Identification Of Flutter Derivatives Research Articles

Bayesian spectral density approach for identification of bridge section’s flutter derivatives operated in turbulent flow

This study presents a Bayesian spectral density approach for identification of flutter derivatives of bridge sections utilizing buffeting displacement responses, where the wind tunnel test is conducted in turbulent flow. Different from traditional time-domain approaches (e.g., least square method and stochastic subspace identification), the newly-proposed approach is operated in frequency domain. Based on the affine invariant ensemble sampler algorithm, Markov chain Monte-Carlo sampling is employed to accomplish the Bayesian inference. The probability density function of flutter derivatives is modeled based on complex Wishart distribution, where probability serves as the measure. By the Bayesian spectral density approach, the most probable values and corresponding posterior distributions (determined by conditions of measured signals) of each flutter derivative can be obtained at the same time. Firstly, numerical simulations are conducted and the identified results are accurate. Secondly, thin plate model, flutter derivatives of which have theoretical solutions, is chosen to be tested in turbulent flow for the sake of verification. The identified results of thin plate model are consistent with the theoretical solutions. Thirdly, the center-slotted girder model, which is widely-utilized long-span bridge sections in current engineering practice, is employed to investigate the applicability of the proposed approach on a general bridge section. For the center-slotted girder model, the flutter derivatives are also extracted by least square method in uniform flow to cross validate the newly-proposed approach. The identified results by two different approaches are compatible.

Experimental Uncertainty Quantification of Flutter Derivatives for a PK Section Girder and Its Application on Probabilistic Flutter Analysis

Aerodynamic flutter instability could lead to the catastrophic collapse of flexible long-span bridges and needs to be prevented. This study investigated the variability of eight experimentally measured flutter derivatives (FDs) for a commonly used a Pasco–Kennewick (PK) section girder using a free vibration technique in a wind tunnel, which provided some new insights into the identification of FDs and supplemented the reliability analysis for buffeting and flutter performance. The aerodynamic uncertainties in terms of the dispersion of flutter coefficients were studied and two implications behind the extraction of FDs were discussed. The statistical and probabilistic behaviors of FDs at different reduced wind speeds were examined before generating sufficient independent random samples using the Monte Carlo (MC) approach. The intercorrelations between experimental FDs quantified by correlation coefficients were also examined and were employed to randomly sample the correlated FDs. The probabilistic flutter solutions in terms of critical wind speed propagated from the FDs uncertainties were studied utilizing step-by-step analysis, which resulted in several multimodal probability distributions of flutter onset. In addition, the role played by each FD on the variation of critical wind speed was discussed.

Stochastic identification of flutter derivatives of long span bridge deck by gust response

Stochastic identification of flutter derivatives of long span bridge deck by gust response

Identifikacija parametara treperenja testovima prisilnih vibracija

Identifikacija parametara treperenja testovima prisilnih vibracija

On the identification of flutter derivatives of bridge decks via RANS turbulence models: Benchmarking on rectangular prisms

In this paper, the ability of two RANS-based turbulence models, the standard k–ω and the k–ω sst (shear-stress-transport formulation), in predicting flutter derivatives of elongated rectangular prisms with different aspect ratios is investigated. Strengths and limitations of the employed methodology are highlighted via comparisons with available experimental results, aiming at identifying some operative indications for choosing a suitable modeling approach (not much time-consuming and suitably accurate), useful for engineers facing the aerodynamic design of bridge structures. The influence of discrepancies among experimental measurements and RANS-based numerical results on the aeroelastic stability of bridge-like structures is also discussed.

