基于信号时频分解的模态参数识别

给出了基于响应信号Gabor展开与重构的模态参数辨识的时频分析方法。通过响应信号的展开与重构，单频特征振动可从复杂的响应信号中分离出来，由它些特征振动信号可进一步提取系统物模态振动参数。论述了频率、阻尼和特征振型的估计方法以及估计方法对系统响应信号的特殊要求。此方法可适用于平衡、非平衡的响应信号，且无需输入信号，属于环境激励下的一种参数辨识方法。仿真结果说明明频展开与重构方法是模态参数辩识的有效手段之一。     

Substructured formulations of nonlinear structure problems – influence of the interface condition

We investigate the use of non‐overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a framework where we can swap Newton and DD so that we solve independent nonlinear problems for each substructure and linear condensed interface problems. The objective is to decrease the number of communications between subdomains and to improve parallelism. Depending on the interface condition, we derive several formulations that are not equivalent, contrarily to the linear case. Primal, dual and mixed variants are described and assessed on a simple plasticity problem. Copyright © 2015 John Wiley & Sons, Ltd.     

Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis

In this paper, we develop Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve the initial-boundary value problems for linear advection or advection-reaction equations. In contrast to many methods for advection-type problems, our ELLAM scheme naturally incorporates the inflow boundary conditions into its formulations and does not need an artificial outflow boundary condition. It does conserve mass. Moreover, optimal-order error estimates for ELLAM have been obtained. In contrast, many methods have only suboptimal-order estimates when applied to solve these problems. Furthermore, our ELLAM scheme provides a systematic approach to treat the interface problems of advection-type equations and can be naturally combined with domain decomposition and local refinement techniques to solve these problems. Numerical results in one and two dimensions are presented and discussed.     

Suppression of smeared spectrum ECM signal

Abstract

Three electronic counter‐countermeasures (ECCM) techniques for suppressing smeared spectrum (SMSP) jamming, a new electronic counter measures (ECM) technique, are presented. The analytical representations of the SMSP ECM signal in the time domain and the frequency domain are first derived, and then the differences between the SMSP jamming signal and the radar linear frequency modulation (LFM) signal are analyzed. Based on the differences, a jamming suppression system specifically for SMSP jamming interference excision is designed, which applies three different signal processing tools, i.e. fractional Fourier transform (FRFT), Fourier transform (FT) and atomic decomposition (AD). The jamming suppression performance of the presented methods is evaluated through simulations. The simulation results show that the presented methods can successfully suppress SMSP jamming.     

A coupling strategy for adaptive local refinement in space and time with a fixed global model in explicit dynamics

In dynamics, domain decomposition methods (DDMs) enable one to use different spatial and temporal discretizations depending on the physical phenomenon being taken into account. Thus, DDMs provide the analyst with key tools for dealing with problems in which phenomena occur on different temporal and spatial scales. This paper focuses on a less intrusive variation of this type of method which enables the global (industrial) mesh to remain unchanged while the local problem is being refined in space and in time where needed. This property is particularly useful in the case of a local problem whose localization evolves rapidly with time, as is the case for delamination. The downside is that the technique is iterative. The method is presented in the context of linear explicit dynamics, but, as with domain decomposition, its extension to other integration schemes and to nonlinear problems should be possible.     

RS-LOD方法及其在旋转机械故障特征提取中的应用

局部波动特征分解(LOD)方法是一种新的自适应时频分析方法。该方法通过采用微分、坐标域变换、分段线性变换三种运算,可以高效地将信号自适应分解为一系列的单一波动分量(MOC),非常适合于处理多分量信号。然而,由于分段线性变换的使用,虽可以显著提高算法的计算效率,但会使MOC分量缺乏光滑性,从而导致失真。对此,将样条曲线形状可调可控的有理样条函数引入LOD方法替代分段线性变换,提出了基于有理样条函数的局部波动特征分解(RS-LOD)方法。在详细阐述RS-LOD分解原理的基础上,通过仿真信号将RS-LOD、LOD和经验模态分解(EMD)进行了对比分析,结果表明RS-LOD方法可以明显改善原LOD方法中MOC分量光滑度差的问题。此外,针对旋转机械故障振动信号的多分量调制特点,将RS-LOD方法应用于旋转机械的故障特征提取,对滚动轴承和齿轮箱故障振动信号的分析结果表明,RS-LOD方法可以有效地提取旋转机械振动信号的故障特征。     

