中心刚体-柔性梁刚柔耦合动力学模型降阶研究

有限单元法被广泛的采用来描述柔性体的弹性变形,然而有限元节点坐标数目庞大,将会给动力学方程求解带来巨大的计算负担.如何降低柔性体的自由度,是当前柔性多体系统动力学研究的一个重要命题.本文以中心刚体-柔性梁系统为例,采用Krylov方法和模态方法进行降价.然后分别采用有限元全模型、Krylov降阶模型和模态降阶模型,对中心刚体-柔性梁进行刚-柔耦合动力学仿真.仿真结果表明,与采用模态降阶方法相比,采用Krylov模型降阶方法只需要较低的自由度,就可以得到与采用有限元方法完全一致的结果.说明Krylov模型降阶方法能够有效的用于柔性多体系统的模型降价研究.     

变截面Z型折叠机翼振动特性的有限元与实验分析

Z型变截面折叠机翼作为一种可变体机翼结构,不同的折叠角对机翼稳定性有着重要的影响,因此研究不同折叠角度下的特性参数对机翼动态稳定性有着重要的意义.本文首先设计加工了Z型变截面可折叠机翼结构的实验模型,通过建立与实验模型相匹配的有限元模型,仿真得到不同折叠角度下机翼的前5阶固有频率和振型,针对不同折叠角度下机翼的固有特性,通过扫频实验得到机翼前5阶固有频率和模态振型,以及横向外激励作用下三段翼的频响曲线,对比分析有限元仿真与实验结果,验证结果的可靠性,这将对机翼结构设计以及特性参数的选取提供参考依据.     

变截面Z型折叠机翼振动特性的有限元与实验分析

Z型变截面折叠机翼作为一种可变体机翼结构,不同的折叠角对机翼稳定性有着重要的影响,因此研究不同折叠角度下的特性参数对机翼动态稳定性有着重要的意义.本文首先设计加工了Z型变截面可折叠机翼结构的实验模型,通过建立与实验模型相匹配的有限元模型,仿真得到不同折叠角度下机翼的前5阶固有频率和振型,针对不同折叠角度下机翼的固有特性,通过扫频实验得到机翼前5阶固有频率和模态振型,以及横向外激励作用下三段翼的频响曲线,对比分析有限元仿真与实验结果,验证结果的可靠性,这将对机翼结构设计以及特性参数的选取提供参考依据.     

柔性航天器动力学建模及模型降阶研究

针对柔性航天器振动影响飞行器姿态稳定性和精度.为了解决上述问题,提出了多柔体航天器的动力学建模.首先,根据工程实现的假设振型法,采用拟坐标拉格朗日方程,推导出带有刚体模态的二阶系统刚柔耦合动力学模型,其中,为了减少模型计算量,通过坐标变换将刚体模态和柔性模态解耦,利用一种刚体模态解耦的二阶不稳定系统的模型降阶方法,并对航天器多柔体系统动力学方程进行了仿真分析,结果飞行姿态稳定,满足了精度要求,表明了动力学建模与模型降阶法的有效性和正确性.     

几种模型降阶方法的仿真对比研究

算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考.利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界.最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小.仿真算例证明了最小二乘法较前两者具有优越性.     

基于非对称Lanczos 算法的线性分数阶系统模型降阶方法

采用非对称Lanczos 算法研究线性分数阶系统的模型降阶问题, 提出一种保持系统传递函数一定数量的分数阶矩的模型降阶方法. 根据Caputo 导数的运算法则给出线性分数阶系统的分数阶矩的计算方法; 利用非对称Lanczos 算法构造对应的非对称三对角矩阵; 根据非对称三对角矩阵的性质证明降阶系统与原系统具有相同的一定数量的分数阶矩; 给出降阶系统与原系统传递函数的误差估计, 为合理选择降阶系统的阶次提供理论依据. 数值实例的计算结果验证了所提出方法的有效性.

     

柔性板的模态价值降阶及其主动控制研究

对柔性板的模型降阶和主动控制进行研究,并且进行实验验证.首先采用假设模态方法给出系统的动力学方程,然后采用价值模态分析方法进行降阶研究.考虑到弱阻尼系统,文中给出了一种价值模态分析方法的近似公式.控制律采用最优控制方法进行设计.仿真和实验结果显示,价值模态分析方法能够有效地显示出系统各阶模态的重要程度,因此能够有效地对系统模型进行降阶.     

