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CONTENTS
Volume 63, Number 6, September25 2017
 

Abstract
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Key Words
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Address
Hua-Peng Chen: Department of Engineering Science, University of Greenwich, UK
Ying Lei: School of Architecture and Civil Engineering, Xiamen University, China


Abstract
The composite blades of offshore wind turbines accumulate structural damage such as fatigue cracking due to harsh operation environments during their service time, leading to premature structural failures. This paper investigates various fatigue crack models for reproducing crack development in composite blades and proposes a stochastic approach to predict fatigue crack evolution and to analyse failure probability for the composite blades. Three typical fatigue models for the propagation of fatigue cracks, i.e., Miner model, Paris model and Reifsnider model, are discussed to reproduce the fatigue crack evolution in composite blades subjected to cyclical loadings. The lifetime probability of fatigue failure of the composite blades is estimated by stochastic deterioration modelling such as gamma process. Based on time-dependent reliability analysis and lifecycle cost analysis, an optimised maintenance policy is determined to make the optimal decision for the composite blades during the service time. A numerical example is employed to investigate the effectiveness of predicting fatigue crack growth, estimating the probability of fatigue failure and evaluating an optimal maintenance policy. The results from the numerical study show that the stochastic gamma process together with the proper fatigue models can provide a useful tool for remaining useful life predictions and optimum maintenance strategies of the composite blades of offshore wind turbines.

Key Words
composite blade; offshore wind turbine; fatigue crack; stochastic modelling; reliability analysis; maintenance strategy

Address
Hua-Peng Chen, Chi Zhang: Department of Engineering Science, University of Greenwich, Chatham Maritime, Kent, ME4 4TB, UK
Tian-Li Huang: School of Civil Engineering, Central South University, Changsha, Hunan Province, 410075, China

Abstract
As a new type of ballastless track, longitudinal continuous slab track (CST) has been widely used in China. It can partly isolate the interaction between the ballastless track and the bridge and thus the rail expansion device would be unnecessary. Compared with the traditional track, CST is composed of multi layers of continuous structures and various connecting components. In order to investigate the performance of CST on a long-span bridge, the spatial finite element model considering each layer of the CST structure, connecting components, bridge, and subgrade is established and verified according to the theory of beam-rail interaction. The nonlinear resistance of materials between multilayer track structures is measured by experiments, while the temperature gradients of the bridge and CST are based on the long-term measured data. This study compares the force distribution rules of ballasted track and CST as respectively applied to a long span bridge. The effects of different damage conditions on CST structures are also discussed. The results show that the additional rail stress is small and the CST structure has a high safety factor under the measured temperature load. The rail expansion device can be cancelled when CST is adopted on the long span bridge. Beam end rotation caused by temperature gradient and vertical load will have a significant effect on the rail stress of CST. The additional flexure stress should be considered with the additional expansion stress simultaneously when the rail stress of CST requires to be checked. Both the maximum sliding friction coefficient of sliding layer and cracking condition of concrete plate should be considered to decide the arrangement of connecting components and the ultimate expansion span of the bridge when adopting CST.

Key Words
continuous slab track; continuous welded rail; long-span bridge; temperature gradient; damage conditions; additional rail stress

Address
Gonglian Dai, Hao Ge, Wenshuo Liu: Department of Civil Engineering, Central South University, Changsha, China
Y. Frank Chen: Department of Civil Engineering, Xijing University, Xian, China; Department of Civil Engineering, Pennsylvania University, Middletown, USA

Abstract
This paper investigated the effects of rebar corrosion on bond performance between rebar and two different concrete mixes (compressive strengths of 20.7 MPa and 44.4 MPa). The specimen was designed as a rebar centrally embedded in a 200 mm concrete cube, with two stirrups around the rebar to supply confinement. An electrochemical accelerated corrosion technique was applied to corrode the rebar. 120 specimens of two different concrete mixes with various reinforcing steel corrosion levels were manufactured. The corrosion crack opening width and length were recorded in detail during and after the corrosion process. Three different loading schemes: monotonic pull-out load, 10 cycles of constant slip loading followed by pullout and varied slip loading followed by pull-out, were carried out on the specimens. The effects of rebar corrosion with two different concrete mixes on corrosion crack opening, bond strength and corresponding slip value, initial slope of bond-slip curve, residual bond stress, mechanical interaction stress, and energy dissipation, were discussed in detail. The mean value and coefficient of variation of these parameters were also derived. It was found that the coefficient of variation of the parameters of the corroded specimens was larger than those with intact rebar. There is also obvious difference in the two different concrete mixes for the effects of rebar corrosion on bond-slip parameters.

