Vehicle Bridge Research Articles

Damage localization using low-frequency bridge acceleration component under a moving vehicle

Monitoring the health of short-span and medium-span bridges in urban transportation systems is a crucially important issue in civil engineering, as is locating damage. Earlier studies have attempted to use bridge deflection or acceleration to locate damage. However, the deflection is not so sensitive to enable damage location. Few studies have investigated low-frequency acceleration responses. For this study, a proposed model-free method is evaluated for damage localization using low-frequency bridge acceleration under a moving vehicle. First, the bridge dynamic responses in a vehicle–bridge interaction (VBI) system are derived theoretically, where the bridge is modeled as a simply supported beam, the vehicle as a moving sprung mass, and damage as a reduction of the beam’s bending stiffness. A partially moving loading model is proposed to explain the influence of the structural damage on the dynamic behavior of the beam. A simple relation was found between low-frequency bridge acceleration and the damage location. Specifically, an abnormal “bump” occurred on the low-frequency bridge acceleration when a vehicle passes over the damaged area. Using this relation, one can directly locate potential damage from the low-pass filtered acceleration time history of the beam. A series of numerical analyses and laboratory and field experiments were conducted to validate the proposed damage localization method.

Evolution of modal properties in the non-proportionally damped coupled vehicle–bridge system

The modal properties of bridges are crucial parameters in engineering applications, and their variation caused by moving vehicles has been increasingly recognized in recent years. However, existing closed-form analytical expressions for the varying modal properties during vehicle passage exist only for simple structural configurations. This paper proposes an innovative method for analyzing the instantaneous modal properties of the system, considering general boundary conditions and the damping effect. First, only general boundary conditions are considered, and the results show that the location of the maximum system frequency shift depends on the mode shape. Then the damping effect is considered, observing that the system is non-proportionally damped in most cases, making it difficult to obtain a closed-form solution using existing methods. To solve this, we transform the system of second-order ordinary differential equations into a set of fourth-order ordinary differential equations and derive the closed-form solution for system’s modal properties. Based on this solution, we introduce the concept of Critical Coupling Damping (CCD), which defines the transition between the coupled description and the moving mass case. This work deepens understanding of changing modal properties during the traverse of sprung masses, and so has numerous potential engineering applications.

Bridge Damage Localization Through Response Reconstruction with Multiple BP-ANNs Under Vehicular Loading

Damage detection is a critical aspect of bridge health monitoring. While data reconstruction has been posited as a promising method for damage detection, its effectiveness in this context has rarely been empirically validated. In this study, we introduce a novel approach to pinpoint potential bridge damage by reconstructing bridge inclination data. For an intact bridge, we selected reference cross-sections and trained multiple Backpropagation Artificial Neural Networks (BP-ANNs) to simulate transfer matrices for inclination between these base sections and other sections of the bridge. These BP-ANNs were then employed to reconstruct inclination data at the same cross-sections on a bridge with artificial damage. We demonstrated that damage localization is feasible through a comparison of the reconstructed and actual measured responses. The theoretical underpinnings of the transfer matrix and the damage localization method were initially elucidated through an analysis of the dynamics of a simplified vehicle–bridge interaction (VBI) system. A series of finite element models were constructed to substantiate the theoretical basis of the damage localization method. Additionally, a large-scale laboratory experiment was carried out to assess the practical effectiveness of the proposed method. The proposed method has been demonstrated to effectively pinpoint the location of potential structural damage. It successfully differentiates between areas in close proximity to the damage and those that are more distant. Compared to existing research, our method does not necessitate prior knowledge of factors such as mode shape functions, traffic conditions, or the constraint of inspecting with a single vehicle. This approach is anticipated to be more convenient for engineering applications, particularly in the development of online monitoring systems, due to its streamlined requirements and robust performance in identifying damage localization.

