprehensive framework for parametric semi-automatic BIM and bridge member segmentation. • The parametric algorithm accounted for diverse types of bridge members and produced BIM bridge models using shape information automatically extracted per parameter. • The parametrically generated bridge BIM model was converted into PCD, serving as deep learning train data for automatic segmentation of bridge members. • The trained deep learning model showed high accuracy for segmenting superstructures, indicating promise for automated segmentation of bridge members. • The segmentation accuracy increased when accounting for the point density of members corresponding to the different sizes of bridge members. This paper proposes a comprehensive framework for parametric semi-automatic BIM and bridge member segmentation. For this, a parametric algorithm was developed to accommodate diverse superstructures, piers, abutments, and bearings. Each structural member in a bridge was classified to designate its shape information as parameters. The range of each parameter was defined to account for various dimensions of the shape of the bridge member. Therefore, libraries for each member were established to produce BIM bridge models using shape information automatically extracted per parameter. Then, the framework includes an algorithm that is developed to convert bridge BIM models generated by the parametric algorithm into PCD data. The virtually generated PCD is used as deep learning train data for automatic member segmentation based on the Point-Net algorithm. The trained algorithm using the virtual PCD was applied to a real bridge PCD. The segmentation of the bridge members showed high accuracy for the superstructure but low accuracy for the bearing. The segmentation accuracy of the algorithm including the bearing member could increase by modifying the density of PCD to account for the different sizes of bridge members. Furthermore, the proposed framework was applied to a UK bridge PCD and showed its applicability for use in bridges in different countries. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) systems are used to analyze the health of infrastructures such as bridges, using data from various types of sensors. While SHM systems consist of various stages, feature extraction and pattern recognition steps are the most important. Consequently, signal processing techniques in the feature extraction stage and machine learning algorithms in the pattern recognition stage play an effective role in analyzing the health of bridges. In other words, there exists a plethora of signal processing techniques and machine learning algorithms, and the selection of the appropriate technique/algorithm is guided by the limitations of each technique/algorithm. The selection also depends on the requirements of SHM in terms of damage identification level and operating conditions. This has provided the motivation to conduct a Systematic literature review (SLR) of feature extraction techniques and pattern recognition algorithms for the structural health monitoring of bridges. The existing literature reviews describe the current trends in the field with different focus aspects. However, a systematic literature review that presents an in-depth comparative study of different applications of machine learning algorithms in the field of SHM of bridges does not exist. Furthermore, there is a lack of analytical studies that investigate the SHM systems in terms of several design considerations including feature extraction techniques, analytical approaches (classification/ regression), operational functionality levels (diagnosis/prognosis) and system implementation techniques (data-driven/model-based). Consequently, this paper identifies 45 recent research practices (during 2016–2023), pertaining to feature extraction techniques and pattern recognition algorithms in SHM for bridges through an SLR process. First, the identified research studies are classified into three different categories: supervised learning algorithms, neural networks and a combination of both. Subsequently, an in-depth analysis of various machine learning algorithms is performed in each category. Moreover, the analysis of selected research studies (total = 45) in terms of feature extraction techniques is made, and 25 different techniques are identified. Furthermore, this article also explores other design considerations like analytical approaches in the pattern recognition process, operational functionality and system implementation. It is expected that the outcomes of this research may facilitate the researchers and practitioners of the domain during the selection of appropriate feature extraction techniques, machine learning algorithms and other design considerations according to the SHM system requirements. [ABSTRACT FROM AUTHOR]

It is a promising method to identify structural damage using bridge dynamic response under moving vehicle excitation, but the lack of accurate information about road roughness and vehicle parameters will lead to the failure of this method. The paper proposed a step-by-step EKF damage identification method, which transforms the inversion problem of unknown structural parameters under unknown loads (vehicle and road roughness) into two separate inversion problems: moving contact force identification and damage parameters identification. Firstly, the VBI model is converted into bridge vibration model under a moving contact force, and the moving contact force covering the information of road roughness and vehicle parameters can be calculated by EKF iteration. Secondly, the moving contact force identified in the first step is loaded on the bridge as a known condition, and the bridge damage problem is also solved by the EKF method. Numerical analyses of a simply-supported bridge under the moving vehicle are conducted to investigate the accuracy and efficiency of the proposed method. Effects of the vehicle speed, the damage cases, the measurement noise, and the roughness levels on the accuracy of the identification results are investigated. The results demonstrate the proposed algorithm is efficient and robust, and the algorithm can be developed into an effective tool for structural health monitoring of bridges. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm to solve vehicle–bridge interaction (VBI) problems. It describes the VBI system in a linear second-order differential-algebraic equation (DAE) manner, incorporating the motions of both the vehicle and the bridge subsystems, together with the contact forces. On account of the conjugation between the VBI system's motions and contact forces, the key feature of the proposed algorithm is to solve the DAE with the the algebraic method of elimination by substitution, avoiding the singularity of the differential operator. It enables a versatile and consensus solution scheme for different types of contact mechanisms, including the rigid contact model with constraints, the elastic contact model with the compliance method, and the creep tangential contact model, as well as different wheel–rail profiles. Combined with an appropriate numerical integration scheme, it allows an explicit expression of the contact forces, subsequently leading to the partitioned non-iterative analysis of the motions of both the vehicle and the bridge subsystems. In addition, by incorporating the dynamic condensation of wheels' degrees of freedom into those of upper components in a matrix form, i.e. a reduced system approach, the proposed algorithm can avoid the numerical drift associated with the kinematic constraints on the acceleration level. To demonstrate the accuracy of the proposed approach, this study first examines a benchmark example of a single degree of freedom sprung mass model traversing a simply supported bridge. Further, it considers a more realistic problem of one and eight train vehicles crossing three three-span continuous bridges. The comparisons and the agreements with existing algorithms prove the accuracy and computational efficiency of the proposed analysis scheme. [ABSTRACT FROM AUTHOR]

