Aeroelastic modeling and stability analysis: A robust approach to the flutter problem

In this paper, a general approach to address modeling of aeroelastic systems, with the final goal to apply μ analysis, is discussed. The chosen test bed is the typical section with unsteady aerodynamic loads, which enables basic modeling features to be captured and so extend the gained knowledge to practical problems treated with modern techniques. The aerodynamic operator has a nonrational dependence on the Laplace variable s, and hence, 2 formulations for the problem are available: frequency domain or state‐space (adopting rational approximations). The study attempts to draw a parallel between the 2 consequent linear fractional transformation modeling processes, emphasizing critical differences and their effect on the predictions obtained with μ analysis. A peculiarity of this twofold formulation is that aerodynamic uncertainties are inherently treated differently and therefore the families of plants originated by the possible linear fractional transformation definitions are investigated. One of the main results of the paper is to propose a unified framework to address the robust modeling task, which enables the advantages of both the approaches to be retained. On the analysis side, the application of μ analysis to the different models is shown, emphasizing its capability to gain insight into the problem.     

Application of output feedback sliding mode control to active flutter suppression of two-dimensional airfoil

The effectiveness of the sliding mode control(SMC) method for active flutter suppression(AFS) and the issues concerning control system discretization and control input constraints were studied using a typical two-dimensional airfoil.The airfoil has a trailing-edge flap for flutter control.The aeroelastic system involves a two-degrees-of-freedom motion(pitch and plunge),and the equations were constructed by utilizing quasi-steady aerodynamic forces.The control system,designed by the output feedback SMC metho...     

Analytical approach to sensitivity analysis of flutter speed in bridges considering variable deck mass

Design techniques based upon sensitivity analysis are not usual in the current design of suspension bridges. However, sensitivity analysis has been proved to be a useful tool in the car and aircraft industries. Evaluation of sensitivity analysis is a mandatory step in the way towards an efficient automated optimum design process which would represent a huge jump in the conception of long span bridges. Some of the authors of this paper were pioneers in establishing a methodology for obtaining the sensitivity analysis of flutter speed in suspension bridges a few years ago. That approach was completely analytical and required the evaluation of many matrices related to the phenomenon. In those works the total mass of the deck was considered as constant and such a circumstance supposed a limitation of the method. In the present paper the complete analytical formulation of the sensitivity analysis problem in bridges considering variable deck mass is presented, as well as its application to the design problem of the Great Belt Bridge. Analytical evaluation of sensitivities is a time demanding task, and in order to avoid excessive computation times, distributed computing strategies have been implemented which can be considered as an additional benefit of this approach. For the application example, it has been found that deck cross-section area and torsional inertia are the structural properties with the greatest influence on the flutter performance.     

Sensitivity of optimal shapes of artificial grafts with respect to flow parameters

The difficulties arising in the numerical solution of PDE-constrained shape optimization problems are manifold. Key ingredients are the optimization strategy and the shape deformation method. Furthermore, the robustness of the optimal shape with respect to simulation parameters is of great interest. In this paper, we consider fluid flows described by the incompressible Navier–Stokes equations. Previous studies on artificial bypass grafts indicated the need for specific constitutive models to account for the non-Newtonian nature of blood; in particular, the constitutive model was shown to affect the solution of the shape optimization problem. We employ a shape optimization framework that couples a finite element solver with quasi-Newton-type optimizers and a Bezier spline shape parametrization. To compute derivatives of the optimal shapes with respect to viscosity, we transform the entire optimization framework by combining the automatic differentiation tools Adifor2 and TAPENADE. We demonstrate the impact of the geometry parametrization and of geometric constraints on the optimization outcome. Finally, we employ the transformed framework to compute the sensitivity of the optimal shape of bypass grafts with respect to kinematic viscosity. The resulting sensitivities predict very accurately the influence of viscosity changes on the optimal shape. The proposed methodology provides a powerful tool to further investigate the necessity of intricate constitutive models by taking derivatives with respect to model parameters.     

