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This study investigates the enhancement of optimal sensor placement (OSP) algorithms by incorporating modal reduction constraints and developing combined techniques. The primary goal is to optimize sensor placement for structural health monitoring (SHM), thereby improving the efficiency of information acquisition within practical constraints. The proposed methodology utilizes iterative elimination and combined criteria to evaluate various sensor configurations. Numerical experiments demonstrate distinct sensor layouts derived from diverse algorithmic approaches. The study's novel contributions include the integration of modal strain energy, effective independence (EI), and modal assurance criterion (MAC) techniques into a unified framework, enhancing adaptability to a wide range of SHM scenarios. [ABSTRACT FROM AUTHOR]

In order to improve sensitivity and noise immunity of a single index to damage in damage identification, based on modal strain energy theory, a two-level feature fusion method combining principal component analysis (PCA) and entropy weight method (EWM) were proposed. The northern goshawk optimization (NGO) algorithm combined with gated recurrent unit (GRU) were used for bridge damage degree prediction. Firstly, based on traditional modal strain energy theory, the diagonal modal strain energy ratio was constructed, and then change rate of the diagonal modal strain energy ratio, dissipation rate of the diagonal modal strain energy ratio, and normalized difference index of the diagonal modal strain energy ratio were derived. Secondly, principal component analysis was used to extract features within the index, and entropy weight method was used to fuse features between indexes. Finally, weighted decision index (WDI) was constructed. The single modal strain energy derivative index was input into the NGO-GRU hybrid neural network, as well as damage degree was output, so as to established the relationship between index value and damage degree, and then realized damage quantification. The proposed method was verified by a three-span continuous beam bridge numerical model. The results show that weighted decision index has good damage location ability and noise immunity. The hybrid neural network has high damage prediction accuracy, with a prediction accuracy rate of 91. 14% . [ABSTRACT FROM AUTHOR]

Passive damping treatments using viscoelastic materials (VEMs) are widely applied as addon solutions to control the dynamic response of light structures. These surface treatments are simple, reliable, and can be optimized by using proper design rules and simulation tools. In this work, a new treatment configuration is proposed, simulated, and assessed, being compared with the most effective configuration currently used. The novelty resides in the VEM layer's geometry, which in the proposed configuration assumes a waved shape. This waved shape is imposed to the viscoelastic layer due to indentations created in the inner faces of the host structure and the constraining layer. The results demonstrate that the wavy configuration, designated as corrugated viscoelastic layer (CVL), outperforms the typical damping treatments for relatively thick host structures and when using thick VEM layers. In addition, this new configuration reduces the stiffness decoupling effect due to the soft VEM layer, restoring the flexural stiffness of the original undamped structure. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of structural damage localization, a method to locate structural damages is proposed by combining the cross-model modal strain energy and the wavelet analysis(WA). Firstly, indices based on cross-modelmodal strain energy of all elements have been calculated. Secondly, the wavelet analysis is conducted on the sequence composed of the calculated indices of all elements, with high-frequency detail coefficients extracted to form the improved damage index. Finally, damage locations are judged according to the improved index. A planar truss is taken as the numerical example, with the Monte Carlo analysis carried out in consideration of 5% noise level. The result shows that the improved index is more robust to resist noise interference and can better indicate damage locations.

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In this study, an efficient method for determining the accurate location of damage to structures is introduced using an optimal sensor placement (OSP) and modal strain energy-based index (MSEBI). The research is implemented in two main stages. In the first stage, a correlation function between the reconstructed mode shapes using the iterated improved reduced system (IRS) method and the complete mode shapes of a structure is defined and then the function is minimized via the binary differential evolution (BDE) algorithm to find the optimal sensor placement of the structure. In the second stage, the location of damage is determined using MSEBI based on the optimum place of sensors obtained already. In order to assess the efficiency of the proposed method, two standard examples, including a two-dimensional (2-D) frame structure with 45 elements and a 2-D truss with 47 elements, are examined. Numerical results, considering different conditions, demonstrate that the integration of OSP method and MSEBI can provide an efficient tool for accurate and rapid identification of the damage location. The parametric study shows that the proposed method has a low sensitivity to the number of modes and noise level, and it can properly identify damage by considering a few modes and the high level of noise.

