基于区间B样条小波有限元的移动荷载识别

小波有限元以区间B样条小波尺度函数为插值函数构造小波有限元单元,并通过单元转换矩阵建立小波空间与物理空间各参数之间的关系.采用动态规划法与Tikhonov正则化法识别移动荷载,避免了直接处理反问题时的振荡与数值计算病态解等问题.算例采用所测得的部分离散点的动态响应数据为已知信息,验证了小波有限元的优越性及小波的多尺度特...     

一种改进多分辨率图像融合算法

提出一种基于局部熵的多分辨图像融合算法。利用小波变换得到待融合图像的多分辨结构,同时得到图像的多分辨局部熵序列。以局部熵为判据,在图像多分辨结构相应各级上进行融合,得到融合图像的多分辨结构,利用小波逆变换重构融合图像。实验结果表明,该图像融合方法在保留TM多光谱图像光谱分辨率的同时,通过融合SPOT全色图像提高了空间分辨率,丰富了图像细节信息。     

基于小波变换的自适应图像融合算法

针对现有图像融合方法存在的光谱信息和空间细节信息不能较好兼顾的问题,建立了图像内容自适应的融合准则和一致性选取准则,提出了一种基于小波变换的自适应图像融合算法,实现了多光谱图像与全色图像的融合,并对融合图像进行了主、客观评价。着重从图像融合如何提高目标的区分度和识别率的角度给出主观评价,通过光谱扭曲度、清晰度客观分析多光谱与全色图像的融合效果。实验结果表明,该算法充分利用了全色图像的空间细节特征、图像边缘和方向性特征信息,保留了多光谱图像的光谱信息特征,提高了融合图像的主观效果,有利于信息的提取和目标解译。在光谱和空间细节综合保持方面,该算法优于IHS融合方法和传统的二进小波融合方法。     

基于加权正交多项式的M进制类小波基的构造

本文运用加权正交多项式和频带有限小波函数构造了L^2（[c,d]）空间的M进制类小波基,使该类小波基具有解析表达式和消失距性质,并给出了它的小波分解与重构算法和L^2（[c,d]）空间的多分辨分解.     

基于小波包和LMS自适应降噪的柴油机振动诊断

由于柴油机振动信号的特征频带和噪声频带存在重叠现象,利用小波阈值消噪时难以选取合适的小波阈值,针对该问题提出一种基于小波包的LMS自适应滤波降噪方法。该方法将小波包与LMS自适应滤波相结合,首先利用小波包变换对信号进行多层分解,然后以噪声干扰对应尺度上的第一层“细节”分量及最大分解尺度上的逼近分量重构信号,将重构后的信号作为LMS自适应滤波器原始输入信号,再以小波包最大分解尺度上的高频细节信号作为自适应抵消器的参考输入信号,进行LMS自适应滤波降噪处理。仿真计算和工程应用表明,该方法参数设置较少,易于控制,不涉及小波阈值降噪中阈值的选取问题,对比试验信号的分析验证了方法的有效性,将该法应用在柴油机振动诊断中提高了故障识别率。     

基于小波有限元的移动荷载识别

小波有限元桥梁模型以区间B样条小波尺度函数为插值函数,构造了小波有限元梁单元,并通过单元转换矩阵建立了小波空间与物理空间各参数之间的关系;代表车载的移动力则投影到小波空间,从而建立基于小波的车桥系统相互作用模型。采用动态规划技术与T ikhonov正则化方法识别移动力,避免了直接处理反问题时的两端振荡与数值计算病态解等问题。仿真算例表明,与传统有限元模型相比,在相同条件下,小波有限元模型以较少的单元,在相似的识别时间内可获得相似的移动力识别精度。     

三维力传感器静态解耦算法的研究与应用

介绍了三维腕力传感器维间耦合基本原理,并建立了耦合误差模型,阐述了传感器静态标定的基本方法。对传统的基于求解矩阵广义逆的静态解耦算法中容易产生病态矩阵,进而影响解耦稳定性和精度的问题进行了研究。提出了基于耦合误差建模的静态解耦算法。对十字梁型三维腕力传感器进行静态标定试验,使用2种解耦算法对标定数据进行分析。试验结果表明,基于耦合误差建模的静态解耦算法具有高可靠性和高解耦精度,且能够反应各维力之间的耦合关系。     

自适应多小波混合构造方法及在故障诊断中应用

小波理论中基函数的逼近阶和消失矩特性都是信号处理中非常重要的性质。传统自适应多小波构造方法仅能对逼近阶或消失矩单一特性进行改造,并且所生成的多个基函数时频特征和波形差异较小,难以有效实现复杂动态故障的自适应提取与识别。为此,提出基于两尺度相似变换和提升方法相结合的自适应多小波混合构造框架,对原有多尺度函数和多小波函数进行线性与非线性组合,扩大多小波改造空间,获得具有高阶逼近阶的多尺度函数和消失矩涵盖多阶次的多小波函数,增强多小波正则性、光滑性、信号逼近能力和局部定位能力,并提高信号分析精度,为复杂动态信号中微弱和复合故障特征提取与识别提供优良性质的自适应基函数及诊断方法;为按需优选自适应基函数,提出改进局部故障域谱熵最小化原则的自适应基函数优选方法,实现轴系、齿轮和轴承故障的分门别类优选,简化故障分类模式。工程实例表明该方法可以有效识别复杂背景噪声干扰下的轴承内圈微弱损伤,并成功诊断出空气分离压缩机组齿轮箱止推夹板碰撞与摩擦的多特征复合故障。     

基于提升小波的发动机振动信号相关分析

发动机的振动信号一般呈非平稳时变特征.傅立叶变换只能确定一个函数奇异性的整体性质,而难以确定奇异点在空间的位置及分布情况.经典的小波变换具有空间局部化性质,但多数性质都是通过傅立叶变换性质来实现的.提升算法摆脱了这种局限,它从一个简单的多分辨分析开始,然后向具有某一特性的MRA逐渐逼近.根据信号与噪声在各尺度下的不同传播特性,通过各层之间相关性分析滤除噪声,有效的提取出信号特征.     