Dynamic Intelligent Analysis of Single-Column Pier Bridges Considering Vehicle–Bridge Interaction

With its advantages of low engineering cost, minimal space occupancy, and aesthetically pleasing shape, the single-column pier bridge is frequently utilized in urban viaducts and interchange ramps. Due to structural peculiarities, the bridge subjected to eccentric loading, flexural and torsional interaction, and centrifugal force may undergo tipping accidents. To better comprehend the overturning resistance of the bridge, the vibration governing equation of the bridge (idealized as an orthotropic thin plate with point supports in the domain model) is established considering vehicle–bridge interaction. An approximate dynamic analysis formula is subsequently derived via a hybrid method using the grey wolf optimizer. Compared with the outcomes of finite element analysis, the maximal deviation arising from this derived analytical formula is approximately [Formula: see text]% with the greater discrepancy being observed in scenarios featuring minimal support reactions. Compared with the finite element method, the proposed method in this study has higher computational efficiency with precision. This analytical solution is then utilized in the parametric study to scrutinize the influences of span, road surface roughness, and vehicle velocity on a single-column pier bridge under four vehicles. The analysis findings indicate that the proposed approach is reasonably precise, remarkably efficient, and efficacious.

Dynamic Analysis of a Vehicle–Bridge System Under Excitation of Random Road Irregularities

This paper presents a comprehensive study of the dynamic response analysis of vehicle–bridge coupled systems, with detailed simulation methods for the vehicles, bridges, and wheel–road coupling relationships. The simulation of the entire vehicle–bridge coupling system is carried out using the open-source finite element analysis platform OpenSees. A novel three-dimensional wheel–road coupling element is introduced to model the interactions between the wheel and road nodes. This element facilitates precise computation of the dynamic responses within the vehicle–bridge coupled system, including both vehicle and bridge behaviors, along with the interaction forces between the wheels and the bridge surface. The coupling element consists of a wheel node and all potential road nodes on the bridge surface that the wheel may traverse. This configuration preserves the finite element model of the entire vehicle–bridge coupled system throughout the vehicle’s movement, thereby improving the efficiency of numerical simulations of vehicle–road interactions. The study accounts for the impact of random road irregularities on the dynamic responses of both the vehicle and the bridge. These irregularities are treated as input parameters for the wheel–road coupling element rather than being accounted for through the wheel–road interaction constraint equations, thereby improving the convenience of simulating random road irregularities.

Study on the Degradation Model of Service Performance in Railway Steel–Concrete Composite Beams Considering the Cumulative Fatigue of Steel Beams and Studs Based on Vehicle–Bridge Coupling Theory

The steel–concrete composite beam, as a structural form that combines the advantages of steel and concrete, has been applied in railway engineering. However, with the increase in railway operation time, the degradation pattern of the service performance of steel–concrete composite bridges remains unclear. This paper proposes a method for calculating the long-term service performance of railway steel–concrete composite beams, considering the cumulative fatigue damage of steel beams and studs, based on the vehicle–bridge coupling theory and Miner’s linear cumulative damage criterion. The proposed method is validated using measured data from an in-service steel–concrete composite railway bridge with spans of 40 + 50 + 40 m. The calculated mid-span vertical displacement and the first two natural frequencies of the composite beam deviated from the measured results by only 2.1%, 7.7%, and 9.5%, respectively. The research results can provide a basis for extending the service life of composite beams and preventing the occurrence of safety accidents.

Bridge Monitoring Using Smartphones Installed on Driving Vehicles: Oriented to Crowdsourcing Model

The acquisition of bridge frequency by using the ubiquitous ordinary passenger vehicles and smartphones in cities has attracted an increasing amount of attention. This study proposes a bridge monitoring method and develops a vehicle–bridge crowdsourcing monitoring (VBCM) platform for public participation. It takes smartphones carried by vehicles as monitoring terminals for a long-term bridge monitoring task. To validate the feasibility of available smartphone brands as a signal collector, a small shake table test is carried out and the processing scheme for the smartphone sampling data is investigated. A smartphone sensor frequency gain technique is proposed to satisfy the fusion of multisensor data in different smartphones. Furthermore, a magnetic target identification technique is proposed to pick up and extract the bridge response signal segment corresponding to the vehicle’s entering and leaving, as well as to eliminate redundant data. To this end, the network of multiple smartphones is synchronized. For the sake of applicability and feasibility, a series of scaled experiments are conducted in the laboratory considering an adapted toy car driving over a simply supported steel bridge. The results demonstrated the practicality of the proposed methodology. The combination of easily accessible smartphones oriented to a crowdsourcing model and a driving vehicle lowers the threshold for the bridge monitoring process, which also pinpoints a potential for future structural health monitoring development.