Vibration-based damage detection is a range of methods that utilizes the dynamic response of a structure to evaluate its condition and detect damage. It is an important approach for structural health monitoring and has drawn much attention from researchers. While multiple reviews have been published focusing on different aspects of this field, there has not been a study specifically examining the recent development across the range of methods, including natural frequency, mode shape, modal curvature, modal strain energy, and modal flexibility-based damage detection methods. This paper aims to fill this gap by reviewing the recent application of these methods in civil structures, including beams, plates, trusses, frames, and composite structural members. The merits and limitations of each method are discussed, and research opportunities are presented. This broader review also provides an opportunity for critical comparison across this range of methods. While predominantly reviewing experiment-based studies, this review also considers some numerical studies that may motivate further research.

A damage detection and localization method for wooden beams was proposed based on the modal strain energy (MSE) change and evidence fusion. The fused damage indicator was deduced using the first three mode shapes of the wooden beams before and after damage. The finite element modal analysis of the free-supported undamaged and damaged wooden beams with different damage severities at one or two locations was performed. The first three mode shapes were extracted from the corresponding modal analysis, with which the damage indicator based on the MSE change and the fused damage indicator of each damage case were computed. The simulation results show that the fused damage indicator accurately detected and located the damage with different severities at one or two locations. Finally, the modal test was completed using the same damage cases as the finite element simulation. The frequency functions of the whole beam were first obtained, with which the first three experimental mode shapes were then acquired, and the damage indicator based on the MSE change and the fused indicator were further computed. The test results verified the validity and reliability of the proposed damage indicator.

• A continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. • Combination of modal truncation order and sensor layout optimization by modal strain energy. • The proposed algorithm has better accuracy and noise immunity than SSM and GKFM. • For continuous systems, the proposed algorithm has a solution time of 0.38s and is insensitive to the time step. • The proposed algorithm has good accuracy in experimental validation. Dynamic load identification based on structural responses is an important problem in the field of engineering and plays an important role in the condition assessment of mechanical structures. Current popular load identification methods such as the state-space method (SSM) and the Green's kernel function method (GKFM) are implemented on discrete systems with outstanding performance, but when dealing with complex continuous systems, there are some limitations such as low efficiency and inaccuracy. In this paper, a continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. Using modal coordinate transformation and modal truncation methods, the number of infinite vibration differential equations of a continuous system in physical space are converted to a finite number of vibration differential equations in modal space, where the modal truncation order and the optimal layout of the sensors are combined by modal strain energy. The Newmark-β method in modal space is derived and thus combined with SSM to obtain a load identification model Y =HF called SSM-Newmark-β method, which reduces the size of the transfer matrix H. The solution time of the proposed algorithm is 0.38 s for continuous systems, which is rather shorter than that for discrete systems. Furthermore, the simulations show that it has better accuracy and noise immunity than SSM and GKFM in the identification of sinusoidal load, impact load, and random load. The effect of time step is also discussed which reveals that the larger time step has less effect on the proposed algorithm. An experimental study is carried out on a cantilever beam system. The result verifies that the SSM-Newmark-β algorithm has better accuracy in load identification for the continuous system. This research provides a new sight for the real-time identification of dynamic loads for complex structures. [ABSTRACT FROM AUTHOR]

Identification of crack location and severity is a vital step in assessment of deteriorated structures. The current research addresses the sensitivity of using modal displacement, modal curvature, and modal strain energy functions as Damage Indices (D.I.s) for crack detection. Comparison of these indicators at cracked and undamaged conditions was performed. Firstly, Damage Index (D.I.) method was utilized on synthetic data obtained with the aid of finite element modelling on different flexural elements. The technique was again used to identify cracks for physical scaled-down masonry walls. Three clayey bricks walls with different thicknesses and crack configurations were prepared for this purpose. Each wall was tested in its virgin and damaged states. Formal modal analysis was conducted. It was concluded that all the used D.I.s were accepted as damage indicators. It can also be stated that the relative severity between cracks can be obtained. Numerically, D.I. method was found effective in cases of multiple or inclined cracks. Generally, the identification based on curvature functions, were better than displacement functions for the same number of monitoring points and crack severity. Curvature can’t, however, be easily obtained for sophisticated structures with limited data. Moreover, the detection process became easier as the crack dimensions increased.

