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Rail transit’s wheel–rail system periodically encounters defects such as wheel polygons, rail corrugation, and rail fastener failure, which are intricately linked to the modal parameters of track structures. Identifying these modal parameters is essential for refining wheel–rail dynamics models, understanding track defect mechanisms, and defect detection. This study reviews the current methodologies for identifying track structure modal parameters, emphasizing their significance in track engineering. It categorizes various identification techniques, examines their development, and highlights their application in updating track dynamics theoretical models. The relationship between track modal parameters and wheel–rail defects is discussed, alongside a summary of modal parameter-based defect remediation strategies globally. The paper also evaluates the current state of defect identification research utilizing track modal parameters. In the “prospects” section, three forward-looking research avenues are proposed. These approaches are poised to streamline and improve the efficiency of modal parameter extraction, marking potential breakthroughs in the field.

An accurate finite element model (FEM) plays a critical role in the structural damage identification. However, due to the existence of the uncertainties, such as material properties and modeling errors, it always exists some gaps between the analytical FEM and experimental structure. While an artificial neural network (ANN)-based model updating methods have been widely adopted to narrow the gap and obtain a baseline FEM, it still faces inaccurate results and fails to meet the physical law. In this regard, the study proposes a novel physics-based loss function inspired by modal sensitivity analysis and incorporates it into the residual neural network, thereby forming a novel physics-guided neural network (PGNN) method. The mapping relationship between the input of structural responses and output of model updating variables is constrained to retain its physical meaning by guiding the training process instead of pure data association, which aims to improve the accuracy of the ANN-based method and achieve accurate and high-efficiency model updating. An experimental example of a continuous rigid frame bridge is adopted to verify the feasibility of the proposed method. Additionally, other common model updating methods, including moth-flame optimization and regularization method, are used to make a comparison. The noise-robustness of the proposed method is investigated as well. Compared to the existing method, the results illustrate that the proposed PGNN method can achieve better model updating and good noise-robustness under high uncertainties, which means the introduction of the physics-based loss function significantly enhances the parameters updating ability of the neural network. The proposed method exhibits high efficiency and promising potential for large-scale bridge structure model updating.

The modeling, updating and validation of a structural health monitoring oriented finite element model (FEM) of the Tsing Ma suspension bridge towers are presented in this paper. The portal-type bridge tower is composed of two hollow reinforced concrete legs and four deep pre-stressed cross-beams with a steel truss cast in the concrete of each cross-beam to form a narrow corridor for access between two legs. Except that steel trusses are modeled by beam elements, all structural components are modeled by solid elements to facilitate local damage detection, in particular at member joints. The established tower model is then updated using sensitivity-based model updating method taking the natural frequencies identified from field measurement data as reference. Furthermore, a two-level validation criterion is proposed and implemented to examine the replication performance of the updated finite element model of the bridge tower in terms of (1) natural frequencies in higher modes of vibration and (2) dynamic characteristics of the tower-cable system. The validation results show that a good replication of dynamic characteristics is achieved by the updated tower model when compared to the field measurement results. Finally, stress distribution and concentration of the bridge tower are investigated through nonlinear static analysis of the tower-cable system.

In this paper, the simple genetic algorithm (SGA) is improved by combining with the simulated annealing algorithm (SAA) for the parameter identification of a reinforced concrete (RC) frame on elastic foundation. SGA adopts parallel search strategy, which is based on the concept of "survival of the fittest" in optimization while SAA adopts a serial form and the process is endowed with time-variety probable jumping property so that local optimization could be prevented. The global searching ability is developed by combining the two methods and the new algorithm is named genetic annealing hybrid algorithm (GAHA). Modal experiments were carried out on a four-storey RC frame structural model with isolated embedded footings in laboratory. The measured natural frequencies and mode shapes have been utilized to identify the physical parameters of the frame by the proposed method. Four cases of concrete elastic modulus and foundation dynamic shear modulus are identified, and the results are compared with the usual sensitivity methods (SM). By model updating, the results show that the elastic modulus of concrete increases with respect to the storey. The identified elastic modulus of the concrete is generally larger than that found by compressive testing because the dynamic modulus of concrete is larger than the static modulus of concrete. The identified soil dynamic shear modulus also increases with the storey since the soil property depends on the pressure exerted on the soil. It is also shown that the identified results by GAHA are better than that of SM.

