Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Measurement of wind field characteristics at a long-span suspension bridge

In order to provide a reliable basis for wind resistant evaluation of a long-span suspension bridge, a structural health monitoring system is installed on a bridge in the East China Sea and the simultaneous wind data at the bridge deck and at the top of the bridge tower are recorded. The average wind speeds and directions, variations of wind speeds with height, turbulent characteristics, spatial correlation and characteristics of wind flow around the bridge deck are analyzed by using statistical methods and spectral analysis. It is found that the average wind speeds along the bridge girder are almost identical; however, the mean wind directions vary greatly at different locations. The dimensionless exponent decreases as the average wind speed increases. The measured turbulence intensities are greater than the recommended values, and the turbulence power spectrum can well fit the standard spectrum. However, the measured spectral values are considerably smaller in low frequency ranges. The mean wind speed of the wake flow decreases and the turbulence intensity increases significantly, and the spectral characteristics of the wake flow change obviously while the feature frequency of vortex shedding has not yet been observed.

Damage alarming of long-span suspension bridge based on GPS-RTK monitoring

Structure damage identification and alarming of long-span bridge were conducted with three-dimensional dynamic displacement data collected by GPS subsystem of health monitoring system on Runyang Suspension Bridge.First,the effects of temperature on the main girder spatial position coordinates were analyzed from the transverse,longitudinal and vertical directions of bridge,and the correlation regression models were built between temperature and the position coordinates of main girder in the longitudinal and vertical directions;then the alarming indices of coordinate residuals were conducted,and the mean-value control chart was applied to making statistical pattern identification for abnormal changes of girder dynamic coordinates;and finally,the structural damage alarming method of main girder was established.Analysis results show that temperature has remarkable correlation with position coordinates in the longitudinal and vertical directions of bridge,and has weak correlation with the transverse coordinates.The 3%abnormal change of the longitudinal coordinates and 5%abnormal change of the vertical ones caused by structural damage are respectively identified by the mean-value control chart method based on GPS dynamic monitoring data and hence the structural abnormalities state identification and damage alarming for main girder of long-span suspension bridge can be realized in multiple directions.

Advanced aerostatic analysis of long-span suspension bridges

As the span length of suspension bridges increases, the diameter of cables and thus the wind load acting on them, the nonlinear wind-structure interaction and the wind speed spatial non-uniformity all increase consequently, which may have unnegligible influence on the aerostatic behavior of long-span suspension bridges. In this work, a method of advanced aerostatic analysis is presented firstly by considering the geometric nonlinearity, the nonlinear wind-structures and wind speed spatial non-uniformity. By taking the Runyang Bridge over the Yangtze River as example, effects of the nonlinear wind-structttre interaction, wind speed spatial non-uniformity, and the cable＇s wind load on the aerostatic behavior of the bridge are investigated analytically. The results showed that these factors all have important influence on the aerostatic behavior, and should be considered in the aerostatic analysis of long and particularly super long-span suspension bridges.

Structural condition assessment of long-span suspension bridges using long-term monitoring data

This paper focuses on developing an online structural condition assessment technique using long-term monitoring data measured by a structural health monitoring system. The seasonal correlations of frequency-temperature and beam-end displacement-temperature for the Runyang Suspension Bridge are performed, first. Then, a statistical modeling technique using a six-order polynomial is further applied to formulate the correlations of frequency-temperature and displacement-temperature, from which abnormal changes of measured frequencies and displacements are detected using the mean value control chart. Analysis results show that modal frequencies of higher vibration modes and displacements have remarkable seasonal correlations with the environmental temperature and the proposed method exhibits a good capability for detecting the micro damage-induced changes of modal frequencies and displacements. The results demonstrate that the proposed method can effectively eliminate temperature complications from frequency and displacement time series and is well suited for online condition monitoring of long-span suspension bridges.

Non-linear buffeting response analysis of long-span suspension bridges with central buckle

The rigid central buckle employed in the Runyang Suspension Bridge (RSB) was the first time it was used in a suspension bridge in China. By using a spectral representation method and FFT technique combined with measured data,a 3D fluctuating wind field considering the tower wind effect is simulated. A novel FE model for buffeting analysis is then presented,in which a specific user-defined Matrix27 element in ANSYS is employed to simulate the aeroelastic forces and its stiffness or damping matrices are parameterized by wind velocity and vibration frequency. A nonlinear time history analysis is carried out to study the influence of the rigid central buckle on the wind-induced buffeting response of a long-span suspension bridge. The results can be used as a reference for wind resistance design of long-span suspension bridges with a rigid central buckle in the future.

