An accelerated iterative method for contact analysis

An iterative solution procedure for a frictionless contact problem is presented. Convergence to the exact solution is guaranteed by an error reduction method, and the rate of convergence is drastically improved by reduction of the ratio of extreme eigenvalues of the iteration matrix. For an ordinary linear equation, the present technique has the same theoretical value of convergence rate as the Chebyshev acceleration technique. The present acceleration technique can be directly extended for complicated frictional contact problems.     

Stability analysis of constrained multibody systems

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems usually assume the rows of the constraint Jacobian matrix to be linearly independent. But during the motion, at instantaneous configurations, the Jacobian matrix may become less than full rank resulting in singularities. This occurs when the closed-loop goes from 3D to 2D type of configuration. In this paper the linearly dependent rows are identified by an uptriangular decomposition process. The corresponding constraint equations are modified so that the singularities in the numerical procedure are avoided. The conditions for the validity of the modified equations are described. Furthermore, the constraint equations expressed in accelerations are modified by Baumgarte's approach to stabilize the accumulation of the numerical errors during integration. A computational procedure based on Kane's equations is presented. Two and three-link robotic manipulators will be simulated at singular configurations to illustrate the use of the modified constraints.     

A direct violation correction method in numerical simulation of constrained multibody systems

 A new direct violation correction method for constrained multibody systems is presented. It can correct the value of state variables of the systems directly so as to satisfy the constraint equations of motion. During the integration of the dynamic equations of constrained multibody systems, this method can efficiently control the violations of constraint equations within any given accuracy at each time-step. Compared to conventional indirect methods, especially Baumgarte's Constraint Violation Stabilization Method, this method has clear physical meaning, less calculation and obvious correction effect. Besides, this method has minor effect on the form of the dynamic equations of systems, so it is stable and highly accurate. A numerical example is provided to demonstrate the effectiveness of this method. Received: 17 December 1999     

A hybrid variational method for multibody dynamics

This paper presents a hybrid variational method to minimize computational effort in forming and solving the equations of motion for broad classes of rigid multibody mechanical systems. The hybrid method combines the O(n) and O(n³) recursive variational methods for forming the equations of motion in terms of joint relative co-ordinates. While the O(n³) method is more efficient than the O(n) method for systems with short chains and decoupled loops, the converse is true when the number of bodies in chains is large. The computational complexity of the O(n³) and O(n) methods in forming and solving the equations of motion is analysed as a function of the numbers of bodies, decoupled loops, joints, cut joints, cut-joint constraint equations and force elements. Based on complexity estimates, the method presented in this paper uses either the O(n) or O(n³) variational method to formulate the equations of motion for each open chain and decoupled loop in the system, to minimize the computational effort.     

An iterative rounding search-based algorithm for the disjunctively constrained knapsack problem

This article proposes an iterative rounding search-based algorithm for approximately solving the disjunctively constrained knapsack problem. The problem can be viewed as a variant of the well-known knapsack problem with some sets of incompatible items. The algorithm considers two key features: a rounding strategy applied to the fractional variables of a linear relaxation and a neighbouring strategy used for improving the quality of the solutions at hand. Both strategies are iterated into a process based on adding a series of (i) valid cardinality constraints and (ii) lower bounds used for bounding the objective function. The proposed algorithm is analysed computationally on a set of benchmark instances of the literature. The proposed algorithm outperforms the Cplex solver and the results obtained improve on most existing solutions.     

An effective solver for absolute variable formulation of multibody dynamics

This paper presents an effective and general method for converting the equations of motion of multibody systems expressed in terms of absolute variables and Lagrange multipliers into a convenient set of equations in a canonical form (constraint reaction-free and minimal-order equations). The method is applicable to open-loop and closed-loop multibody systems, and to systems subject to holonomic and/or nonholonomic constraints. Being aware of the system configuration space is a metric space, the Gram-Schmidt ortogonalization process is adopted to generate a genuine orthonormal basis of the tangent (null, free) subspace with respect to the constrained subspace. The minimal-order equations of motion expressed in terms of the corresponding tangent speeds have the virtue of being obtained directly in a resolved form, i.e. the related mass matrix is the identity matrix. It is also proved that, in the case of absolute variable formulation, the orthonormal basis is constant, which leads to additional simplifications in the motion equations and fits them perfectly for numerical formulation and integration. Other useful peculiarities of the orthonormal basis method are shown, too. A simple example is provided to illustrate the convertion steps.The research leading to this paper was supported in part by the State Committee for Scientific Research, Grant No. 3 0955 91 01     