Some new insights into the identification of bridge deck flutter derivatives

In the identification of flutter derivatives using coupled free vibration technique, the influences of implied approximations are assessed in this study. For a thin flat plate section and three representative deck sections of long-span bridges, KH1∗, KH2∗, KA1∗, KA2∗, K2H3∗, K2H4∗, K2A3∗, and K2A4∗ are demonstrated to be dependent on reduced wind velocity, especially at lower reduced wind velocities. This is contrary to the commonly used assumption of these parameters being constants. Kh is conventionally used to quantify H1∗, H4∗, A1∗, A4∗, and Kα for H2∗, A2∗, H3∗, A3∗. This means the direct components of aeroelastic motions (h1,α2) are comparatively predominant than the incentive cross components (h2,α1). However, this approximation is only valid for weak modal coupling cases at lower wind velocities. Novel perspectives are provided regarding the subtle underlying complexities in extracting flutter derivatives using coupled free vibration technique. The accuracy in identifying flutter derivatives can be effectively improved by setting close frequencies of coupled modes. The mechanical damping ratio, mass, and mass moment of inertia can be artificially increased to postpone the occurrence of flutter and extend the reduced wind velocity region to acquire sufficient flutter derivatives for flutter analysis. This study may serve as a building block for improving the understanding of flutter derivative identification from coupled free vibration responses, and practical strategies are proposed to improve the identification accuracy.

A modification to the flutter derivative model

There is an ambiguity in the original equations for the identification of flutter derivatives. The analysis in this paper shows that, for the two degrees of freedom (2DOF) model, these derivatives in these equations are, in fact, three-dimensional functions instead of one dimensional functions of reduced frequency. Alternative governing equations are proposed in this paper to solve this problem. These new equations “decouple” the aeroelastic coupling effect by approximated modeling strategy. The number of independent aeroelastic parameters is reduced from eight to five. Nonlinear nature of the aeroelastic coupling effect is unveiled. The nonlinear identification method is presented to retrieve the new set of aeroelastic parameters. Wind tunnel experiments were conducted to show the effectiveness of the newly proposed equations.

Identification of flutter derivatives of bridge decks using CFD-based discrete-time aerodynamic models

This paper presents a method to extract flutter derivatives of bridge decks based on a combination of the computational fluid dynamics (CFD), system simulations and system identifications. The incompressible solver adopts an Arbitrary Lagrangian-Eulerian (ALE) formulation with the finite volume discretization in space. The imposed sectional motion in heaving or pitching relies on exponential time series as input, with aerodynamic forces time histories acting on the section evaluated as output. System identifications are carried out to fit coefficients of the inputs and outputs of ARMA models, as to establish discrete-time aerodynamic models. System simulations of the established models are then performed as to obtain the lift and moment exerting on the sections to a sinusoidal displacement. It follows that flutter derivatives are identified. The present approaches are applied to a hexagon thin plate and a real bridge deck. The results are compared to the Theodorsen closed-form solution and those from wind tunnel tests. Satisfactory agreements are observed.

Identification of flutter derivatives from full-scale ambient vibration measurements of the Clifton Suspension Bridge

The estimated response of large-scale engineering structures to severe wind loads is prone to modelling uncertainties that can only ultimately be assessed by full-scale testing. To this end ambient vibration data from full-scale monitoring of the historic Clifton Suspension Bridge has been analysed using a combination of a frequency domain system identification method and a more elaborate stochastic identification technique. There is evidence of incipient coupling action between the first vertical and torsional modes in strong winds, providing unique full-scale data and making this an interesting case study. Flutter derivative estimation, which has rarely previously been attempted on full-scale data, was performed to provide deeper insight into the bridge aerodynamic behaviour, identifying trends towards flutter at higher wind speeds. It is shown that, as for other early suspension bridges with bluff crosssections, single-degree-of-freedom flutter could potentially occur at wind speeds somewhat below requirements for modern designs. The analysis also demonstrates the viability of system identification techniques for extracting valuable results from full-scale data.

Identification of Flutter Derivatives of Bridge Deck Under Multi-Frequency Vibration

:A multi-frequency vibration method (MFVM) is proposed to identify flutter derivatives of bridge deck. In this method, a bridge deck is forced in vertical or torsional harmonic vibration with linear combination of multi-frequency. Computational Fluid Dynamic (CFD) simulation is conducted using 2D unsteady incompressible Navier-Stokes equations combined with renormalization group (RNG) k  turbulence model, based on improved domain decomposition method. The non-dimensional time histories of lift and moment are fitted by least square method to identify the flutter derivatives of bridge deck. Flutter derivatives of a thin flat plate and the 2nd Nanjing Yangtze River Bridge section are computed. The results are in good agreement with Theodorsen’s theory and wind tunnel test data, which demonstrates the reliability and efficiency of the present approach.