Performance-based system seismic assessment for long-span suspension bridges under two-level seismic hazard

Since there are few studies on the performance-based seismic evaluation of the long-span suspension bridge system under two-level earthquake hazard in Chinese code,the developed procedure of this study can be regarded as a general program to assess the seismic performance of the overall system for long-span suspension bridges.In the procedure,the probabilistic seismic demand models of multiple bridge components were developed by nonlinear time-history analyses incorporating the related uncertainties,and the component-level fragility curves were calculated by the reasonable definition of limit states of the corresponding components in combination with seismic hazard analysis.The bridge repair cost ratios used to evaluate the system seismic performance were derived through the performance-based methodology and the damage probability of critical components.Furthermore,the repair cost ratios of the overall bridge system that was retrofitted with fluid viscous dampers for the main bridge and changed restraint systems for the approach bridges were compared.The results show that peak ground velocity and peak ground acceleration can be selected as the optimal intensity measurements of long-span suspension bridges using the TOPSIS(technique for order preference by similarity to an ideal solution).The bridge repair cost ratios can serve as accurate evaluation indicators to provide an efficient evaluation of retrofit measures.The seismic evaluation of long-span bridges is misled when ignoring the interaction of adjacent structures.However,the repair cost ratios of a bridge system that has optimum seismic performance are less sensitive to the relative importance of adjacent structures.

Three-dimensional nonlinear flutter analysis of long-span suspension bridges during erection

In this work, the aerodynamic stability of the Yichang Suspension Bridge over Yangtze River during erection was determined by three dimensional nonlinear flutter analysis, in which the nonlinearities of structural dynamic characteristics and aeroelastic forces caused by large deformation are fully considered. An interesting result obtained was that the bridge was more stable when the stiffening girders were erected in a non symmetrical manner as opposed to the traditional symmetrical erection schedule. It was also found that the severe decrease in the aerodynamic stability was due to the nonlinear effects. Therefore, the nonlinear factors should be considered accurately in aerodynamic stability analysis of long span suspension bridges during erection.

Influence of rigid central buckle on seismic response of long-span suspension bridges

A rigid central buckle is employed in Runyang Suspension Bridge （RSB） to replace commonly used short suspenders in the main span. Based on the seismic waves with 2% probabilities of exceedance, the nonlinear seismic response time-domain analysis are then conducted and influence of central buckles on seismic response of long-span suspension bridge is specially studied. Analysis resuits show that the central buckle can effectively control the longitudinal floating vibration mode of the deck, and therefore reduce earthquake-excited longitudinal displacement at the end of the deck. However, the central buckle may cause increment of longitudinal displacement at the top of main tower and bending moment at the bottom of the main tower, which should be paid special attention to. Results provide references for anti-earthquake analysis and design of long-span suspension bridges using rigid central buckles.

Analysis on Bearing Capacity of Tunnel-Type Anchorage of a Long-Span Suspension Bridge

Due to complicated rock structure and environment, a prototype test for a tunnel-type anchorage is infeasible. Based on the rock mass parameters from tests, a three-dimensional （3D） elastoplastic analysis was performed to simulate the influence of the construction procedure of Siduhe bridge with tunnel-type anchorage （TTA） in Hubei Province, China. The surrounding rock and concrete anchorage body were simulated by 8 nodes 3D brick elements. The geostatic state of the complex geometric structure was established with initial data. The in-situ concrete casting of the anchorage body and excavation of the rock mass were simulated by tetrahedral shell elements. The results show that the surrounding rock is in an elastic state under the designed cable force. The numerical overloading analysis indicates that the capacity of the surrounding anchorage is 7 times that of the designed cable force. The failure pattern shows that two anchorage bodies would be pulled out in the end. The maximum shear stress appears 10 m before the back anchorage face. The maximum range influenced by the TTA under ultimate loads is about 16 m.

