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.     

Parametric study on flutter derivatives of bridge decks

The method for identification of flutter derivatives of bridge decks developed by the authors is first briefly described in this paper. To investigate the effects of dynamic parameters of a bridge deck model on the flutter derivatives a test of the sectional Jiangyin Bridge deck's models with different dynamic parameters was carried out in a boundary layer wind tunnel using the present identification method. In both smooth and simulated turbulent flow conditions, a plate model and the sectional deck model of the Jiangyin Bridge were tested to further survey the effects of turbulence on flutter derivatives. The identified results tend to indicate that the effects of parameters of the model and turbulence on the flutter derivatives are negligible.     

紊流风场中桥梁气动导数识别的随机方法

气动导数是大跨桥梁结构颤振和抖振分析的重要依据。本文提出采用随机系统识别方法来识别紊流风场中的气动导数, 与当前应用较广的瞬态激励法及强迫激励法相比, 这类方法的优势在于: (1) 将紊流看作是激励, 而不是噪声, 更能反映结构实际工作状态下的特性; (2) 识别精度不受风速的制约, 可以获得较高折减风速下的气动导数; (3) 可直接在紊流风场中结构随机响应上进行识别, 无需任何人为外在激励, 试验更为简单易行。在风洞中完成了紊流风场中桥梁节段模型测振试验, 进一步利用本文的方法识别出气动导数。与相关文献提供的类似模型在均匀场和紊流场中识别结果的对比表明: 本文识别的气动导数是可靠的, 所提出的采用随机系统识别方法来识别紊流风场中气动导数的思路是可行的。     

全桥气弹模型颤振导数识别

将节段模型颤振导数识别方法用于全桥气弹模型,对其可行性和便利性进行详细论述;给出气弹模型模态质量的确定方法;采用随机子空间方法和随机搜索方法识别均匀流场和紊流场中苏通大桥气弹模型的18颤振导数,并和特征系统实现算法识别结果进行对比分析。研究结果表明:节段模型颤振导数识别方法是识别气弹模型颤振导数的有效和实用方法;模型模态质量可以方便地根据几何缩尺比由实桥对应值直接推算得到,且比通过模型试验实测精度更高;不同方法识别得到的均匀流场中苏通大桥气弹模型大部分颤振导数基本吻合;相对于紊流场中的气弹模型而言,均匀流场中的节段模型颤振导数识别精度更高。     

Identification of aerodynamic parameters for eccentric bridge section model

The equations of motion for bridge deck section model elastically suspended in wind tunnel are formulated about mass center of the system using the Lagrangian approach, accommodating both the elasticity and damping eccentricities in the formulation. The Subsection Extended-Order Iterative Least Square (SEO-ILS) algorithm is developed in the state space for direct identification of system matrices from free vibration data of section model obtained from wind tunnel testing. The flutter derivatives can be extracted straightforwardly from the difference in the system matrices identified at zero wind velocity and at a specific wind velocity, respectively. By making use of complex modal decomposition technique, a procedure is employed to correct the system matrix at zero wind velocity considering both eccentricities. The proposed method is applied to identify the flutter derivatives of a thin plate section model and the section model of a suspension bridge. The results show a favorable agreement between the flutter derivatives of a thin plate obtained with the proposed method and those derived from the analytic formulae. The identified direct flutter derivatives of the suspension bridge section model also are in good agreements with those obtained using Scanlan's method. It is shown that the use of the corrected system matrix at zero wind velocity leads to better accuracy in identifying the flutter derivatives especially at high reduced wind velocity than using the original system matrix, and the eccentricity is found to have more influence on the cross flutter derivatives than on the direct flutter derivatives.     

桥梁气动导纳识别的阶跃函数拟合法

基于桥梁主梁断面气动导数、阶跃函数与气动导纳之间的关系,提出一种获取气动导纳的阶跃函数拟合法。首先根据紊流风场中的抖振响应,识别桥梁结构气动导数和等效气动导纳,然后由气动导数可拟合得到阶跃函数,并根据阶跃函数系数计算得到竖向脉动风对应的气动导纳,最后结合等效气动导纳计算水平向脉动风对应的气动导纳。阶跃函数拟合法直接根据抖振响应完成了桥梁断面完整气动导纳的识别,实例研究表明,该方法对于桥梁断面气动导纳识别而言是可行的。     

Determination of flutter derivatives by a taut strip model

The taut strip model is a kind of aeroelastic model, which can be regarded as an in-between model between the sectional model and the full aeroelastic bridge model. Determination of flutter derivatives by taut strip models has rarely been studied. In this paper, a theory of determination of flutter derivatives using the taut strip model is established based on the eigensystem realization algorithm. Considering the restriction of measuring points, modal coordinate expansion technique is introduced to get the information of unknown measuring points. Generalized inverse matrix theory is employed to obtain the stiffness matrix and damping matrix of taut strip models. Then, the flutter derivatives can be extracted by the subtraction of stiffness and damping matrixes. A method of identifying of flutter derivatives in turbulence flow is also proposed through the random decrement technique. Experimental study of determination of flutter derivatives by taut strip model is carried out based on the theory discussed in the paper. A taut strip model of a thin plate is designed, and it is used in smooth flow to determine flutter derivatives as well as in turbulence flow in TJ-2 wind tunnel of Tongji University. In the end, comparisons with theoretical flutter derivatives of a thin-plate section are undertaken to validate the reliability of the theory.     