Identification of crack location and severity is a vital step in assessment of deteriorated structures. The current research addresses the sensitivity of using modal displacement, modal curvature, and modal strain energy functions as Damage Indices (D.I.s) for crack detection. Comparison of these indicators at cracked and undamaged conditions was performed. Firstly, Damage Index (D.I.) method was utilized on synthetic data obtained with the aid of finite element modelling on different flexural elements. The technique was again used to identify cracks for physical scaled-down masonry walls. Three clayey bricks walls with different thicknesses and crack configurations were prepared for this purpose. Each wall was tested in its virgin and damaged states. Formal modal analysis was conducted. It was concluded that all the used D.I.s were accepted as damage indicators. It can also be stated that the relative severity between cracks can be obtained. Numerically, D.I. method was found effective in cases of multiple or inclined cracks. Generally, the identification based on curvature functions, were better than displacement functions for the same number of monitoring points and crack severity. Curvature can't, however, be easily obtained for sophisticated structures with limited data. Moreover, the detection process became easier as the crack dimensions increased. [ABSTRACT FROM AUTHOR]

A convolutional neural network (CNN)-based structural damage detection (SDD) method using populations of structures and modal strain energy (MSE) is proposed. In this study, sufficient samples of the CNN are provided by numerical simulations, and the size of the model can be changed by modifying the coordinates of some nodes, thereby establishing a series of numerical models (i.e., a population). Finally, three groups are investigated, the effects of multiple indices on damage detection based on population are compared. The results demonstrate that the MSE as a damage index is superior to the other indices. [ABSTRACT FROM AUTHOR]

The conventional modal strain energy (MSE), as a practical objective function, suffers from the lack of access to the damaged stiffness matrix and uses the intact stiffness matrix of the structure instead. To overcome the aforementioned deficiency of the MSE, this study proposes a reformed elastic strain energy-dissipation criterion called the "augmented modal strain energy" (AMSE) which is composed of relative differences of natural frequency and mode shape. In the AMSE not only the effects of the energy-dissipation criterion as a function of natural frequency but also the equilibria of the elastic strain energy as a function of mode shape are considered. Hereupon, the AMSE is implemented along with the interactive autodidactic school (IAS) optimization algorithm to investigate the effectiveness of the proposed identification method. In this regard, the AMSE is verified by assessing three benchmark truss and frame structures. The obtained results confirm the reliable performance of AMSE in both terms of intensification and diversification. Furthermore, it is observed that despite using noise-polluted modal data, the proposed AMSE not only identifies the damage location accurately, but also anticipates the extent of damage precisely. Consequently, the proposed energy-dissipation-based objective function (AMSE) is suggested, along with the IAS optimization algorithm, as a robust technique for the damage detection of structures. [ABSTRACT FROM AUTHOR]

Change in modal strain energy is one of the indicators used to detect damage in structures. However, in structures with high degrees of freedom, such as double-layer grids, this method requires a relatively large number of mode shapes which in practice is difficult to determine. Therefore, it is necessary to reduce the number of required mode shapes. In this study, a damage detection technique based on modal strain energy and Dempster-Shafer evidence theory is presented for locating damage in double layer grids using only a few number of mode shapes. First, by calculating mode shapes of the grid in undamaged and damaged states, the modal strain energy based index for each mode shape is determined. Then, the results obtained from separate mode shapes are combined using Dempster-Shafer theory to achieve better results. In order to investigate the effect of noise on damage detection, 3% random noise is added to mode shapes. To demonstrate the performance of the proposed method, different single and multiple damage cases with different damage intensities are considered. Numerical results show that using 5 mode shapes, the presented technique can detect up to 3 damaged elements with different damage intensities in different parts of the grid with good accuracy (probability of 92.3%). Considering the fact that the classical modal strain energy method fails to distinguish even 1 damaged element in the double layer grid, the result shows significant improvement.

