Bridge damage identification methods based on contact point response of vehicle-bridge system are promising as they can effectively reduce the sensor number and the adverse effects of road roughness. However, such methods normally fail to consider the transverse distribution characteristics of damage and quantify damage severity of plate bridge. This paper proposes a damage localization and quantification method based on contact point response of vehicle-bridge system for plate bridge. Firstly, a spatial vehicle-bridge model is established for plate bridge and the indirect estimation approach for contact point response of the vehicle-bridge system is derived for practical application. Secondly, the damage localization index based on region curvature of instantaneous amplitude squared (IAS) of the driving component of the contact point response in damage state is constructed, and the corresponding preliminary damage localization procedure is provided. Thirdly, finite element model (FEM) updating with object function formed by region curvature of IAS is employed to obtain precise damage identification results. Finally, numerical and experimental examples are conducted to verify the effectiveness of the proposed method. The results indicate that it can reasonably consider the transverse distribution characteristics of damage and effectively quantify the damage severity.

Damage identification of hinge joints is crucial for ensuring the operational safety of prefabricated bridges. However, the engineering application of existing data-driven methods is restricted by scarce labeled data in actual bridges and significant domain shifts between simulation (source domain) and monitoring data (target domain). Furthermore, actual bridges typically exhibit only limited bridge states, which can induce negative transfer in conventional domain adaptation. This paper proposes an attention-guided Partial Domain Adaptation (PDA) method for damage identification of hinge joints in prefabricated bridges subjected to random traffic flow. First, a transformer feature extractor is employed to learn discriminative representations from acceleration responses at mid-span measured by limited sensors. Then, a transferability evaluation module and linear cosine cross-domain attention mechanism are introduced to construct Weighted Maximum Mean Discrepancy (WMMD), which facilitates fine-grained alignment of shared classes between the source and target domains at the instance level, and effectively suppresses interference from private classes in the source domain. Besides, the cross-domain attention weight distribution provides visual explanations for transfer effectiveness and the decision mechanisms of the network model. Numerical examples demonstrate that even under the dual challenges of random traffic excitation and limited sensors, the proposed method effectively mitigates the adverse effects from label space differences and environmental noise. The identification accuracy is significantly improved compared with traditional supervised methods and the global domain adaptation method, offering a low-cost and effective solution for hinge joint damage identification with sparse observations.

With the increase of bridge service life, various loads, environmental corrosion and material aging may lead to the accumulation of structural damage, it is significant to identify structural damage to provide maintenance strategies and prevent collapse accidents. Abridge damage identification method based on fused multi-point deflection influence line area is proposed in this study. Initially, the variational mode decomposition (VIVID) technique is introduced to decompose the structural dynamic deflection under moving load, which will separate the dynamic fluctuation disturbance component from the structural low-frequency deflection response. In order to reduce the number of unknown variables to be solved and smooth the local fluctuations in the solution caused by noise, the B-spline basis functions are used to expand the influence line, which will transform the identification of influence line into solving the weight coefficients of base functions. Subsequently, the influence lines of the simply supported bridge before and after damage are derived, and a damage index based on the area difference of influence lines of fusing multi-point is proposed. Finally, a numerical simulating and experimental testing under various damage cases are studied to validate the feasibility of the proposed method. The dynamic fluctuation interference can effectively eliminate and the influence line can be accurately identified by proposed method. The fused damage index can effectively identify and localize structural damage under various damage cases, and the identification result is better and more stable than the damage index of single measurement point.

It is crucial to calculate the dynamic response of bridge induced by moving load which is the main live load during operation. Physics-informed neural network (PINN) is powerful in calculating structural response induced by static load as it can provide the prior knowledge for neural network. This paper extends the PINN for dynamic response analysis of bridge subjected to moving load. Firstly, nondimensional partial differential equations of uniform and non-uniform bridges subjected to moving loads are derived. Then, the Dirac function is approximated by Gaussian function, and the corresponding sampling strategy is proposed. Thirdly, the Fourier embedding layer and causal weight are added in the deep neural network and loss function of PINN, respectively. Fourthly, the implementation procedures of the PINN based moving load induced dynamic response analysis method are provided accordingly. Finally, numerical experiments are conducted to verify the effectiveness and superiority proposed method. The results indicate that the moving load induced dynamic response can be obtained by PINN driven by physics (PINN-DP) when the bridge parameters are known, and the response of bridge with unknown parameters can be obtained by PINN driven by both physics and data (PINN-DPD) with small amount of monitored response. Besides, the sampling strategy and causal weights added in the PINN can improve the accuracy of the analyzed results.