Defect Inspection Technology for Steel Truss Suspension Bridges

Steel truss suspension bridges are prone to developing defects after prolonged use.These defects may include corrosion of the main cable or the steel truss.To ensure the normal and safe functioning of the suspension bridge,it is necessary to inspect for defects promptly,understand the cause of the defect,and locate it through the use of inspection technology.By promptly addressing defects,the suspension bridge’s safety can be ensured.The author has analyzed the common defects and causes of steel truss suspension bridges and proposed specific inspection technologies.This research is intended to aid in the timely discovery of steel truss suspension bridge defects.

Deformation monitoring of long-span railway bridges based on SBAS-InSAR technology

The deformation monitoring of long-span railway bridges is significant to ensure the safety of human life and property.The interferometric synthetic aperture radar(In SAR)technology has the advantage of high accuracy in bridge deformation monitoring.This study monitored the deformation of the Ganjiang Super Bridge based on the small baseline subsets(SBAS)In SAR technology and Sentinel-1A data.We analyzed the deformation results combined with bridge structure,temperature,and riverbed sediment scouring.The results are as follows:(1)The Ganjiang Super Bridge area is stable overall,with deformation rates ranging from-15.6 mm/yr to 10.7 mm/yr(2)The settlement of the Ganjiang Super Bridge deck gradually increases from the bridge tower toward the main span,which conforms to the typical deformation pattern of a cable-stayed bridge.(3)The sediment scouring from the riverbed cause the serious settlement on the bridge’s east side compared with that on the west side.(4)The bridge deformation negatively correlates with temperature,with a faster settlement at a higher temperature and a slow rebound trend at a lower temperature.The study findings can provide scientific data support for the health monitoring of long-span railway bridges.

Safety of the express freight train running over a long-span bridge

Purpose-Express freight transportation is in rapid development currently.Owing to the higher speed of express freight train,the deformation of the bridge deck worsens the railway line condition under the action of wind and train moving load when the train runs over a long-span bridge.Besides,the blunt car body of vehicle has poor aerodynamic characteristics,bringing a greater challenge on the running stability in the crosswind.Design/methodology/approach-In this study,the aerodynamic force coefficients of express freight vehicles on the bridge are measured by scale model wind tunnel test.The dynamic model of the train-long-span steel truss bridge coupling system is established,and the dynamic response as well as the running safety of vehicle are evaluated.Findings-The results show that wind speed has a significant influence on running safety,which is mainly reflected in the over-limitation of wheel unloading rate.The wind speed limit decreases with train speed,and it reduces to 18.83 m/s when the train speed is 160 km/h.Originality/value-This study deepens the theoretical understanding of the interaction between vehicles and bridges and proposes new methods for analyzing similar engineering problems.It also provides a new theoretical basis for the safety assessment of express freight trains.

Multi-type sensor placement and response reconstruction for structural health monitoring of long-span suspension bridges

This study is devoted to the experimental validation of the multi-type sensor placement and response reconstruction method for structural health monitoring of long-span suspension bridges. The method for multi-type sensor placement and response reconstruction is briefly described. A test bed, comprising of a physical model and an updated finite element （P-E） model of a long-span suspension bridge is also concisely introduced. The proposed method is then applied to the test bed; the equation of motion of the test bed subject to ground motion, the objective function for sensor location optimization, the principles for mode selection and multi-type response reconstruction are established. A numerical study using the updated FE model is performed to select the sensor types, numbers, and locations. Subsequently, with the identified sensor locations and some practical considerations, fiber Bragg grating （FBG） sensors, laser displacement transducers, and accelerometers are installed on the physical bridge model. Finally, experimental investigations are conducted to validate the proposed method. The experimental results show that the reconstructed responses using the measured responses from the limited number of multitype sensors agree well with the actual bridge responses. The proposed method is validated to be feasible and effective for the monitoring of structural behavior of longspan suspension bridges.