Structural damage inspection is a key structural engineering technique that strives for ensuring structural safety. In this regard, one of the major intelligent approaches is the inverse analysis of structural damage using evolutionary computation. By considering the recent advances in this field, an efficient hybrid objective function that combines the global modal kinetic and modal strain energies is introduced. The newly developed objective function aims to extract maximum dynamic information from the structure and overcome noisy conditions. Moreover, the original methods are usually vulnerable to the associated high multimodality and uncertainty of the inverse problem. Therefore, the oppositional learning (OL) for population initialization and convergence acceleration is first adopted. Thereafter, the unified particle swarm algorithm (UPSO) mechanism is combined with another newly developed algorithm, the gradient-based optimizer (GBO). The new algorithm, called the oppositional unified particle swarm gradient-based optimizer (OL-UPSGBO), with the convergence acceleration feature of (OL), enhances balanced exploration-exploitation of UPSO, and the local escaping operator of GBO is designed to specifically deal with the complex inverse analysis of structural damage problems. To authenticate the performance of the OL-UPSGBO, the complex benchmark set of CEC 2017 is adopted to compare the OL-UPSGBO with several original metaheuristics. Furthermore, the developed approach for structural damage identification is tested using several damage scenarios in a multi-story frame structure. Results show that the developed approach shows superior performance and robust behavior when tackling the inverse analysis of structural damage. [ABSTRACT FROM AUTHOR]

In this paper, two typical examples are used to illustrate the weak position of aircraft structure in the process of vibration. Through the modal analysis of the typical composite plate and I-shaped beam, the first 20-order modal strain energy of the plate is extracted, which is difficult to locate the weak spot due to the highly scattered location of the higher modal strain energy. The modal participation factor is introduced as the weight factor of the summation of the modal strain energy. The modal participation factor is large, the weighting factor is large, and the high modal strain energy of the composite plate moves diagonally in the 45° direction of the composite plate and the high strain energy region is consistent with the previous modes of the plate. This is the result of the weak in-plane shear stiffness of the composite panel, which shows the effectiveness of the mode weighted summation method. The I-shaped composite beam uses the modal strain energy summation of the weight factor, and the higher modal strain energy is concentrated on the middle part of the beam and at 1/4 and 3/4 of it. Therefore, the weak part of the vibration can be clearly identified. The higher modal strain energy is extracted by the method proposed to this paper, which can be used as a reference to structural design and dynamic on-line monitoring. [ABSTRACT FROM AUTHOR]

Damage detection is a critical aspect of structural health monitoring. The Kalman filter (KF) has been used in various methods for detecting structural damage based on online measurement data. Due to noise in the sensor responses and errors in the damage detection process, the damage detection process's accuracy is reduced. This study proposes a novel method for resolving this issue by integrating the Kalman filter and sensitivity analysis (KFSA). The damage detection problem has been considered as a state estimation problem in this method, with the system's state estimated using the KF. In this problem, the damage is considered a random phenomenon in the state equation, and the damage detection equation is used as the observation equation via sensitivity analysis (SA). Due to the randomization of the state equation and the resulting increase in accuracy, damages are accurately detected among the suspected damaged elements obtained via modal strain energy. The numerical validation of structures is carried out under various damage scenarios. The comparative results demonstrate that the proposed method for detecting damage is exact and can be used for the structural health monitoring of in-service civil structures. [ABSTRACT FROM AUTHOR]