Timely and accurate damage identification can provide necessary guidance for bridge operation and maintenance. As the moving load is the main live load during service period, this paper proposes a damage identification method for bridges subjected to moving load based on fractional Fourier transform (FRFT). First, bridge response induced by moving load in time domain is rotated into fractional Fourier domain by using FRFT. Filtering and decomposing are conducted on the transformed moving load induced response by adjusting the angle parameter of FRFT and inverse FRFT to obtain the first intrinsic mode function. Then the relative FRFT entropy (RFE) index is defined based on the first intrinsic mode function for damage localization. The functional relationship between RFE and damage severity is established for damage quantification. Numerical and experimental examples of a simply supported beam with positive damage and negative damage under the excitation of moving load are carried out to investigate the performance of the proposed method. The results reveal that the proposed method can effectively and rapidly localize and quantify damages of the bridge subjected to moving load with a single sensor.

Data-driven acoustic emission (AE) damage location methods yield promising performances in large-scale complex structures like orthotropic steel decks (OSDs), but rely on abundant training data that are generally obtained by pencil lead break (PLB) tests. A new data-driven AE location method based on spectral element simulation and machine learning is proposed for more efficient practical applications. Especially, a CPU-GPU heterogeneous parallel computing framework is developed for three-dimensional time-domain spectral element method (SEM) simulation. It helps to generate high-quality numerical AE waves without excessive computational resources for training the artificial neural network (ANN)-based location model. Through the experiment on a full-scale OSD model, the method was proved to achieve an accuracy significantly higher than the widely-used time of arrival (TOA) method and comparable to the traditional data-driven method with experimental input data. The innovation lied in obviating burdensome PLB tests to collect training data for the AE location machine learning model.

Accurate identifying moving load is of great significance for bridge design, operation and maintenance. As the condition state of actual bridges is complex, moving load is subjected to time-varying uncertainty. Traditional probability theory uses stochastic process to describe uncertain moving load time history, which relies on plenty of samples. This paper proposes a bridge moving load identification method based on interval process with a small number of samples. Firstly, the establishment approach for non-probabilistic interval process model of moving load is presented based on ellipsoidal convex model. Then, the interval process identification of moving load problem is transformed into median time history identification which is achieved by deterministic identification method, and radius time history identification which is realized by matrix decomposition. Finally, the effectiveness of the proposed method is verified through numerical and experimental examples. The results manifested that compared with the Monte Carlo method, the required sample amount of the prosed method is significantly reduced, while compared with the stochastic process method, the results obtained by the proposed method are more accurate with the same sample amount. Besides, the influences of vehicle weight and velocity, road roughness, measurement noise, and measurement location on the identification results are systematically investigated.

Bridge influence line has an important application in structural performance evaluation, damage identification, model correction and bridge weigh-in-motion. Influence line identification method based on dynamic testing is often interfered by the vehicle-bridge coupling vibration and the measurement noise. A deflection influence line identification method based on VMD and B-spline basis function was proposed in this article. The VMD was introduced to eliminate the dynamic fluctuation component, and then the quasi-static response could be extracted. The optimal decomposition parameters of VMD were determined by permutation entropy and GWO algorithm. The B-spline basis function was used to expand the influence line, and the identification of influence line was transformed to solve the weight coefficients of the basis function, which would greatly reduce the number of unknown variables and smooth the local fluctuations caused by noise. Finally, the feasibility and accuracy of the proposed method were verified by a numerical simulating and experimental testing, and the influence of various parameters such as vehicle speed, vehicle weight and road roughness were investigated. The results showed that the proposed method could effectively eliminate the fluctuation disturbance, and the deflection influence line could be identified with accuracy acceptable for engineering applications.

It is extremely challenging to directly measure the dynamic displacement which is essential in bridge state evaluation. The indirect physical-driven displacement reconstruction methods are restricted by the deviation existing between mechanism model and actual bridge, while indirect data-driven methods are restricted by requirement for a large amount of data. This paper proposes a physics-informed recurrent neural network (PI-RNN) based dynamic displacement reconstruction method. Firstly, the recurrent neural network is established, and the physical equation between data of measured points and target points are derived. Then, the derived physical equation is represented as physical information and added in the loss function of the network. Thus, the loss function contains a physical-based regularization term, which can guide the training direction of the network model, alleviate the over-fitting problem, and improve the generalization ability of the network. Subsequently, the displacement response reconstruction procedure based on PI-RNN is provided in detail. Finally, the effectiveness and superiority of the proposed method are verified by numerical and experimental examples. The results indicate that the PI-RNN is superior to RNN in terms of accuracy and efficiency in reconstruction bridge displacement.