An Experimental and Numerical Study on the Lateral Stiffness Limits of Straddle-Type Monorail Tour-Transit Systems

The development of the straddle-type monorail tour-transit system (MTTS) has received keen attention. Regarding the unspecified regulations on the lateral stiffness limit of steel substructures, which is essential for the design of MTTSs, this work presents a comprehensive assessment of the issue. Firstly, a wind–vehicle–bridge coupling model was established, integrating multibody dynamics and finite element methods. This model was then validated against field test results, considering measured track irregularities and simulated wind loadings as the excitations. Afterwards, a trend analysis and a variance-based sensitivity analysis was performed to investigate the effect of various factors on the dynamic response of the MTTS. Results indicate that the pier height significantly impacts the lateral displacement of the pier top, accounting for 87% of the first-order sensitivity index and 75% of the total sensitivity index. In comparison, the lateral stiffness of track beams contributes over 70% to the maximum responses at the mid-span. Based on this, two responses, the lateral displacement of the pier top and the lateral deflection–span ratio of the track beam, were utilized as evaluation indicators. With the analysis of indicators in terms of lateral acceleration, Sperling index, and lateral wheel force, the limited values for the two indicators were determined as 8.04 mm and L/4200, respectively. These findings can serve as valuable references for future research and designs in this field.

Physically Guided Estimation of Vehicle Loading-Induced Low-Frequency Bridge Responses with BP-ANN

The intersectional relationship in bridge health monitoring refers to the mapping function that correlates bridge responses across different locations. This relationship is pivotal for estimating structural responses, which are then instrumental in assessing a bridge’s service status and identifying potential damage. The current research landscape is heavily focused on high-frequency responses, especially those associated with single-mode vibration. When it comes to low-frequency responses triggered by multi-mode vehicle loading, a prevalent strategy is to regard these low-frequency responses as “quasi-static” and subsequently apply time-series prediction techniques to simulate the intersectional relationship. However, these methods are contingent upon data regarding external loading, such as traffic conditions and air temperatures. This necessitates the collection of long-term monitoring data to account for fluctuations in traffic and temperature, a task that can be quite daunting in real-world engineering contexts. To address this challenge, our study shifts the analytical perspective from a static analysis to a dynamic analysis. By delving into the physical features of bridge responses of the vehicle–bridge interaction (VBI) system, we identify that the intersectional relationship should be inherently time-independent. The perceived time lag in quasi-static responses is, in essence, a result of low-frequency vibrations that are aligned with driving force modes. We specifically derive the intersectional relationship for low-frequency bridge responses within the VBI system and determine it to be a time-invariant transfer matrix associated with multiple mode shapes. Drawing on these physical insights, we adopt a time-independent machine learning method, the backpropagation–artificial neural network (BP-ANN), to simulate the intersectional relationship. To train the network, monitoring data from various cross-sections were input, with the responses at a particular section designated as the output. The trained network is now capable of estimating responses even in scenarios where time-related traffic conditions and temperatures deviate from those present in the training data set. To substantiate the time-independent nature of the derived intersectional relationship, finite element models were developed. The proposed method was further validated through the in-field monitoring of a continuous highway bridge. We anticipate that this method will be highly effective in estimating low-frequency responses under a variety of unknown traffic and air temperature conditions, offering significant convenience for practical engineering applications.

Dynamic Analysis of Rockfall Impact on Bridges: Implications for Train Safety

The threat of rockfall impacting bridges in mountainous areas poses a great risk to the safety of passing trains. This study delves into the dynamics of rockfall impact and its implications on the interaction between train vehicles and bridges. Leveraging LS-DYNA, this study first captured the force–time history of rockfall impact on bridge structures. Subsequently, there was a comparison with the impact forces generated at various speeds with those predicted by established formulas, validating the accuracy of simulations. Employing BANSYS software, the dynamic responses of both bridge structures and the vehicle–bridge coupling system to falling rocks were analyzed. The investigation encompassed parameters such as impact speed, position, and train location. The findings reveal that escalating impact speeds correlate with increased average and maximum impact forces from falling rocks. Notably, the average impact force does not linearly correspond with rock speed and often exceeds values calculated by conventional formulas. Impact position minimally affects maximum impact force, yet alterations in position prolong impact duration, consequently reducing average impact force. Rockfall-induced impacts precipitate notable spikes in train lateral acceleration, lateral wheelset force, wheel unloading rate, and derailment coefficient, albeit with a comparatively lesser impact on vertical acceleration. Increasing impact speed and altering position intensifies the vehicle’s response, particularly when the train is in close proximity to the impact site.

