The integration of graphene nanoplatelets (GnPs) into cementitious construction yields a multifunctional real‐time structural health monitoring (SHM) material for self‐sensing. Above a percolation threshold of 3.2 wt% GnP, a conductive network forms in the cementitious material, leading to a sharp decrease in electrical resistance (∼ 4 orders of magnitude) and a sensitive and stable sensory response under cyclic compressive loading. The values of fractional change in resistance (FCR) upon compression were found to be linearly correlated with stress, reaching 40% at a maximum stress of 11 MPa. The correlation between stress and resistance was calibrated using the stress sensitivity factor (SF = ((FCR)/( σ ))·100). The obtained SF was 3.6%/MPa, which is a significant improvement over previously reported studies (twice as high). The reproducible response was independent of the load direction with respect to orientation of the electrodes (parallel or perpendicular to the force direction). Currently used sensors mostly provide global information on large structures and are based on complex, fragile external devices such as cameras, lasers, or ultrasound sensors, which require extensive data analysis and operational overhead. In contrast, the findings of this study highlight the potential of the cementitious composite itself as a scalable, durable, and local sensor for SHM applications in concrete elements.
The practical application of active control for base‐isolated structures must contend with a host of real‐world challenges, including the physical limits of isolator displacement and actuator force, mandatory building separation distances, and sensor noise and parameter uncertainties. While passive and semiactive systems remain the preferred solutions for most seismic applications, active control offers a unique advantage for near‐fault regions where long‐period ground motions can drive passive isolators beyond their displacement capacity. This study develops a model predictive controller (MPC) specifically for such demanding scenarios. Our MPC design carefully balances tracking error against control effort and explicitly enforces hard constraints on the control force and its rate of change associated with the real hydraulic actuators. While traditional tracking MPC is employed here, the framework is positioned as a baseline for future economic MPC (EMPC) formulations that directly optimize actuator energy consumption and displacement limits. The prediction horizon is also tuned to the structure’s dominant dynamics to ensure reliable performance. We test our controller on a 10‐degree‐of‐freedom (DOF) base‐isolated building model subjected to three historic earthquakes: Chi‐Chi, Shinjuku, and Kobe. The simulation framework, built in MATLAB/MPC3S, is made robust by incorporating a second‐order filter to clean sensor noise and by modeling uncertainties in stiffness and damping. The results are clear: Our proposed MPC substantially outperforms an equivalent input disturbance (EID) controller. It achieves dramatic reductions in both floor displacements and velocities, strengthens overall stability, and critically maintains strict adherence to all operational limits, even when faced with significant noise and parameter uncertainties.
Accurate evaluation of chloride‐induced corrosion in reinforced concrete (RC) structures is essential for effective maintenance, yet conventional diagnostic approaches require full‐depth coring and laboratory testing to determine chloride profiles and diffusion coefficients. These procedures are costly and invasive for large‐scale routine inspection. This study proposes a data‐driven framework that enables corrosion initiation assessment using only surface chloride measurements combined with machine‐learning (ML)–based estimation of chloride diffusion coefficients. To address the large uncertainty associated with unknown mix proportions in existing structures, regional mix‐design statistics were incorporated to constrain ML model inputs and reduce prediction variability. The resulting diffusion coefficient distributions were then integrated into a probabilistic chloride ingress model based on fib Model Code 2010, allowing explicit propagation of uncertainties in material properties, cover depth, and environmental exposure through Monte Carlo simulation. Field validation was conducted using concrete cores extracted from roadside barriers and bridge components located in inland and coastal environments. Comparison between predicted and measured chloride profiles demonstrated that the proposed approach successfully captures the range and depth of chloride penetration observed in practice. The results indicate that this minimally invasive method can support early‐stage depassivation probability screening, optimize locations requiring detailed testing, and enhance decision‐making in infrastructure asset management. It should be noted that this approach assesses the risk of corrosion initiation (i.e., depassivation onset) and not the actual condition or section loss of the embedded reinforcement.