Because of overloading, damage accumulation, and inadequate maintenance, many early RC hollow-slab bridges are experiencing a decline in a technical condition, with some even facing insufficient load-bearing capacity. Therefore, estimating the deflection verification coefficient (DVC) for evaluating the load-bearing capacity in a timely manner is crucial to ensuring the safe operation of such bridges. The normally used technical condition evaluation in China can only determine the grade of a bridge's technical condition, without directly providing the DVC for assessing the actual load-bearing capacity, which means that the data of technical condition evaluation are still underutilized. This paper develops a method for estimating the DVC of an RC hollow-slab bridge based on the technical condition index (TCI). Firstly, TCIs associated with load-bearing capacity are extracted from the qualitative and quantitative descriptive information regarding diseases and local damage from periodic inspection reports of an RC hollow-slab bridge. Secondly, an extreme learning machine (ELM) correlation model is established between the TCIs and the DVC of the RC hollow-slab bridge. Subsequently, a method for estimating the DVC of the RC hollow-slab bridge based on the measured TCIs is proposed. Finally, numerical examples and field tests are conducted to validate the effectiveness and applicability of the proposed method. The results indicate that it effectively leverages technical condition evaluation data to estimate the DVC with high accuracy and connects the gap between technical condition evaluation and load-bearing capacity evaluation. The established ELM correlation model is universally applicable to similar-type bridges, which is of benefit to address the traditional issues of traffic disruption, heavy workload, and high costs associated with a static load test.

Bridge dynamic displacement reconstruction methods based on neural networks usually use single-input neural networks, and most of the hyperparameters are determined by experience, which seriously affect the reconstruction accuracy. In this paper, a reconstruction method for bridge displacement response induced by moving load is proposed by using a small number of sensors and a triple-input IPSO-BiLSTM network. Firstly, the input strain and acceleration data are normalized in advance for data fusion. Secondly, IPSO-BILSTM network model with three-time sequence responses as input is constructed, and IPSO algorithm is used to optimize the network hyperparameters. Finally, three-time sequence responses are input into the trained iterative particle swarm optimization (IPSO)-Bidirectional LSTM (IPSO-BiLSTM) neural network to reconstruct the bridge displacement response. The proposed IPSO-BiLSTM network realizes the data fusion of three-time sequence responses and automatically establishes the relationship between input response and output displacement. Numerical examples indicate that the reconstruction accuracy is sensitive to road roughness and measurement noise. Experimental studies reveal that the reconstruction accuracy is insensitive to vehicle velocity and weigh.

Full-field dynamic displacement (FFDD) is important for bridge condition assessment. However, it is challenging to monitor the FFDD with high accuracy due to limited sensors and environment variation. This paper proposes a FFDD reconstruction method for bridge based on modal learning. Firstly, the transfer function of dynamic strain response of finite points (SRFP) and FFDD are derived based on the beam bending theory and modal superposition method. Then iterative particle swarm optimization (IPSO) is employed to facilitate self-learning of mode shape with the ability of adapting environment variation. Subsequently, the procedure for reconstructing bridge FFDD by utilizing SRFP and the learned transfer function is provided. Finally, the effectiveness of the proposed method is verified by numerical and experimental examples of bridge under random load, impact load, and moving load excitation, and effects of sensor placement, road roughness, and measurement noise on the reconstruction accuracy are systematically investigated. The results indicate that the proposed method can accurately reconstruct the FFDD in the presence of environment variation, road roughness, and measurement noise at the cost of limited sensors.

Finite element model (FEM) updating is widely used in damage identification for its clear physical meaning and standardized process. However, the traditional FEM is updated by an iterative algorithm, which suffers from low-computational efficiency. There are too many parameters that need to be updated and hence it is difficult to converge during optimization. Besides, the FEM and the information used for updating are uncertain for real bridges, which seriously affect the effectiveness of damage identification. This paper proposes a probabilistic identification method for structural damage by using the non-iterative eigenstructure assignment (ESA)-based FEM updating. First, a non-iterative ESA-based FEM updating approach is proposed by using the frequency and mode shape. Second, the damage location is determined by comparing the global stiffness matrix of the FEM before and after updating. Third, the elemental damage severity is estimated according to the functional relationship between the principal diagonal element variation in the global stiffness matrix and the elemental damage severity. Then, a probabilistic damage identification method is presented considering the uncertainty effects by combining Monte Carlo and non-iterative ESA- based FEM updating. Finally, the effectiveness and superiority of the proposed damage identification method are verified by numerical and experimental examples. The results indicate that the non-iterative technique substantially improves the efficiency of FEM updating and damage identification of bridges considering its uncertainty.

