Neurocomputing method based on structural finite element analysis of discrete model

Based on structural finite element analysis of discrete models, a neurocomputing strategy is developed in this paper. Dynamic iterative equations are constructed in terms of neural networks of discrete models. Determination of the iterative step size, which is important for convergence, is investigated based on the positive definiteness of the finite element stiffness matrix. Consequently, a method of choosing the step size of dynamic equations is proposed and the computational formula of the best step size is derived. The analysis of the computing model shows that the solution of finite element system equations can be obtained by the method of neural network computation efficiently. The proposed method can be used for parallel computation of structural finite element in a large-scale integrated circuit (LSI).     

A systematic method for eigenstructure assignment and application to response shaping

The simultaneous assignment of eigenvalue and eigenvector in a dynamic system using a constant-gain state-feedback controller is formulated as a static optimization problem. Response shaping by adequately damping the dominant modes or by eliminating the uncontrollable modes is possible in this formulation. Systematic solution through a standard LP routine makes the method attractive for practical implementation. The proposed eigenstructure-assignment algorithm is illustrated through two examples, one of which is the stabilization of a single machine connected to an infinite-bus power system.     

H.264帧内预测模式快速选择算法

为降低帧内预测的复杂度,提出一种快速的帧内预测算法。该算法利用帧内4×4块最优预测模式与和它相邻的预测模式之间率失真代价（RDCost）的高相关性,以及绝对变换误差和（SATD）与率失真（RD）性能之间的强相关性,有效减少了预测模式,避免了不必要的RDCost计算。实验结果显示,该算法提高编码时间效率约为50%,同时保持视频的图像质量几乎不变。     

Computational aspects of sensitivity calculations in linear transient structural analysis

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. Several existing sensitivity calculation methods and two new methods are compared for three example problems. All of the methods considered are computationally efficient enough to be suitable for largeorder finite element models. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the convergence of both response quantities and sensitivities as a function of the number of vectors used.Two types of sensitivity calculation techniques were considered. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. This was found to result in poor convergence of stress sensitivities in several cases. To overcome this poor convergence, two semianalytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in very good convergence of the stress sensitivities. In both techniques the computational cost is much less than would result if the vibration modes were recalculated and then used in an overall finite difference method.     

The construction of free–free flexibility matrices for multilevel structural analysis

This article considers a generalization of the classical structural flexibility matrix. It expands on previous papers by taking a deeper look at computational considerations at the substructure level. Direct or indirect computation of flexibilities as “influence coefficients” has traditionally required pre-removal of rigid body modes by imposing appropriate support conditions, mimicking experimental arrangements. With the method presented here the flexibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free–free stiffness matrix. This generalized inverse preserves the stiffness spectrum. The definition is element independent and only involves access to the stiffness generated by a standard finite element program and the separate construction of an orthonormal rigid-body mode basis. The free–free flexibility has proven useful in special application areas of finite element structural analysis, notably massively parallel processing, model reduction and damage localization. It can be computed by solving sets of linear equations and does not require processing an eigenproblem or performing a singular value decomposition. If substructures contain thousands of d.o.f., exploitation of the stiffness sparseness is important. For that case this paper presents a computation procedure based on an exact penalty method, and a projected rank-regularized inverse stiffness with diagonal entries inserted by the sparse factorization process. These entries can be physically interpreted as penalty springs. This procedure takes advantage of the stiffness sparseness while forming the full free–free flexibility, or a boundary subset, and is backed by an in-depth null space analysis for robustness.     

An adaptive boundary element for eigenvalue problems with the Helmholtz equation: simplified h-scheme

A simplified h-version of the adaptive boundary elements is proposed for the eigenvalue analysis of the Helmholtz equation. The new scheme considers the effect of each local boundary element refinement, not on the eigenvalue but on the eigenvector, which is devised for possible application of the conventional adaptive mesh construction strategy for boundary value problems. In this paper, for improvement of computational efficiency, the local reanalysis for obtaining the eigenvector is employed. The error indicator of the eigenvector in place of that of the eigenvalue, the global value, decides selectively the boundary elements to be refined. Utility of the proposed method is compared, through some examples, with those previously developed.     