Key Words
reinforcement; concrete; corrosion; bond; cyclic-loading; performance degradation

Address
Haijun Zhou, Xuebing Liang, Zeqiang Wang, Xiaolin Zhang and Feng Xing: Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, China

Abstract
Steel cables as the most important components are widely used in the certain types of structures such as cablesupported bridges, but the long-span structures may result in an increase in fatigue under high stress and corrosion of steel cables. The traditional steel cable is becoming a more evident hindrance. Fiber Reinforced Polymer (FRP) cables with lightweight, high-strength are widely used in civil engineering, but there is little research in vibrational characteristics of FRP cables, especially on the damping characteristic. This article studied the two methods to evaluate dynamical damping characteristic of basalt FRP(BFRP) and glass FRP(GFRP) cables. First, the vibration tests of the B/G FRP cables with different diameter and different cable force were executed. Second, the cables forces were calculated using dynamic strain, static strain and dynamic acceleration respectively, which were further compared with the measured force. Third, experimental modal damping of each cables was calculated by the half power point method, and was compared with the calculation by Rayleigh damping theory and energy dissipation damping theory. The results indicate that (1) The experimental damping of FRP cables decreases with the increase of cable force, and the trend of experimental damping changes is roughly similar with the theoretical damping. (2) The distribution of modal damping calculated by Rayleigh damping theory is closer to the experimental results, and the damping performance of GFRP cables is better than BFRP cables.

Key Words
cable force; damping ratio; B/GFRP cable; long-gauge strain; vibration test

Address
Qi Xia, JiaJia Wu, XueWu Zhu and Jian Zhang: Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, P.R. China

Abstract
Modal parameter identification plays a key role in the structural health monitoring (SHM) for civil engineering. Eigensystem realization algorithm (ERA) is one of the most popular identification methods. However, the complex environment around civil structures can introduce the noises into the measurement from SHM system. The spurious modes would be generated due to the noises during ERA process, which are usually ignored and be recognized as physical modes. This paper proposes an improved stabilization diagram method in ERA to distinguish the spurious modes. First, it is proved that the ERA can be performed by any two Hankel matrices with one time step shift. The effect of noises on the eigenvalues of structure is illustrated when the choice of two Hankel matrices with one time step shift is different. Then, a moving data diagram is proposed to combine the traditional stabilization diagram to form the improved stabilization diagram method. The moving data diagram shows the mode variation along the different choice of Hankel matrices, which indicates whether the mode is spurious or not. The traditional stabilization diagram helps to determine the concerned truncated order before moving data diagram is implemented. Finally, the proposed method is proved through a numerical example. The results show that the proposed method can distinguish the spurious modes.

Key Words
eigensystem realization algorithm (ERA); spurious mode; stabilization diagram; Hankel matrix; singular value decomposition (SVD)

Address
Chun-Xu Qu: School of Civil Engineering, Dalian University of Technology, Dalian, 116024, China; State Key Laboratory of Building Safety and Built Environment, Beijing, 100013, China
Ting-Hua Yi, Xiao-Mei Yang, Hong-Nan Li: School of Civil Engineering, Dalian University of Technology, Dalian, 116024, China

Abstract
In recent years, multifractal-based analysis methods have been widely applied in engineering. Among these methods, multifractal detrended cross-correlation analysis (MFDXA), a branch of fractal analysis, has been successfully applied in the fields of finance and biomedicine. For its great potential in reflecting the subtle characteristic among signals, a structural health monitoring (SHM) system based on MFDXA is proposed. In this system, damage assessment is conducted by exploiting the concept of multifractal theory to quantify the complexity of the vibration signal measured from a structure. According to the proposed algorithm, the damage condition is first distinguished by multifractal detrended fluctuation analysis. Subsequently, the relationship between the q-order, q-order detrended covariance, and length of segment is further explored. The dissimilarity between damaged and undamaged cases is visualized on contour diagrams, and the damage location can thus be detected using signals measured from different floors. Moreover, a damage index is proposed to efficiently enhance the SHM process. A sevenstory benchmark structure, located at the National Center for Research on Earthquake Engineering (NCREE), was employed for an experimental verification to demonstrate the performance of the proposed SHM algorithm. According to the results, the damage condition and orientation could be correctly identified using the MFDXA algorithm and the proposed damage index. Since only the ambient vibration signal is required along with a set of initial reference measurements, the proposed SHM system can provide a lower cost, efficient, and reliable monitoring process.