The main girder dynamic alignment (MGDA) is important in condition assessment of cable-stayed bridges during operation. However, it is challenging to measure the MGDA of cable-stayed bridge with high-accuracy due to the limited sensor number. This paper proposes an indirect reconstruction method for MGDA of cable-stayed bridge based on physics-informed neural network (PINN) and few sensors. Firstly, the cables of cable-stayed bridge are simplified as continuously elastic supports, and the dimensionless motion equation of the simplified model is derived accordingly. Then, two surrogate models are developed with neural network to simulate MGDA and external excitation, and the Fourier embedding layer is incorporated into the network. Besides, the spatial and temporal causal weights are added in to the physics-informed loss function to improve the model approximation, and different total loss functions are calculated for training the two surrogate models. Thirdly, the procedures for reconstructing the MGDA of cable-stayed bridge based on the developed PINN are provided in detail. Finally, the effectiveness of the proposed method is verified by numerical experiments, and the effects of sensor number, road roughness, damage state and measurement noise are systematically explored. The results indicate that the proposed method takes advantage of the PINN in calculating structural response with sparse data, and can accurately monitor the MGDA of a cable-stayed bridge indirectly with limited sensor number.

To advance the intelligent operation and maintenance of bridges, a deep learning-based acoustic emission (AE) data clustering framework was developed for evaluating fatigue cracks in welded joints under conditions of operational noise interference and complex damage mechanisms. Specifically, a convolutional autoencoder (CAE) model was implemented to extract damage-sensitive features from AE wavelet images. Additionally, a physics-guided single-and-cross-case strategy using Gaussian mixture models (GMMs) was presented to diagnose overlapping microscopic noise and damage mechanisms across different cases with various crack lengths. Field tests demonstrated the efficiency of the proposed framework to distinguish AE data induced by noise, crack propagation, surface fretting, and impact, enabling accurate identification of no-damage, minor-damage, and serious-damage cases according to their characteristic mechanisms. Future work will incorporate long-term monitoring data from additional cases to further refine the damage quantification and enhance the overall robustness.

A mode shape identification (MSI) approach is developed based on the instantaneous frequency (IF) of moving vehicle-bridge system (VBS) in this study. Firstly, the relational expression between the IF of VBS and the bridge mode shape (MS) is deduced. Then, the system IF is tracked through synchroextracting transform and used to reconstruct MS accordingly. A numerical case is performed to manifest the precision of the proposed approach.

Transfer learning-based damage identification is widely explored as it can utilize prior damage knowledge from finite element model (FEM) to identify damage without real structure damage labels. However, lacking a substantial amount of real structure data and overlooking the variances in conditional (local) distributions between source domain (data generated by FEM) and target domain (real structure data) severely restrict its practical application. This paper proposes a transfer learning-based damage identification method by combining Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and Dynamic Adversarial Adaptation Network (DAAN). Firstly, WGAN-GP generative model is employed to augment real structure samples to address the issue of insufficient data. Then, an optimization transfer model with the capability of balancing the importance of marginal and conditional distributions between FEM data and real structure data is proposed based on DAAN transfer model. It dynamically learns damage-invariant features for damage identification. Thirdly, damage identification procedures are provided by combining the generative model WGAN-GP and the transfer model DAAN with moving load induced responses as inputs. Numerical and experimental examples indicate that the proposed method achieves superior transfer effect with limited real structure data and maintains high damage identification accuracy compared to the traditional transfer learning-based methods.

Uncertain parameters with spatial dependency exist in actual bridges inevitably, which significantly affect the bridge dynamic response. However, such spatial dependency is often neglected when investigating its influence on bridge response. This study proposes a bridge dynamic response analysis method considering the spatial dependency of uncertain parameters. Firstly, the bridge uncertain parameter is described by a non-probabilistic interval field model, and the spatial dependency between adjacent values of the interval field is quantified by the Karhunen-Loe`ve like expansion. Thus the bridge is transformed into a system with multidimensional interval parameters by finite element method. Then, the system with multidimensional interval parameters is decomposed into several one-dimensional subsystems with only one interval parameter. Finally, the interval parameters of each one-dimensional system are divided into several subintervals with small uncertainties, and the dynamic response is obtained by combining analysis of subinterval results. Numerical examples are used to verify the accuracy and efficiency of the proposed method, and the results indicate that the proposed method significantly reduces the computational effort and improves the computational efficiency. Higher level of spatial dependency of the interval field, larger subinterval number, and lower uncertainty level of the non-probabilistic interval field leads to higher dynamic analysis accuracy.

This paper presents a moving force identification (MFI) approach based on dictionary learning (DL) with double sparsity.Firstly, the MFI equation is established, and a sparse dictionary model is designed.Then the sparse K-singular-value-decomposition (K-SVD) algorithm is employed for dictionary learning.Finally, the moving forces is identified via force dictionary and double sparse codes.Numerical example of a simply supported beam subjected to a moving force is used to verify the effectiveness of the proposed approach.

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