A comparative study is performed for the direct and iterative methods for updating the structural matrices based on measured data. The former was derived from the orthogonality constraints by replacing the modal vector of concern by the modal matrix in computing the correction matrices. ¹ The iterative method used is the improved inverse eigensenstivity method. ² Through the numerical studies, it was demonstrated that both methods yield good results. However, the direct updating method is found to be more suitable for engineering applications due to its ease in treating multi-modes and higher efficiency, especially for complicated structures.

Traditional structural system identification and damage detection methods use vibration responses under single excitation. This paper presents an auto/cross-correlation function-based method using acceleration responses under multiple ambient white noise or impact excitations. The auto/cross-correlation functions are divided into two parts. One is associated with the structural parameters and the other with the energy of the excitation. These two parts are updated sequentially using a two-stage method. Numerical and experimental studies are conducted to demonstrate the accuracy and robustness of the proposed method. The effects of measurement noise and number of measurement points on the identification results are also studied.

This study proposes a new correlation improvement technique for the optimum node removal location to get improved modal assurance criterion (MAC) matrix. The technique is applied to updating of the finite element model (FEM) of a structure. The developed routine is tried on a utility helicopter. It is proven that it is capable of showing better performance than the coordinate MAC (coMAC), commonly used in such analyses. Commercial software is utilized for the finite element analysis of the helicopter fuselage and tail. Experimental modal analyses are also performed for updating the model for tail of the helicopter to demonstrate the effectiveness of the new technique.

Accurate modeling of damping is essential for prediction of vibration response of a structure. This paper presents a study of damping matrix identification method using experimental data. The identification is done by performing finite element (FE) model updating using normal frequency response functions (FRFs). The paper addresses some key issues like data incompleteness and computation of the normal FRFs for carrying out the model updating using experimental data. The effect of various levels of damping in structures on the performance of the identification techniques is also investigated. Experimental studies on three beam structures made up of mild steel, cast iron and acrylic are presented to demonstrate the effectiveness of the identification techniques for different levels of damping.

This paper presents a novel method to localize and quantify damage in a jack arch structure by introducing a linkage modeling technique to overcome issues caused by having limited sensors. The main strategy in the proposed Frequency Response Function (FRF)-based sensitivity model updating approach is to divide the specimen into partitions. The Young’s modulus of each partition is then updated to detect stiffness reduction caused by damage. System Equivalent Reduction Expansion Process (SEREP) is used to reduce the full finite element (FE) model to a linkage model. The number of measured degrees of freedom (DOFs) is then expanded to the linkage model using the mass and stiffness matrices of the linkage model for the synthesis of interpolated FRFs. The FRF sensitivities are then formulated using the linkage model along with the interpolated FRFs to iteratively calculate the values of the updating parameters until convergence is achieved. The methodology and theory behind this procedure are discussed and verified using a numerical and experimental study. The successful implementation of this method has the potential to detect the location and severity of damage where sensor placement is limited.

The necessity of detecting structural damages in an early stage has led to the development of various procedures for structural model updating. In this regard, sensitivity-based model updating methods utilizing mode shape data are known as effective tools. For this purpose, accurate estimation of the mode shape changes is desired to achieve successful model updating. In this paper, Wang’s method is improved by including measured natural frequencies of the damaged structure in derivation of the sensitivity equation. The sensitivity equation is then solved using an incomplete subset of mode shape data in evaluation of the changes of the structural parameters. A comparative study of the results obtained by the proposed method with those by the modal method for a truss and a frame model indicated that the former is significantly more effective for damage detection than the latter. Furthermore, the capability of the proposed method for model updating in the presence of measurement and mass modeling errors is investigated.