Summary: The identification of traffic loads, including the axle weight (AW) and the gross vehicle weight (GVW) of vehicles, plays an important role in bridge design refinement, safety evaluation, and maintenance strategies. Bridge weigh in motion (BWIM) is a promising technique to weigh vehicles passing through bridges. Though the state‐of‐the‐art BWIM can accurately identify the GVW, unacceptable weighing errors are reported when identifying the AW of vehicles, particularly for those with closely spaced axles. To address the axle weighing problem, this paper aims to improve the performance of BWIM in weighing individual axle loads apart from the gross vehicle weight. The work first theoretically analyzes the possible sources of errors of existing BWIM algorithms, which are observational errors residing in the BWIM equation, no constraint imposed on individual axle loads, and ill‐conditioned nature. Accordingly, three measures are taken to establish a novel robust BWIM algorithm, which is based on regularized total least squares, as well as imposing constraints on the relationship between axles. To validate the proposed algorithm, a series of weighing experiments are carried out on a high‐fidelity vehicle‐bridge scale model. The corresponding results indicate that the proposed BWIM algorithm significantly outperforms other existing BWIM algorithms in terms of the accuracy and robustness of identifying individual axle weight, while retaining satisfactory identification of the gross vehicle weight as well. [ABSTRACT FROM AUTHOR]

Summary: This paper develops a trend line‐based algorithm for signal decomposition in which the adjusted Savitzky–Golay filter is utilized to initiate the decomposition process. In this line, the proposed algorithm determines some special trend lines, mainly composed of the natural frequency of a bridge. An easy‐to‐implement algorithm is then provided to formulate this process and to decompose the given signal into its components in a systematic way. Additionally, a residual signal is generated by the proposed algorithm to store the detected noise and to reconstruct the original signal. To verify the proposed algorithm in the field of bridge health monitoring, a set of numerical and experimental examples are offered in which the proposed algorithm is employed to decompose the signal and provide the constituent components. Moreover, the application of the proposed algorithm in damage localization of the bridge is addressed in the appendix using a simply supported bridge under a moving vehicle. Finally, the bridge example is solved by empirical mode decomposition, as a promising benchmark method, to further illustrate the accuracy of the results and compare them in detail. [ABSTRACT FROM AUTHOR]

Vulnerability analysis has become a recent concern for bridge administration authorities. This paper presents a Bayesian network-based vulnerability evaluation methodology for a large-scale national highway (NH) bridge network, using the improved ORDER-II-Dijkstra algorithm. The NH bridge network consists of 1772 bridges, and includes their spatial locations, types, completion years, and assessment states. The network vulnerability was defined by combining edge failure and its influence on network connectivity. Using the equivalent bridge concept for simplicity, the edge failure probability was determined by a series system composed of all bridges in the same edge, where the failure probability for one bridge could be calculated by incorporating its assessment state and design load. The large-scale bridge network connectivity probability was approximately evaluated using the Bayesian network. To avoid the NP-hard problem, the ORDER-II algorithm evaluated the most probable state combinations of equivalent bridges, by adding or deleting ordered state combinations to the minimum heap. The improved Dijkstra's algorithm was chosen to determine the network connectivity under each state combination by seeking the shortest paths between node pairs. The application of vulnerability to the bridge network illustrates the effectiveness and accuracy of this method, and can provide guidance for decision-making. [ABSTRACT FROM AUTHOR]

Vehicle on-board monitoring methods use responses of running vehicles to identify track irregularity in real time. But the parameters of both the bridges and the vehicles in such processes may have a non-negligible degree of uncertainty or randomness that will inevitably lead to uncertainty in the track irregularity identification. Quantifying such uncertainty is a great challenge as the vehicle-bridge system (VBS) to be treated with is time-dependent and random. This paper proposes an on-board track irregularity identification algorithm that realizes an inverse random dynamic analysis of the VBS to quantify estimation uncertainty by using a Bayesian Kalman filter technology. The proposed algorithm utilizes sigma point sets to simulate the random parameters and the noises, and is therefore capable of implementing high-fidelity probability density propagation in the nonlinear state transfer and observation functions describing the VBS. The proposed algorithm is validated by numerical examples with various running states and parameter uncertainty levels. [ABSTRACT FROM AUTHOR]

Modal parameter identification is considered to be one of the most important tasks in structural health monitoring because it provides a reliable reference for structural vibration control, damage severity, and operational state. Moreover, at present, the combined deterministic-stochastic subspace algorithm is cogitated as one of the key algorithms in the modal parameter identification, which is why it is widely used in the modal parameter identification of bridge structures. In this paper, a novel method is proposed, which is a time-domain identification algorithm, based on sliding window-fuzzy C-means clustering algorithm-combined with deterministic-stochastic subspace identification (SC-CDSI), to achieve online intelligent tracking and identification of modal parameters for nonlinear time-varying structures. First of all, to realize the online tracking and identification process, it is necessary to divide the input and output signal of the nonlinear time-varying structure by windowing; for that, to determine the window function, window size and window step length according to the characteristics of the signal are analyzed. Secondly, in order to satisfy the intelligent identification of effective modals in stability diagram, the fuzzy C-means clustering algorithm is kept as a base, whereas frequency, damping ratio, and modal shapes serve as clustering elements, applied to fuzzy C-means clustering algorithm, and then the intelligent selection of effective modals is achieved. Finally, a shaking table test bridge is used as a modal parameter identification in lab, and its results are compared with the MIDAS finite element results. The compared results show that the proposed SC-CDSI identification algorithm can accurately achieve the intelligent identification of online tracking of the structural frequency, and the identification results are reliable to be used in real-life bridge structures. [ABSTRACT FROM AUTHOR]