Seismic isolation systems have been employed in bridges to increase their lateral flexibility and thereby improve their performance by reflecting seismic energy away from the structure. In recent years, stiffness devices that could passively generate both positive and negative tangential stiffness that varies with displacement were introduced within bridge isolation systems in an attempt to further improve seismic performance by reducing their lateral stiffness to near‐zero values and thus increasing the fundamental natural period to near‐infinity. Previous investigations on such displacement‐dependent stiffness devices have focused on their effect on the seismic response of existing bridges, where design parameters that characterize the behavior of stiffness devices often had values from preliminary designs or, at best, values obtained from sensitivity studies. A potentially different level of performance could be realized in the design of a new bridge if the isolation system components (bearings, dampers, and stiffness devices) were designed simultaneously through optimization. This study concentrates on an evaluation of the effectiveness of displacement‐dependent stiffness devices in improving the response of a bridge with a well‐designed (optimized) seismic isolation system. A design framework is developed that optimizes configurations of the isolation system for multiple performance objectives. It is found that for a bridge with an isolation system comprised only of lead‐rubber bearings, the inclusion of stiffness devices can, in certain cases, result in improved seismic performance. In contrast, for a bridge with a high‐performance isolation system comprised of lead‐rubber bearings and dampers, the inclusion of stiffness devices provides negligible improvement in seismic performance.
Multiple site damage (MSD) is often concealed and can lead to interacting cracks under dynamic loading conditions, resulting in failures of bolted connection structures. Therefore, extensive research has focused on crack detection and prediction in MSD‐affected connection structures. However, existing methods typically involve high computational costs, neglect global structural responses, and still face challenges in early crack detection. In this study, a fatigue damage identification method for bolted connection structures with MSD is proposed based on statistical time‐domain features. A vibration fatigue experiment is conducted under sinusoidal excitation at the resonant frequency to induce progressive damage in a bolted connection structure with MSD. During the fatigue process, the excitation is periodically interrupted, and Gaussian white noise excitation is applied to measure structural responses at different damage stages. The responses are collected using an accelerometer and recorded by a National Instruments (NI) data acquisition system. Fifteen statistical time‐domain features are extracted from the measured responses to characterize structural condition variations. Welch’s t ‐test is then employed to identify the most sensitive features for fatigue damage detection. Among the extracted features, the root mean square (RMS) and square mean root (SMR) are found to be particularly effective for identifying damage in MSD‐affected bolted connection structures. The experimental results demonstrate that the proposed method achieves high classification performance using global vibration responses from a limited number of sensors, without requiring complex nonlinear feature extraction.
Wind turbine drivetrains operate under variable aerodynamic loading, fluctuating speed, and harsh field environments, making condition monitoring difficult when fault samples are scarce and imbalanced. To address this challenge, this paper proposes a small‐sample data augmentation method that fuses variational mode decomposition–particle swarm optimization–symmetric dot pattern (VMD–PSO–SDP) feature optimization with a prior knowledge–guided Wasserstein conditional generative adversarial network (PK‐WCGAN). First, VMD is used to decompose vibration signals into informative modal components. In combination with an improved PSO algorithm for optimizing SDP parameters, high‐order fault feature maps are generated to enhance feature transferability. Then, real feature maps are used to pretrain the discriminator as prior knowledge, guiding the Wasserstein conditional generative adversarial network (WCGAN) to learn the target domain distribution. A gradient penalty mechanism is introduced to improve the quality of generated samples and training stability. Finally, generated samples are fused with real training samples to construct a hybrid dataset. Experimental results demonstrate that the generated data effectively reduce small‐sample distribution mismatch. When the target data samples are expanded from 50 to 1000, the average recognition accuracy of the five models increases from 54.6% to 94.0%, and the risk of overfitting is reduced by up to 26.5 percentage points under the 10‐sample setting. This method provides an effective solution for small‐sample fault diagnosis in the wind turbine drivetrain.
In tensegrity and cable‐strut tensile structure design, determining the initial configuration with suitable prestress distributions that ensure structural stability constitutes a critical design phase. To address the limitations of conventional prestress design methods—specifically, low computational efficiency and difficulty in obtaining feasible solutions for complex cable‐strut systems—this paper proposes a deep learning approach based on a graph neural network (GNN) to predict prestress distributions. The methodology abstracts tensegrity or cable‐strut systems into graph structures: Node features encode spatial coordinates and support conditions, while edge features encode topological connectivity, member orientation vectors, member lengths, and member‐type indicators (struts in compression and cables in tension); the prestress values are treated as edge‐level prediction targets. A composite loss function combining mean squared error and equilibrium equation loss is formulated to evaluate discrepancies between predicted and SDP reference prestress distributions. Leveraging extensive existing datasets of prestress design cases for various tensegrity and cable‐strut tensile structures, the trained model achieves end‐to‐end prediction, directly outputting prestress distributions from the graph‐based input representation. Comparative numerical experiments demonstrate that the proposed method rapidly generates prestress designs without iterative computations, while tests on unseen configurations sampled from the structural families represented in the dataset indicate its generalization capability within the considered data distribution. This approach provides a novel paradigm for the rapid end‐to‐end prestress design of tensegrity and cable‐strut systems.