A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis

This paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis. The methods comprise a penalty approach, Lagrange multiplier methods, and a Nitsche‐type method. For the Nitsche method, a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity. All these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2D. In particular, focus is put on non‐uniform rational B‐spline patches which join nonconformingly along their common interface. Thus, the application of isogeometric analysis is extended to multi‐patches, which can have an arbitrary parametrization on the adjacent edges. Moreover, it has been shown that the unique properties provided by isogeometric analysis, that is, high‐order functions and smoothness across the element boundaries, carry over for the analysis of multiple domains. Copyright © 2013 John Wiley & Sons, Ltd.     

A meshless method for conjugate heat transfer problems

Mesh reduction methods such as boundary element methods, method of fundamental solutions, and spectral methods all lead to fully populated matrices. This poses serious challenges for large-scale three-dimensional problems due to storage requirements and iterative solution of a large set of non-symmetric equations. Researchers have developed several approaches to address this issue including the class of fast-multipole techniques, use of wavelet transforms, and matrix decomposition. In this paper, we develop a domain decomposition, or the artificial sub-sectioning technique, along with a region-by-region iteration algorithm particularly tailored for parallel computation to address the coefficient matrix issue. The meshless method we employ is based on expansions using radial-basis functions (RBFs).An efficient physically based procedure provides an effective initial guess of the temperatures along the sub-domain interfaces. The iteration process converges very efficiently, offers substantial savings in memory, and features superior computational efficiency. The meshless iterative domain decomposition technique is ideally suited for parallel computation. We discuss its implementation under MPI standards on a small Windows XP PC cluster. Numerical results reveal the domain decomposition meshless methods produce accurate temperature predictions while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.     

基于集合经验模态分解的脑电信号高阶张量特征提取

为了实现脑机接口系统需要有效的特征提取算法。针对二维主成分分析(2DPCA)的特征提取方法忽略脑电信号(EEG)频域特征的缺点和基于小波分解构建EEG高阶张量时小波参数难以确定的局限性,提出了基于集合经验模态分解(EEMD)构建高阶张量结合多线性主成分分析(MPCA)降维的特征提取方法。设计了3种不同特征提取方法的对照实验,并结合Fisher线性判别分析分类方法取得分类准确率。结果表明:新提出的方法相比基于小波分解构建高阶张量结合MPCA进行降维和2DPCA的特征提取方法,平均识别准确率分别提高4.75%和2.6%,且识别准确率的方差分别减小72.69%和23.86%。该方法在提高单次运动想象脑电信号识别准确率的同时还具有更好的适用性,为实现运动想象脑电信号解码奠定了基础。     

A new impedance accounting for short‐ and long‐range effects in mixed substructured formulations of nonlinear problems

An efficient method for solving large nonlinear problems combines Newton solvers and domain decomposition methods. In the domain decomposition method framework, the boundary conditions can be chosen to be primal, dual, or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance), which can increase the convergence rate. The optimal value for this parameter is usually too expensive to be computed exactly in practice: An approximate version has to be sought, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance, which combines short‐ and long‐range effects at a low computational cost.     