Summary: Mode shapes have been playing a vital role in the research and application of bridge structural health monitoring. This paper presents a novel indirect method identifying bridge mode shapes using dynamic responses of a tractor–trailer vehicle model, which consists of one tractor and three instrumented trailers. In an effort to eliminate the road roughness effect, accelerations of adjacent trailers are firstly subtracted. Wavelet analysis is then employed to identify bridge mode shapes from the subtracted accelerations in an iterative manner. Furthermore, wavelet denoising algorithm is adopted to improve the identification accuracy in the presence of measurement noise. Systematic numerical simulations, in which a tractor–trailer model passes over an expressway bridge, are conducted in order to investigate the performance of the proposed method. Sensitivity analysis including vehicle speed, class of road roughness, and noise level are studied in this numerical investigation. Results demonstrate that the proposed method is able to identify bridge modal frequencies and mode shapes with satisfactory resolution, accuracy, and robustness. [ABSTRACT FROM AUTHOR]

This paper proposes a new cable element and a novel formation procedure of unbalanced loads for cable-stayed bridges. The proposed method couples the effects of geometric nonlinearity and concrete creep/shrinkage. An improved catenary cable element with arbitrary rigid arms is introduced to reduce the degree of freedoms in simulations. An explicit expression of tangent stiffness of the new cable element is derived. Then, an incremental stiffness equation under co-rotational coordinate system is established by introducing a recurrence equation of creep loads. Following this, a new formation method is proposed to evaluate the unbalanced loads on the current deformed equilibrium configuration. This method is illustrated and validated by two actual long span cable-stayed bridges in Yangtze River. The results indicate that the coupled algorithm can significantly enhance the computational efficiency and accuracy for the bridge analysis during construction. [ABSTRACT FROM AUTHOR]

Summary: Modal parameter variation plays an important role in bridge health monitoring. But tracking the long‐term variation of modal parameters is restricted by the modal identifiability. Since some modes cannot be identified due to the limitations of sensor locations or excitation conditions, the identified modes will be missing or misclassification in the tracking process. In this paper, the multistage tracking technique based on subspace correlations is proposed. To avoid missing the identified modes, the reference mode list should be complete to cover all identified modes. Thus, the first stage is to update the reference list adaptively, where the correlations between the observability vectors of identified modes and the subspaces of existing reference modes are taken. The second stage is to cluster each traceable mode and the specified reference mode together without misclassification, where the modal similarity is measured by the similarity of observability vectors (SOV). The proposed algorithm is verified by the vibration data of a numerical model and a highway bridge, respectively. The results show that the proposed method can link with modes in the same order correctly and update the reference mode list adaptively to avoid missing the identified modes. [ABSTRACT FROM AUTHOR]

An enhanced method to determine the best-fit auto-regressive model (AR model) for structural damage identification is proposed in this paper. Whereby, two parameters of the model, including the number of model order and the window size of data, are analyzed simultaneously in order to accomplish the optimized values by means of Akaike's Information Criterion (AIC) algorithm. The damage condition of structures can be detected by defined damage indicators obtained from the first three AR coefficients of the best-fit AR models. The ability of the proposed damage identification method is compared with the process that only utilizes conventional AR models without concern of parameter selection. The proposed method is verified using experimental data previously collected from a large-size bridge structure in the Structural Laboratory at the University of Central Florida. The results indicate that this method can detect and locate damage more effectively. [ABSTRACT FROM AUTHOR]

This paper describes a novel method to determine a road profile through the analysis of accelerations in a passing vehicle. A direct integration algorithm is proposed to determine the profile from the measured vehicle acceleration response. A sprung mass model and a half-car model are used to represent the vehicles in separate analyses. Combining the direct integration algorithm with the Cross Entropy (CE) optimisation method, a vehicle fleet monitoring concept is proposed for the monitoring of roads and/or bridges. In this approach, the profile can be calculated using accelerations from multiple vehicles without prior knowledge of the vehicle properties. Numerical results show that calculated profiles are the same as the 'true' profiles which were used to generate the 'simulated measured' accelerations. [ABSTRACT FROM AUTHOR]

In recent years, bridge health monitoring system has been widely used to deal with massive data produced with the continuous growth of monitoring time. However, how to effectively use these data to comprehensively analyze the state of a bridge and provide early warning of bridge structure changes is an important topic in bridge engineering research. This paper utilizes two algorithms to deal with the massive data, namely Kohonen neural network and long short-term memory (LSTM) neural network. The main contribution of this study is using the two algorithms for health state evaluation of bridges. The Kohonen clustering method is shown to be effective for getting classification pattern in normal operating condition and is straightforward for outliers detection. In addition, the LSTM prediction method has an excellent prediction capability which can be used to predict the future deflection values with good accuracy and mean square error. The predicted deflections agree with the true deflections, which indicate that the LSTM method can be utilized to obtain the deflection value of structure. What's more, we can observe the changing trend of bridge structure by comparing the predicted value with its limit value under normal operation. [ABSTRACT FROM AUTHOR]

An important issue in classifying rational 3-tangles is how to know whether or not a given tangle is the trivial rational 3-tangle called ∞-tangle. The author [4] provided a certain algorithm to detect the ∞-tangle. In this paper, we give a much simpler method to detect the ∞-tangle by using the bridge arc replacement. We hope that this method can help prove many application problems such as a classification of 3-bridge knots. • Bridge arc replacement. • Detecting ∞-tangle. [ABSTRACT FROM AUTHOR]

