Accelerating Krawczyk-like interval algorithms for the solution of nonlinear systems of equations by using second derivatives

Recently the properties of Krawczyk-like iterative interval methods for the solution of systems of nonlinear equations have been discussed in several papers (e.g. [2], [3], [5], [6]). These methods converge to a solution under relatively weak conditions provided an initial inclusion vector is known. In the present paper we describe a method that improves the convergence speed for an important class of problems by using second partial derivatives. This method is particularly interesting for large systems with a Jacobi matrix whose off-diagonal coefficients are all constant.     

An Algebraic Multigrid Method for Higher-order Finite Element Discretizations

In this paper, we will design and analyze a class of new algebraic multigrid methods for algebraic systems arising from the discretization of second order elliptic boundary value problems by high-order finite element methods. For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid. With any given classical algebraic multigrid solver for linear finite element stiffness matrix, a corresponding algebraic multigrid method can then be designed for the quadratic or higher order finite element stiffness matrix by combining with a standard smoother for the original system. This method is designed under the assumption that the sparse matrix to be solved is associated with a specific higher order, quadratic for example, finite element discretization on a finite element grid but the geometric data for the underlying grid is unknown. The resulting new algebraic multigrid method is shown, by numerical experiments, to be much more efficient than the classical algebraic multigrid method which is directly applied to the high-order finite element matrix. Some theoretical analysis is also provided for the convergence of the new method.     

In-plane vibration of plates by continuous mass matrix method

The continuous mass matrix method derived for frameworks is extended to the analysis of in-plane vibration of plates. A continuous mass distribution which is the same as the actual mass distribution of the plate is considered over each rectangular finite element. Taking into account that the rigid body movement produces inertial forces in dynamic analysis for a rectangular plate element eight independent conditions are provided to satisfy eight independent freedoms. Each condition is obtained from an independent displacement distribution satisfying the equations of motion at any point of the element and not only at the nodes of the rectangle. The dynamic element stiffness matrix thus obtained is a function of the natural circular frequency. The limit of the dynamic element stiffness matrix when the value of the natural circular frequency tends to zero is the static, stress compatible element stiffness matrix. The analysis of plates under forcing forces is performed by modal analysis after the natural circular frequencies and the corresponding modal shapes have been obtained from the free vibrations, for all the forcing forces are assumed to be function of the same time variation. Otherwise one must recur to a numerical analysis. The effect of the sizes, number of the meshes, the additional static load on the plate and the rigidity of the boundaries on the vibration of the plate is discussed. Few example problems are solved in order to illustrate the above mentioned effects. The numerical results obtained by continuous mass matrix method are compared with those of consistent mass matrix method. The convergence in terms of the sizes of meshes and the limit of convergence are examined.     

VIBEX: an expert system for vibration fault diagnosis of rotating machinery using decision tree and decision table

This paper proposes an expert system called VIBEX (VIBration EXpert) to aid plant operators in diagnosing the cause of abnormal vibration for rotating machinery. In order to automatize the diagnosis, a decision table based on the cause-symptom matrix is used as a probabilistic method for diagnosing abnormal vibration. Also a decision tree is used as the acquisition of structured knowledge in the form of concepts is introduced to build a knowledge base which is indispensable for vibration expert systems. The decision tree is a technique used for building knowledge-based systems by the inductive inference from examples and plays a role itself as a vibration diagnostic tool. The proposed system has been successfully implemented on Microsoft Windows environment and is written in Microsoft Visual Basic and Visual C++. To validate the system performance, the diagnostic system was tested with some examples using the two diagnostic methods.     

Transfer matrix method for linear multibody system

A new method for linear hybrid multibody system dynamics is proposed in this paper. This method, named as transfer matrix method of linear multibody system (MSTMM), expands the advantages of the traditional transfer matrix method (TMM). The concepts of augmented eigenvector and equation of motion of linear hybrid multibody system are presented at first to find the orthogonality and to analyze the responses of the hybrid multibody system using modal method. If using this method, the global dynamics equation is not needed in the study of linear hybrid multibody system dynamics. The MSTMM has a small size of matrix and higher computational speed, and can be applied to linear multi-rigid-body system dynamics, linear multi-flexible-body system dynamics and linear hybrid multibody system dynamics. This method is simple, straightforward, practical, and provides a powerful tool for the study on linear hybrid multibody system dynamics. This method can be used in the following: (1) Solve the eigenvalue problem of linear hybrid multibody systems. (2) Obtain the orthogonality of eigenvectors of linear hybrid multibody systems. (3) Realize the accurate analysis of the dynamics response of linear hybrid multibody systems. (4) Find the connected parameters between bodies used in the computation of linear hybrid multibody systems. A practical engineering system is taken as an example of linear multi-rigid-flexible-body system, the dynamics model, the transfer equations and transfer matrices of various bodies and hinges; the overall transfer equation and overall transfer matrix of the system are developed. Numerical example shows that the results of the vibration characteristics and the response of the hybrid multibody system received by MSTMM and by experiment have good agreements. These validate the proposed method.     