Comparisons of bridges flutter derivatives and generalized ones

The causes of the nonlinearity of self-excited aerodynamic force of bridge are interpreted from such two aspects as amplitude and wind velocity. The concept of “generalized flutter derivative” is proposed, and its physical meaning is illustrated. The graphs of the generalized flutter derivatives of plate and Sutong Bridge section model are plotted. The characteristics of all generalized flutter derivatives are compared and analyzed, and their superiorities are verified. The results indicate that the physical meaning of generalized flutter derivatives are more explicit compared to the traditional ones. It is more convenient to understand the nonlinearity properties of self-excited aerodynamic force of bridge according to the generalized flutter derivatives graphs with the wind velocity as the horizontal coordinate.     

桥梁颤振的随机有限元分析

在众多桥梁颤振分析的实验加理论方法中，ＰＫ－Ｆ法是一种通用性很强的等效颤振分析方法。本文以１８个气动导数的桥梁颤振分析ＰＫ－Ｆ法为基础，将随机有限元法应用于随机桥梁颤振分析中，着重研究自激气动力或气动导数的随机影响，建立了桥梁颤振分析的随机有限元法──随机有限元颤振分析方法，用该方法对江阴长江大桥的随机颤振进行了分析。     

桥梁断面几种气动导纳模型的合理性剖析

首先介绍非定常运动状态下的薄机翼的升力产生机制,机翼的相对运动速度用一系列固定分布模态表达成一种级数形式的广义模式。在这些速度分布模式中包括有平动模式、转动模式以及其他高阶的非线性模式。与此相对应,机翼所受的非定常升力也可根据环量理论求解成一种广义模式。由于所有频率特性的脉动风均可采用Bessel函数展开成广义形式,因而这一类方法直接得出机翼气动导纳的表达式。目前,桥梁风致抖振计算中几种应用较广的气动导纳模型均与机翼理论有关,该文的主要目标是通过对机翼理论的回顾,剖析桥梁风工程中气动导纳模型的合理性与所存在问题的根源。分析表明,任何试图通过气动导数求出气动导纳的方法都是在逻辑上不正确的。通过气动导纳的本质特征的分析,对试验测试钝体桥梁断面气动导纳的方法提出一些建议。     

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.     

Flutter mechanism for rectangular prisms in smooth and turbulent flow

The aim of the present work is to clarify the flutter mechanism for suspended long span bridges via a parametric analysis on flutter instability for a set of given deck profiles. Several wind tunnel tests in the DIC-CRIACIV boundary layer wind tunnel (BLWT) have been carried out on spring suspended section models such as rectangular cylinders of different slenderness ratios B/D=5 and 12.5, where B is the longitudinal length of the prism and D is the height of the prism. The main experimental parameters needed for examining whether a given bridge profile is flutter-prone below a certain mean wind velocity are the flutter derivatives, so a system identification procedure (combined system identification method, CSIM) has been developed to extract simultaneously all flutter derivatives from two degrees of freedom (2DoF) section model test results (coupled vertical-torsional free vibration tests). The parametric analysis includes the investigation on (1) the effects of model dynamic properties on BLWT test results, (2) the consequence of turbulence on bridge stability, (3) the possible definition of an aerodynamic stability performance index (β) for rectangular cylinders for designing purposes.     

风雨联合作用下大跨桥梁颤振稳定性试验研究

针对风雨联合作用下的大跨桥梁颤振稳定性,以一开槽双箱梁桥梁为研究对象,通过在大气边界层风洞中搭建的风雨联合作用试验系统,完成基于自由振动法的节段模型颤振试验。通过分析不同雨强下该桥梁主梁的颤振导数以及颤振临界风速,进而获取降雨对大跨桥梁颤振稳定性的影响规律。试验结果显示:颤振导数随雨强变化而变化,其中体现扭转气动阻尼特性的颤振导数变化较为显著,随雨强增大,颤振临界风速先增大后减小。试验结果表明:降雨对大跨桥梁的颤振导数以及颤振临界风速均有一定影响。     