A discernible correlation emerged between global bridge disasters and bridge deterioration in recent years. To assist bridge inspectors in conducting deterioration identification, this paper presents a Pilgrimage Walk Optimization (PWO) algorithm inspired by Taiwan's unique Matsu bobee custom. The search behavior of the PWO algorithm simulates the gathering of devotees following Matsu's palanquin and their collective movements based on folk belief activities, including divination block casting, pilgrimage, the leisure ceremony, crawling beneath the palanquin, palanquin robbing, and the return palanquin ceremony. Analysis results show that the PWO outperformed contemporary metaheuristic algorithms on various multidimensional benchmark functions and was effectively applied to image segmentation for multiple types of bridge deterioration collected by an unmanned aerial vehicle. In the increasing number of engineering problems requiring edge computing to process big data, the proposed PWO algorithm is a low-cost and robust method with fault tolerance. • Presenting the innovative Pilgrimage Walk Optimization (PWO) algorithm, a revolutionary metaheuristic approach. • The new algorithm is tested on benchmark functions and applied to optimize image segmentation. • PWO algorithm outperforms contemporary metaheuristic algorithms in terms of achieving optimal solutions. • Exploring diverse bridge deterioration patterns auto-segmented using metaheuristic clustering algorithms. • PWO algorithm holds potential applications in AIoT technology and automation within the construction industry. [ABSTRACT FROM AUTHOR]

• A preconditioned least square QR-factorization approach is developed for moving force identification. • The regularization matrix L is introduced to improve the ill-posed problems. • The number of iterations j is introduced to avoid noise disturbance and ensure the robustness. • Preconditioned least square QR-factorization approach is validated through numerical simulation. This paper develops a novel method for moving force identification (MFI) called preconditioned least square QR-factorization (PLSQR) method. The algorithm seeks to reduce the impact of identification errors caused by unknown noise. The biaxial moving forces travel on a simply supported bridge at three different speeds is used to generate numerical simulations to assess the effectiveness and applicability of the algorithm. Results indicate that the method is more robust towards ill-posed problem and has higher identification precision than the conventional time domain method (TDM). In addition, the robustness and ill-posed immunity of PLSQR are directly affected by two kinds of regularization parameters, namely, number of iterations j and regularization matrix L. Compared with the standard form of least square QR-factorization (LSQR), i.e., the regularization matrix L being the identity matrix I n , the PLSQR with the optimal number of iterations j and regularization matrix L has many advantages on MFI and it is more suitable for field trials due to better adaptability with type of sensors and number of sensors. [ABSTRACT FROM AUTHOR]

Highlights • For precast concrete bridge decks, HSS-formed shear pockets should be designed to ensure ductile behavior. • Concrete strength and shear pocket dimensions are key parameters in the design of shear pocket connections. • Using HSS in forming shear pockets is an efficient way for confining pocket concrete/grout and controlling splitting cracks. • FEA can be utilized in modeling the predicting the behavior of HSS-formed shear pockets. Abstract Current bridge design codes do not provide adequate criteria/procedures for designing full-depth precast concrete deck systems, especially those with shear pocket connections. Instead, these systems and their connections are designed on a case-by-case basis by either conducting necessary testing or adopting the design criteria/procedures developed primarily for cast-in-place concrete deck systems. Shear pocket connections formed using steel hollow structural sections (HSS) provide a promising solution to connecting precast concrete deck panels to the supporting girders due to their superior structural performance and simplicity of panel fabrication. The main objective of this paper is to develop criteria/procedures for designing HSS formed shear pocket connections in full-depth precast concrete deck systems. These procedures will assist bridge designers in selecting pocket dimensions, HSS thickness, pocket anchorage and reinforcement necessary to maximize the connection capacity while allowing adequate construction tolerance. Experimental investigation (push-off testing) and finite element analysis (FEA) were performed to validate the developed design criteria/procedures. Analysis and testing results indicated that the developed design criteria/procedures for HSS formed shear pocket connections are satisfactory. [ABSTRACT FROM AUTHOR]

Finding the shortest path in road networks becomes one of important issues in location based services (LBS). The problem of finding the optimal meeting point for a group of users has also been well studied in existing works. In this paper, we investigate a new problem for two users. Each user has his/her own source and destination. However, whether to meet before going to their destinations is with some uncertainty. We model it as minimum path pair ( MPP) query, which consists of two pairs of source and destination and a user-specified weight $\alpha$ to balance the two different needs. The result is a pair of paths connecting the two sources and destinations respectively, with minimal overall cost of the two paths and the shortest route between them. To solve MPP queries, we devise algorithms by enumerating node pairs. We adopt a location-based pruning strategy to reduce the number of node pairs for enumeration. An efficient algorithm based on point-to-point shortest path calculation is proposed to further improve query efficiency. We also give two fast approximate algorithms with approximation bounds. Extensive experiments are conducted to show the effectiveness and efficiency of our methods. [ABSTRACT FROM AUTHOR]

Bridge health monitoring system produces much monitored data during the long-term service periods. How to properly handle with these data is one of the main difficulties in the field of Structural Health Monitoring (SHM). To predict the structural reliability with these data, the objectives of this paper are to present: (1) a nonlinear dynamic model, (2) nonlinear Mixed Gaussian Particle Filtering (MGPF) algorithm, (3) a dynamic reliability prediction approach combining nonlinear MGPF algorithm and SHM data with first order second moment (FOSM) method. And the monitored extreme stress data of an actual bridge is provided to illustrate the application and feasibility of the proposed models and methods. [ABSTRACT FROM AUTHOR]