Identifying relatively weak areas is of great significance for improving the seismic reliability of structures. In this paper, a modal strain energy decomposition method is proposed, which can realize the decoupling of the comprehensive modal strain energy of a planar structure into three basic modal strain energies. According to the decomposition results, the modal strain energy decomposition diagram and the modal strain energy cloud diagram can be drawn so as to realize the quantitative and visual analysis of the vibration modes. The method is independent of load cases and can identify relatively weak areas of a structure from the perspective of inherent characteristics. The comparison with the shaking table test results of the two-story shear wall shows that the modal strain energy decomposition method can effectively identify the type of the relatively weak area of a structure and locate the position of the relatively weak area. Finally, the 6-story shear wall is analyzed by the modal strain energy decomposition method, and the relatively weak areas under the first two vibration modes are identified. [ABSTRACT FROM AUTHOR]

Structural health monitoring is used to control the health of regularly deteriorating special structures or those subjected to sudden loading. Damage localization and severity estimation are important goals of researchers. In this study, an existing modal strain energy-based approach is enhanced by a proposed updating procedure to detect damage and estimate severity. Numerical validation is conducted on a cantilever beam and a portal frame. The updated results obtained using the suggested technique are better compared with those of the existing method. On the basis of only the fundamental mode shape, the updating technique can successfully localize damaged elements regardless of the complexity of damage scenarios, and it can estimate severity with acceptable accuracy levels as long as the modal data are free of noise or submerged in noise at low levels. [ABSTRACT FROM AUTHOR]

The subject of structural health monitoring and damage identification of structures at the earliest possible stage has been a noteworthy topic for researchers in the last years. Modal strain energy (MSE) based index is one of the efficient methods which are commonly used for detecting damage in structures. It is also more effective and economical to employ some methods for reducing the degrees of freedom in large-scale structures having a large number of degrees of freedom. The purpose of this study is to identify structural damage via an index based on MSE and reconstructed mode shapes. The Guyan reduction method (GRM) is utilized here to reconstruct the mode shapes. Therefore, in the first step by employing GRM, mode shapes in slave degrees of freedom are estimated by those of master degrees of freedom. In the second step, the modal strain energy based index (MSEBI) is used to find the location of damaged elements. In order to assess the efficiency of the method, two standard examples are considered. Damage is identified with considering complete mode shapes and reconstructed mode shapes, and the results are compared together. The outcomes show that the combination of MSE and GRM can be useful for the structural damage detection, when considering the noise.

The structural health of operational metro tunnels is closely related to public safety. Prior research has focused on the locations of structural damage, but few researchers have examined both the location of damage and identifying the degree of damage, especially in metro shield tunnels. This paper proposes a new method for identifying structural damage that entails locating and detecting the degradation of tunnel performance, with a special focus on characterizing the degree of damage. First, the dynamic behaviors (modal frequencies and shapes) of different damage levels are obtained from an analytical model of the original tunnel structure. Second, a modal strain energy damage indicator (MSEDI) is introduced to locate the damage, regardless of size. Once the location of the damage is identified using MSEDI, a fuzzy logic-based damage identification (FLBDI) method is used to determine the actual extent of the damage. Finally, a simplified model of the tunnel is created using the Euler-Bernoulli beam theory and Winkler's foundation, to further test the procedure under an incomplete modal information condition and with differing noise levels. The results reveal that the fuzzy logic- based system can identify the degree of damage and structural degradation with very high accuracy, in which the location of damage and the prediction of performance degradation is satisfactorily confirmed. [ABSTRACT FROM AUTHOR]

Change in modal strain energy is one of the indicators used to detect damage in structures. However, in structures with high degrees of freedom, such as double-layer grids, this method requires a relatively large number of mode shapes which in practice is difficult to determine. Therefore, it is necessary to reduce the number of required mode shapes. In this study, a damage detection technique based on modal strain energy and Dempster-Shafer evidence theory is presented for locating damage in double layer grids using only a few number of mode shapes. First, by calculating mode shapes of the grid in undamaged and damaged states, the modal strain energy based index for each mode shape is determined. Then, the results obtained from separate mode shapes are combined using Dempster-Shafer theory to achieve better results. In order to investigate the effect of noise on damage detection, 3% random noise is added to mode shapes. To demonstrate the performance of the proposed method, different single and multiple damage cases with different damage intensities are considered. Numerical results show that using 5 mode shapes, the presented technique can detect up to 3 damaged elements with different damage intensities in different parts of the grid with good accuracy (probability of 92.3%). Considering the fact that the classical modal strain energy method fails to distinguish even 1 damaged element in the double layer grid, the result shows significant improvement. [ABSTRACT FROM AUTHOR]