Model reduction tools for nonlinear structural dynamics

Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their derivatives with respect to modal coordinates contain much beneficial reduction information. Three approaches to obtain modal derivatives are presented, including a newly introduced numerical way. Direct and reduced integration results of truss examples show that tangent modes do not describe the nonlinear system sufficiently well, whereas combining tangent modes with modal derivatives and/or static modes provides much better reduction results.     

Vibration reanalysis using frequency-shift combined approximations

In the structural dynamic optimization procedure, many repeated analyses are conducted to evaluate vibration performance of successively modified structural designs. A new procedure for structural vibration (or eigenproblem) reanalysis is developed based on iteration and inverse iteration method with frequency-shift and linear combination acceleration to reduce the high computational cost of structure reanalysis. With a suitable frequency-shift factor, the Frequency-Shift Combined Approximations (FSCA) method allows to calculate higher modes accurately. Three numerical examples are presented to demonstrate the accuracy of the proposed method. Excellent results can be obtained in cases where large modifications are made and higher modes are needed.     

Modal representation of geometrically nonlinear behavior by the finite element method

A method is described for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of the solution of a certain eigenvalue problem. This eigenvalue problem, commonly known as the linear or bifurcation buckling problem for a restricted class of so-called “perfect” structural situations, is thus seen to have a broader significance. The applied loading nonlinearly amplifies the contributions of each mode (eigenvector) present in the linear finite dement solution, and the amplification factors are easily computable functions of the eigenvalues. Computational results for braced frames and arches under asymmetric loading are presented.     

Computation of optical modes in axisymmetric open cavity resonators

The computation of optical modes inside axisymmetric cavity resonators with a general spatial permittivity profile is a formidable computational task. In order to avoid spurious modes the vector Helmholtz equations are discretised by a mixed finite element approach. We formulate the method for first and second order Nédélec edge and Lagrange nodal elements. We discuss how to accurately compute the element matrices and solve the resulting large sparse complex symmetric eigenvalue problems. We validate our approach by three numerical examples that contain varying material parameters and absorbing boundary conditions (ABC).     

New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

基于核的双子空间方法及其快速求解算法

针对现有的双子空间方法中存在的问题,提出一种基于核的双子空间判别分析(KDS-DA)方法。此外,还提出一种基于镶边矩阵求逆运算的快速KDS-DA特征求解算法。该算法运用高阶镶边矩阵的求逆运算可转化为低阶镶边矩阵的求逆运算这一性质,使得当顺序求解样本类内散射矩阵主空间中第r+1个KDS-DA判别矢量时,可充分利用求解第r个判别矢量时所得到的计算结果来减少算法复杂度。通过在ORL和AR人脸库上的实验证实文中方法的有效性。     

A Multigrid Method for Helmholtz Transmission Eigenvalue Problems

In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.     

Eigenfilter design of linear-phase FIR digital filters using neural minor component analysis

This paper proposes a minor component analysis-based neural learning algorithm for designing linear-phase finite impulse response digital filters. The objective function to be minimized in the least-squares design can be formulated as the eigenvalue problem for solving an appropriate real, symmetric, and positive-definite matrix. To achieve the eigenfilter design, an alternative neural learning rule based on the minor component analysis algorithm is exploited. The optimal filter coefficients corresponding to the eigenvector of the smallest eigenvalue of the positive-definite matrix can be achieved in an iterative manner, avoiding the complex computation of eigenvalue decomposition. Furthermore, the learning step parameter that affects the convergence performance is investigated empirically. The simulation results indicate that the proposed neural-based approach can be applied to eigenfilter design and yields a lower computational complexity compared with traditional matrix algebraic-based approaches.     