In order to relieve traffic congestion, irregularly-shaped bridges have been widely used in urban overpasses. However, the analysis on modal characteristics of irregularly-shaped bridges is not exhaustive, and the effect of design parameters on modal characteristics will be deeply investigated in future studies. In this paper, a novel strategy based on a free-interface mode synthesis algorithm is proposed to evaluate the parameters' effect on the modal characteristics of irregularly-shaped bridges. First, a complicated, irregularly-shaped bridge is divided into several substructures based on its properties. Then, the modal characteristics of the overall structure can be obtained, only by a few low-order modal parameters of each substructure, using a free-interface mode synthesis method. A numerical model of a typical irregularly-shaped bridge is employed to verify the effectiveness of the proposed strategy. Simulation results reveal that the free-interface mode synthesis method possesses favorable calculation accuracy for analyzing the modal characteristics of irregularly-shaped bridges. The effect of design parameters such as ramp curve radius, diaphragm beam stiffness, cross-section feature, and bearing conditions on the modal characteristics of an irregularly-shaped bridge is evaluated in detail. Analysis results can provide references for further research into and the design of irregularly-shaped bridges. [ABSTRACT FROM AUTHOR]

Recent studies show that individuals in a social network can be divided into different groups of densely connected communities, and these individuals who bridge different communities, referred to as structural hole spanners, have great potential to acquire resources/information from communities and thus benefit from the access. Structural hole spanners are crucial in many real applications such as community detections, diffusion controls, viral marketing, etc. In spite of their importance, little attention has been paid to them. Particularly, how to accurately characterize the structural hole spanners and how to devise efficient yet scalable algorithms to find them in a large social network are fundamental issues. In this paper, we study the top-$k$ structural hole spanner problem. We first provide a novel model to measure the quality of structural hole spanners through exploiting the structural hole spanner properties. Due to its NP-hardness, we then devise two efficient yet scalable algorithms, by developing innovative filtering techniques that can filter out unlikely solutions as quickly as possible, while the proposed techniques are built up on fast estimations of the upper and lower bounds on the cost of an optimal solution and make use of articulation points in real social networks. We finally conduct extensive experiments to validate the effectiveness of the proposed model, and to evaluate the performance of the proposed algorithms using real world datasets. The experimental results demonstrate that the proposed model can capture the characteristics of structural hole spanners accurately, and the structural hole spanners found by the proposed algorithms are much better than those by existing algorithms in all considered social networks, while the running times of the proposed algorithms are very fast. [ABSTRACT FROM AUTHOR]

Bridge engineers increasingly prefer to use the Ground-Penetrating Radar (GPR) technique. GPR can yield data with very high spatial resolution, the data can be acquired rapidly and even during traffic, causing very low interferences. This paper presents a novel GPR system that is designed and developed for bridge applications. In addition it proposes a new algorithm for cracks tracking in a three-dimensional domain. The effectiveness and accuracy of the procedure have been calibrated and validated on four different bridges. In this paper, three-dimensional visualisations of cracks and two-dimensional tomographies and sections are shown to demonstrate the potentialities of the GPR system associated to the signal-processing algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a solution in which a wireless interface is employed to replace the cables in bridge-sensor measurement applications. The most noticeable feature of the presented approach is the fact that the wireless interface simply replaces the cables without any additional hardware modification to the existing system. In this approach, the concept of reciprocal topology is employed, where the transmitter side acquires signals with its own transfer function and the receiver side reconstructs them with the transfer function reciprocal to the transmitter transfer function. In this paper the principle of data acquisition and reconstruction is described together with the implementation details of the signal transfer from the sensor to the signal-monitoring equipment. The wireless data communication was investigated and proprietary data-reduction methods were developed. The proposed methods and algorithms were implemented using two different wireless technologies. The performance was evaluated with a dedicated data-acquisition system and finally, the test results were analyzed. The two different sets of results indicated the high level of amplitude and the temporal accuracy of the wirelessly transferred sensor signals. [ABSTRACT FROM AUTHOR]

Dynamic response analysis of a nonlinear train-track-bridge system under earthquakes is a time-consuming task. In this paper, a fast computing strategy is proposed to reduce the simulation time by solving the shortcomings of classical time integration algorithms in the computation of the coupled system. The core of the strategy focuses on completely explicit computational processes and unconditional stability. Based on the loosely coupling scheme, the model of the train-track-bridge system is divided into two parts, namely, the train substructure established using multibody dynamics and the track-bridge substructure established using the finite element method. Track-bridge substructure and train substructure are separately integrated by the unconditionally stable explicit algorithm, CQ3, and its degenerate form, respectively. The interaction of the two substructures depends on wheel-rail forces. The track-bridge substructure is further decoupled to describe its nonlinear behavior and to improve the speed of solving algebraic equations. The proposed strategy not only avoids the complex iterative process of the nonlinear train-track-bridge system but also eliminates the limitation of the integration time step caused by the minimum natural period of the track-bridge substructure. This paper first simulates the dynamic response of a train under a sinusoidal displacement excitation and extends the simulation strategy to analyze the vibration of the coupling system under an earthquake. The applicability, efficiency, and accuracy of the strategy are illustrated through three numerical analyses. The strategy proposed in this paper provides a convenient and greatly computationally efficient option for simulating the nonlinear dynamic response of a large-scale train-track-bridge system. • The unconditionally stable explicit algorithm is introduced to the large-scale nonlinear train-track-bridge system. • Compared with using the classical algorithms, the proposed method achieves the same accuracy and higher efficiency. • The proposed method can greatly improve the computational efficiency of train-track-bridge coupling simulation. [ABSTRACT FROM AUTHOR]

This paper describes a methodology to optimize cost and CO 2 emissions when designing precast–prestressed concrete road bridges with a double U-shape cross-section. To this end, a hybrid glowworm swarm optimization algorithm (SAGSO) is used to combine the synergy effect of the local search with simulated annealing (SA) and the global search with glowworm swarm optimization (GSO). The solution is defined by 40 variables, including the geometry, materials and reinforcement of the beam and the slab. Regarding the material, high strength concrete is used as well as self-compacting concrete in beams. Results provide engineers with useful guidelines to design PC precast bridges. The analysis also revealed that reducing costs by 1 Euro can save up to 1.75 kg in CO 2 emissions. Finally, the parametric study indicates that optimal solutions in terms of monetary costs have quite a satisfactory environmental outcome and differ only slightly from the best possible environmental solution obtained. [ABSTRACT FROM AUTHOR]

