• Wind and Structures
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• v.9 no.2
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• pp.159-178
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• 2006

For the slender and flexible cable supported bridges, identification of all the flutter derivatives for the vertical, lateral and torsional motions is essential for its stability investigation. In all, eighteen flutter derivatives may have to be considered, the identification of which using a three degree-of-freedom elastic suspension system has been a challenging task. In this paper, a system identification technique, known as covariance-driven stochastic subspace identification (COV-SSI) technique, has been utilized to extract the flutter derivatives for a typical bridge deck. This method identifies the stochastic state-space model from the covariances of the output-only (stochastic) data. All the eighteen flutter derivatives have been simultaneously extracted from the output response data obtained from wind tunnel test on a 3-DOF elastically suspended bridge deck section-model. Simplicity in model suspension and measurements of only output responses are additional motivating factors for adopting COV-SSI technique. The identified discrete values of flutter derivatives have been approximated by rational functions.

• Wind and Structures
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• v.7 no.3
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• pp.173-186
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• 2004

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. In this paper, one popular stochastic system identification technique, covariance-driven Stochastic Subspace Identification(SSI in short), is firstly presented for estimation of the flutter derivatives of bridge decks from their random responses in turbulent flow. Secondly, wind tunnel tests of a streamlined thin plate model and a ${\Pi}$ type blunt bridge section model are conducted in turbulent flow and the flutter derivatives are determined by SSI. The flutter derivatives of the thin plate model identified by SSI are very comparable to those identified by the unifying least-square method and Theodorson's theoretical values. As to the ${\Pi}$ type section model, the effect of turbulence on aerodynamic damping seems to be somewhat notable, therefore perhaps the wind tunnel tests for flutter derivative estimation of those models with similar blunt sections should be conducted in turbulent flow.

• Wind and Structures
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• v.14 no.5
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• pp.413-434
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• 2011

Without output covariance estimation, one reference-based Stochastic Subspace Technique (SST) for extracting modal parameters and flutter derivatives of bridge deck is developed and programmed. Compared with the covariance-driven SST and the oscillation signals incurred by oncoming or signature turbulence that adopted by previous investigators, the newly-presented identification scheme is less time-consuming in computation and a more desired accuracy should be contributed to high-quality free oscillated signals excited by specific initial displacement. The reliability and identification precision of this technique are confirmed by a numerical example. For the 3-DOF sectional models of Sutong Bridge deck (streamlined) and Suramadu Bridge deck (bluff) in wind tunnel tests, with different wind velocities, the lateral bending, vertical bending, torsional frequencies and damping ratios as well as 18 flutter derivatives are extracted by using SST. The flutter derivatives of two kinds of typical decks are compared with the pseudo-steady theoretical values, and the performance of $H_1{^*}$, $H_3{^*}$, $A_1{^*}$, $A_3{^*}$ is very stable and well-matched with each other, respectively. The lateral direct flutter derivatives $P_5{^*}$, $P_6{^*}$ are comparatively more accurate than other relevant lateral components. Experimental procedure seems to be more critical than identification technique for refining the estimation precision.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.331-351
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• 2012

In this study an output-only system identification technique for civil structures under ambient vibrations is carried out, mainly focused on using the Stochastic Subspace Identification (SSI) based algorithms. A newly developed signal processing technique, called Singular Spectrum Analysis (SSA), capable to smooth a noisy signal, is adopted for preprocessing the measurement data. An SSA-based SSI algorithm with the aim of finding accurate and true modal parameters is developed through stabilization diagram which is constructed by plotting the identified system poles with increasing the size of data matrix. First, comparative study between different approaches, with and without using SSA to pre-process the data, on determining the model order and selecting the true system poles is examined in this study through numerical simulation. Finally, application of the proposed system identification task to the real large scale structure: Canton Tower, a benchmark problem for structural health monitoring of high-rise slender structures, using SSA-based SSI algorithm is carried out to extract the dynamic characteristics of the tower from output-only measurements.

• Smart Structures and Systems
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• v.11 no.1
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• pp.19-34
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• 2013

The objective of this paper is to develop on-line system parameter estimation and damage detection technique from the response measurements through using the Recursive Covariance-Driven Stochastic Subspace identification (RSSI-COV) approach. To reduce the effect of noise on the results of identification, discussion on the pre-processing of data using recursive singular spectrum analysis (rSSA) is presented to remove the noise contaminant measurements so as to enhance the stability of data analysis. Through the application of rSSA-SSI-COV to the vibration measurement of bridge during scouring experiment, the ability of the proposed algorithm was proved to be robust to the noise perturbations and offers a very good online tracking capability. The accuracy and robustness offered by rSSA-SSI-COV provides a key to obtain the evidence of imminent bridge settlement and a very stable modal frequency tracking which makes it possible for early warning. The peak values of the identified $1^{st}$ mode shape slope ratio has shown to be a good indicator for damage location, meanwhile, the drastic movements of the peak of $2^{nd}$ mode slope ratio could be used as another feature to indicate imminent pier settlement.