A Fast Multi-Objective Optimization Method for Control Parameters of High-Speed Maglev Vehicle-Bridge System

A fast multi-objective optimization method (FMOOM) is proposed by optimizing control parameters to improve the dynamic performance of a high-speed maglev vehicle–bridge system. This approach involves generating the corresponding dynamic response to the sampled control parameters using a theoretical model of a high-speed maglev vehicle–bridge system, followed by establishing an adaptive surrogate model for the relationship between the control parameters and the dynamic response extrema. In the second step, we combine the adaptive surrogate model and the multi-objective gradient-based optimizer (MOGBO) algorithm to obtain the Pareto solution set satisfying different performance indexes. Additionally, the control parameters are optimized using the fuzzy comprehensive evaluation method. In the numerical simulation, we investigate five maglev trains and ten-span simply supported beam bridges and the theoretical model is verified by comparing the calculations with the measured results. The optimization effect of FMOOM is analyzed under different working conditions. The results show that the adaptive surrogate model has good prediction accuracy based on the radial basis function. Furthermore, the Pareto solution distribution of different schemes using FMOOM is reasonable, and the optimization results are as expected. Compared with the reference scheme, the dynamic response of the maglev vehicle–bridge system is smaller after being subjected to FMOOM optimization, and the six performance indexes are dramatically improved.

Study on Vibration and Noise of Railway Steel–Concrete Composite Box Girder Bridge Considering Vehicle–Bridge Coupling Effect

A steel–concrete composite beam bridge fully exploits the mechanical advantages of the concrete structure and steel structure, and has the advantages of a fast construction speed and large stiffness. It is of certain research value to explore the application of this bridge type in the field of railway bridges. However, with the rapid development of domestic high-speed railway construction, the problem of vibration and noise radiation of high-speed railway bridges caused by train loads is becoming more and more serious. A steel–concrete composite beam bridge combines the tensile characteristics of steel and the compressive characteristics of concrete perfectly. At the same time, it also has the characteristics of a steel bridge and concrete bridge in terms of vibration and noise radiation. This feature makes the study of the vibration and noise of the bridge type more complicated. Therefore, in this paper, the characteristics of vibration and noise radiation of a high-speed railway steel–concrete composite box girder bridge are studied in detail from two aspects: the theoretical basis and a numerical simulation. The main results obtained are as follows: Relying on the idea of vehicle–rail–bridge coupling dynamics, a structural dynamics analysis model of a steel–concrete combined girder bridge for a high-speed railroad was established, and numerical program simulation of the vibration of the vehicle–rail–bridge coupling system was carried out based on the parametric design language of ANSYS 18.0 and the language of MATLAB R2021a, and the structural vibration results were analyzed in both the time domain and frequency domain. By using different time-step loading for the vehicle–rail–bridge coupling vibration analysis, the computational efficiency can be effectively improved under the condition of guaranteeing the accuracy of the result analysis within 100 Hz. Based on the power flow equilibrium equation, a statistical energy method of calculating the high-frequency noise radiation is theoretically derived. Based on the theoretical basis of the statistical energy method, the high-frequency noise in the structure is numerically simulated in the VAONE 2021 software, and the average contribution of the concrete roof plate to the three acoustic field points constructed in this paper is as high as 50%, which is of great significance in the study of noise reduction in steel–concrete composite girders.

A bridge dynamic response analysis and load recognition method using traffic imaging

As the primary variable load of bridges, vehicle load is an important parameter for bridge health monitoring. However, traditional Weigh-in-Motion (WIM) systems and the commonly used method of placing sensors on the bridge are challenging to apply in load monitoring for many small and medium-sized bridges. Therefore, this paper proposes a bridge vehicle load identification method based on traffic surveillance video data. Leveraging the surveillance video data on the bridge, without introducing additional hardware devices, the displacement of target points is detected through sub-pixel level image detection algorithms, enabling non-contact measurement of bridge structural response through imaging. A spatiotemporal relationship model of structural displacement, vehicle load, and load distribution is established to solve for vehicle load. Finally, model bridge tests under various loading conditions and engineering practice experiments are conducted to validate the feasibility of the method. The results of the model bridge tests show that the structural displacement measured using traffic video measurement has a deviation of less than 10% compared to the measurements obtained using contact displacement sensors (LVDT), and it can accurately reflect the displacement characteristics of the structure. The results of the field tests demonstrate that the average estimation deviation for heavy vehicle loads ranging from 12 to 18 tons is approximately 18%, meeting the engineering requirements. The proposed method can provide load statistical information for the extensive health monitoring of small and medium-sized bridges and offer a new technical pathway for obtaining bridge load information.