Reliable gearbox fault diagnosis is an important component of condition monitoring and predictive maintenance in industrial systems. Vibration‐based approaches are widely used for this purpose; however, raw vibration signals are often noisy, nonstationary, and affected by changing operating conditions. In this study, a hybrid deep learning framework combining a convolutional neural network (CNN), bidirectional long short‐term memory (BiLSTM), and gated recurrent unit (GRU) is investigated for gearbox fault diagnosis directly from raw vibration time‐series data. Within the proposed framework, the CNN module is used to extract localized fault‐related patterns, the BiLSTM module models bidirectional temporal dependencies, and the GRU layer provides compact temporal summarization for classification. The model is evaluated on an industrial‐grade gearbox vibration dataset using stratified cross‐validation, out‐of‐fold (OOF) predictions, and an independent holdout set. Performance is assessed using ROC–AUC, F1 score, and accuracy, together with threshold optimization, bootstrap‐based confidence interval estimation, statistical comparison, and interpretability analysis. On the considered benchmark, the CNN–BiLSTM–GRU model achieves strong diagnostic performance, reaching a ROC–AUC of 0.998, an F1 score of 0.979, and an accuracy of 0.980, while generally outperforming standalone and reduced hybrid variants. Additional analyses using bootstrap confidence intervals, the DeLong test, LIME, and SHAP further support the stability and interpretability of the obtained results. The findings suggest that the proposed hybrid structure is effective for raw vibration‐based gearbox fault diagnosis on the evaluated binary benchmark. However, the results should be interpreted within the scope of the employed dataset, which represents a relatively constrained fault scenario. Accordingly, the main contribution of the study lies in the integration of hybrid temporal modeling, leakage‐aware evaluation, threshold analysis, and interpretability within a single diagnosis framework, rather than in claiming universal generalization across all industrial gearbox conditions.
Finite element (FE) model updating methods are widely used in the field of structural health monitoring as well as performance evaluation. Whenever modeling is involved, whether it is a theoretical model or a FE model, the modeling error is a factor that will not be eliminated and has a significant impact on the model update results. It usually leads to residual errors in the update results, and large discrepancies between the determined model parameters and the corresponding physical values in the actual situation. In this paper, a new two-stage Bayesian updating theory is developed to study the model updating problem considering modeling errors. The model updating parameters are explicitly divided into traditional model parameters and modeling error parameters, and these two parameters are updated separately. Meanwhile, the modeling error is also divided into measurement error and FE error, whose manifestations in the objective function are discussed separately. The FE computational errors are divided into frequency-dependent modeling errors and modal computational errors, and a simulated numerical simulation model is used to verify the feasibility of model updating and the effects of model updating results after considering the modeling errors. Subsequently, to verify the practical application of the method, for a real bridge, the modified parameters and modes are screened to avoid the situation of too many parameters of the objective function, and a suitable optimization algorithm is selected during the calculation process so as to improve the computational efficiency. The results show that the algorithm considering the modeling error will make the bridge update more accurate and effectively improve the accuracy of the model update.
A passive resettable stiffness damper is presented for controlling vibrations in seismically excited structures. The damper generates forces in proportion to the piston displacement, making it effective over a wide range of vibration amplitudes and frequencies. Energy dissipation occurs by resetting the damper force to zero at each change in piston direction. This is achieved using a special resetting mechanism that is integrated with the damper body. A model of the resetting mechanism was developed that considers the detailed geometry of its components, and the model was validated using CAD software. The model was used to investigate the influence of the mechanism geometry on its performance, leading to a design methodology that ensures the mechanism operates properly and without interruption during a dynamic event. A prototype was constructed and subjected to multiple cycles of sinusoidal loading at different amplitudes and frequencies. The results showed that the damper force increased with input amplitude but was independent of input frequency. However, the energy dissipation capacity of the damper was found to be frequency dependent. The damper hysteresis loops showed stable force-displacement characteristics over several hundred cycles of motion, thereby validating the damper concept and demonstrating the reliability of the resetting mechanism.