Damage detection through an inverse optimization problem has been investigated by many researchers. Recently, Modal Strain Energy (MSE) has been utilized as an index (MSEBI) for damage localization that serves to guide the optimization. This guided approach considerably reduces the computational cost and increases the accuracy of optimization. Although this index mostly exhibits an acceptable performance, it fails to find some damaged elements' locations in some cases. The aim of this paper is twofold. Firstly, a Graph-based Adaptive Threshold (GAT) is proposed to identify some of those elements that are not detected by basic MSEBI. GAT relies on the concepts from graph theory and MSE working as a simple anomaly detection technique. Secondly, an Improved version of the Water Strider Algorithm (IWSA) is introduced, applied to the damage detection problems with incomplete modal data and noisecontaminated inputs. Several optimization algorithms, including the newly-established Water Strider Algorithm (WSA), are utilized to test the proposed method. The investigations on several damage detection problems demonstrate the GAT and IWSA's satisfactory performance compared to the previous methods. [ABSTRACT FROM AUTHOR]

Structural damage inspection is a key structural engineering technique that strives for ensuring structural safety. In this regard, one of the major intelligent approaches is the inverse analysis of structural damage using evolutionary computation. By considering the recent advances in this field, an efficient hybrid objective function that combines the global modal kinetic and modal strain energies is introduced. The newly developed objective function aims to extract maximum dynamic information from the structure and overcome noisy conditions. Moreover, the original methods are usually vulnerable to the associated high multimodality and uncertainty of the inverse problem. Therefore, the oppositional learning (OL) for population initialization and convergence acceleration is first adopted. Thereafter, the unified particle swarm algorithm (UPSO) mechanism is combined with another newly developed algorithm, the gradient-based optimizer (GBO). The new algorithm, called the oppositional unified particle swarm gradient-based optimizer (OL-UPSGBO), with the convergence acceleration feature of (OL), enhances balanced exploration-exploitation of UPSO, and the local escaping operator of GBO is designed to specifically deal with the complex inverse analysis of structural damage problems. To authenticate the performance of the OL-UPSGBO, the complex benchmark set of CEC 2017 is adopted to compare the OL-UPSGBO with several original metaheuristics. Furthermore, the developed approach for structural damage identification is tested using several damage scenarios in a multi-story frame structure. Results show that the developed approach shows superior performance and robust behavior when tackling the inverse analysis of structural damage.

Structural performance and safety in composites have become a major issue of modern engineering technology. The composite structure fails catastrophically due to lack of monitoring. The use of composite structures in automotive vehicles has increased drastically in recent years. To overcome this problem, damage detection at early stage is a serious concern in the structures. Among the various Structural Health Monitoring (SHM) techniques, the vibration-based methodologies have emerged as one of the potential monitoring techniques. In the paper, Modal Strain Energy (MSE) is used to inspect the artificially created crack in Mono Composite Leaf Spring (MCLS). Initially, eigenvalues and eigenvectors are determined for modeled baseline and cracked leaf spring using MATLAB programming. Then, element damage indices are calculated using stiffness of both springs. Finally, elemental modal strain energies and its variation among both the spring are determined. The presence of crack is identified based on variation of natural frequencies, location by damage index and severity by sensitivity of MSE. It has been concluded that the proposed method precisely evaluates the presence, position, and severity of crack. [ABSTRACT FROM AUTHOR]

