基于频域的挠性摆式加速度计表头参数辨识方法

鉴于挠性摆式加速度计表头频率特性的传统振动台测试方法存在低频和高频段的动态误差较大的缺点,给出了系统开路和闭合两种状态的电激励测试方法;在此基础上,针对挠性摆式加速度计表头参数的理论计算值和实际工作状态有一定的误差,研究并提出了基于频域的Levy法和山下法的表头参数辨识方法,并运用Householder变换解决了辨识过程中的病态问题.实验和辨识结果表明,电激励测试的方法更便于实验和在线动态测试,而且这种通过利用实测的频率特性来反推辨识表头参数的方法,有着很高的辨识精度和工程实用价值.     

密集模态挠性结构模型多变量频域辨识和控制

密集模态挠性结构的模态不仅阻尼小而且耦合程度高,给模型辨识带来了很大困难.频域辨识是获取空间挠性结构模型的一个有效方法,但是目前频域辨识要么模型结构定义有缺陷,要么是集中在单变量情形,不适合作大型空间挠性结构多变量模型的辨识.本文提出了多变量极大似然频域辨识,给出了其模型结构定义、算法推导及实现,并将其应用于H型密集模态挠性板的模型辨识,根据辨识结果,设计主动控制律,实现了对密集模态挠性板振动的有效抑制,表明了辨识算法及主动控制的可行性.     

力学复合环境下挠性陀螺仪的动力学分析

为研究分析挠性陀螺仪在过载振动复合环境下附加误差形成的机理和建立误差补偿模型,从结构分析入手,采用有限元分析软件ANSYS建立陀螺仪的实体模型和有限元模型,计算陀螺仪的章动频率,并与实验测量值进行比较,验证了模型的正确性;对挠性陀螺仪在过载-振动复合环境中的动力学特性进行分析研究,得到了各节点轴向位移,结合施加的载荷即可以计算得到陀螺仪的漂移角速度;同时通过模态分析计算得到陀螺仪的固有频率及相应振型.     

基于ASYM的激光陀螺捷联惯性系统温度误差模型辨识

为减小温度对导航精度的影响,实现系统级的温度补偿,在实验中采用静态条件下的标定方法;基于激光陀螺捷联惯性系统的误差模型方程,用广义逆算法顺利分离求得陀螺各零偏及标度因数值;根据以往温度误差模型的结构特点,运用渐近辨识方法(ASYM)中的最终输出误差准则(FOE)对温度误差模型中非线性部分的阶次进行准确的计算,确定了合理的温度误差模型结构。为了解决用最小二乘法辨识模型结构的系数时,信息矩阵求逆容易溢出的问题,采用了自适应的岭估计算法确定陀螺零偏温度误差模型的系数,实现了系统级的温度误差建模。所得到的温度误差模型补偿效果比定阶前明显提高。     

基于控制响应的时变系统模态参数辨识的改进子空间方法

提出了一种基于系统控制信号激发的响应数据来辨识时变系统模态参数的改进子空间方法。该方法以系统控制响应信号建立系统的状态空间输出方程并构造了一个广义Hankel矩阵,通过对该矩阵做奇异值分解(SVD),用广义能观阵的估计代替输出矩阵,然后利用奇异值矩阵的正交性,有效地降低了噪声敏感性和计算量,从而容易地辨识出等效状态下的系统矩阵,最后采用转换矩阵辨识出时变系统的模态参数。通过理论分析、仿真和实验,讨论了不同信噪比对辨识结果的影响,验证了该方法的有效性。     

恒温法测爆热的快速系统辨识方法

为了降低经典恒温法爆热测量中出现系统故障而导致测量失败的风险,提出了基于故障前内桶水温升曲线辨识爆热值的测量方法。首先,分析了测量过程的传热机制,建立了量热计的传热模型,解算得到了各测量阶段的内桶水温升曲线;然后,基于系统辨识理论,提出了中间参数的辨识算法,并基于隔离易振荡参数的思路,给出了修正温升与爆热的快速系统辨识算法,通过误差分析证明了爆热辨识值近似收敛于经典值;最后,应用爆热值分布在4～9 kJ/g的8个炸药样品的实验数据对算法进行了检验,并提出了判断收敛时刻的实验判据。结果表明,辨识算法有效隔离了振荡参数的影响,对内桶水温度变化有较强的预测能力,爆热辨识值能在40 min（主末期1/3）内快速稳定地收敛到3.5%的相对误差上限水平内,实验判据能较准确地判断爆热辨识值收敛时刻。本方法理论上还可拓展至绝热法爆热值计算。     

一种改进的螺旋桨相同步控制噪声模型辨识方法

阐述了相同步控制降噪的原理及简化噪声模型的建立方法;针对传统的辨识方法无法满足分布式方案的缺点,提出一种简化噪声模型的改进辨识方法,该方法能大大降低模块之间的通信实时性需求,提高相角寻优方案的可实施性,还能提高简化噪声模型的辨识精度;并采用HS-DY混合共轭梯度法提高求解速度,使改进的方法满足控制实时性要求;研究了不同的数据采集条件对辨识精度的影响,得到了合适的采集条件为取5~10个周期的数据;基于本文搭建的实验平台对改进的方法进行了验证,结果表明改进的方法比传统方法能更准确地预测最优相角,辩识精度提高约7°。     