Drive-By Identification of Joint Bridge Damage and Surface Roughness Based on Sensitivity Analysis of Residual Contact Point Deflections

Drive-by inspection of bridge damage using a passing vehicle’s dynamic response has great potential in bridge damage identification. Among the current drive-by methodologies, the methods based on bridge modeling have been proposed for the quantitative identification of bridge damage and bridge surface roughness. However, the coupling of bridge damage and unknown surface roughness increases the difficulty of the identification problem and most previous studies conduct the identification task of bridge damage or bridge surface roughness separately. In this paper, a novel method is proposed for the identification of joint bridge damage and bridge surface roughness based on the residual bridge deflections from the front and rear wheels contact points of an instrumented passing vehicle. The vehicle–bridge interaction is analyzed using a half-car model of a four degrees of freedom (4-DOF) with front and rear vehicle wheels. First, the vehicle–bridge unknown forces and displacement of the vehicle axles are identified by the generalized Kalman filter under unknown input (GKF-UI) proposed by the authors. The sensors can be installed conveniently on the vehicle body due to GKF-UI. Then, the residual bridge deflections from the front and rear vehicle wheels contact points are utilized to eliminate the effect of road surface roughness. Afterward, bridge structural damage is identified based on the sensitivity analysis of residual bridge deflections from the front and rear contact points with [Formula: see text]1-norm regularization. Finally, bridge road surface roughness is estimated based on the identified unknown forces and updated bridge model with damage. The results of numerical identification examples demonstrate the effectiveness of the proposed method for the identification of joint bridge damage and surface roughness.

Ride comfort and impact factor of a seven-span continuous cable-stayed bridge

This study was conducted to investigate the vibration serviceability and impact coefficient of a seven-span continuous cable-stayed bridge planned for an expressway extension using a three-dimensional vehicle–bridge coupled vibration analysis. For the bridge design, deflection under the designed live load of the continuous cable-stayed bridge did not meet the deflection limit specified in “Japanese Design Specifications for Highway Bridges.” The excessive deflection indicates the possibility of poor vibration serviceability. To clarify the bridge vibration serviceability, the dynamic responses of the bridge and passing vehicles were examined using the three-dimensional vehicle–bridge coupled vibration analysis. The three-dimensional analysis was validated by comparing the vibration response of a single-span steel cable-stayed bridge in service subjected to vehicle running tests with those numerical responses from the three-dimensional analysis. The ride comfort of vehicles on the bridge was assessed in terms of vibration serviceability according to the ISO 2613-1 international standard for evaluating whole-body vibration exposure. The observation from the simulation-based investigation demonstrated that the vehicle response does not exceed the ride comfort limit irrespective of vehicle, road, and running conditions. In other words, the findings confirmed a negligible effect of large deflections on driving safety. The impact factors were found to be less than 1.05 for the main girder, less than 1.03 for the main tower base, and less than 1.04 for the cable. The impact factor was greatest when several vehicles were running at resonant headway.

Indirect Identification and Analysis of Bridge Damage Using Vehicle–Bridge Coupled Vibration and Deep Learning

Indirect Identification and Analysis of Bridge Damage Using Vehicle–Bridge Coupled Vibration and Deep Learning

Bridge damage identification based on synchronous statistical moment theory of vehicle–bridge interaction