Optimization with respect to covariance sequence parameters

A general problem involving optimization of a covariance sequence is considered in the paper. One difficulty with this class of problems is to ensure that the covariance sequence is nonnegative definite (in other words, realizable). It is suggested that this difficulty can be overcome by reformulating the optimization problem in terms of the partial autocorrelation coefficients (PAC). One need only constrain these coefficients to lie in the range (−1, 1) to guarantee that the corresponding covariance sequence is nonnegative definite. The synthesis of a signal realizing the optimizing covariance sequence is also discussed. Special emphasis is given to the case when some of the PACs are either +1 or −1.     

Sensitivity analysis of the scattering parameters of microwave filters using the adjoint network method

A novel approach is presented to calculate the sensitivities of the scattering parameters of microwave filters obtained with the full‐wave mode‐matching (MM) technique. Using only the MM simulation of the original network, the sensitivities of the scattering parameters with respect to all designable parameters are obtained. The adjoint network method (ANM) is applied to the generalized scattering matrices of the different filter components. This guarantees good accuracy of the calculated sensitivities. The implementation details are discussed for N‐resonator ridge waveguide filters. Excellent agreement is obtained between the sensitivities calculated using ANM and those obtained using the expensive central differences. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Sensitivity analysis in the single-machine scheduling problem with max–min criterion

In this paper, the single‐machine scheduling problem 1∣prec∣f_max is considered. It is one of the most general scheduling problems for which an efficient, polynomial algorithm has been developed. It is always possible to calculate quickly one optimal solution (a sequence of jobs) in that problem. However, the set of all optimal solutions may contain a lot of other sequences, so it is important to give a full characterization of that set. This paper consists of two parts. In the first part, some sufficient and necessary conditions of optimality of a given solution to the problem 1∣prec∣f_max are proved. In the second part, an application of these conditions to the sensitivity analysis is presented.     

Sensitivity analysis of the setup knapsack problem to perturbation of arbitrary profits or weights

The setup knapsack problem can be viewed as a more complex version of the well‐known classical knapsack problem. An instance of such a problem may be defined by a set of n items that is divided into m different classes For each class, only one item is considered as a setup item. The aim of the problem is to pack a subset of items in a knapsack of a predefined capacity that maximizes an objective function. In this paper, we analyze the sensitivity of an optimal solution depending on the variation of the profits or weights of arbitrary items. The optimality of the solution at hand is guaranteed by establishing the sensitivity interval that is characterized by both lower and upper values (called limits). First, two cases are distinguished when varying the profits: perturbation of the profit of an item (either ordinary or setup item) and, variation of the profits of a couple of items containing both setup and ordinary items belonging to the same class. Second, two cases are studied, where the perturbation concerns the weights: the variation is relied on the weight of an item and, the case of the variation of the weights of a subset of items. The established results are first illustrated throughout a didactic example, where both approximate and exact methods are used for analyzing the quality of the proposed results. Finally, an extended experimental part is proposed in order to evaluate the effectiveness of the proposed limits.     

超音速下热壁板的颤振分析

首先研究了热效应对壁板结构动力学特性的影响.将基于超音速活塞理论的非定常气动力模型与壁板的结构动力学方程相结合,得到了热壁板的颤振方程.利用p-k法进行了热壁板的颤振计算,讨论了气流偏角对颤振速度的影响.数值结果表明,热效应对壁板的固有特性有较大影响,进而影响壁板的颤振特性.     