Moving Least Squares (MLS) Method for Identification of Flutter Derivatives of Bridge Decks

Moving Least Squares (MLS) Method for Identification of Flutter Derivatives of Bridge Decks

Identification of flutter derivatives of bridge decks with free vibration technique

The flutter derivatives of bridge decks can be determined in a unique manner on condition that the complex modal parameters of the system at one reduced frequency are obtained. Based on the idea, a new method of identifying the flutter derivatives of bridge decks is proposed and it can overcome some shortcoming of the existing method and extend the applicability of the free vibration technique at high wind velocity. The identified results have agreements with the target ones of an ideal thin-plate section and those of a thin-plate section measured by the forced vibration technique. The proposed method is reliable and effective to extract the flutter derivatives from coupled free vibration.

Data-driven stochastic subspace identification of flutter derivatives of bridge decks

Most of the previous studies on flutter derivatives have used deterministic system identification techniques, in which the buffeting forces and the associated responses are considered as noises. In this paper, one of the most advanced stochastic system identification, the data-driven stochastic subspace identification technique (SSI-DATA) was proposed to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of the stochastic method is that it considers the buffeting forces and the responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under a smooth flow by the free decay and the buffeting tests were used to validate the applicability of the SSI-DATA method. The results were compared with those from the widely used covariance-driven SSI method. Wind tunnel tests of a two-edge girder blunt type of Industrial-Ring-Road Bridge deck (IRR) were then conducted under both smooth and turbulent flows. The identified flutter derivatives of the thin plate model based on the SSI-DATA technique agree well with those obtained theoretically. The results from the thin plate and the IRR Bridge deck helped validate the reliability and applicability of the SSI-DATA technique to various experimental methods and wind flow conditions. The results for the two-edge girder blunt type section show that applying the SSI-DATA yields better results than those of the SSI-COV. The results also indicate that turbulence tends to delay the onset of flutter compared with the smooth flow case.

Experimental and numerical identification of flutter derivatives for nine bridge deck sections

This paper presents the results of a study into experimental and numerical methods for the identification of bridge deck flutter derivatives. Nine bridge deck sections were investigated in a water tunnel in order to create an empirical reference set for numerical investigations. The same sections, plus a wide range of further sections, were studied numerically using a commercially available CFD code. The experimental and numerical results were compared with respect to accuracy, sensitivity, and practical suitability. Furthermore, the relevance of the effective angle of attack, the possible assessment of non-critical vibrations, and the formulation of lateral vibrations were studied. Selected results are presented in this paper. The full set of raw data is available online to provide researchers and engineers with a comprehensive benchmarking tool.

Identification of Flutter Derivatives of Bridge Decks in Wind Tunnel Test by Stochastic Subspace Identification

Problem statement: Flutter derivatives are the essential parameters in the estimations of the flutter critical wind velocity and the responses of long-span cable supported bridges. These derivatives can be experimentally estimated from wind tunnel test results. Generally, wind tunnel test methods can be divided into free decay test and buffeting test. Compared with the free decay method, the buffeting test is simpler but its outputs appear random-like. This makes the flutter derivatives extraction from its outputs more difficult and then a more advanced system identification is required. Most of previous studies have used deterministic system identification techniques, in which buffeting forces and responses are considered as noises. These previous techniques were applicable only to the free decay method. They also confronted some difficulties in extracting flutter derivatives at high wind speeds and under turbulence flow cases where the buffeting responses dominate. Approach: In this study, the covariance-driven stochastic subspace identification technique (SSI-COV) was presented to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of this method is that it considers the buffeting forces and responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under smooth flow by the free decay and the buffeting tests were used to validate the applicability of the SSI-COV method. Then, wind tunnel tests of a two-edge girder blunt type of Industrial-Ring-Road Bridge deck (IRR) were conducted under smooth and turbulence flow. Results: The identified flutter derivatives of the thin plate model by the SSI-COV technique agree well with those obtained theoretically. The results from the thin plate and the IRR Bridge deck validated the reliability and applicability of the SSI-COV technique to various experimental methods and conditions of wind flow. Conclusion/Recommendations: The SSI-COV was successfully employed to identify flutter derivatives of bridge decks with reliable results. It is a proven technique that can be readily applied to identify flutter derivatives of other bridge decks either by the free decay or the buffeting tests.

