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CONTENTS
Volume 17, Number 3, March 2016
 

Abstract
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Key Words
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Address
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Abstract
Deficient modes that cannot be always identified from different sets of measurement data may exist in the application of operational modal analysis such as the stochastic subspace identification techniques in large-scale civil structures. Based on a recent work using the long-term ambient vibration measurements from an instrumented cable-stayed bridge under different wind excitation conditions, a benchmark problem is launched by taking the same bridge as a test bed to further intensify the exploration of mode identifiability. For systematically assessing this benchmark problem, a recently developed SSI algorithm based on an alternative stabilization diagram and a hierarchical sifting process is extended and applied in this research to investigate several sets of known and blind monitoring data. The evaluation of delicately selected cases clearly distinguishes the effect of traffic excitation on the identifiability of the targeted deficient mode from the effect of wind excitation. An additional upper limit for the vertical acceleration amplitude at deck, mainly induced by the passing traffic, is subsequently suggested to supplement the previously determined lower limit for the wind speed. Careful inspection on the shape vector of the deficient mode under different excitation conditions leads to the postulation that this mode is actually induced by the motion of the central tower. The analysis incorporating the tower measurements solidly verifies this postulation by yielding the prevailing components at the tower locations in the extended mode shape vector. Moreover, it is also confirmed that this mode can be stably identified under all the circumstances with the addition of tower measurements. An important lesson learned from this discovery is that the problem of mode identifiability usually comes from the lack of proper measurements at the right locations.

Key Words
stochastic subspace identification; cable-stayed bridge; mode identifiability; alternative stabilization diagram; hierarchical sifting process

Address
Wen-Hwa Wu, Chien-Chou Chen and Gwolong Lai: Department of Construction Engineering, National Yunlin University of Science and Technology,123 University Road, Touliu, Yunlin 640, Taiwan
Sheng-Wei Wang: Graduate School of Engineering Science and Technology, National Yunlin University of Science and Technology, 123 University Road, Touliu, Yunlin 640, Taiwan


Abstract
This study investigates the mode identifiability of a multi-span cable-stayed bridge in terms of a benchmark study using stabilization diagrams of a system model identified using stochastic subspace identification (SSI). Cumulative contribution ratios (CCRs) estimated from singular values of system models under different wind conditions were also considered. Observations revealed that wind speed might influence the mode identifiability of a specific mode of a cable-stayed bridge. Moreover the cumulative contribution ratio showed that the time histories monitored during strong winds, such as those of a typhoon, can be modeled with less system order than under weak winds. The blind data Acc 1 and Acc 2 were categorized as data obtained under a typhoon. Blind data Acc 3 and Acc 4 were categorized as data obtained under wind conditions of critical wind speeds around 7.5 m/s. Finally, blind data Acc 5 and Acc 6 were categorized as data measured under weak wind conditions.

Key Words
benchmark study; cable-stayed bridge; cumulative contribution ratio; operational modal identification

Address
Y. Goi and C.W. Kim:Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto 615-8540, Japan

Abstract
The recent research on proper orthogonal decomposition (POD) has revealed the linkage between proper orthogonal modes and linear normal modes. This paper presents an investigation into the modal identifiability of an instrumented cable-stayed bridge using an adapted POD technique with a band-pass filtering scheme. The band-pass POD method is applied to the datasets available for this benchmark study, aiming to identify the vibration modes of the bridge and find out the so-called deficient modes which are unidentifiable under normal excitation conditions. It turns out that the second mode of the bridge cannot be stably identified under weak wind conditions and is therefore regarded as a deficient mode. To judge if the deficient mode is due to its low contribution to the structural response under weak wind conditions, modal coordinates are derived for different modes by the band-pass POD technique and an energy participation factor is defined to evaluate the energy participation of each vibration mode under different wind excitation conditions. From the non-blind datasets, it is found that the vibration modes can be reliably identified only when the energy participation factor exceeds a certain threshold value. With the identified threshold value, modal identifiability in use of the blind datasets from the same structure is examined.

Key Words
cable-stayed bridge; modal identifiability; deficient mode; proper orthogonal decomposition; energy participation factor

Address
M. Li and Y.Q. Ni: Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong


Abstract
This paper was written in the context of a benchmark study promoted by The Hong Kong Polytechnic University using data samples collected in an instrumented cable-stayed bridge. The main goal of the benchmark test was to study the identification of the bridge modes of vibration under different wind conditions. In this contribution, the tools developed at ViBest/FEUP for automated data processing of setups collected by dynamic monitoring systems are presented and applied to the data made available in the context of the benchmark study. The applied tools are based on parametric output only modal identification methods combined with clustering algorithms. The obtained results demonstrate that the proposed algorithms succeeded to automatically identify the modes with relevant contribution for the bridge response under different wind conditions.