Modified triangular factors in the incremental finite element analysis with nonsymmetric stiffness changes

A method is presented for modifying the triangular factors of the global stiffness matrix with nonsymmetric stiffness modifications. The proposed procedure is based on the Bennett's algorithm and applies to nonlinear structural analysis by the finite element method. The appropriate computational cost analysis is included and states the conditions of the economical use of the method.     

Accelerated subspace iteration with aggressive shift

The subspace iteration method is a very classical method for solving large general eigenvalue problems, and it is accepted as one of the reliable methods to solve large size eigenvalue problems through 1970–1980s. However, the classical subspace method is less efficient than Lanczos iteration method in terms of CPU time, because its parameters and iteration procedure were selected for today’s small and medium size eigenvalue problems. In the last 30 years, researchers have been trying to accelerate the classical subspace iteration method in different ways, such as, power acceleration, relaxation acceleration, so that it can deal with larger and larger eigenvalue problems arising in finite element analysis. Shifting technique is recognized as an efficient way to speed up the convergence rate for small and medium size eigenvalue problems. However the shifting cost for large size eigenvalue problems is expensive and thus makes it unacceptable. That is why almost all improvements in the last 20 years did not deal with shifts. In this paper, an aggressive shifting strategy is proposed based on a computable convergence criterion involving both eigenvalue and eigenvector instead of eigenvalue only. A wide range of numerical tests shows that the proposed aggressive shifting strategy can greatly decrease CPU time.     

Finite prism method based topology optimization of beam cross section for buckling load maximization

The use of the finite element method (FEM) for buckling topology optimization of a beam cross section requires large numerical cost due to the discretization in the length direction of the beam. This investigation employs the finite prism method (FPM) as a tool for linear buckling analysis, reducing degrees of freedom of three-dimensional nodes of FEM to those of two-dimensional nodes with the help of harmonic basis functions in the length direction. The optimization problem is defined as the maximization problem of the lowest eigenvalue, for which a bound variable is introduced and set as the design objective to treat mode switching phenomena of multiple eigenvalues. The use of the bound formulation also helps the proposed optimization to treat beams having local plate buckling modes as the fundamental modes as well as beams having global buckling modes. The axial stress is calculated according to the distribution of material modulus which is interpolated using the SIMP approach. Optimization problems finding cross-section layouts from rectangular, L-shaped and generally-shaped design domains are solved for various beam lengths to ascertain the effectiveness of the proposed method.     

A Multilevel Correction Method for Interior Transmission Eigenvalue Problem

In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction method can transform the transmission eigenvalue solving in the finest finite element space to a sequence of linear problems and some transmission eigenvalue solving in a very low dimensional spaces. Since the main computational work is to solve the sequence of linear problems, the multilevel correction method improves the overfull efficiency of the transmission eigenvalue solving. Some numerical examples are provided to validate the theoretical results and the efficiency of the proposed numerical scheme.     

On a multimode test sequencing problem

Test sequencing is a binary identification problem wherein one needs to develop a minimal expected cost test procedure to determine which one of a finite number of possible failure states, if any, is present. In this paper, we consider a multimode test sequencing (MMTS) problem, in which tests are distributed among multiple modes and additional transition costs will be incurred if a test sequence involves mode changes. The multimode test sequencing problem can be solved optimally via dynamic programming or AND/OR graph search methods. However, for large systems, the associated computation with dynamic programming or AND/OR graph search methods is substantial due to the rapidly increasing number of OR nodes (denoting ambiguity states and current modes) and AND nodes (denoting next modes and tests) in the search graph. In order to overcome the computational explosion, we propose to apply three heuristic algorithms based on information gain: information gain heuristic (IG), mode capability evaluation (MC), and mode capability evaluation with limited exploration of depth and degree of mode Isolation (MCLEI). We also propose to apply rollout strategies, which are guaranteed to improve the performance of heuristics, as long as the heuristics are sequentially improving. We show computational results, which suggest that the information-heuristic based rollout policies are significantly better than traditional information gain heuristic. We also show that among the three information heuristics proposed, MCLEI achieves the best tradeoff between optimality and computational complexity.     

Erratum to: New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.