This study evaluates the accuracy of satellite Interferometric Synthetic Aperture Radar (InSAR) for the structural health monitoring (SHM) of civil infrastructures, focusing on bridge displacements. A comparative analysis is conducted between displacement data obtained from InSAR and traditional topographic techniques, using the Colle Isarco Viaduct in Italy as a case study. The analysis involves satellite images from the COSMO-SkyMed constellation and topographic data from total stations collected over 4 years. Results indicate that InSAR-derived displacements are accurate in areas with high temporal coherence, demonstrating minor differences from and strong correlation with topographic measurements. Phase ambiguity issues in regions with significant displacements are identified and addressed through a data-fusion method, enhancing the accuracy of InSAR-derived results. The unpaired t-test confirms the robustness of the findings, indicating no significant differences between InSAR and topographic measurements. Findings suggest that InSAR has considerable potential as both a standalone and complementary tool for bridge SHM.
A theoretical framework is developed to investigate the influence of nonclassical damping on frequency and damping variations in vehicle-bridge interaction systems, a topic that has received basically no attention to date. An explicit dimensionless expression is first derived to estimate damping variation, together with analytical and semianalytical solutions for the undamped and pseudo-undamped frequencies, respectively. As existing approaches for quantifying nonclassical damping effects are not directly applicable to vehicle-bridge interaction systems, a novel index specifically tailored to these systems is proposed to characterize the degree of nonclassical damping. The validity of the proposed framework and index is verified through numerical simulations. Both theoretical analysis and numerical results indicate that (1) vehicle-bridge interaction-induced frequency variation is generally suppressed by nonclassical damping; (2) the use of undamped theory may lead to significant errors in estimating frequency variation, particularly near resonance and for systems with high vehicle damping; (3) vehicle-bridge interaction-induced damping variation is more sensitive to the internal frequency ratio and damping characteristics of the system than the corresponding frequency variation.
The identification of road roughness using the dynamic responses of passing vehicles is of practical value. However, with vehicle parameters unknown a priori, unknown vehicle parameters and road roughness are coupled in the identification. In existing methods, vehicle parameters and road roughness are identified based on complex stage identification or mutual iteration. Moreover, road roughness is random in nature, but there is a lack of research on the identification of statistical road roughness. In this paper, an efficient method is proposed for the direct identification of joint vehicle parameters and road roughness field using dynamic response data fusion of three-dimensional (3D) moving vehicles. First, the extended Kalman filter with unknown inputs is used to identify vehicle parameters, except tire stiffness, and unknown forces in a 3D moving vehicle. Then, the tire stiffness and road roughness are identified based on the property that front and rear vehicle wheels pass same road surface. Furthermore, it is extended to study the identification of joint vehicle parameters and Gaussian random road roughness field. Based on the vehicle parameters identified using the above deterministic method, the Karhunen-Lo & egrave;ve (KL) expansion is performed on vehicle responses to obtain their truncated KL components, which are used as the observations of the Kalman filter with unknown inputs to identify the corresponding KL components of random road roughness. Finally, statistics of Gaussian random road roughness are estimated. The proposed deterministic and stochastic methods are tested by numerical simulation of 3D vehicle responses with different road roughness levels.
Bridge deterioration modeling plays a crucial role in infrastructure maintenance and lifespan prediction. Current methodologies evolve along three axes: (1) Mechanism‐driven models, which leverage structural mechanics and material degradation theories to provide detailed insights into the physical processes underlying deterioration, constrained by computational intensity; (2) probabilistic frameworks, which are used to quantify degradation uncertainties, effective for long‐term reliability yet insensitive to anomalies; and (3) data‐driven models, which are used for high‐dimensional pattern mining, limited by data dependency and interpretability barriers. The hybrid intelligence paradigm emerges as a transformative solution, integrating physical laws, stochastic processes, and machine learning. This review systematically evaluates contemporary techniques across computational efficiency, predictive robustness, and engineering applicability. In addition, comprehensive structural health monitoring of bridges is advancing through the investigation of deterioration mechanisms, the application of nondestructive damage detection tools, and the exploration of emerging technologies such as AI‐based tools, data fusion integrated with digital twin systems. Priority innovations should focus on (1) developing resilient data processing methods, (2) novel multisensor joint reconstruction algorithms that can effectively mitigate simultaneous data loss, (3) creating prescriptive analytics systems that synchronize real‐time structural responses with probabilistic multihazard simulations, and (4) incorporating attention mechanisms and robust recursive algorithms into time‐series models to better capture long‐term dependencies and mitigate error accumulation.