Key Words
automated operational modal analysis; cable-stayed bridge; benchmark study

Address
Filipe Magalhães and Álvaro Cunha: CONSTRUCT – ViBest, Faculty of Engineering, University of Porto (FEUP),
Rua Dr. Roberto Frias, 4200-465 Porto, Portugal


Abstract
In this study, the Bayesian probabilistic framework is investigated for modal identification and modal identifiability based on the field measurements provided in the structural health monitoring benchmark problem of an instrumented cable-stayed bridge named Ting Kau Bridge (TKB). The comprehensive structural health monitoring system on the cable-stayed TKB has been operated for more than ten years and it is recognized as one of the best test-beds with readily available field measurements. The benchmark problem of the cable-stayed bridge is established to stimulate investigations on modal identifiability and the present paper addresses this benchmark problem from the Bayesian prospective. In contrast to deterministic approaches, an appealing feature of the Bayesian approach is that not only the optimal values of the modal parameters can be obtained but also the associated estimation uncertainty can be quantified in the form of probability distribution. The uncertainty quantification provides necessary information to evaluate the reliability of parametric identification results as well as modal identifiability. Herein, the Bayesian spectral density approach is conducted for output-only modal identification and the Bayesian model class selection approach is used to evaluate the significance of different modes in modal identification. Detailed analysis on the modal identification and modal identifiability based on the measurements of the bridge will be presented. Moreover, the advantages and potentials of Bayesian probabilistic framework on structural health monitoring will be discussed.

Key Words
Bayesian inference; structural health monitoring; cable-stayed bridge; modal identification; modal identifiability

Address
Sin-Chi Kuok:Department of Civil and Environmental Engineering, Cornell University, Ithaca, New York, USA 14853
Ka-Veng Yuen: Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macao, China


Abstract
Modal identification based on ambient vibration data has attracted extensive attention in the past few decades. Since the excitation for ambient vibration tests is mainly from the environmental effects such as wind and traffic loading and no artificial excitation is applied, the signal to noise (s/n) ratio of the data acquired plays an important role in mode identifiability. Under ambient vibration conditions, certain modes may not be identifiable due to a low s/n ratio. This paper presents a study on the mode identifiability of an instrumented cable-stayed bridge with the use of acceleration response data measured by a long-term structural health monitoring system. A recently developed fast Bayesian FFT method is utilized to perform output-only modal identification. In addition to identifying the most probable values (MPVs) of modal parameters, the associated posterior uncertainties can be obtained by this method. Likewise, the power spectral density of modal force can be identified, and thus it is possible to obtain the modal s/n ratio. This provides an efficient way to investigate the mode identifiability. Three groups of data are utilized in this study: the first one is 10 data sets including six collected under normal wind conditions and four collected during typhoons; the second one is three data sets with wind speeds of about 7.5 m/s; and the third one is some blind data. The first two groups of data are used to perform ambient modal identification and help to estimate a critical value of the s/n ratio above which the deficient mode is identifiable, while the third group of data is used to perform verification. A couple of fundamental modes are identified, including the ones in the vertical and transverse directions respectively and coupled in both directions. The uncertainty and s/n ratio of the deficient mode are investigated and discussed. A critical value of the modal s/n ratio is suggested to evaluate the mode identifiability of the deficient mode. The work presented in this paper could provide a base for the vibration-based condition assessment in future.

Key Words
mode identifiability; cable-stayed bridge; ambient vibration; fast Bayesian FFT method; uncertainty

Address
Feng-Liang Zhang and Yan-Chun Ni:1Research Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai, China
Yi-Qing Ni: Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong


Abstract
A benchmark problem for modal identification of a cable-stayed bridge was proposed by a research team at Hong Kong Polytechnic University. By taking an instrumented cable-stayed bridge as a test bed, nineteen sets of vibration records with known/unknown excitations were provided to invited researchers. In this paper, the vibration responses of the bridge under a series of excitation conditions are examined to estimate the wind and traffic-induced variations of its dynamic characteristics. Firstly, two output-only experimental modal identification methods are selected. Secondly, the bridge and its monitoring system are described and the nineteen sets of vibration records are analyzed in time-domain and frequency-domain. Excitations sources of blind datasets are predicted based on the analysis of excitation conditions of known datasets. Thirdly, modal parameters are extracted by using the two selected output-only modal identification methods. The identified modal parameters are examined with respect to at least two different conditions such as traffic- and typhoon-induced loadings. Finally, the typhoon-induced effects on dynamic characteristics of the bridge are estimated by analyzing the relationship between the wind velocity and the modal parameters.

Key Words
cable-stayed bridge; experimental modal analysis; typhoon-induced; traffic-induced; dynamic characteristics

Address
Jae-Hyung Park, Thanh-Canh Huynh, Kwang-Suk Lee and Jeong-Tae Kim: Department of Ocean Eng., Pukyong National University, Busan, Korea

Abstract
The ambient vibration measurement is an output-data-only dynamic testing where natural excitations are represented, for instance, by winds and typhoons. The modal identification involving output-only measurements requires the use of specific modal identification techniques. This paper presents the application of a reliable method (the Stochastic Subspace Identification – SSI) implemented in a general purpose software. As a criterion toward the robustness of identified modes, a bio-inspired optimization algorithm, with a highly nonlinear objective function, is introduced in order to find the optimal deployment of a reduced number of sensors across a large civil engineering structure for the validation of its modal identification. The Ting Kau Bridge (TKB), one of the longest cable-stayed bridges situated in Hong Kong, is chosen as a case study. The results show that the proposed method catches eigenvalues and eigenvectors even for a reduced number of sensors, without any significant loss of accuracy.

Key Words
ambient vibration; cable-stayed bridge; modal frequencies; mode shapes; parameter identification; sensor deployment

Address
F. Casciati, L. Elia and L. Faravelli:Department of Civil Engineering and Architecture, DICAr, University of Pavia, via Ferrata 3, I-27100 Pavia, Italy
S. Casciati: Department of Civil Engineering and Architecture, DICAR, University of Catania at Siracusa,
Piazza Federico di Svevia 1, I-96100 Siracusa, Italy




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