节流管孔流动参数与雷诺数关系的数值研究

对初始静止状态的流体,在其压力差为阶跃变化的情况下,通过节流孔的流动过程进行了数值解析计算。特别注目于再附着点距离zats、流量系数cd、惯性长,以及时间常数τq、τz与雷诺数Re的关系。做出了流动参数与雷诺数Re的关系图,并给出了用雷诺数计算时间常数的计算式。数值计算结果说明了对应于流量变化的时间常数τq随着Re数的增加而减少,而对应于流场变化的时间常数τz几乎为一定值。     

Sensitivity analysis of the additive model in data envelopment analysis while inputs and outputs are fuzzy data

Data envelopment analysis (DEA) requires input and output data to be precisely known. This is not always the case in real applications. Sensitivity analysis of the additive model in DEA is studied in this paper while inputs and outputs are symmetric triangular fuzzy numbers. Sufficient conditions for simultaneous change of all outputs and inputs of an efficient decision-making unit (DMU) which preserves efficiency are established. Two kinds of changes on inputs and outputs are considered. For the first state, changes are exerted on the core and margin of symmetric triangular fuzzy numbers so that the value of inputs increase and the value of outputs decrease. In the second state, a non-negative symmetric triangular fuzzy number is subtracted from outputs to decrease outputs and it is added to inputs to increase inputs. A numerical illustration is provided.     

Sensitivity analysis of steel moment frames accounting for geometric and material nonlinearity

A procedure for sensitivity analysis of planar steel moment frameworks accounting for second-order displacement effects and inelastic material behavior under combined bending moment and axial force is presented in the context of performance-based design for seismic loading. Analytical formulations defining the sensitivity of nodal displacements to modifications in member cross-section sizes are derived. A nine-story moment frame example illustrates the applicability and accuracy of the developed formulations.     

不确定性参数灵敏度分析的随机响应面法

动力学和控制系统中往往包含有不确定性参数,为此提出了一种基于随机响应面的不确定性参数灵敏度分析方法,以量化参数不确定性对响应变异性的影响.文中首先利用随机响应面建立不确定性参数和响应之间的表达式,然后通过求偏导方式推导参数的灵敏度系数,该系数综合反映了参数均值和标准差的影响.最后通过一根包含几何、材料不确定参数的数值梁来验证所提出方法,并与方差分析法结果进行了比较.     

悬索桥主缆初应力对桥梁动力特性的影响

为掌握主缆初应力对桥梁动力特性的影响,以悬索桥为例,采用静力非线性分析方法计算应力变化过程中悬索桥的跨中挠度、缆索轴力及加劲梁的轴力变化;将得到的内力作为结构的预加应力进行有预应力的模态分析. 应用ANSYS软件进行分析,其中有限元建模时采用4种单元类型:空间梁单元BEAM4用于模拟加劲梁和塔;空间杆单元LINK10用于模拟主缆及吊杆;通过设定BEAM4和LINK10单元初应变进行有预应力的模态分析;采用MASS21单元模拟横隔板、吊杆锚固装置和桥面上的栏杆,并分别考虑质量和质量惯性矩的作用. 分析表明,悬索桥主梁竖弯振动频率受主缆初应力的影响较大,而侧弯振动频率和扭转振动频率受此影响较小. 该结果为同类桥梁的动力特性分析提供参考.     

Sensitivity analysis of prefiltering in identification of two-time scaled systems

System identification is an important field of modeling that allows obtaining mathematical models capable of reproducing the experimental behavior of dynamical systems accurately. When dealing with complex systems that involve more than one time and/or space scale, the identification task is not so trivial. In this context, this works focuses on the study of two-time scaled systems (TTSSs), comprising a theoretical sensitivity analysis of prefiltered estimators for system identification purposes. It is worth mentioning that prefiltered estimators are a very important class of estimators when frequency-domain identification is required rather than its time-domain counterpart. Thus, the sensitivity analysis is performed for the identification of a Lockheed F104G aircraft model, which corresponds to a TTSS. Numerical simulations are also performed to validate the theoretical analysis.     