风驱雨作用下桥梁主梁颤振节段模型试验研究

针对风驱雨作用下桥梁主梁的颤振问题,依据风驱雨作用和主梁振动特点,给出了分别考虑雨滴冲击和表面积水后的降雨相似关系,并探讨了其选取原则。选取大跨度桥梁较常采用的典型断面,通过节段模型试验模拟了风驱雨对主梁断面的颤振导数和颤振发生过程的影响。试验结果表明:主梁断面的颤振气动导数随雨强的变化无明显规律,各导数的变化量值相当,随风速增加,降雨引起的导数变化有所加大,但基本没有改变其随风速变化的整体趋势,试验雨强120mm/h时,模型颤振临界风速会有20%～30%左右的提高,但考虑雨强相似比后可以认为降雨对桥梁主梁的风致颤振失稳特征的影响基本可以忽略。     

苏通大桥气弹模型气动失稳分析

大跨柔性桥梁气弹模型在风荷载作用下会产生明显的竖向、侧向位移和附加攻角。推导气弹模型实测位移修正表达式,对苏通大桥气弹模型高风速时实测位移进行修正,对比分析修正前后差异。绘制了苏通大桥主跨跨中断面、1/4断面和边跨跨中3个典型断面扭转中心的运动轨迹,分析其特点,对苏通大桥气弹模型气动失稳现象进行解释。基于随机搜索方法和随机子空间方法识别得到的模态参数,对苏通大桥气弹模型进行复模态颤振分析。分析结果表明:苏通大桥气弹模型可视为一种非常规索网复合系统,其气动失稳振动表现为保持平衡状态的竖向、侧向和扭转耦合滚动,扭转频率成分在竖弯和侧弯振动中参与很多,而竖弯和侧弯频率成分在其他两种振动中参与很少。     

Comparisons of bridges flutter derivatives and generalized ones

The causes of the nonlinearity of self-excited aerodynamic force of bridge are interpreted from such two aspects as amplitude and wind velocity. The concept of “generalized flutter derivative” is proposed, and its physical meaning is illustrated. The graphs of the generalized flutter derivatives of plate and Sutong Bridge section model are plotted. The characteristics of all generalized flutter derivatives are compared and analyzed, and their superiorities are verified. The results indicate that the physical meaning of generalized flutter derivatives are more explicit compared to the traditional ones. It is more convenient to understand the nonlinearity properties of self-excited aerodynamic force of bridge according to the generalized flutter derivatives graphs with the wind velocity as the horizontal coordinate. __________ Translated from Journal of Wuhan University of Technology (Transportation Science and Engineering), 2008, 32(4): 607–610 [译自: 武汉理工大学学报(交通科学与工程版)]     

Application of the k-ω turbulence model for a wind-induced vibration study of 2D bluff bodies

This paper is concerned with the question of an appropriate turbulence model for the computational modelling of bridge deck aero-elasticity. A detailed examination of the suitability of different turbulence models for simulating various aero-elastic phenomena leads to the conclusion that the two equation k-ω RANS turbulence model strikes the right balance between computational efficiency and accuracy in simulating the flow regime. In order to test this hypothesis a rectangular prism with B/D=4 is taken as an example structure and the flutter derivatives are identified from FSI simulations for both low and medium turbulent flow regimes. The simulations are carried out using a block iterative sequential coupling routine that allows for the exploitation of existing fluid and structural solvers. The results show that the k-ω can adequately model the motion induced shear layer dynamics that are necessary for simulating FSI. The results also demonstrate the potential benefits of computational FSI studies in that flutter derivatives (and other aerodynamic coefficients) can readily be obtained without some of the problems encountered in wind tunnel tests.     

高墩连续刚构桥线性抖振时程响应分析

采用Miyata T准定常气动力模型,通过双变量泰勒展开,导出12阶单元气动阻尼矩阵和气动刚度矩阵,并在ANSYS中以Matrix27单元输入来考虑桥梁结构风致抖振自激力模型,结合桥址处脉动风场的模拟,对某连续刚构桥最大双悬臂阶段和成桥运营阶段进行线性抖振时程响应分析。最后对脉动风荷载作用下的结构响应值和静阵风荷载作用结果进行了比较,得到脉动增大系数值。     

根据随机交通状况修正横截面尺寸的大跨桥梁的风致性能

现有的交通状况对细长大跨桥梁(SLB)面板主要影响有两类:1)桥梁横截面尺寸发生改变,这可能会反过来改变颤振导数及作用在桥梁上的风致气动弹性荷载;2)作用于桥梁上的附加动力荷载,包括来自于车辆的动力相互作用。与外部动力荷载——车辆相比,通过改变桥梁横截面尺寸来研究其影响是很少见的。在桥面板上分布车辆模型,在风洞实验室模拟随机交通流对按比例制作的桥梁截面模型进行试验。在风洞试验中通过改变桥梁的横截面尺寸来获得不同的颤振导数,目前的研究是从数值上评估其对大跨桥梁的风致性能,如气动弹性性能、风致响应和潜在疲劳累积性能的影响。