Constrained layer damping treatment is widely used to suppress the vibration and noise of thin-walled structures. However, full coverage of constrained damping layer will increase unnecessary additional mass, resulting in material waste and cannot effectively improve the damping performance of the composite structure. In this article, a topology optimization approach is proposed to realize the optimal distribution of constrained damping layer. The design objective is to maximize modal loss factors solved by the modal strain energy method under the constraint of volume. Taking the relative density of the finite element of the constrained damping layer as design variable, the solid isotropic material with penalization method is used to realize the optimal topological distribution of the damping material on the surface of the metal substrate. Then the moving asymptote method is adopted as an optimizer to search the optimal layout of the constrained damping layer. Based on a modified modal superposition method, the sensitivities of the objective function with respect to the design variables are obtained. Numerical examples and experiments are presented for illustrating the validity and efficiency of this approach. The results show that the objective function converges to the optimal value smoothly, and the optimized modal loss factors have been significantly improved. The layouts of the constrained damping layer after optimization are clear and reasonable, and its distributions are affected by both the damping layer and the constraining layer. Each part of the constrained damping layer after optimizing can greatly improve the damping performance of the structure. [ABSTRACT FROM AUTHOR]

The present study aims to propose a robust method to detect the damage severity and location of the structural elements, focusing on the data type and acquisition method and promoting the model updating tools. The novelty of this method lies in its rotational mode shape acquisition that provides valuable information on the damage. In this method, the damaged elements were indirectly identified by detecting the healthy elements and eliminating them from the search space. Moreover, this method could minimize the modal strain energy difference between the damaged reference model and the numerical model using an optimization algorithm. An improved genetic algorithm was then employed to perform the optimization task. In this study, four numerical and two experimental damage scenarios were applied to a simply supported beam to examine the performance of the proposed method. Data acquisition systems were implemented using vision-based and accelerometer-based methods. The results indicated that this method could accurately identify the location and severity of damage using only the first mode shape since the rotational mode shapes were more sensitive to damage than the vertical mode shapes. [ABSTRACT FROM AUTHOR]

Disease in the liner back cavities of operational metro tunnels is alternately affected by groundwater environment, train cyclic load, and ambient environment conditions. Cavity disease is characterized by high levels of hiddenness and uncertainty; it also easily induces other tunnel diseases which can reduce the structure's bearing capacity and degrade structural safety and stability throughout the tunnel. This paper proposes a novel cavity-locating method for operational shield tunnels, with special focus on single- and multiple-cavity diseases. Based on perturbation theory, dynamic behaviors (modal frequencies and shapes) of different cavity cases were obtained from an analytical model of the original tunnel structure. A modal strain energy cavity indicator (MSECI) was established to reveal the locations of both single cavity and multiple cavities. A typical shield tunnel was modeled as an Euler-Bernoulli beam on a Winkler foundation and evaluated to validate the proposed method. The perturbation theory appears to effectively characterize the dynamic characteristics of liner back cavities in metro tunnels. MSECI can be used to locate cavities accurately. This work may provide a valuable theoretical basis for the detection and analysis of tunnel cavity disease and other tunnel health-monitoring applications. [ABSTRACT FROM AUTHOR]

The number of structural elements plays a significant role in detecting damage location and severity; such methods have sometimes failed to provide correct solutions due to the entrapment of damage detection algorithms in the local optimum. To resolve this problem, this study proposed the simultaneous use of mathematical and statistical methods to narrow down the search space. To this end, a two-step damage detection method was proposed. In the first step, the structural elements were initially divided into different clusters using the k-means method. Subsequently, the possibly damaged elements of each cluster were identified. In the second step, the elements selected in the first step were placed in a new set, and a process was applied to identify their respective damage location and severity. Thus, the proposed method reduced the search space as well as the possibility of entrapment in the local optimum. Other advantages of the proposed method include the use of fewer dynamic properties. Accordingly, by narrowing down the search space and the dimensions of the system for governing equations, the proposed method could significantly increase the chance of obtaining favorable results in structures with many elements and those with few vibration modes. A meta-heuristic method, called the colliding bodies optimization (CBO), was used in the proposed damage detection optimization algorithm. The optimization problem was based on the modal strain energy equations. According to the results, the proposed method was able to detect the location and severity of damage, even at its slightest percentage. [ABSTRACT FROM AUTHOR]