基于复模态方法的二维夹层壁板颤振分析

本文研究二维夹层壁板在一侧受超音速气动力的情况下的颤振现象.利用复模态方法和伽辽金方法分析颤振临界马赫数以及夹芯粘性阻尼对颤振的影响.结果发现考虑前四阶模态时,由于一二阶频率重合而使振动能量积聚发生颤振.考虑中间层的粘弹性时,发现随着粘性阻尼的增加,颤振临界马赫数和临界颤振频率均呈现先降低后升高的现象,其原因是粘弹性一方面降低系统固有频率使得临界马赫数降低,另一方面又使能量耗散使得临界马赫数升高,在这两种作用的影响下出现了上述复杂的现象.本文的研究结果有利于颤振抑制时的设计优化.     

Comparison of numerical techniques for 3D flutter analysis of cable-stayed bridges

This paper presents the results of a comparison study of the numerical techniques of structural and aerodynamic force models developed based on the spline finite strip method with the conventional finite element approach in three-dimensional flutter analysis of cable-stayed bridges. In the new formulation, the bridge girder is modelled by spline finite strips. The mass and stiffness properties of the torsional behaviour of complex bridge girder, which have a significant influence on the wind stability of long-span bridges, are modelled accurately in the formulation. The effects of the spatial variation of the aerodynamic forces can be taken into account in the proposed numerical model by distributing the loads to the finite strips modelling the bridge deck. The numerical example of a 423 m long-span cable-stayed bridge is presented in the comparison study. The accuracy and effectiveness of the proposed finite strip model are compared to the results obtained from the equivalent beam finite element models. The advantages and disadvantages of these different modelling schemes are discussed.     

Development of an autonomous bridge deck inspection robotic system

The threat to safety of aging bridges has been recognized as a critical concern to the general public due to the poor condition of many bridges in the United States. Currently, the bridge inspection is conducted manually, and it is not efficient to identify bridge condition deterioration in order to facilitate implementation of appropriate maintenance or rehabilitation procedures. In this paper, we report a new development of the autonomous mobile robotic system for bridge deck inspection and evaluation. The robot is integrated with several nondestructive evaluation (NDE) sensors and a navigation control algorithm to allow it to accurately and autonomously maneuver on the bridge deck to collect visual images and conduct NDE measurements. The developed robotic system can reduce the cost and time of the bridge deck data collection and inspection. For efficient bridge deck monitoring, the crack detection algorithm to build the deck crack map is presented in detail. The impact‐echo (IE), ultrasonic surface waves (USW), and electrical resistivity (ER) data collected by the robot are analyzed to generate the delamination, concrete elastic modulus, corrosion maps of the bridge deck, respectively. The presented robotic system has been successfully deployed to inspect numerous bridges in more than ten different states in the United States.     

Sensitivity analysis and optimization of stochastic Petri nets

In this paper we define the notion of controlled stochastic Petri net (CSPN), which is a stochastic Petri net with controlled parameters and performance indices. Specifically, transition times and/or conflict resolution rules can depend on controlled parameters and transition times can have arbitrary distribution functions. A method for computing statistical estimates of performance indices and their gradients (sensitivities) with respect to controlled parameters is described. This method, which needs only one simulation of a CSPN, is considerably superior to conventional finite differences both in terms of precision and required amount of simulation and is based on likelihood ratio/score function approach, other possibilities based on extensions of infinitesimal perturbation analysis are outlined. These gradient estimates are used in stochastic optimization algorithms to obtain the optimal value of the aggregated performance function of the CSPN. A combined optimization and simulation tool is developed which includes approaches to the gradient estimation mentioned above. The numerical experiments presented in this paper confirm the efficiency of the proposed techniques.     

Active control of supersonic/hypersonic aeroelastic flutter for a two-dimensional airfoil with flap

The flutter, post-flutter and active control of a two-dimensional airfoil with control surface operating in supersonic/hypersonic flight speed regions are investigated in this paper. A three-degree-of-freedom dynamic model is established, in which both the cubic nonlinear structural stiffness and the nonlinear aerodynamic load are accounted for. The third order Piston Theory is employed to derive the aerodynamic loads in the supersonic/hypersonic airflow. Nonlinear flutter happens with a phenomenon of limit...