Model updating methods based on structural vibration data have been developed and applied to detecting structural damages in civil engineering. Compared with the large number of elements in the entire structure of interest, the number of damaged elements which are represented by the stiffness reduction is usually small. However, the widely used $l_2$ regularized model updating is unable to detect the sparse feature of the damage in a structure. In this paper, the $l_1$ regularized model updating based on the sparse recovery theory is developed to detect structural damage. Two different criteria are considered, namely, the frequencies and the combination of frequencies and mode shapes. In addition, a one-step model updating approach is used in which the measured modal data before and after the occurrence of damage will be compared directly and an accurate analytical model is not needed. A selection method for the $l_1$ regularization parameter is also developed. An experimental cantilever beam is used to demonstrate the effectiveness of the proposed method. The results show that the $l_1$ regularization approach can be successfully used to detect the sparse damaged elements using the first six modal data, whereas the $l_2$ counterpart cannot. The influence of the measurement quantity on the damage detection results is also studied.

Damage identification using the sensitivity of the dynamic characteristics of the structure of concern has been studied considerably. Among the dynamic characteristics used to locate and quantify structural damages, the frequency response function (FRF) data has the advantage of avoiding modal analysis errors. Additionally, previous studies demonstrated that strains are more sensitive to localized damages compared to displacements. So, in this study, the strain frequency response function (SFRF) data is utilized to identify structural damages using a sensitivity-based model updating approach. A pseudo-linear sensitivity equation which removes the adverse effects of incomplete measurement data is proposed. The approximation used for the sensitivity equation utilizes measured natural frequencies to reconstruct the unmeasured SFRFs. Moreover, new approaches are proposed for selecting the excitation and measurement locations for effective model updating. The efficiency of the proposed method is validated numerically through 2D truss and frame examples using incomplete and noise polluted SFRF data. Results indicate that the method can be used to accurately locate and quantify the severity of damage.

In the literature, modal kinetic energy (MKE) has been commonly utilized for optimal sensor placement strategies. However, there have been very few studies on its application to structural damage detection. This paper introduces a new two-stage structural damage assessment method by combining the modal kinetic energy change ratio (MKECR) and symbiotic organisms search (SOS) algorithm. In the first stage, an efficient damage indicator, named MKECR, is used to locate the potential damaged sites. Meanwhile, for the purpose of comparison with MKECR, three other indices are also used. In the second stage, an SOS-based finite element (FE) model updating strategy is adopted to estimate the damage magnitude of identified sites, while excluding false warnings (if any), where an objective function is proposed using a combination of the flexibility matrix and modal assurance criterion (MAC). The performance of the SOS algorithm is also verified by comparing with four other meta-heuristic algorithms. Finally, three numerical examples of 2D truss and frame structures with various hypothetical damage scenarios are carried out to investigate the capability of the proposed method. The numerical results indicate that the proposed method not only can accurately locate and quantify single- and multi-damage in the structures, but also shows a great saving in computational cost.

In order to predict more accurately the structural vibration and noise of elevated tracks induced by moving trains, a new prediction method based on the scaled model test is proposed in this paper. A 32-m simply supported box girder bridge used in the Beijing–Shanghai high-speed railway is selected as the prototype for designing and constructing a scaled model test with 10:1 geometric similarity ratio. Both experimental tests and finite element analyses were carried out to verify the similarity relationship between the model and prototype. The test result shows that the scaled model can predict the structural vibration and noise of the prototype, as long as the similarity constants between the prototype and scaled model are correctively determined. Furthermore, a standard finite element analysis model for the scaled model is built. Based on the sensitivity analysis, the model parameters for finite element analysis are updated by minimizing the errors between the measured and calculated modes. The computational results show that the updated model based on the local parameters partitioning works best, and the precision of the modal frequency calculated is noticeably improved after updating, with the average relative error reduced from 5.46% to 3.09%, and the difference of the peak values reduced from $0.358\times 10^3$m/s² to $0.189\times 10^3$m/s². The calculated dynamic response of the finite element model after updating is basically in line with experimental results, indicating that the updated model can better reflect the dynamic properties of the scaled box girder model. The updated finite element model is useful both for verification with the model test result and for reliable prediction of the dynamic characteristics of the prototype.