The development of high-resolution satellite imaging sensors has enhanced the collection of remotely sensed data and offers a cost-effective way to obtain information over large areas. The main structural features that are to be detected through satellite imaging are roads, buildings, and bridges. Detection of clouds and shadows supports the extraction of these features. However, the type of satellite images provided by different imaging sensors varies widely depending on spatial and spectral resolutions, which makes the process of feature extraction more complicated. This paper presents a detailed analysis of different algorithms developed to extract structural features using a variety of satellite images available for a single region. A comparative study of various techniques is done to justify the best method for the extraction of each feature. [ABSTRACT FROM PUBLISHER]

An optimization approach of network arch bridges using a global optimization algorithm EVOP is presented in this paper. The objective is to minimize the cost of superstructure particularly arches and hangers of network arch bridge by optimizing the geometric shape, rise to span ratio, cross section of arch, and the number, arrangement and cross sectional dimensions of hangers. Constraints for design are formulated as per AASHTO, AISC and ACI Specifications. The minimum cost design problem is characterized by having a combination of continuous, discrete, and integer sets of design variables and is subjected to highly nonlinear, implicit and discontinuous constraints. An optimization algorithm, evolutionary operation (EVOP), is used that is capable of locating directly with high probability the global minimum without requiring information on gradient or sub-gradient of the objective function. EVOP is interfaced with finite element analysis software, ANSYS for evaluation of structural response of the bridge to verify the constraints and also to evaluate objective function. Within the range of design constant parameters considered, it is observed that 38% to 40% of total cost can be saved for circular and parabolic arches respectively, if design is optimized. Results also show that parabolic arch with optimum design variables is more economic than the optimized arch bridges with circular arch geometry. [ABSTRACT FROM AUTHOR]

This paper develops a novel form of a well-known signal processing technique, so as to be applicable to the interaction between a heavy truck and a supporting bridge structure. Motivated by the problem of structural health monitoring of bridges, a new modal coherency function is defined. This relates the input action of moving wheel loads to the dynamic response of the bridge, including the effects of unevenness of the road surface and the vertical dynamics of the truck suspension. The analysis here is specifically aimed at future experimental testing - the validation of axle load estimators obtained from sensors on the truck. It is applicable even when no independent ‘ground truth’ for the dynamic loads is available. The approach can be more widely used in the analysis of dynamic interactions involving suspended moving loads on deformable structures, e.g. for structural vibrations due to high-speed trains. [ABSTRACT FROM AUTHOR]

Bridges are one of the fundamental infrastructure assets that are vital for economic growth and public welfare. Over the past few decades, the numbers of deteriorating bridges have drastically escalated raising concerns for serviceable, safe and functional transportation networks. This state of affairs poses a paramount challenge especially when coupled with the need to address social and environmental constraints. Accordingly, this current research paper proposes an automated three-component model for bridge maintenance optimization at both project and network levels. The first component aims at identifying the physical characteristics of the tackled bridge inventory. The second component encompasses designing a multi-objective optimization model to determine the optimal set of maintenance plans through four principal objective functions. These functions comprise maximization of performance condition of bridge elements, minimization of agency and user costs, minimization of duration of traffic disruption and minimization of environmental impact. In the multi-objective optimization model, an exponential chaotic differential evolution (ECDE) algorithm is introduced in an attempt to circumvent the drawbacks of convergence speed and search behavior of classical meta-heuristics. The third component combines criteria importance through inter-criteria correlation (CRITIC), complex proportional assessment (COPRAS) and grey relational analysis (GRA) to select the most optimum maintenance plan for each study period. Comparison results revealed that ECDE-based Sinusoidal algorithm managed to improve the performance diagnostics of classical meta-heuristics by values ranged from 49.2% to 73.1% over the multi-year maintenance plans. The results of benchmark test functions exemplified that ECDE-based Sinusoidal algorithm performed better than genetic and differential evolution algorithms by 114.2% and 79.5%, respectively. The developed integrated model is expected to assist infrastructure managers in executing optimized and sustainable maintenance budget plans within various planning scenarios. • Bibliometric map is presented to derive the key shortcomings of previous research. • A chaotic-based optimization model is formulated for bridge maintenance planning in both project and network levels. • A hybrid multi-criteria decision-making algorithm is designed for prioritizing the Pareto optimum maintenance plans. • A computer aided application is developed using C#.net and Matlab. • The developed multi-objective optimization model is validated using actual case studies and benchmark test functions. [ABSTRACT FROM AUTHOR]

This paper presents a performance-based optimisation approach for conducting trade-off analysis between safety (roads) and condition (bridges and roads). Safety was based on potential for improvement (PFI). Road condition was based on surface distresses and bridge condition was based on apparent age per subcomponent. The analysis uses a non-monetised optimisation that expanded upon classical Pareto optimality by observing performance across time. It was found that achievement of good results was conditioned by the availability of early age treatments and impacted by a frontier effect preventing the optimisation algorithm from realising of the long-term benefits of deploying actions when approaching the end of the analysis period. A disaggregated bridge condition index proved capable of improving levels of service in bridge subcomponents. [ABSTRACT FROM PUBLISHER]

Accurate assessment of the quality of concrete bridge decks and identification of corrosion induced delamination lead to economic management of bridge decks. It has been demonstrated that ground penetrating radar (GPR) can be successfully used for such purposes. The growing demand on GPR has brought into the challenge of developing automatic processes necessary to produce a final accurate interpretation. However, there have been few publications targeting at automatic detection of bridge deck delamination from GPR data. This paper proposes a novel method using partial differential equations to detect rebar (or steel-bar) mat signatures of concrete bridges from GPR data so that the delamination within the bridge deck can be effectively located. The proposed algorithm was tested on both synthetic and real GPR images and the experimental results have demonstrated its accuracy and reliability, even for diminished image contrast and low signal-to-noise ratio. Therefore, an accurate deterioration map of the bridge deck can be generated automatically. [ABSTRACT FROM PUBLISHER]