Effect of rain on flutter derivatives of bridge decks

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 , and thus the flutter critical wind speeds of bridges.

Computational models and methods for aerodynamic flutter of long-span bridges

The evaluation of bridge aerodynamic instability is traditionally based on direct wind tunnel testing and theoretical analysis method with experimentally identified parameters from wind tunnel tests. With the development of computer technology and computational fluid dynamics, the theoretical analysis method is expected to be developed to theoretical models and pure computational methods for numerically analyzing aerodynamic flutter of long-span bridges. This paper introduces the models and methods for computationally determining aerodynamic instability of long-span bridges, and emphasis is placed on three aspects including self-excited aerodynamic force model, numerical identification of flutter derivatives and two-dimensional or three-dimensional flutter analysis method. Through a serious analysis of the thin-plate cross-section and its cantilevered structure, the H-shaped section and Nanpu cable-stayed bridge, the closed-box section and Höga Kusten Bridge, the main problems and the key prospects are concluded.

Wind Tunnel and CFD Study on Identification of Flutter Derivatives of a Long‐Span Self‐Anchored Suspension Bridge

Abstract: The Sanchaji Bridge with a main span of 328 m, located in Changsha City across Xiangjiang River, is one of the longest self‐anchored suspension bridges completed in China. This article presents the results from a combined wind tunnel and CFD (computational fluid dynamics) study on identification of flutter derivatives of the bridge deck. Based on the Covariance Block Hankel Matrix (CBHM) algorithm in time domain, sectional model wind tunnel tests are conducted in smooth flow to recover modal parameters and to further identify flutter derivatives from free‐decay vibration records. On the other hand, based on the ALE (Arbitrary Lagrangian Eulerian) description and a second‐order projection algorithm, the CFD study uses the FVM (Finite Volume Method) on staggered grids and a forced vibration manner of the bridge deck to evaluate the flow field around the bridge deck. With the obtained aerodynamic forces acting on the bridge deck, flutter derivatives can be evaluated based on system identification. Finally, both of the suggested methods are applied to identification of flutter derivatives of the bridge deck of the Sanchaji Bridge. The results of the present methods have the same trends with Theodorsen analytical solutions, while the results from the CFD study compare well with those from the wind tunnel test. The agreement on the present results suggests that the aeroelastic phenomenon of bridge decks with sharp edges does not appear sensitive to the Re number and turbulence modeling.

Identification of flutter derivatives of bridge decks using stochastic search technique

A more applicable optimization model for extracting flutter derivatives of bridge decks is presented, which is suitable for time-varying weights for fitting errors and different lengths of vertical bending and torsional free vibration data. A stochastic search technique for searching the optimal solution of optimization problem is developed, which is more convenient in understanding and programming than the alternate iteration technique, and testified to be a valid and efficient method using two numerical examples. On the basis of the section model test of Sutong Bridge deck, the flutter derivatives are extracted by the stochastic search technique, and compared with the identification results using the modified least-square method. The Empirical Mode Decomposition method is employed to eliminate noise, trends and zero excursion of the collected free vibration data of vertical bending and torsional motion, by which the identification precision of flutter derivatives is improved.

Direct identification of flutter derivatives and aerodynamic admittances of bridge decks

Flutter derivatives and aerodynamic admittances provide 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 first presented for estimation of the flutter derivatives and aerodynamic admittances of bridge decks from their random responses in turbulent flow. Numerical simulations of an ideal thin plate are adopted to extract these aerodynamic parameters to evaluate the applicability of the present method. Then wind tunnel tests of a streamlined thin plate model and a Π type blunt bridge section model were conducted in turbulent flow and the flutter derivatives and aerodynamic admittances are determined by the SSI technique. The identified aerodynamic parameters are compared with the theoretical ones and the results indicate the applicability of the current method.