模型过程差异下的ALSTOM气化装置控制结构选择(英文)

相对扰动增益矩阵是分析控制结构抗干扰性的一个有用工具,但它的结果受模型不确定性影响.提出基于优化来确定相对扰动增益矩阵范围的方法并用来选择ALSTOM气化装置的控制结构.利用过程运行仿真数据和输出误差系统辨识方法得到降阶线性模型.在不同运行状况统辨几个模型并通过这些模型得到模型不确定性范围.计算出ALSTOM气化装置在模型不确定性下的广义相对扰动增益范围并用来选择鲁棒控制结构.     

一种基于可观测标准型的模型降阶算法

模型降阶方法在大规模集成电路的仿真中有着广泛的应用.由于对互联网络提取寄生参数后电路的规模巨大,使用传统的电路仿真方法将会消耗大量的资源,而模型降阶使得仿真计算量显著减小的同时精度并没有多少损失.文章针对互连线网络的MNA(Modified Nodal Analysis)矩阵通常可观测性较弱的特点,提出了一种基于可观测标准型的模型降阶算法:MOROC.文中推导证明了该算法能够匹配原系统的前q个矩,且具有形式简单和容易检验稳定性的特点.并给出了应用该算法对耦合互连线的降阶建模和仿真结果.     

基于解释结构模型的产品零部件拆卸序列规划

为了快速准确地对复杂产品层次结构进行划分以实现拆卸序列规划,将解释结构模型(ISM)引入到对复杂产品的描述中,提出一种产品零部件拆卸序列规划方法.在对复杂产品零部件连接关系提取与表达、产品零部件连接关系邻接矩阵和有向图进行分析的基础上,构建了基于ISM的产品零部件连接关系模型;通过计算ISM连接关系可达矩阵建立了其有向图,并给出一种产品零部件结构深度的计算及拆卸序列规划方法.最后以确定洗碗机产品门体的拆卸序列规划和目标件的结构深度为例,对文中方法进行了验证,结果表明,该方法能够在短时间内确定复杂产品的结构层次,进而实现其拆卸序列的规划.     

具有单调性非线性项的非线性系统降维观测器设计

Based on the discussion about the existence and design method of full-order observer for systems with monotone nonlinearities, a reduced-order observer design method is developed under the assumption that a linear matrix inequality (LMI) has positive definite matrix solution and the reduced-order observer gain matrix is computed by the solution of LMI. By a linear transformation, a reduced-order observer which does not contain the information of the derivative of the system output is provided. A model is simulated and some conclusions are drawn based on the comparison of the results of reduced-order observer to that of full-order observer. The simulation shows that the design method developed by this paper has good performance.     

Proper orthogonal decomposition and incompressible flow: An application to particle modeling

The proper orthogonal decomposition (POD) is a reduced-order modeling technique that is used to compactly represent unsteady flows. In this paper, we use the POD to capture the parametric variation of a flow with Reynolds number. We study incompressible, axisymmetric, steady flow over spherical particles at various Reynolds numbers in order to give an alternative to correlation-based approaches for predicting the drag on a sphere. In most previous applications of the POD for reduced-order modeling of incompressible flow, the POD modes typically have only described the velocity field; the pressure field was not directly modeled. Since we are interested in drag, which is dependent on the pressure, we formulate the method to directly include the pressure field of an incompressible flow. The POD modes are then derived from numerical flow solutions obtained using an hp-finite element method. A reduced-order model is created by performing a streamwise-upwind-Petrov-Galerkin (SUPG) projection of the incompressible Navier-Stokes equations onto the space spanned by the POD modes. The SUPG approach is taken because when pressure modes are included the Galerkin method fails to give unique solutions for incompressible flow. This is demonstrated for some simple test cases. An efficient numerical implementation is also developed using a Taylor expansion of the SUPG projection of the Navier-Stokes equations. Finally, values of drag are computed from the reduced-order model. Drag can be calculated to within 1.0% of the direct numerical simulations using only a small number of modes while still retaining all of the essential physics around the particle.     