Abstract: Bridges and tunnels are semantically meaningful objects in Geographical Information Systems (GIS), playing an important role in terms of reachability between locations. From a topological point of view, bridges and tunnels on surfaces are captured by the notion of a handle. In this paper, we extend an existing axiomatic characterization of 3D surfaces, which guarantees consistency between geometry and topology, to the case of handles. Furthermore, we present a method which verifies the occurrence of handles in surfaces, thereby contributing to the semantic-topological consistency in GIS. We close the gap between the global topological definition of handles in surfaces and the local definition of semantical handle objects in GIS – tunnels, bridges, arcades. Our method bases on a classification of cycles in two types. We give an efficient algorithm for discriminating both using standard methods from graph theory. This classification in addition contributes to the correctness of editing operations in GIS. [Copyright &y& Elsevier]

Abstract: The lifetime reliability of existing structures may be quantified by lifetime functions. Redundancy is an additional type of structural performance indicator that is defined as a measure of warning available prior to system collapse. Lifetime functions provide a basis on which lifetime redundancy can be evaluated and its quantification can be formulated. The objective of this paper is to present a novel approach for the evaluation of the lifetime redundancy of structural systems. Measures of lifetime redundancy based on lifetime functions are investigated. The effects of maintenance on lifetime functions and redundancy are also presented. Furthermore, the lifetime redundancy is incorporated in a maintenance optimization algorithm. This optimization algorithm is illustrated on an existing highway bridge. [Copyright &y& Elsevier]

The parametric approach to eliminating the temperature-caused modal variability in vibration-based structural damage detection requires a correlation model between the modal properties and environmental temperatures. This paper examines the generalization capability of neural network models, established using long-term monitoring data, for correlation between the modal frequencies and environmental temperatures. A total of 770 h modal frequency and temperature data obtained from an instrumented bridge are available for this study, which are further divided into three sets: training data, validation data, and testing data. A two-layer back-propagation neural network (BPNN) is first trained using the training data by the conventional training algorithm, in which the number of hidden nodes is optimally determined using the validation data. Then two new BPNNs are configured with the same data by applying the early stopping technique and the Bayesian regularization technique, respectively. The reproduction and prediction capabilities of the two new BPNNs are examined in respect of the training data and the unseen testing data, and compared with the performance of the baseline BPNN model. This study indicates that both the early stopping and Bayesian regularization techniques can significantly ameliorate the generalization capability of BPNN-based correlation models, and the BPNN model formulated using the early stopping technique outperforms that using the Bayesian regularization technique in both reproduction and prediction capabilities. [ABSTRACT FROM AUTHOR]

While numerous studies have been published concerning the application of a variety of system identification techniques in conjunction with vibration measurements from civil infrastructure systems, there is a paucity of publications addressing the influence of algorithm-specific control parameters that impact the correct and efficient application of the selected identification scheme. Furthermore, as dense sensor arrays become widely accessible in civil infrastructure applications, voluminous amounts of multichannel data streams are becoming available for processing, thus imposing new demands on identification procedures regarding high-dimensionality (in both the spatial as well as the temporal domains) requirements that may render some methods inapplicable if careful attention is not paid to practical implementation issues. This paper provides a comprehensive study of three time-domain identification algorithms applied in conjunction with the Natural Excitation Technique in order to extract the modal parameters of a newly constructed long-span bridge that was monitored, in its virgin state, over a relatively long period of time with a state-of-the-art dense sensor array. The three methods used are: the eigensystem realization algorithm (ERA), the ERA with data correlations, and the least squares algorithm. One of the critical issues in the mentioned algorithms, is selection of the reference degree-of-freedom (DOF). Previous experiences have shown that one cannot rely on a single reference DOF for identification of all modes. Consequently, the aforementioned identification formulations were modified to include multiple reference DOF, simultaneously, or one at a time. An autonomous algorithm was presented to distinguish the genuine structural modes from spurious noise or computational modes. Based on some parameter studies, some useful guidelines for the selection of critical user-selectable parameters are presented. [ABSTRACT FROM AUTHOR]

Abstract: Current terrain modelling algorithms are not capable of reconstructing 3D surfaces, but are restricted to so-called 2.5D surfaces: for one planimetric position only one height may exist. The objective of this paper is to extend terrain relief modelling to 3D. In a 3D terrain model overhangs and caves, cliffs and tunnels will be presented correctly. Random measurement errors, limitations in data sampling and the requirement for a smooth surface rule out a triangulation of the original measurements as the final terrain model. A new algorithm, starting from a triangular mesh in 3D and following the subdivision paradigm will be presented. It is a stepwise refinement of a polygonal mesh, in which the location of the vertices on the next level is computed from the vertices on the current level. This yields a series of triangulated terrain surfaces with increasing point density and smaller angles between adjacent triangles, converging to a smooth surface. With the proposed algorithm, the special requirements in terrain modelling, e.g. breaklines can be considered. The refinement process can be stopped as soon as a resolution suitable for a specific application is obtained. Examples of an overhang, a bridge which is modelled as part of the terrain surface and for a 2.5D terrain surface are presented. The implications of extending modelling to 3D are discussed for typical terrain model applications. [Copyright &y& Elsevier]