In practice, a model-based structural damage detection (SDD) method is helpful for locating and quantifying damages with the aid of reasonable finite element (FE) model. However, only limited information in single or two structural states is often used for model updating in existing studies, which is not reasonable enough to represent real structures. Meanwhile, as an output-only damage indicator, transmissibility function (TF) is proven to be effective for SDD, but it is not sensitive enough to change in structural parameters. Therefore, a multi-state strategy based on weighted TF (WTF) is proposed to improve sensitivity of TF to change in parameters and in order to further obtain a more reasonable FE model for SDD in this study. First, WTF is defined by TF weighted with element stiffness matrix, and relationships between WTFs and change in structural parameters are established based on sensitivity analysis. Then, a multi-state strategy is proposed to obtain multiple structural states, which is used to reasonably update the FE model and detect structural damages. Meanwhile, due to fabrication errors, a two-stage scheme is adopted to reduce the global and local discrepancy between the real structure and the FE model. Further, the $l_1$-norm and the $l_{1∕2}$-norm regularization techniques are, respectively, introduced for both model updating and SDD problems by considering the characteristics of problems. Finally, the effectiveness of the proposed method is verified by a simply supported beam in numerical simulations and a six-storey frame in laboratory. From the simulation results, it can be seen that the sensitivity to structural damages can be improved by the definition of WTF. For the experimental studies, compared with the FE model updated from the single structural state, the FE model obtained by the multi-state strategy has an ability to more reasonably describe the change of states in the frame. Moreover, for the given structural damages, the proposed method can detect damage locations and degrees accurately, which shows the validity of the proposed method and the reliability of the updated FE model.

Model updating is a widely adopted method to minimize the error between test results from the real structure and outcomes from the finite element (FE) model for obtaining an accurate and reliable FE model of the target structure. However, uncertainties from the environment, excitation and measurement variability can reduce the accuracy of predictions of the updated FE model. The Bayesian model updating method using multiple Markov chains based on differential evolution adaptive metropolis (DREAM) algorithm is explored, which runs multiple chains simultaneously for a global exploration, and it automatically tunes the scale and orientation of the proposal distribution during the evolution of the posterior distribution. The performance of the proposed method is illustrated numerically with a beam model and a three-span rigid frame bridge. Results show that the DREAM algorithm is capable for updating the FE model in civil engineering. It extends the Bayesian model updating method to multiple Markov chains scenario, which provides higher accuracy than single chain algorithm such as the delayed rejection adaptive metropolis-hastings (DRAM) method. Moreover, results from both examples indicate that the proposed method is insensitive to values of initial parameters, which avoid errors resulting from inappropriate prior knowledge of parameters in the FE model updating.

Marine platforms are located in complex environments, and safety deteriorates throughout the day. It is necessary to analyze the jacket platform structure by the finite element method. Problems such as platform structure variation and fatigue corrosion lead to model deviation. In this paper, a finite element model correction method based on deep learning is proposed with a jacket platform as the engineering background. First, different platform design parameters are selected, and the corresponding fundamental frequencies are obtained by finite element simulation. Second, the input features are extended as necessary to increase the damage-sensitive information, with the nonlinear differences between the two reduced by an improved ResNet50 network. Finally, the correction values of the finite element model are obtained by combining the measured data with the inherent structural frequencies obtained by covariance-driven stochastic subspace identification (Cov-SSI). The results show that the error after correction is less than 4%, which can reflect the real marine platform state well.