Energy‐momentum consistent algorithms for dynamic thermomechanical problems—Application to mortar domain decomposition problems

An energy‐momentum consistent integrator for non‐linear thermoelastodynamics is newly developed and extended to domain decomposition problems. The energy‐momentum scheme is based on the first law of thermodynamics for strongly coupled, non‐linear thermoelastic problems. In contrast to staggered algorithms, a monolithic approach, which solves the mechanical as well as the thermal part simultaneously, is introduced. The approach is thermodynamically consistent in the sense that the first law of thermodynamics is fulfilled. Furthermore, a domain decomposition method for the thermoelastic system is developed based on previous developments in the context of the mortar method. The excellent performance of the new approach is illustrated in representative numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure

The direct methods for the solution of systems of linear equations with a symmetric positive‐semidefinite (SPS) matrix A usually comprise the Cholesky decomposition of a nonsingular diagonal block A _???? of A and effective evaluation of the action of a generalized inverse of the corresponding Schur complement. In this note we deal with both problems, paying special attention to the stiffness matrices of floating structures without mechanisms. We present a procedure which first identifies a well‐conditioned positive‐definite diagonal block A _???? of A , then decomposes A _???? by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S of A _????. The Schur complement S is typically very small, so the generalized inverse can be effectively evaluated by the singular value decomposition (SVD). If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any ‘epsilon’. Moreover, if the kernel of A is known, then the SVD can be replaced by effective regularization. The results of numerical experiments show that the proposed method is useful for effective implementation of the FETI‐based domain decomposition methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Strict lower bounds with separation of sources of error in non‐overlapping domain decomposition methods

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element and domain decomposition methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a domain decomposition iterative solver) from the discretization error (due to the finite element), which enables the steering of the iterative solver by the discretization error. These lower bounds are also used to improve the goal‐oriented error estimation in a substructured context. Assessments on 2D static linear mechanic problems illustrate the relevance of the separation of sources of error and the lower bounds' independence from the substructuring. We also steer the iterative solver by an objective of precision on a quantity of interest. This strategy consists in a sequence of solvings and takes advantage of adaptive remeshing and recycling of search directions. Copyright © 2016 John Wiley & Sons, Ltd.     

Stress intensity factor computation using the method of fundamental solutions: mixed‐mode problems

The method of fundamental solutions is applied to the computation of stress intensity factors in linear elastic fracture mechanics. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy–Navier equations of elasticity and the leading terms for the displacement near the crack tip. Two algorithms are developed, one using a single domain and one using domain decomposition. Numerical results are given. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐level BDDC in two dimensions

Balancing Domain Decomposition by Constraints (BDDC) methods are non‐overlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from discretization of elliptic boundary value problems. They are similar to the balancing Neumann–Neumann algorithm. However, in BDDC methods, a small number of continuity constraints are enforced across the interface, and these constraints form a new coarse, global component. An important advantage of using such constraints is that the Schur complements that arise in the computation will all be strictly positive definite. The matrix of the coarse problem is generated and factored by direct solvers at the beginning of the computation. However, this problem can ultimately become a bottleneck, if the number of subdomains is very large. In this paper, two three‐level BDDC methods are introduced for solving the coarse problem approximately in two‐dimensional space, while still maintaining a good convergence rate. Estimates of the condition numbers are provided for the two three‐level BDDC methods and numerical experiments are also discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Inexact Schwarz‐algebraic multigrid preconditioners for crack problems modeled by extended finite element methods

Traditional algebraic multigrid (AMG) preconditioners are not well suited for crack problems modeled by extended finite element methods (XFEM). This is mainly because of the unique XFEM formulations, which embed discontinuous fields in the linear system by addition of special degrees of freedom. These degrees of freedom are not properly handled by the AMG coarsening process and lead to slow convergence. In this paper, we proposed a simple domain decomposition approach that retains the AMG advantages on well‐behaved domains by avoiding the coarsening of enriched degrees of freedom. The idea was to employ a multiplicative Schwarz preconditioner where the physical domain was partitioned into “healthy” (or unfractured) and “cracked” subdomains. First, the “healthy” subdomain containing only standard degrees of freedom, was solved approximately by one AMG V‐cycle, followed by concurrent direct solves of “cracked” subdomains. This strategy alleviated the need to redesign special AMG coarsening strategies that can handle XFEM discretizations. Numerical examples on various crack problems clearly illustrated the superior performance of this approach over a brute force AMG preconditioner applied to the linear system. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust and efficient domain decomposition preconditioners for adaptive hp finite element approximations of linear elasticity with and without discontinuous coefficients