Bridge engineers need to group bridges to determine adequate let projects based on their proximities, types of work, costs, and cost constraints for each clustered let project after bridges to be treated yearly are identified. This process is time-consuming and typically performed manually. First, this paper presents the formulation of a bridge clustering problem for determining let projects by considering the bridge proximity and type of work with preference membership functions to simulate the actual decision-making process. Second, a constrained fuzzy c-mean (FCM) clustering algorithm is presented to resolves this problem. A case study using the subset of bridges in the state of Georgia with the hypothetical treatments and costs was used to test the developed algorithm and to demonstrate its capability. The results show that the developed constrained FCM clustering algorithm can, in seconds, effectively determine adequate let projects by clustering bridges while meeting cost constraints. The presented formulation also allows incorporation of additional factors such as preference of clustering bridges with the same route number or same route type that are important to other state Departments of Transportation. Finally, conclusions about the benefits and characteristics of the developed algorithm are summarized, and recommendations for future research are discussed. [ABSTRACT FROM AUTHOR]

A nondestructive crack detection (NCD) scheme to locate a crack and estimate the crack size by using changes in the modal parameters of a class of bridges is presented in this paper. First, the theory underlying a nondestructive crack localization and crack-size estimation algorithm for beam-type structures is outlined. Next, a field experiment to verify the feasibility and applicability of the NCD scheme is detailed. In that experiment, predamage and postdamage modal data extracted from a full-scale plate–girder bridge are described. The modal data are fed into the NCD scheme that localizes crack and estimates crack size in the test structure. The result of the analysis indicates that the proposed NCD algorithm correctly locates the crack and accurately estimates the size of the crack. [ABSTRACT FROM AUTHOR]

The paper aims to develop a unified variational framework to bridge the gap between the non-ordinary state-based peridynamics (NOSB-PD) and the classical continuum mechanics (CCM). First, a new force state vector is proposed by introducing the first Piola–Kirchhoff stress. This new force state vector enables the stress divergence of each material point to be expressed by averaging all the force state vectors in its support domain. The new force state vector also ensures the mathematical consistency between the strong form of PD and CCM when the horizon of a material point approaches to zero. Second, the displacement and traction boundaries in CCM are transformed into the non-local fictious boundary layers in PD, and a non-local Gauss's formulation is presented by transforming the displacement and traction boundaries in CCM into the non-local fictious boundary layers in PD, and this formulation unifies the variational framework and boundary conditions of PD and CCM. Third, a fully implicit algorithm is developed to obtain the general nonlinear problems such as fracture and large deformation of solid materials. Further, a penalty method is employed to eliminate the zero-energy mode oscillation inherently observed in NOSB-PD, and the penalty force and penalty stiffness matrix are derived for the proposed implicit algorithm and numerical implementation. Numerical results demonstrate that the proposed method is accurate and can well capture the fracture and large deformation of solid materials. Results also indicate that the method can effectively prevent the zero-mode oscillations inherently observed in the original NOSB-PD, and thus ensures the computational stability. • A unified variational framework is proposed to bridge the gap between PD and CCM. • A new force state vector is introduced to ensure the consistency between PD and CCM. • The proposed variational framework unifies boundary conditions in PD and CCM. • A fully implicit algorithm is developed to simulate general nonlinear problems. • A penalty method is employed to obtain a stable numerical solutions in NOSB-PD. [ABSTRACT FROM AUTHOR]

Nowadays, many precision farming applications rely on the use of GNSS-RTK. However, when it comes to autonomous agricultural vehicles, GNSS cannot be used as a stand-alone system for positioning. To ensure high availability and robustness of the positioning solution, GNSS-RTK must be fused with additional sensors. This paper presents a novel sensor fusion algorithm tailored to tracked agricultural vehicles. GNSS-RTK, an IMU and wheel speed sensors are fused in an error-state Kalman filter to estimate position and attitude of the vehicle. An odometry model for tracked vehicles is introduced which is used to propagate the filter state. By using both IMU and wheel speed sensors, specific motion characteristics of tracked vehicles such as slippage can be included in the dynamic model. The presented sensor fusion algorithm is tested at a composting site using a tracked compost turner. The sensor measurements are recorded using the Robot Operating System (ROS). To analyze the achievable accuracies for position and attitude of the vehicle, a precise reference trajectory is measured using two robotic total stations. The resulting trajectory of the error-state filter is then compared to the reference trajectory. To analyze how well the proposed error-state filter is suited to bridge GNSS outages, GNSS outages of 30 s are simulated in post-processing. During these outages, the vehicle's state is propagated using the wheel speed sensors, IMU, and the dynamic model for tracked vehicles. The results show that after 30 s of GNSS outage, the estimated horizontal position of the vehicle still has a sub-decimetre accuracy. [ABSTRACT FROM AUTHOR]

A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm. [ABSTRACT FROM AUTHOR]

Due to insufficient test data, insufficient constraint equations and uncertain objective function, the local optimal solution and the global optimal solution of the objective function in finite element model updating may represent the actual parameters of the structure. Based on this, this paper proposes an improved artificial fish school algorithm. By combining the niche technology with the artificial fish school algorithm, the improved algorithm can systematically find multiple global optimal solutions and local optimal solutions of the objective function. Aiming at the difficulty of determining the niche radius, an adaptive niche radius mechanism is proposed. The improved algorithm is used to study the multi-alternatives problem of finite element model updating after verifying its feasibility through numerical simulation analysis. In the case of benchmark framework model updating, it is confirmed that multi-alternative problems exist and the global optimal solution of the objective function does not necessarily represent the true parameters of the structure. In case 2, the improved algorithm combined with the Kriging model is applied to the model updating of a cable-stayed footbridge, and 15 sets of solutions are obtained, in which the error objective function values of the measured and theoretical values of the bridge modes are close but the solutions are completely different. Combining with the actual bridge condition and reanalysis technology, the author takes the suboptimal solution 2 as the most representative solution of the bridge parameters, which reduces the possibility of misjudgment of structural parameters. [ABSTRACT FROM AUTHOR]