变分多尺度方法在一维力学模型中的应用

将变分多尺度方法应用于一维缆索模型,导出受力缆索的宏观有限元模型并求得细观位移解析解,总结出变分多尺度方法应用于具体模型的关键点和缺陷. 假定刚度为常值,数值模拟一定边界和受力下的缆索,得到宏观和细观位移. 将细观与宏观位移叠加,相比于精确位移得出：细观位移可视为常规有限元模型的后验误差. 变分多尺度方法在一维力学模型中的成功应用,推进了其实用性,为其在更多力学及工程问题中的运用和发展提供了参考.     

求非线性转子－轴承系统周期响应的一种计算方法

本文把求非线性转子－轴承系统瞬态响应的分块Ｎｅｗｍａｒｋ方法与打靶法结合求系统的周期解，该方法利用了分块Ｎｅｗｍａｒｋ方法求解速度快的优点和Ｊａｃｏｂｉ矩阵求解时每步不需迭代的特点。本文首先给出周期解的求解公式，然后用一个算例，讨论了周期解的稳定性及失稳后的分岔行为。     

陀螺零偏二次模型参数的系统级辨识算法

以单轴旋转光学捷联惯性导航系统为原型,假设水平陀螺常值漂移的影响得以完全调制,方位陀螺漂移为随时间变化的二次模型,在水平阻尼工作模式下推导了系统位置误差与方位陀螺漂移之间严格的数学关系。分别设置了方位陀螺漂移仅有常值项、一次项、二次项和全系数误差的误差模型,利用递推最小二乘算法成功辨识出设定的二次模型中各个参数值。仿真结果表明,常值项首先被辨识出来,估计时间约为14 h,估计误差为6.54e-6(°)/h;一次项系数估计时间约为30 h,估计误差为2.73e-8(°)/h;二次项系数估计时间约为42 h,估计误差为1.51e-9(°)/h;全系数估计需要45 h,估计误差为7.28e-6(°)/h。辨识结果验证了该算法的正确性。实际系统中,可适当增加总的辨识估计时间,以达到更高精度的辨识结果。     

The analysis of thin walled composite laminated helicopter rotor with hierarchical warping functions and finite element method

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free bending as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method is introduced to form a numerical algorithm. Both static and natural vibration problems of sample box beams are analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor. The project supported by the National Natural Science Foundation of China (19932030)     

Dynamics of flexible multibody systems with tree topologies

The dynamic equations of flexible multibody systems with tree topological configuration are derived by using the Jourdain's principle. The independent joint coordinates are introduced to describe the large displacements of the bodies, and the modal coordinates are used to describe small deformations of flexible bodies based on the consistent mass finite element method and normal vibration mode analysis. The minimum differential equations are developed, which are compatible with the equations of multi-rigid body systems or structural dynamics. The stiff problem in the numerical integration is thus alleviated effectively. The method used in this paper can be extended to deal with systems with other topological configurations. Finally, the validity and feasibility of the presented mathematical model are demonstrated by a numerical example of a manipulator with two elastic links. The project supported by National Natural Science Foundation of China     

Some improvements on free surface simulation by the particle finite element method

The Lagrangian method has become increasingly popular in numerical simulation of free surface problems. In this paper, after a brief review of a recent Lagrangian method, namely the particle finite element method, some issues are discussed and some improvements are made. The least‐square finite element method is adopted to simplify the solving of the Navier–Stokes equations. An adaptive time method is derived to obtain suitable time steps. A mass correction procedure is imported to improve the mass conservation in long time calculations and time discretization scheme is adopted to decrease the pressure oscillations during the calculations. Finally, the method is used to simulate a series of examples and the results are compared with the commercial FLOW3D code. Copyright © 2008 John Wiley & Sons, Ltd.     

The three-dimensional prolonged adaptive unstructured finite element multigrid method for the Navier–Stokes equations

This paper presents the development of the three- dimensional prolonged adaptive finite element equation solver for the Navier–Stokes equations. The finite element used is the tetrahedron with quadratic approximation of the velocities and linear approximation of the pressure. The equation system is formulated in the basic variables. The grid is adapted to the solution by the element Reynolds number. An element in the grid is refined when the Reynolds number of the element exceeds a preset limit. The global Reynolds number in the investigation is increased by scaling the solution for a lower Reynolds number. The grid is refined according to the scaled solution and the prolonged solution for the lower Reynolds number constitutes the start vector for the higher Reynolds number. Since the Reynolds number is the ratio of convection to diffusion, the grid refinements act as linearization and symmetrization of the equation system. The linear equation system of the Newton formulation is solved by CGSTAB with coupled node fill-in preconditioner. The test problem considered is the three-dimensional driven cavity flow. © 1997 John Wiley & Sons, Ltd.     