• Smart Structures and Systems
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• v.23 no.1
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• pp.15-29
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• 2019

This paper addresses the problem of damage detection in suspension bridge hangers, with an emphasis on the modal flexibility method. It aims at evaluating the capability and the accuracy of the modal flexibility method to detect and locate single and multiple damages in suspension bridge hangers, with different level of severity and various locations. The study is conducted numerically and experimentally on a laboratory suspension bridge mock-up. First, the covariance-driven stochastic subspace identification is used to extract the modal parameters of the bridge from experimental data, using only output measurements data from ambient vibration. Then, the method is demonstrated for several damage scenarios and compared against other classical methods, such as: Coordinate Modal Assurance Criterion (COMAC), Enhanced Coordinate Modal Assurance Criterion (ECOMAC), Mode Shape Curvature (MSC) and Modal Strain Energy (MSE). The paper demonstrates the relative merits and shortcomings of these methods which play a significant role in the damage detection ofsuspension bridges.

• Smart Structures and Systems
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• v.20 no.2
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• pp.115-126
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• 2017

The modal identification of large civil structures such as bridges under the ambient vibrational conditions has been widely investigated during the past decade. Many operational modal analysis methods have been proposed and successfully used for identifying the dynamic characteristics of the constructed bridges in service. However, there is very limited research available on reliable criteria for the robustness of these identified modal parameters of the bridge structures. In this study, two time-domain operational modal analysis methods, the data-driven stochastic subspace identification (SSI-DATA) method and the covariance-driven stochastic subspace identification (SSI-COV) method, are employed to identify the modal parameters from field recorded ambient acceleration data. On the basis of the SSI-DATA method, the modal contribution indexes of all identified modes to the measured acceleration data are computed by using the Kalman filter, and their applicability to evaluate the robustness of identified modes is also investigated. Here, the benchmark problem, developed by Hong Kong Polytechnic University with field acceleration measurements under different excitation conditions of a cable-stayed bridge, is adopted to show the effectiveness of the proposed method. The results from the benchmark study show that the robustness of identified modes can be judged by using their modal contributions to the measured vibration data. A critical value of modal contribution index of 2% for a reliable identifiability of modal parameters is roughly suggested for the benchmark problem.

• Wind and Structures
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• v.21 no.6
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• pp.677-691
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• 2015

In this study, the geometrical setup of a turbine blade is tracked. A research-scale rotating turbine blade system is setup with a single 3-axes accelerometer mounted on one of the blades. The turbine system is rotated by a controlled motor. The tilt and rolling angles of the rotating blade under operating conditions are determined from the response measurement of the single accelerometer. Data acquisition is achieved using a prototype wireless sensing system. First, the Rodrigues' rotation formula and an optimization algorithm are used to track the blade rolling angle and pitching angles of the turbine blade system. In addition, the blade flapwise natural frequency is identified by removing the rotation-related response induced by gravity and centrifuge force. To verify the result of calculations, a covariance-driven stochastic subspace identification method (SSI-COV) is applied to the vibration measurements of the blades to determine the system natural frequencies. It is thus proven that by using a single sensor and through a series of coordinate transformations and the Rodrigues' rotation formula, the geometrical setup of the blade can be tracked and the blade flapwise vibration frequency can be determined successfully.

• Wind and Structures
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• v.11 no.3
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• pp.209-220
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• 2008

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. Many studies have been performed on the methods and applications of identification of flutter derivatives of bridge decks under wind action. In fact, strong wind, especially typhoon, is always accompanied by heavy rain. Then, what is the effect of rain on flutter derivatives and flutter critical wind speed of bridges? Unfortunately, there have been no studies on this subject. This paper makes an initial study on this problem. Covariance-driven Stochastic Subspace Identification (SSI in short) which is capable of estimating the flutter derivatives of bridge decks from their steady random responses is presented first. An experimental set-up is specially designed and manufactured to produce the conditions of rain and wind. Wind tunnel tests of a quasi-streamlined thin plate model are conducted under conditions of only wind action and simultaneous wind-rain action, respectively. The flutter derivatives are then extracted by the SSI method, and comparisons are made between the flutter derivatives under the two different conditions. The comparison results tentatively indicate that rain has non-trivial effects on flutter derivatives, especially on and $H_2$ and $A_2$thus the flutter critical wind speeds of bridges.

• Wind and Structures
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• v.30 no.6
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• pp.633-648
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• 2020

The objective of this work was to investigate the interference effects of two-parallel bridge decks on aerodynamic coefficients, vortex-induced vibration, flutter instability and flutter derivatives. The two bridges have significant difference in cross-sections, dynamic properties, and flutter speeds of each isolate bridge. The aerodynamic static tests and aeroelastic tests were performed in TU-AIT boundary layer wind tunnel in Thammasat University (Thailand) with sectional models in a 1:90 scale. Three configuration cases, including the new bridge stand-alone (case 1), the upstream new bridge and downstream existing bridge (case 2), and the downstream new bridge and the upstream existing bridge (case 3), were selected in this study. The covariance-driven stochastic subspace identification technique (SSI-COV) was applied to identify aerodynamic parameters (i.e., natural frequency, structural damping and state space matrix) of the decks. The results showed that, interference effects of two bridges decks on aerodynamic coefficients result in the slightly reduction of the drag coefficient of case 2 and 3 when compared with case 1. The two parallel configurations of the bridge result in vortex-induced vibrations (VIV) and significantly lower the flutter speed compared with the new bridge alone. The huge torsional motion from upstream new bridge (case 2) generated turbulent wakes flow and resulted in vertical aerodynamic damping H1^* of existing bridge becomes zero at wind speed of 72.01 m/s. In this case, the downstream existing bridge was subjected to galloping oscillation induced by the turbulent wake of upstream new bridge. The new bridge also results in significant reduction of the flutter speed of existing bridge from the 128.29 m/s flutter speed of the isolated existing bridge to the 75.35 m/s flutter speed of downstream existing bridge.