Vibration‐based health monitoring (VHM) has emerged as a promising technique for assessing the integrity of deep foundations by interpreting variations in dynamic response governed by soil–pile interaction. This review presents the theoretical background of foundation failure mechanisms, sensing technologies, and numerical approaches that underpin VHM for pile foundations, with emphasis on recent advances in fiber‐optic sensing, piezoceramic transducers, and acoustic emission measurement. Developments in optimal sensor placement, high‐rate data acquisition, and advanced signal‐processing techniques including time‐ and frequency‐domain analysis and machine‐learning‐based interpretation are examined in relation to their capability to identify damage mechanisms such as cracking, scouring, buckling, degradation of bearing capacity and shaft resistance, and postearthquake damage. A critical evaluation of physical model tests, field studies, and numerical investigations highlights the strong influence of pile geometry, embedment depth, material type, excitation method, and sensor configuration on the sensitivity of vibration‐based indicators. While VHM has demonstrated strong potential during installation and under controlled monitoring conditions, its application to existing and aging foundations, particularly deeply embedded and large‐diameter piles, remains limited. The findings underscore the need for unified VHM protocols, scalable and nonintrusive sensing strategies, and field‐validated diagnostic indicators that explicitly account for soil–pile interaction to support reliable long‐term performance assessment of pile foundations, especially for postdisaster damage evaluation.
During long-term service, the mechanical properties of laminated rubber bearings are altered by earthquakes, sustained loads, temperature variations, and other factors, thereby reducing their seismic isolation performance. To address the limitation that existing methods cannot achieve in situ, high-precision detection of bearing mechanical properties, this study proposes an innovative detection framework, DamageYOLO. This framework integrates active sensing, the Continuous Wavelet Transform (CWT), and a pretrained YOLOv5s model enhanced with attention mechanisms. The pretrained YOLOv5s model is fine-tuned to adapt to the bearing damage detection task, and the Squeeze-and-Excitation (SE) and Multihead Attention (MHA) modules are introduced to enhance the model's feature representation capability. To validate the effectiveness of the DamageYOLO framework, a database containing 2880 samples was established through accelerated aging and active-sensing experiments. The corresponding detection signals were converted into two-dimensional wavelet scalograms using CWT and used as input features for the model. The results show that, on the test set, the developed model, DamageYOLO-shear, achieved a coefficient of determination (R2) of 0.9996 and a mean absolute error (MAE) of 0.8 N/mm. Furthermore, the proposed model exhibits superior predictive performance compared with deep learning models developed using time-domain images and wavelet packet energy spectra. This suggests that the DamageYOLO framework provides a new and effective approach for damage detection in laminated rubber bearings.
Fatigue‐induced damage in reinforced concrete bridge slabs subjected to traffic loading evolves gradually, often with limited visible signs until critical damage occurs. Monitoring this process is essential for timely maintenance and improved assessment of structural safety. This paper investigates how concrete microcracking evolves spatially and temporally under traffic loading and temperature variations and how microcracking can be characterized using acoustic emission (AE) monitoring. An 18‐month AE monitoring campaign was conducted on a reinforced concrete bridge slab, combining Ib‐value analysis, absolute energy quantification, and three‐dimensional localization of AE events. Two novel fatigue damage indices, one for progressive damage and another for stationary damage, are proposed to quantitatively differentiate microcracking mechanisms and assess fatigue progression. The results show that early‐fatigue damage of the concrete in the reinforced concrete slab is dominated by stationary microcracking, with occasional progressive microcracking events. Spatial analysis revealed concentrated microcracking in regions experiencing significant shear and bending stresses. Additionally, microcracking displayed seasonal cyclic patterns linked to temperature‐induced stress variations. The developed fatigue damage indices and integrated monitoring approach provide practical methods for early‐stage fatigue assessment, supporting proactive management of reinforced concrete structures under in situ operational conditions.