A method for calculating strand tension in the anchor span of a suspension bridge considering the rotation of a splay saddle

This paper reports a method for strand tension in anchor spans considering rotation.A kind of co-moved coordinate system,a saddle local coordinate system,was set up.This system implemented the rotation of the splay saddle through the rotation of the coordinate system,and all calculations proceeded in this coordinate system.Considering the rotation of the anchoring surface by the rotation of the local coordinate system of the anchoring surface,the anchorage point coordinates of strands were transformed to the local sadle coordinate system.There was a two-layer iteration adopted in the calculation.In the inner iteration,the cable force at the end of the vertical bend was taken as the variable,and the ordinate of the anchorage point was taken as the target value.In the outer iteration,the vertical tangential angle at the end of the vertical bend was taken as the variable,and the ordinate of the anchorage point was taken as the target value.The method carried out the rotation of the splay saddle and anchor surface and was simple,convenient and without approximation.The effect of rotation was considered precisely;it showed stability during the process of two-layer iteration,powerful adaptation and higher efficiency and had been successfully applied in the construction control of the Wufengshan Yangtze River Bridge,the world's first kilometer-level combined highway and railway suspension bridge.

Mechanical deformation properties of Continuous Welded Rail on kilometer-span suspension bridge for high-speed railway

The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.

Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.

Accurate stress analysis on rigid central buckle of long-span suspension bridges based on submodel method

Runyang Suspension Bridge (RSB) with the main span of 1490 m is the longest bridge in China and the third longest one in the world. In this bridge the rigid central buckle is employed for the first time in the mid-span of the suspension bridge in China. For such a super-long-span bridge, the traditional finite element (FE) modeling technique and stress analysis methods obviously cannot satisfy the needs of conducting accurate stress analysis on the central buckle. In this paper, the submodel method is in- troduced and for the first time used in analyzing the stresses of the central buckle. After an accurate FE submodel of the central buckle was specially established according to the analysis results from the whole FE model, the connection technique between the two-scale FE models was realized and the ac- curate stresses of the central buckle under various vehicle load cases were then conducted based on the submodel method. The calculation results were testified to be accurate and reliable by the field measurements, which show the efficiency and reliability of the submodel method on analyzing the mechanical condition of the central buckle of long-span suspension bridges. Finally, the working be- havior and mechanical characteristics of the central buckle of the RSB under vehicle loads were ana- lyzed based on the calculation and measurement results. The results obtained in this paper can provide theoretic references for analyzing and designing the rigid central buckle in long-span suspension bridges in future.

Damper placement for seismic control of super-long-span suspension bridges based on the first-order optimization method

To ensure the anti-earthquake performances of super-long-span suspension bridges, effective devices should be employed to control the seismic response of key sections. In this paper, four kinds of assessment functions for seismic response control effect are formulated based on the mechanism of seismic response control with dampers and the seismic response characteristics of long-span suspension bridges. A new optimal placement method of dampers using penalty function and first-order optimization theory is then proposed. Runyang suspension bridge (RSB) with a main span of 1490 m is then taken as an example. After seismic response time-history analyses on RSB using different placements of dampers, the analysis results are optimized by employing the optimal placement method and the optimal placements of dampers with the four assessment functions are then achieved respectively. Comparison of the four optimal control effects show that different assessment functions can lead to different optimal placements when the number of dampers is certain, but all placements of dampers can reduce the seismic response of RSB significantly. The selection of assessment functions and damper optimal placement should be determined by the structural characteristics and by what is considered in the structures. Results also show that the first-order optimization is an effective method on determining the optimal placement of dampers.

Temperature gradient and its effect on flat steel box girder of long-span suspension bridge

The temperature field variation law and distribution characteristics of an orthotropic flat steel box girder under sunny conditions were analyzed through a field temperature test on the steel box girder of the operational Runyang Yangtze River Bridge(the suspension bridge part).Function optimization fitting and error analysis of the test data were conducted.A temperature gradient distribution curve applicable to a hexagonal flat steel box girder was proposed.Based on the measurement results,the temperature effect of an orthotropic flat steel box girder was analyzed using finite element method and the effects of different temperature gradient modes on the mechanical characteristics and stress distribution of the steel box girder were compared.Under sunny conditions,heat conduction in the flat steel box girder structure shows distinct "box-room effect" characteristics,and the actual temperature gradient distribution is inconsistent with the one suggested by the existing standards.The thermal stress of a steel box girder calculated from the measured temperature gradient mode exceeds that calculated from the standard,and the intensity approximates that under the action of designed vehicle loads.The temperature-induced stress is distributed centrally near the manufacturing welds of the orthotropic steel box girder,which should be considered in design,construction and research.Results from this study could supplement the existing bridge and culvert design standards.