AbstractConsidering the weak noise resistance and low identification efficiency of traditional bridge damage identification methods, a data‐driven approach based on synchronous statistical moment theory and vehicle–bridge interaction vibration theory is proposed. This method involves two main steps. First, a two‐axle test vehicle is used to collect acceleration response signals synchronously from adjacent designated measurement points while stationary. This operation is repeated to calculate the second‐order statistical moment curvature (SOSMC) difference of entire bridge points corresponding signals in different states. By comparing with the reference value, the preliminary damage location of the bridge can be obtained. Second, the first‐order modal shape curve is constructed using the second‐order statistical moment (SOSM). The refined identification of bridge damage is then based on an improved direct stiffness back calculation of the bridge's stiffness. This article proposes the synchronization theory for the first time and combines it with the statistical moment clustering method, forming an innovative approach to obtaining structural vibration modes. The effectiveness of this method has been well validated through numerical simulations with different parameters and on‐site bridge tests. The research results indicate that SOSMC indicators have better noise resistance and higher recognition efficiency in identifying damage locations, compared to modal curvature and flexibility curvature indicators. Additionally, compared to transfer rate and random subspace methods, the SOSM method results in smaller error and higher identification efficiency.

Simulation and Experimental Study on Bridge–Vehicle Impact Coupling Effect under Pavement Local Deterioration

With the rapid development of China’s transportation network, the demand for bridge construction is increasing, the traffic volume is increasing yearly, and the average vehicle speed and the frequency of overloaded vehicles crossing bridges are soaring. When a vehicle passes over a highway bridge, it can easily form a coupling vibration between the vehicle and bridge due to the excitation of the expansion joint, the unevenness of the bridge deck, and the existing coating-hole. The impact effect is significant, which seriously affects the operation safety of both the vehicle and bridge, seriously damaging the service life of the bridge. Due to the influence of construction technology, it is common for the vibration to meet transverse and longitudinal expansion joints of a prefabricated girder bridge, where an aging bridge deck frequently results in bulges and potholes in asphalt pavement. The bridge vibration amplification effect under the dynamic load of heavy, high-speed vehicles is significant, and research about the large impact coefficient of bridges with local pavement deterioration is urgently needed. This study used SIMULINK simulation software and involved conducting several bridge model tests. Dynamic simulation analyses and running vehicle tests on scaled and real bridge models were carried out to study the coupling vibration response of bridge decks in the presence of different pothole sizes. The results show that the impact effect of low-speed vehicles passing through a larger-sized pothole is relatively significant, and the impact coefficient can be amplified to 214% of the original value under good road surfaces in extreme cases. The vehicle–bridge coupling impact effect of potholes is similar to bulges. This relevant work could provide suggestions for the operational performance evaluation and maintenance of bridges with local pavement deterioration.

Coupled Vibration of a Vehicle Group–Bridge System and Its Application in the Optimal Strategy for Bridge Health Monitoring

The accuracy of bridge performance monitoring and evaluation is easily affected by unfavorable factors such as vehicle coupling and test noise. In order to accurately evaluate the dynamic response and health monitoring threshold of the bridge under different operating conditions, a time-varying dynamic vehicle group model including the main uniform mass and the coupling mass was established, and the influence of road roughness was considered in the coupling equation. A bridge monitoring strategy considering signal noise ratio and vehicle–bridge interaction was proposed, and the effectiveness of the monitoring strategy was verified by taking a simple supported beam as an example. The results showed that the proposed time-varying dynamic vehicle group model could accurately consider the influence of road roughness and estimate the threshold of health monitoring, and the proposed bridge monitoring strategy could filter out a large amount of low signal-to-noise ratio or meaningless data, thus saving computing resources and realizing the lightweight safety monitoring of bridges.

Fatigue Evaluation of CFST Arch Bridge Based on Vehicle–Bridge Coupling Vibration Analysis

This study proposes a fatigue life analysis method for long-span CFST arch bridges based on a vehicle–bridge coupled vibration analysis model, which can analyze the structural dynamic effects and the excessive fatigue damage caused by the passage of vehicles. In situ test analysis of bridge dynamic characteristics is carried out, and a numerical model considering the vehicle–bridge coupled system is validated according to the measured vibration modes, frequency, and displacement time history. The results indicate that the proposed vehicle–bridge coupled vibration numerical model can be used to simulate the dynamic response of the bridge under various conditions. The factors of vehicle speed, vehicle weight, and road surface condition are further selected to analyze the vehicle–bridge coupled vibration effect, and it is found that the response time history is more sensitive to the vehicle weight factor. In addition, the fatigue life of suspenders at different positions is compared, which is found to decrease significantly with a reduction in suspender length. Due to damage to the suspender caused by environmental erosion, the cross-sectional area decreases and the stress amplitude changes, resulting in a decrease in the fatigue reliability of the suspender under different conditions.