Key Words
multifractal; detrended fluctuation analysis; detrended cross-correlation analysis; structural health monitoring

Address
Tzu-Kang Lin and Yi-Hsiu Chien: Department of Civil Engineering, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan

Abstract
Accurately extracting the axle distribution information of a passing vehicle from bridge dynamic responses experiences a key and challenging step in non-pavement bridge weigh-in-motion (BWIM). In this article, the wavelet transformation is adopted and the wavelet coefficient curve is used as a substitute for dynamic response. The driving frequency is introduced and expanded to multi-axle vehicle, and the wavelet coefficient curve on specific scale corresponding to the driving frequency is confirmed to contain obvious axle information. On this basis, an automatic method for axle distribution information identification is proposed. The specific wavelet scale can be obtained through iterative computing, and the false peaks due to bridge vibration can be eliminated through cross-correlation analysis of the wavelet coefficients of two measure points. The integrand function that corresponds to the maximum value of the cross-correlation function is used to identify the peaks caused by axles. A numerical application of the proposed axle information identification method is carried out. Numerical results demonstrate that this method acquires precise axle information from the responses of an axle-insensitive structure (e.g., girder) and decreases the requirement of sensitivity structure of BWIM. Finally, an experimental study on a full-scale simply supported bridge is also conducted to verify the effectiveness of this method.

Key Words
dynamic strain responses; axle distribution information; automatic identification; wavelet coefficient; driving frequency; specific scale

Address
Ning-Bo Wang: School of Civil Engineering, Central South University, Changsha 410075, Hunan, China
Wei-Xin Ren: Department of Civil Engineering, Hefei University of Technology, Hefei 230009, Anhui, China
Zhi-Wei Chen: Department of Civil Engineering, Xiamen University, Xiamen 361005, Fujian, China

Abstract
The applications of smartphones or other portable smart devices have dramatically changed people\'s lifestyle. Researchers have been investigating useage of smartphones for structural health monitoring, earthquake monitoring, vibration measurement and human posture recognition. Their results indicate a great potential of smartphones for measuring pedestrianinduced loads like walking, jumping and bouncing. Smartphone can catch the device\'s motion trail, which provides with a new method for pedestrain load measurement. Therefore, this study carried out a series of experiments to verify the application of the smartphone for measuring human-induced load. Shaking table tests were first conducted in order to compare the smartphones\' measurements with the real input signals in both time and frequency domains. It is found that selected smartphones have a satisfied accuracy when measuring harmonic signals of low frequencies. Then, motion capture technology in conjunction with force plates were adopted in the second-stage experiment. The smartphone is used to record the acceleration of center-of-mass of a person. The human-induced loads are then reconstructed by a biomechanical model. Experimental results demonstrate that the loads measured by smartphone are good for bouncing and jumping, and reasonable for walking.

Key Words
portable devices; embedded sensor; MEMS technology; human-induced model

Address
Ziye Pan and Jun Chen: Department of Structural Engineering, Tongji University, Shanghai, China

Abstract
System identification and damage detection for structural health monitoring have received considerable attention. Various time domain analysis methodologies based on measured vibration data of structures have been proposed. Among them, recursive least-squares estimation of structural parameters which is also known as parametric Kalman filter (PKF) approach has been studied. However, the conventional PKF requires that all the external excitations (inputs) be available. On the other hand, structural uncertainties are inevitable for civil infrastructures, it is necessary to develop approaches for probabilistic damage detection of structures. In this paper, a parametric Kalman filter with unknown inputs (PKF-UI) is proposed for the simultaneous identification of structural parameters and the unmeasured external inputs. Analytical recursive formulations of the proposed PKF-UI are derived based on the conventional PKF. Two scenarios of linear observation equations and nonlinear observation equations are discussed, respectively. Such a straightforward derivation of PKF-UI is not available in the literature. Then, the proposed PKF-UI is utilized for probabilistic damage detection of structures by considering the uncertainties of structural parameters. Structural damage index and the damage probability are derived from the statistical values of the identified structural parameters of intact and damaged structure. Some numerical examples are used to validate the proposed method.