Stability analysis of constraints in flexible multibody systems dynamics

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems assume that the constraint equations are linearly independent. During the motion, when the system is at a singular configuration, the constraint Jacobian matrix possesses less than full rank and hence it results in singularities. This occurs when the direction of a constraint coincides with the direction of the lost degree of freedom. In this paper the constraint equations for deformable bodies are modified for use in the neighborhood of the singular configuration to yield the system inertia matrix which is nonsingular and also to take the actual generalized constraint forces into account. The procedures developed are applicable to both the augmented approach and the coordinate reduction methods. For the modeling of the constrained flexible multibody systems, a general recursive formulation is developed using Kane's equations, finite element method and modal analysis techniques. The system may contain revolute, prismatic, spherical or other types of joints, as well as geometrical nonlinearities; the rotary inertia is also automatically included. Simulation of a two-link flexible manipulator is presented at a singular configuration to demonstrate the utility of the method.     

An accelerated automatic root search algorithm for iterative methods in vibration analysis

The paper presents an accelerated version of an automatic root searching technique developed by the authors for application to residual function iterative methods in vibration analysis. The power and generality of the accelerated method is demonstrated by application to (i) an 8 rotor torsional vibration system, and (ii) a 15 rotor torsional vibration system specially synthesized so as to have an uneven root distribution including clusters of close frequencies.     

Collisions of multibody systems

This paper presents a computational procedure for studying collisions of multibody systems. It combines the procedures of impact analysis and the methods of modern multibody dynamics (including the use of Kane's equations, lower body arrays, generalized speeds, and differentiation algorithms). By assuming the duration of impact to be very short and that the configurations of the systems have only small changes during the colliding process, we can automatically generate the governing dynamical equations. By using Newton's impact law, the partial velocities of the contact points determine impulse force components. Then by back substituting into the governing equations, the changes of velocities during the collision, the components of internal impulses, and the subsequent motions of the systems after collision may be determined. Received 24 January 2001     

An accelerated subspace iteration method

The subspace iteration method is widely used for the computation of a few smallest eigenvalues and the corresponding eigenvectors of large eigenproblems. Under certain conditions, this method exhibits slow convergence. For improving the convergence of the method, a few acceleration techniques are already available in the literature. In this paper, yet another method is presented. The method has been applied for the computation of a few smallest eigenpairs of some typical eigenprobiems. The results indicate that the acceleration method is efficient for large eigenproblems. Simplicity, ease of computer implementation, absence of parameters whose values are to be chosen based on experience and effectiveness for large problems are the attractive features of the proposed method.     

V-BLAST MIMO-OFDM系统的一种迭代信道估计方案

研究了频率选择性衰落信道条件下Turbo编码V-BLAST MIMO-OFDM系统的信道估计方法,提出了V-BLAST MIMO-OFDM系统的一种新的迭代信道估计方案。该方案首先利用发送的正交导频序列得到导频处的初始信道估计,然后利用导频符号辅助方法对信道进行内插,得到数据处的初始信道估计,经Turbo迭代纠错译码后,将得到的信息位和校验位软值信息反馈给信道估计器,并利用期望最大化(EM)迭代信道估计方法对信道进行更新。仿真结果表明,随着迭代次数的增加,系统的信道估计性能显著提高。     

An iterative algorithm for solving inverse problems in structural dynamics

The pulse-spectrum technique (PST), an iterative numerical algorithm, is presented and extended to solve the inverse problems arising from the dynamic structural identification and structural design problems. A simple one-dimensional shear beam model is used to demonstrate the applicability of PST. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement and design data. It is found that the PST is not only quite robust in providing accurate results but also an excellent numerical method according to the four practical criteria for evaluating numerical methods.     

An iterative solution scheme for systems of boundary element equations

In this paper an iterative scheme of first order is developed for the purpose of solving linear systems of equations. In particular, systems that are derived from boundary integral equations are investigated. The iterative schemes to be considered are of the form Ex^(k+1) = Dx^(k) + d, where E and D are square matrices. It will be assumed that E is a lower matrix, i.e. the coefficients above the central diagonal are zero. It will be shown that by considering matrix D embedded in a vector space and reducing its size with respect to a chosen metric, that convergence rates can be substantially improved. Equation ordering and parameter matrices are used to reduce the magnitude of D. A number of examples are tested to illustrate the importance of the choice of metric, equation ordering and the parameter matrix. Computation times are determined for both the iterative procedure and Gauss elimination indicating the usefulness of iteration which can be orders of magnitude faster.     