The vulnerability of stay cables to vibrations necessitates high-performance control solutions that surpass the performance limitations of passive dampers. This study presents the experimental verification of a novel adaptive semiactive control system for cable vibration mitigation. The system integrates an inverse-dynamic-based adaptive frequency-shaped linear quadratic Gaussian (iAFLQG) controller with a self-sensing magnetorheological (MR) damper, providing collocated force and displacement feedback. The iAFLQG strategy features online weight tuning via the Hilbert-Huang transform (HHT), enabling real-time tracking of the evolving dominant vibration mode. Laboratory tests demonstrate that the proposed control law significantly outperforms both passive MR damping and a standard inverse-dynamics-based LQG (iLQG) control. The iAFLQG control not only provides superior damping across a range of vibration amplitudes but also notably exceeds the theoretical damping limits for an optimal linear viscous damper. This superior effectiveness is attributed to a beneficial negative stiffness effect that amplifies damper motion, thereby enhancing the energy dissipation through the semiactive damping, which is adaptively tuned in real-time for the dominant mode. The study concludes that, for the experimentally investigated cases of dominant in-plane vibration, the iAFLQG strategy constitutes a high-performance adaptive solution for cable vibration mitigation, as validated by its integration with the self-sensing MR damper.
Scissor-jack brace-damper systems (SJBS) are widely utilized in structural applications. However, their performance is constrained by the fixed mode, and solutions based on small deformation cannot accurately capture their mechanical properties. To address this, a hybrid system combining the lever arm system (LAS) and SJBS is proposed. The theoretical framework encompasses geometric properties and establishes the relationship between interstory drift and viscous damper (VD) axial deformation, alongside an analysis of the VD's nonlinear response. By applying bar models of the bilateral lever arm system (B-LAS) and the bilateral lever arm scissor-jack brace-damper system (B-LASJS) to the dynamic analysis of plane steel frame structures in Abaqus software, the derivation of the theoretical model is validated. Subsequently, this study further conducts a seismic performance analysis of steel frames in 10- and 20-story high-rise structures equipped with B-LASJS, comparing them to frame structures with B-LAS and uncontrolled structure (US). The findings demonstrate that B-LASJS-equipped structures exhibit enhanced dynamic performance and energy dissipation capabilities compared to B-LAS-equipped counterparts. Additionally, the parameter analysis of B-LASJS and U-LASJS reveals that structural response is influenced by the angle between the bar and the horizontal axis and the lever ratio, emphasizing the importance of careful parameter design before engineering applications. In conclusion, the proposed B-LASJS provides a more stable, safe, and efficient energy dissipation solution for building structures.
Accurate bridge deflection prediction is vital for structural health monitoring. Compared with traditional methods, it can more effectively uncover complex nonlinear laws from massive monitoring data to achieve forward-looking prediction. Although the current mainstream models have significant advantages in modeling capabilities, they still face the bottlenecks of insufficient feature representation and high computational complexity. To solve this problem, the deflection of the bridge is accurately predicted. In this study, we innovatively construct a transformer architecture by introducing a Gaussian probability density function to establish a likelihood estimation framework. Utilizing maximum likelihood estimation for parameter optimization, it achieves probabilistic interval modeling of deflection time-series signals. For comparison, two additional encoder-decoder models are employed: The SBIGRU model refers to the Sequence-to-Sequence Bidirectional Gated Recurrent Unit, whereas the ASBIGRU model extends this architecture by integrating an attention mechanism to improve bidirectional sequence representation. The experimental data are based on the multisection monitoring data of a long-span suspension bridge in China, covering ambient temperature, vehicle load effect, and deflection signal. The analysis examined correlations among datasets with multiple cross-sections of bridges and validated the robustness of the proposed probabilistic model. The application of the transformer model produced a notably low root mean square error of 2.588 mm alongside a high coefficient of determination of 0.9693 and markedly decreased the time required for training to 28% of that demanded by established techniques. Compared to alternative modeling techniques, transformer models deliver enhanced prediction accuracy as well as greater computational efficiency. This breakthrough provides a theoretical basis for the engineering application of transformer in the intelligent monitoring of cable load-bearing bridges.