The vibration discomfort of standing people: evaluation of multi-axis vibration

Few studies have investigated discomfort caused by multi-axis vibration and none has explored methods of predicting the discomfort of standing people from simultaneous fore-and-aft, lateral and vertical vibration of a floor. Using the method of magnitude estimation, 16 subjects estimated their discomfort caused by dual-axis and tri-axial motions (octave-bands centred on either 1 or 4 Hz with various magnitudes in the fore-and-aft, lateral and vertical directions) and the discomfort caused by single-axis motions. The method of predicting discomfort assumed in current standards (square-root of the sums of squares of the three components weighted according to their individual contributions to discomfort) provided reasonable predictions of the discomfort caused by multi-axis vibration. Improved predictions can be obtained for specific stimuli, but no single simple method will provide accurate predictions for all stimuli because the rate of growth of discomfort with increasing magnitude of vibration depends on the frequency and direction of vibration.     

自动测试设备开关矩阵之研究

对自动测试设备开关矩阵的各种设计方案进行了全面分析比较，提出了一种高适配能力的设计方案，基于此方案设计的混合智能型开关矩阵，解决了自动测试设备与各种被测单元适配难的问题，并已获国家发明专利。     

结合协方差与变异系数的密码芯片能量泄漏评估模型

在信息技术安全性评估通用准则中,必须使用具体的侧信道分析方法来评估密码芯片工作时的能量泄漏情况.为降低评估过程对侧信道分析方法的依赖性,通过分析能量迹各点之间的关系,构建一种基于协方差矩阵变异系数的能量泄漏评估模型.利用协方差矩阵度量能量迹各点间的线性关系,并引入变异系数衡量矩阵内各元素的差异程度,从而评估芯片工作时的...     

Registration based on projective reconstruction technique for augmented reality systems

In AR systems, registration is one of the most difficult problems currently limiting their application. In this paper, we propose a simple registration method using projective reconstruction. This method consists of two steps: embedding and tracking. Embedding involves specifying four points to build the world coordinate system on which a virtual object will be superimposed. In tracking, a projective reconstruction technique is used to track these four specified points to compute the model view transformation for augmentation. This method is simple, as only four points need to be specified at the embedding stage and the virtual object can then be easily augmented onto a real scene from a video sequence. In addition, it can be extended to a scenario using the projective matrix that has been obtained from previous registration results using the same AR system. The proposed method has three advantages: 1) it is fast because the linear least square method can be used to estimate the related matrix in the algorithm and it is not necessary to calculate the fundamental matrix in the extended case. 2) A virtual object can still be superimposed on a related area even if some parts of the specified area are occluded during the whole process. 3) This method is robust because it remains effective even when not all the reference points are detected during the whole process, as long as at least six pairs of related reference points correspondences can be found. Some experiments have been conducted to validate the performance of the proposed method.     

体育馆大跨屋盖空间风振分析

采用高效的完全背景响应法与共振分量法,结合有限元法对某体育馆大跨屋盖进行较为准确的空间风振分析. 在屋盖同步风洞试验的基础上,按空间随机风振分析方法考虑多个振型的影响,计算3个风向下屋盖各节点的静力等效风载荷和最大动位移以及杆件最大动内力,并给出位移和应力两个风振因数,为结构的抗风设计提供风载荷数据. 数值计算结果证明完全背景响应方法与共振分量法在工程应用上的可行性,可为同类屋盖的风振分析提供参考.     

Time domain approximation using digital methods

Two digital methods are proposed for the solution of the time-domain approximation problem. Tho first method, based on a reeursivo algorithm for tho matrix pseudo-iriverso, determines the pulse transfer function of a discrete-timo system of a prescribed order providing the best fit in tho least squares sense at tho samplo points. Tho continuous-time system transfer function is then derived by using a simple transformation provided that tho sampling frequence oxeeeds tho Nyquist rate. Tho method is direct and computationally efficient. The second method is based on using an offieiont gradient search algorithm providing the best fit in the least pti sense at tho samplo points. A number of examples illustrato the methods     

Distributed generic approximate sparse inverses

The need for accuracy in the solution of linear systems derived from the discretization of partial differential equations leads to large sparse linear systems. The solution of sparse linear systems requires efficient scalable methods. Iterative solvers require efficient parallel preconditioning methods to solve effectively sparse linear systems. Herewith, a new parallel algorithm for the generic approximate sparse inverse matrix method for distributed memory systems is proposed. The computation of the distributed generic approximate sparse inverse matrix is based on a column-wise approach, which allows the separation to independent problems that can be handled in parallel without synchronization points or intermediate communications. This is achieved by reforming the generic approximate sparse inverse matrix algorithm and its process of computation with a new partial solution method for the computation of the nonzero elements of each column dictated by the approximate inverse sparsity pattern. Moreover, an algorithmic scheme is proposed for the efficient distribution of data amongst the available workstations, along with a load balancing scheme for problems with large standard deviation in the number of nonzero elements per column. Numerical results are presented for the proposed schemes for various model problems.     