CMRH method as iterative solver for boundary element acoustic systems

Disceretization of boundary integral equations leads to complex and fully populated linear systems. One inherent drawback of the boundary element method (BEM) is that, the dense linear system has to be constructed and solved for each frequency. For large-scale problems, BEM can be more efficient by improving the construction and solution phases of the linear system. For these problems, the application of common direct solver is inefficient. In this paper, the corresponding linear systems are solved more efficiently than common direct solvers by using the iterative technique called CMRH (Changing Minimal Residual method based on Hessenberg process). In this method, the generation of the basis vectors of the Krylov subspace is based on the Hessenberg process instead of Arnoldi's one that the most known GMRES (Generalized Minimal RESidual) solver uses. Compared to GMRES, the storage requirements are considerably reduced in CMRH.     

Impulsive motion of ideally constrained mechanical systems via analytical dynamics

This paper formulates the general variational equation, or principle, for the impulsive motion of mechanical systems subjected to ideal impulsive constraints, in both holonomic and nonholonomic coordinates, then applies it to problems with persistent impulsive constraints and, with the help of Lagrange's method of undetermined multipliers, produces all possible impulsive equations of motion, with or without the associated reactions, in holonomic or nonholonomic coordinates. These equations are the impulsive counterparts of the well-known finite motion equations of Routh/Voss, Maggi, Hadamard, Boltzmann/Hamel, Chaplygin/Voronets, and Appell. Finally, a simple example is presented and solved with several of the above methods.     

An iterative boundary element method for Cauchy inverse problems

 We are interested in this paper in recovering an harmonic function from the knowledge of Cauchy data on some part of the boundary. A new inversion method is introduced. It reduces the Cauchy problem resolution to the determination of the resolution of a sequence of well-posed problems. The sequence of these solutions is proved to converge to the Cauchy problem solution. The algorithm is implemented in the framework of boundary elements. Displayed numerical results highlight its accuracy, as well as its robustness to noisy data. Received 6 November 2000     

A Lagrangian approach to the non-causal inverse dynamics of flexible multibody systems: The three-dimensional case

This paper addresses the problem of end-point trajectory tracking in flexible multibody systems through the use of inverse dynamics. A global Lagrangian approach is employed in formulating the system equations of motion, and an iterative procedure is proposed to achieve end-point trajectory tracking in three-dimensional, flexible multibody systems. Each iteration involves firstly, a recursive inverse kinematics procedure wherein elastic displacements are determined in terms of the rigid body co-ordinates and Lagrange multipliers, secondly, an explicit computation of the inverse dynamic joint actuation, and thirdly, a non-recursive forward dynamic analysis wherein generalized co-ordinates and Lagrange multipliers are determined in terms of the joint actuation and desired end-point co-ordinates. In contrast with the recursive methods previously proposed, this new method is the most general since it is suitable for both open-chain and closed-chain configurations of three-dimensional multibody systems. The algorithm yields stable, non-casual actuating joint torques and associated Lagrange multipliers that account for the constraint forces between flexible multibody components.     

An iterative method for maximum entropy regularization reconstruction in MRI

Many problems in physics involve imaging objects with high spatial frequency content in a limited amount of time. The limitation of available experimental data leads to the infamous problem of diffraction limited data, which manifests itself by causing ringing in the image. This ringing is due to interference phenomena in optics and is known as the Gibbs phenomenon in engineering. In this paper, an iterative maximum entropy regularization (IMER) algorithm for magnetic resonance imaging (MRI) is developed, which produces a super-resolution and optimal signal-to-noise solution to the problem of reconstructing a source from partial Fourier transform data. This method is capable, in principle, of unlimited resolution and is robust with respect to Gaussian white noise perturbation. Comparisons of the IMER method with the conventional Fourier transform method are carried out with the real magnetic resonance data to illustrate the performance of the proposed method. © 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 427–431, 1999     

基于硬判决的BICM-ID系统的迭代载波相位同步算法

在基于迭代译码的比特交织编码调制(BICM-ID)系统中,提出了一种利用译码产生的硬判决信息作引导的迭代载波相位同步的算法.该算法等效于期望最大化(EM)算法,收敛于最大似然(ML)估计,利用Viterbi译码过程中产生的数据比特硬判决信息,通过迭代地在同步和解码之间交换信息来完成联合解码和载波相位同步,实现了联合解码同步.仿真结果验证了该算法的有效性.在相偏θ∈[-20°,20°]时,其误码率性能最佳;在迭代次数达到5次时,误码率性能基本接近理想同步性能,较传统的相位同步算法具有更优的性能.随着信噪比的增大,能更快地逼近理想同步性能.