Adaptive finite element methods (FEM) generate linear equation systems that require dynamic and irregular patterns of storage, access, and computation, making their parallelization difficult. Additional difficulties are generated for problems in which the coefficients of the governing partial differential equations have large discontinuities. We describe in this paper the development of a set of iterative substructuring based solvers and domain decomposition preconditioners with an algebraic coarse‐grid component that address these difficulties for adaptive hp approximations of linear elasticity with both homogeneous and inhomogeneous material properties. Our solvers are robust and efficient and place no restrictions on the mesh or partitioning. Copyright © 2003 John Wiley & Sons, Ltd.     

The DRM‐MD integral equation method: an efficient approach for the numerical solution of domain dominant problems

This work presents a multi‐domain decomposition integral equation method for the numerical solution of domain dominant problems, for which it is known that the standard Boundary Element Method (BEM) is in disadvantage in comparison with classical domain schemes, such as Finite Difference (FDM) and Finite Element (FEM) methods. As in the recently developed Green Element Method (GEM), in the present approach the original domain is divided into several subdomains. In each of them the corresponding Green's integral representational formula is applied, and on the interfaces of the adjacent subregions the full matching conditions are imposed. In contrast with the GEM, where in each subregion the domain integrals are computed by the use of cell integration, here those integrals are transformed into surface integrals at the contour of each subregion via the Dual Reciprocity Method (DRM), using some of the most efficient radial basis functions known in the literature on mathematical interpolation. In the numerical examples presented in the paper, the contour elements are defined in terms of isoparametric linear elements, for which the analytical integrations of the kernels of the integral representation formula are known. As in the FEM and GEM the obtained global matrix system possesses a banded structure. However in contrast with these two methods (GEM and non‐Hermitian FEM), here one is able to solve the system for the complete internal nodal variables, i.e. the field variables and their derivatives, without any additional interpolation. Finally, some examples showing the accuracy, the efficiency, and the flexibility of the method for the solution of the linear and non‐linear convection–diffusion equation are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Fast Computation of Stationary Inviscid Flow Around an Airfoil

The parallel performance of an implicit solver for the Euler equations on a structured grid is discussed. The flow studied is a two-dimensional transonic flow around an airfoil. The spatial discretization involves the MUSCL scheme, a higher-order Total Variation Diminishing scheme. The solver described in this paper is an implicit solver that is based on quasi Newton iteration and approximate factorization to solve the linear system of equations resulting from the Euler Backward scheme. It is shown that the implicit time-stepping method can be used as a smoother to obtain an efficient and stable multigrid process. Also, the solver has good properties for parallelization comparable with explicit time-stepping schemes. To preserve data locality domain decomposition is applied to obtain a parallelizable code. Although the domain decomposition slightly affects the efficiency of the approximate factorization method with respect to the number of time steps required to attain the stationary solution, the results show that this hardly affects the performance for practical purposes. The accuracy with which the linear system of equations is solved is found to be an important parameter. Because the method is equally applicable for the Navier-Stokes equations and in three-dimensions, the presented combination of efficient parallel execution and implicit time-integration provides an interesting perspective for time-dependent problems in computational fluid dynamics.     

Multiscale domain decomposition analysis of quasi‐brittle heterogeneous materials

A hybrid multiscale framework is presented, which processes the material scales in a concurrent manner, borrowing features from hierarchical multiscale methods. The framework is used for the analysis of non‐linear heterogeneous materials and is capable of tackling strain localization and failure phenomena. Domain decomposition techniques, such as the ?nite element tearing and interconnecting method, are used to partition the material in a number of non‐overlapping domains and adaptive re?nement is performed at those domains that are affected by damage processes. This re?nement is performed in terms of material scale and ?nite element size. It is veri?ed that the results are independent of the chosen domain decomposition. Moreover, the multiscale analyses are validated with reference solutions obtained with a full ?ne‐scale solution procedure. Copyright © 2011 John Wiley & Sons, Ltd.