转子振动的主动控制

本文针对转子振动主动控制中系统矩阵中含有陀螺阵这一特点,提出了在频域中的二次型目标函数;根据转子振动故障的特点,明确提出了转子振动主动控制的三个作用,研究了相应的控制器设计方法;并以一悬臂模型转子为例,分析了振动主动控制的可能实施方案及效果;结果表明,本文中所提出的方法效果良好,有重要应用前景。     

随机时滞系统的时滞相关无源控制

研究随机时滞系统的时滞相关无源性分析和控制问题. 利用Lyapunov-Krasovskii方法和松弛矩阵方法, 得到时滞相关的无源性条件. 基于该条件设计时滞相关的随机无源控制器. 文中的结果以线性矩阵不等式(Linear matrix inequalities, LMIs)表示, 可以利用标准的凸优化算法进行有效求解. 通过一个数值例子说明本文方法的有效性.     

一种飞控系统不确定性建模方法及其鲁棒控制

针对大包线飞行控制系统, 本文通过摄动参数标称化及多个工作点的数据拟合, 并将拟合误差视为范数有界不确定性, 给出了一种不确定模型描述方法, 以降低系统描述的保守性. 基于二次稳定性准则, 运用线性矩阵不等式的处理方法, 得到了大包线飞控系统动态输出反馈控制器的存在条件和设计方法. 进一步, 通过合适的匹配摄动参数和求解凸优化问题, 以参数向量2--范数的形式给出了闭环系统保持鲁棒稳定所允许的参数最大摄动范围估计方法, 建立了系统摄动参数与二次稳定性之间的联系. 最后通过对飞行控制系统的算例仿真, 验证了文中方法的有效性和可行性.     

Conservatism reduction for linear parameter‐varying control design facing inexact scheduling parameters illustrated on flight tests

This article addresses the design problem of linear parameter‐varying (LPV) output feedback controllers that depend on inexact scheduling parameters for LPV systems. This problem has already been tackled and several methods have been proposed by overbounding the discrepancies between the actual scheduling parameters and the provided ones in the derivation of controller design condition. However, all methods in literature have conservatism in the overbounding, which is the main issue addressed in this article. We therefore propose a new overbounding for the discrepancies with the reverse use of Elimination lemma, which introduces no conservatism in theory. The new method is formulated in terms of bilinear matrix inequality, which is not tractable compared with linear matrix inequality, thus a practical design procedure composed of line search and iterative algorithm is shown. The effectiveness of our method is illustrated by an application to flight controller design for the lateral‐directional motions of a research airplane MuPAL‐α and the consequently conducted flight tests.     

一类线性时变群体系统稳定性的代数判据

针对在判断群体系统的稳定性时没有一般的方法和程序构造Lyapunov函数这个难点,利用矩阵范数,孤立子系统的矩阵指数函数与比较原理提出了一类线性时变群体系统平凡解一致稳定,所有解一致有界的充分条件。方便此类群体系统的稳定性分析,为研究其他群体系统稳定性的代数判据提供了理论基础。可以在此基础上,进一步研究一类非线性群体系统稳定性的代数判据。同时,还给出了具体算例,说明所提方法的正确性。此代数判据应用简便,灵活,适于实际应用。     

不确定离散时滞分段系统的广义H2弹性控制

针对一类不确定离散时滞分段系统,研究了广义H2稳定性分析和带有时滞的状态反馈弹性控制器设计问题.通过构造适当的离散分段二次李亚普诺夫函数,利用分段二次李亚普诺夫稳定性理论,给出了对于所有的容许参数不确定性,闭环系统是广义H2稳定的充分条件;在此基础上,基于线性矩阵不等式(LMI)处理方法,提出了带有时滞的状态反馈弹性控制器增益阵的设计方案.仿真实例验证了所提方法的有效性.     

不确定广义线性时变系统的鲁棒稳定和二次稳定

针对不确定广义线性时变系统,采用矩阵不等式的分析方法,提出不确定广义线性时变系统鲁棒稳定和二次稳定的概念.建立该类系统的矩阵不等式,将该类系统的鲁棒控制问题转化为求解矩阵不等式问题,得到该类系统鲁棒稳定和二次稳定的充分必要条件,并给出一种状态反馈鲁棒镇定控制器的设计方法.最后,通过数值算例表明了所提出方法的可行性.