• A novel process is proposed to update elemental mass and stiffness matrices. • Both Lanczos bidiagonalization and Tikhonov regularization are combined to develop a new hybrid regularization method. • This method can solve the ill-posed inverse problem of structural model updating in a robust manner. • This method exploits new generalized cross-validation functions for determining an iteration number and a regularization parameter. • The accuracy and effectiveness of the presented approaches are verified numerically and experimentally. Structural model updating (SMU) by sensitivity analysis is a reliable and successful approach to adjusting finite element models of real structures by modal data. However, some challenging issues, including the incompleteness of measured modal parameters, the presence of noise, and the ill-posedness of the inverse problem of SMU may cause inaccurate and unreliable updating results. By deriving a hybrid sensitivity function based on a combination of modal strain and kinetic energies, this article proposes a sensitivity-based SMU method for simultaneously updating the elemental mass and stiffness matrices. The key idea of the proposed sensitivity function originates from the fundamental concepts of the equality-constrained optimization problem and Lagrange multiplier method. By combining the Lanczos bidiagonalization algorithm and Tikhonov regularization technique, a novel hybrid regularization method is presented to solve the ill-posed inverse problem of SMU in a robust manner. This scheme exploits new generalized cross-validation functions directly derived from the outputs of the Lanczos bidiagonalization algorithm to automatically specify the number of iterations and determine an optimal regularization parameter. The accuracy and effectiveness of the presented approaches are verified numerically and experimentally by a steel truss and the full-scale I-40 Bridge. All results show that the proposed methods are effective tools for SMU under incomplete noisy modal data. [ABSTRACT FROM AUTHOR]

Modal strain energy is a sensitive dynamic characteristic for nondestructive damage identification. In previous decades, it was widely used in damage index methods for localization of damage. However, these kind of methods often make misjudgments, especially for beam- and plate-like structures, because their angular displacements cannot usually be directly measured, which plays an important role in calculating element modal strain energy. In this paper, using the Gaussian smoothing technique and a laser scanning vibrometer, a new modal strain energy-based model updating method is proposed for damage assessment of beam-like structures. This method can determine the location and severity of damage at the same time. It calculates the experimental modal strain energy independently from the element stiffness matrix to reduce measurement noise and is baseline free because the mass matrix used for normalization is considered unchanged. A simulated one-crack simply supported beam, a simulate Π–shape framework, and an experimental two-crack cantilever beam are used to demonstrate the effectiveness and robustness of the proposed method. The results show that this method can accurately locate the damaged elements and enable an acceptable assessment of the severity of damage. [ABSTRACT FROM AUTHOR]

Structure-borne noise from railway bridges has become increasingly severe due to increased train speeds and axle loads. Constrained layer damping can suppress structural vibration and noise considerably across a wide frequency range by dissipating vibrational energy via damping layer shear deformation. This paper proposes a theoretical method of calculating the train-induced vibration and noise of a constrained layer damping-enhanced railway bridge based on the train–track–bridge coupled vibration, the modal strain energy method, and statistical energy analysis. First, the vibration responses of bridge decks were obtained via train–track–bridge coupled vibration calculations. Second, the constrained layer damping subsystem modal loss factors were determined via modal strain energy analysis and converted to damping loss factors in 1/3 octave band. Third, upon substituting the vibration energies of the decks and the damping loss factors of constrained layer damping subsystems into the statistical energy analysis power balance equations, the transmitted vibration energy results from various bridge subsystems were determined by solving the referenced equations. The structure-borne noise from the bridge was finally determined by analyzing the vibratory energies of all of the bridge subsystems using vibro-acoustic theory. Numerical analysis and field measurements of vibration and noise from a three-span steel–concrete composite bridge before and after constrained layer damping installation were performed. The predicted train-induced vibration and noise agreed well with the measured results. The stringer web and flange vibration velocity levels were reduced by 10.5 dB and 6.1 dB, respectively, and the sound pressure level at a measurement point 25 m (horizontal) from the track centerline and 1.5 m off the ground decreased by 4.3 dB(A). [ABSTRACT FROM AUTHOR]