Model order reduction via real Schur-form decomposition

A new algorithm is presented for computing Moore's reduced-order transfer-function matrix without calculating the balancing transformation, which tends to be ill-conditioned, especially when the original system is non-minimal or when it has very nearly uncontrollable or unobservable modes. The algorithm is based on finding the eigenspaces associated with large eigenvalues of the cross-gramian matrix W_co using the real Schur-form decomposition. The algorithm does not require a minimal model to start with. The state-space realization obtained by this method is related to the balanced realization by a non-singular matrix. An example is presented to illustrate the proposed algorithm     

随机马尔可夫切换系统的H∞模型降阶

考虑一类带有时滞的不确定马尔可夫切换系统的H∞模型降阶问题.首先得到了一个矩阵不等式形式的充分条件,使该系统的H∞模型降阶问题对于满足条件的任意不确定性都是可解的;然后依据CCL(conecom plem entarity linearization)方法给出了该问题的求解算法,以及降阶模型的参数化方法.仿真算例说明该方法的有效性.     

基于Karhunnen-Loève展开的柔性梁撞击系统的降阶方法

首先基于Euler-Bernoulli原理,建立了一柔性悬臂梁撞击系统的动力学方程,并给出了模态分析方法;然后在若干基本假定和定义的基础上,利用Karhunnen-Loève展开这一正交分解手段,给出了体现动力系统主要特征的降阶模型,可将系统的本征值进行新的表述;最后将所提方法应用于柔性悬臂梁撞击系统的降阶分析过程中,并给出了相应数值例题.结果表明:本方法可以用少量的模态准确模拟可控系统的动力学特性,可为系统控制研究提供基础.     

Mistuning identification for industrial blisks based on the best achievable eigenvector

This paper presents a method of mistuning identification for turbomachinery blisks (integrally bladed disks) from measurements of the system modes and natural frequencies. The procedure is based on the “Best Achievable Eigenvectors” of all measured modes simultaneously combined with a regulation technique. Four illustrative numerical simulations, based on a reduced-order model of the blisk, are given which demonstrate that this technique produces acceptable mistuning identification. To do so, a finite element model of the bladed disk and a computational reduced-order modelling technique, based on component-mode substitution method and combined with a cyclic characteristic of the blade assembly, are developed. Moreover, sensibility coefficients of the mistuning parameter with respect to measured data are derived.     

改进的用于模型降阶的最小信息损失方法

针对最小信息损失方法进行模型降阶时结果不唯一的问题,提出了改进的最小信息损失方法.本方法通过限制系统采用输出正规模型,将系统的能观性格兰姆矩阵限制为单位矩阵,从而使得系统的总信息损失达到最小.并且保证了降阶结果的唯一性.     

Output feedback control using reduced order models

A method is presented for designing linear output feedback controllers using reduced-order models. These reduced-order models retain only the modes that can be most affected by output feedback. A criterion for determining these modes is also derived. Examples are given to demonstrate the advantage of the proposed method over existing well-known techniques.     

A projection approach to covariance equivalent realizations of discrete systems

Covariance equivalent realization theory has been used recently in continuous systems for model reduction [1]-[4] and controller reduction [2], [5]. In model reduction, this technique produces a reduced-order model that matchesq + 1output covariances andqMarkov parameters of the full-order model. In controller reduction, it produces a reduced controller that is "close" to matchingq + 1output covariances of the full-order controller, andqMarkov parameters of the closed-loop system. For discrete systems, a method was devised to produce a reduced-order model that matches theq + 1covariances [6], but not any Markov parameters. This method requires a factorization to obtain the input matrix, and since the dimension of this matrix factor depends upon rank properties not known a priori, this method may not maintain the original dimension of the input vector. Hence, this method [6] is obviously not suitable for controller reduction. A new projection method is described that matchesqcovariances andqMarkov parameters of the original system while maintaining the correct dimension of the input vector.     

A nonlinear POD-Galerkin reduced-order model for compressible flows taking into account rigid body motions

The construction of a nonlinear reduced-order model for fluid–structure interaction problems is investigated in this paper for unsteady compressible flows excited by the rigid body motion of a structure. The reduction is achieved by means of a Galerkin projection of the Navier–Stokes equations on the first POD modes resulting from the proper orthogonal decomposition. In the first part of the paper, the projection technique is carried out on a purely aerodynamic case in order (i) to validate an efficient iterative technique based on an updated QR decomposition to compute the POD modes, and (ii) to discuss the merits of different correction methods introduced to improve the long-term stability of the reduced-order model. The second and most original part of the paper deals with the construction of the reduced set of equations which arise from the projection of the compressible Navier–Stokes equations formulated in a suitable moving frame representing the rigid body motion. The expressions of the resulting non-autonomous terms appearing in the reduced-order model have also been optimized to reduce the computational costs.