Key Words
parametric Kalman filter; unknown Input; structural identification; probabilistic damage detection; uncertainties

Address
Lijun Liu, Han Su and Ying Lei: Department of Civil Engineering, Xiamen University, Xiamen, 361005,China

Abstract
Recently, some integrated structural identification/damage detection and reliability evaluation of structures with uncertainties have been proposed. However, these techniques are applicable for off-line synthesis of structural identification and reliability evaluation. In this paper, based on the recursive formulation of the extended Kalman filter, an on-line integration of structural identification/damage detection and reliability evaluation of stochastic building structures is investigated. Structural limit state is expanded by the Taylor series in terms of uncertain variables to obtain the probability density function (PDF). Both structural component reliability with only one limit state function and system reliability with multi-limit state functions are studied. Then, it is extended to adopt the recent extended Kalman filter with unknown input (EKF-UI) proposed by the authors for on-line integration of structural identification/damage detection and structural reliability evaluation of stochastic building structures subject to unknown excitations. Numerical examples are used to demonstrate the proposed method. The evaluated results of structural component reliability and structural system reliability are compared with those by the Monte Carlo simulation to validate the performances of the proposed method.

Key Words
structural identification; damage detection; uncertainties; probability; reliability evaluation; on-line; Integration; extended Kalman filter; partial measurements

Address
Ying Lei, Longfei Wang, Lanxin Lu: School of Architecture and Civil Engineering, Xiamen University, Xiamen, 361005, China
Dandan Xia: School of Civil & Architecture Engineering, Xiamen University of Technology, Xiamen, 361024, China

Abstract
Failure of a redundant long-span bridge is often described by innumerable failure modes, which make the structural system reliability analysis become a computationally intractable work. In this paper, an innovative procedure is proposed to efficiently identify the dominant failure modes and quantify the structural reliability for a long-span bridge system. The procedure is programmed by ANSYS and MATLAB. Considering the correlation between failure paths, a new branch and bound operation criteria is applied to the traditional stage critical strength branch and bound algorithm. Computational effort can be saved by ignoring the redundant failure paths as early as possible. The reliability of dominant failure mode is computed by FORM, since the limit state function of failure mode can be expressed by the final stage critical strength. PNET method and FORM for system are suggested to be the suitable calculation method for the bridge system reliability. By applying the procedure to a CFST arch bridge, the proposed method is demonstrated suitable to the system reliability analysis for long-span bridge structure.

Key Words
long-span arch bridge; system reliability; dominant failure mode, identification strategy; branch-and-bound

Address
Xin Gao: College of Construction Engineering, Jilin University, 130026 Jilin, P.R. China
Shunlong Li: Department of Civil Engineering, Harbin Institute of Technology, 150090 Harbin, P.R. China

Abstract
The accurate evaluation of wind characteristics and wind-induced structural responses during a typhoon is of significant importance for bridge design and safety assessment. This paper presents an expectation maximization (EM) algorithm-based angular-linear approach for probabilistic modeling of field-measured wind characteristics. The proposed method has been applied to model the wind speed and direction data during typhoons recorded by the structural health monitoring (SHM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. In the summer of 2015, three typhoons, i.e., Typhoon Chan-hom, Typhoon Soudelor and Typhoon Goni, made landfall in the east of China and then struck the Jiubao Bridge. By analyzing the wind monitoring data such as the wind speed and direction measured by three anemometers during typhoons, the wind characteristics during typhoons are derived, including the average wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, and power spectral density (PSD). An EM algorithm-based angularlinear modeling approach is proposed for modeling the joint distribution of the wind speed and direction. For the marginal distribution of the wind speed, the finite mixture of two-parameter Weibull distribution is employed, and the finite mixture of von Mises distribution is used to represent the wind direction. The parameters of each distribution model are estimated by use of the EM algorithm, and the optimal model is determined by the values of R2 statistic and the Akaike

Key Words
structural health monitoring; wind characteristics; typhoon; joint distribution function; angular-linear approach; expectation maximization algorithm