A finite element method for the one‐dimensional extended Boussinesq equations

A new finite element method for Nwogu's (O. Nwogu, ASCE J. Waterw., Port, Coast., Ocean Eng., 119 , 618–638 (1993)) one‐dimensional extended Boussinesq equations is presented using a linear element spatial discretisation method coupled with a sophisticated adaptive time integration package. The accuracy of the scheme is compared to that of an existing finite difference method (G. Wei and J.T. Kirby, ASCE J. Waterw., Port, Coast., Ocean Eng., 121 , 251–261 (1995)) by considering the truncation error at a node. Numerical tests with solitary and regular waves propagating in variable depth environments are compared with theoretical and experimental data. The accuracy of the results confirms the analytical prediction and shows that the new approach competes well with existing finite difference methods. The finite element formulation is shown to enable the method to be extended to irregular meshes in one dimension and has the potential to allow for extension to the important practical case of unstructured triangular meshes in two dimensions. This latter case is discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

A combined finite volumes - finite elements method for a low-Mach model

In this paper, we develop a finite volumes - finite elements method based on a time splitting to simulate some low-Mach flows. The mass conservation equation is solved by a vertex-based finite volume scheme using a τ-limiter. The momentum equation associated with the compressibility constraint is solved by a finite element projection scheme. The originality of the approach is twofold. First, the state equation linking the temperature, the density, and the thermodynamic pressure is imposed implicitly. Second, the proposed combined scheme preserves the constant states, in the same way as a similar one previously developed for the variable density Navier-Stokes system. Some numerical tests are performed to exhibit the efficiency of the scheme. On the one hand, academic tests illustrate the ability of the scheme in term of convergence rates in time and space. On the other hand, our results are compared to some of the literature by simulating a transient injection flow as well as a natural convection flow in a cavity.     

基于混合编码遗传算法和有限元分析的压电结构载荷识别

与传统的优化算法相比,遗传算法不需要计算目标函数的导数信息,便于迭代,可实现全局寻优.因此,本文提出一种采用混合编码的遗传算法与有限元分析相结合,对复合材料层合板、壳进行载荷识别的新方法.在遗传算法求解过程中,设计变量的编码方法选择是其重要环节,二进制编码容易产生连续函数离散化时的映射误差,且其求解精度与染色体的编码长度紧密相关,过长的染色体描述虽可提高精度,但会显著降低算法的求解效率.为此,本文提出采用混合编码的方法进行载荷识别,即用二进制编码表征载荷作用位置,浮点数编码表示载荷的大小.这一方法大大降低了染色体的长度,并显著提高了计算效率和精度.     

Modal parameter identification of flexible spacecraft using the covariance-driven stochastic subspace identification (SSI-COV) method

In this paper, the on-orbit identification of modal parameters for a spacecraft is investigated. Firstly, the cou-pled dynamic equation of the system is established with the Lagrange method and the stochastic state-space model of the system is obtained. Then, the covariance-driven stochas-tic subspace identification (SSI-COV) algorithm is adopted to identify the modal parameters of the system. In this algo-rithm, it just needs the covariance of output data of the system under ambient excitation to construct a Toeplitz matrix, thus the system matrices are obtained by the singular value decom-position on the Toeplitz matrix and the modal parameters of the system can be found from the system matrices. Finally, numerical simulations are carried out to demonstrate the validity of the SSI-COV algorithm. Simulation results indi-cate that the SSI-COV algorithm is effective in identifying the modal parameters of the spacecraft only using the output data of the system under ambient excitation.     

Parameter identification of river current and diffusion by reduced Kalman filter finite element method

The objective of this study is to propose a parameter identification of a river current and diffusion coefficients by using the reduced Kalman filter finite element method, which has been previously presented and now extended by the authors. For comparison, the estimation computations of velocity, water elevation, and chemical oxygen demand (COD) concentration are carried out on the basis of nonlinear shallow water flow and compared with the observations carried out at the Teganuma river in Japan. A marked discrepancy in COD concentration is found between the computed and observed results. The correlation factor between the computed and observed results is 0.51. To reduce the discrepancy, the authors believe that the diffusion coefficients should be identified. Assuming that the diffusion coefficient is constant in the entire domain and over the entire total duration, satisfactory results were not obtained. Thus, the computational domain is divided into four subdomains according to the water depth. Assuming that the diffusion coefficients are constant in each subdomain, the identification is carried out. Relatively good, albeit unsatisfactory, results are obtained. The discrepancy between the computed and observed COD concentration has special features. In some time zones, the computed results are larger whereas in other time zones, they are smaller than the observed results. To compensate this discrepancy, we assumed that the diffusion coefficient is a function of COD concentration. The correlation factor is improved to be 0.73. The identified diffusion coefficients are time functions that change cyclically with a period of 24 h. This fact suggests that biological phenomenas occurred in the river. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.