Real-time hybrid simulation (RTHS) is an economical and reliable method for the evaluation of structural dynamic performances, and the fixed analytical substructure model is often used in RTHS which may affect the accuracy of results. In this study, a real-time hybrid simulation platform (RTHSP) developed by configuring a generic National Instruments (NI) controller with hybrid programming strategy is presented in detail. The dynamic performances of a scaled base isolated structure, where the unscented Kalman filter (UKF) was used to update the analytical substructure Bouc–Wen model during the RTHSs was evaluated by presented RTHSP. RTHS of a base-isolated structure was performed where a lead rubber bearing (LRB) was tested physically as the experimental substructure of a part of the isolation layer and the superstructure with the rest of the isolation layer model updated by UKF was considered as the analytical substructure. Under the excitation of three natural earthquakes, the RTHSs with and without UKF updating were compared and analyzed the differences between the two. The results indicated that the displacements of experimental substructure generated by RTHS with UKF updating are the largest, while the relative displacements and acceleration of superstructure are the smallest overall, and the dynamic characteristics of the isolation layer of the analysis substructure updated by UKF are different from that without updated, which reflected the more authentic dynamic mechanical performance of the base-isolated structure under earthquake excitation. In addition, the RTHSP and the hybrid programming strategy are verified to be reliable in tests and experiments, and the components and implementation of a RTHSP for base-isolated structures is described in detail, providing a reference for research on RTHS method.

The $l_2$ regularization is usually used to deal with the problems of under-determinacy and measurement noise for the conventional sensitivity-based model updating damage detection methods. However, the $l_2$ regularization technique often provides overly smooth solutions and thus cannot exhibit the sparsity of the structural damage due to the promotion of the 2-norm term on smoothness. In the study, a structural damage detection method is proposed based on an improved modal flexibility sensitivity function and an iterative reweighted $l_p$ (IR$l_p)$ regularization. Specifically, the sensitivity function is established by introducing changes in the mode shapes into the derivative of eigenvalue and can be applied to identify the localized damage more accurately. Additionally, IR$l_p$ regularization is proposed to deal with the ill-posed problem of damage detection in a noisy environment. The proposed IR$l_p$ regularization is compared with the $l_1$ and $l_2$ regularizations through a numerical and an experimental examples. The numerical and experimental results indicate that the IR$l_p$ regularization can more accurately locate and quantify the single and multiple damages under the noise situation. The maximum identification errors are only 5.16% and 5.67%, respectively. Moreover, compared to the basic modal flexibility sensitivity function, the improved function is more sensitive to the damage. The maximum identification error of the improved function is less than 6%, while the relative errors are significantly larger in the basic function.

Aiming to enhance the accuracy, stability, and noise robustness of swarm intelligence-based algorithms for structural damage identification (SDI), a novel improved dragonfly algorithm (IDA) is proposed. The IDA integrates the dragonfly algorithm (DA) with three key strategies including enhanced Lévy flight, optimal solution bidirectional search, and greedy preservation. These strategies are introduced to enhance the exploration capability of the original DA and improve the IDA’s capacity to obtain global optima. An objective function is defined using frequency change ratio and flexibility assurance criterion (FAC). Additionally, trace sparse regularization is also incorporated into the objective function since most of the damages in structures tend to be sparsely distributed, so that a sparse result is ensured to improve SDI accuracy. To evaluate the performance of the proposed algorithm, a comparison of the original DA and IDA is conducted using four benchmark functions. The results demonstrate that the proposed algorithm achieves improved convergent rate and accuracy. Furthermore, numerical simulations are performed on a 10-element simply-supported beam and a 31-element planar truss to validate the effectiveness and efficiency of the proposed algorithm in SDI. Significantly, the utilization of IDA instead of DA leads to a substantial reduction in the average calculated relative error for the truly damaged element within the considered damage cases of the simply-supported beam, decreasing from 13.05% to 6.15%. Moreover, an experimental simply-supported beam structure with several assumed damage cases is fabricated in the laboratory. The experimental results further confirm the robustness and capability of the proposed method in real-world SDI applications.