Address
X.W. Ye, P.S. Xi, Y.H. Su and B. Chen: Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China

Abstract
Significant improvements to methodologies on structural damage detection (SDD) have emerged in recent years. However, many methods are related to inversion computation which is prone to be ill-posed or ill-conditioning, leading to lowcomputing efficiency or inaccurate results. To explore a more accurate solution with satisfactory efficiency, a PSO-INM algorithm, combining particle swarm optimization (PSO) algorithm and an improved Nelder-Mead method (INM), is proposed to solve multi-sample objective function defined based on Bayesian inference in this study. The PSO-based algorithm, as a heuristic algorithm, is reliable to explore solution to SDD problem converted into a constrained optimization problem in mathematics. And the multi-sample objective function provides a stable pattern under different level of noise. Advantages of multi-sample objective function and its superior over traditional objective function are studied. Numerical simulation results of a two-storey frame structure show that the proposed method is sensitive to multi-damage cases. For further confirming accuracy of the proposed method, the ASCE 4-storey benchmark frame structure subjected to single and multiple damage cases is employed. Different kinds of modal identification methods are utilized to extract structural modal data from noise-contaminating acceleration responses. The illustrated results show that the proposed method is efficient to exact locations and extents of induced damages in structures.

Key Words
structural damage detection; PSO-INM; multi-sample objective function; benchmark model

Address
Ze-peng Chen: School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, China; MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632, China
Ling Yu: School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, China; MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632, China; College of Civil Engineering and Architecture, China Three Gorges University, Yichang 443002, China

Abstract
An accurate calculation of the stochastic wind field is the foundation for analyzing wind-induced structure response and reliability. In this research, the spatial correlation of structural wind field was considered based on the time domain method. A method for calculating the stochastic wind field based on cross stochastic Fourier spectrum was proposed. A flowchart of the proposed methodology is also presented in this study to represent the algorithm and workflow. Along with the analysis of regional wind speed distribution, the wind speed time history sample was calculated, and the efficiency can therefore be verified. Results show that the proposed method and programs could provide an efficient simulation for the wind-induced structure response analysis, and help determine the related parameters easily.

Key Words
stochastic wind field; cross stochastic Fourier spectrum; wind speed time history; time domain method; fluctuating wind field; structure wind induced respond

Address
Li Lin: School of Civil & Architecture Engineering, Xiamen University of Technology, 600 Ligong Road, Xiamen, China; College of Civil Engineering, Hunan University, 109 Shijiachong Road, Changsha, China; Department of Civil & Environmental Engineering, University of California, Irvine, 4136 Engineering Gateway, USA
A.H.S. Ang: Department of Civil & Environmental Engineering, University of California, Irvine, 4136 Engineering Gateway, USA
Dan-dan Xia, Hai-tao Hu, Huai-feng Wang: School of Civil & Architecture Engineering, Xiamen University of Technology, 600 Ligong Road, Xiamen, China
Fu-qiang He: School of Civil & Architecture Engineering, Xiamen University of Technology, 600 Ligong Road, Xiamen, China; Fujian Provincial Key Laboratory of Fire Retardant Materials, 422 Siming Road, Xiamen, China

Abstract
Excessive vibrations can occur in long-span structures such as floors or footbridges due to occupant\'s daily activity like walking and cause a so-called vibration serviceability issue. Since 1970s, researchers have proposed many human walking load models, and some of them have even been adopted by major design guidelines. Despite their wide applications in structural vibration serviceability problems, differences between these models in predicting structural responses are not clear. This paper collects 19 popular walking load models and compares their effects on structure\'s responses when subjected to the human walking loads. Model parameters are first compared among all these models including orders of components, dynamic load factors, phase angles and function forms. The responses of a single-degree-of-freedom system with various natural frequencies to the 19 load models are then calculated and compared in terms of peak values and root mean square values. Case studies on simulated structures and an existing long-span floor are further presented. Comparisons between predicted responses, guideline requirements and field measurements are conducted. All the results demonstrate that the differences among all the models are significant, indicating that in a practical design, choosing a proper walking load model is crucial for the structure\'s vibration serviceability assessment.

Key Words
walking load model; comparative study; long-span structures; vibration serviceability

Address
Jinping Wang and Jun Chen: Department of Structural Engineering, Tongji University, 1239 Siping Road, Shanghai, P.R. China


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