一种小波和余弦变换组合域内鲁棒的自适应零水印算法

克服了传统数字水印方案在嵌入水印时要对原始图像数据进行一定修改从而导致嵌入水印图像质量下降的局限性,提出了一个基于离散小波变换和离散余弦变换组合域内鲁棒的自适应零水印算法.算法首先对原始数字图像进行适当层次的离散小波变换,并对得到的小波逼近子图进行离散余弦变换,然后依据待嵌入二值字符水印的大小和相应的系数差值要求自适应...     

A spline wavelet finite‐element method in structural mechanics

The wavelet‐based methods are powerful to analyse the field problems with changes in gradients and singularities due to the excellent multi‐resolution properties of wavelet functions. Wavelet‐based finite elements are often constructed in the wavelet space where field displacements are expressed as a product of wavelet functions and wavelet coefficients. When a complex structural problem is analysed, the interface between different elements and boundary conditions cannot be easily treated as in the case of conventional finite‐element methods (FEMs). A new wavelet‐based FEM in structural mechanics is proposed in the paper by using the spline wavelets, in which the formulation is developed in a similar way of conventional displacement‐based FEM. The spline wavelet functions are used as the element displacement interpolation functions and the shape functions are expressed by wavelets. The detailed formulations of typical spline wavelet elements such as plane beam element, in‐plane triangular element, in‐plane rectangular element, tetrahedral solid element, and hexahedral solid element are derived. The numerical examples have illustrated that the proposed spline wavelet finite‐element formulation achieves a high numerical accuracy and fast convergence rate. Copyright © 2005 John Wiley & Sons, Ltd.     

Polycrystal plasticity modeling of bulk forming with finite elements over orientation space

Conventional polycrystal modeling is based primarily upon the association of a material element with a representative aggregate of crystals. In this work we focus on an alternate class of polycrystal schemes developed by applying the finite element method to represent and compute the crystal orientation distribution function over an explicit discretization of orientation space. In particular, we extend the methodology applied previously to planar polycrystals, to the modeling of three dimensional polycrystals. Neo-Eulerian axis angle spaces, and specifically Rodrigues' parameter space, are preferred over the conventional Euler angle spaces for this purpose. Various Eulerian and Lagrangian finite element schemes are considered for the ODF conservation equation, stabilized with appropriate combinations of streamline and artificial diffusion to accommodate its hyperbolic nature. One such stabilized scheme, the incremental Lagrangian is applied to simulate the texturing of FCC crystals under monotonic deformations. Next, the finite element polycrystal scheme is employed to capture the development of spatial texture gradients in a bulk forming process. This involves coupled finite element analyses at two length scales: at the macroscopic scale of the deformation process, over a spatial discretization, and at the microstructural level over the discretized orientation space.This work was supported through Office of Naval Research contract NOOO 14-95-1-0314. Computing resources on the Connection Machine CM-5 were provided by the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign.Dedicated to J. C. Simo     

Multiscale modeling of beam and plates using customized second-generation wavelets

We have designed bicubic Hermite-type finite-element wavelets that decouple the multiresolution stiffness matrix obtained from the discretization of the biharmonic equation. The scale decoupling basis makes the stiffness matrix block diagonal and hence eliminates the coupling between scales. The scale-decoupled system leads to an incremental procedure for systematic enrichment of the solution without the need for costly remeshing of the whole domain and recalculation of the solution. The solution is obtained by injection of finer-scale wavelets at locations with high detail coefficients. We conducted some numerical experiments to demonstrate the customized wavelet-based finite-element method for the problem of bending of Euler’s beam and Kirchhoff’s plates; we also demonstrate the role of wavelets in resolving localized phenomena.     

Shape optimal design of elastic space frames with non-linear response

This paper describes an approach to shape optimal design of elastic space frames with kinematically non-linear response. A space frame structure is treated as to be assembled from several frame design elements each of them being defined as a skeleton lying on a rational Bézier patch. The design variables may influence the control points of each patch and the cross-sectional quantities of beam elements. Highly accurate beam finite elements are employed based on a modified formulation of the beam element proposed by Jelenić and Saje. The modified element is able to account for arbitrary initial curvature and it fits nicely into the context of both the proposed design element technique and the optimization process. The formulation of the shape optimal design problem in form of non-linear mathematical programming problem and its solution by employing gradient-based methods of mathematical programming are discussed briefly. The theory is illustrated in detail with three numerical examples. © 1998 John Wiley & Sons, Ltd.     

基于多变量小波有限元的一维结构分析

基于区间B样条小波(B-Spline Wavelet on the Interval, BSWI)和多变量广义势能函数,该文构造了二类变量小波有限单元,并用于一维结构的弯曲与振动分析。基于广义变分原理,从多变量广义势能函数出发,推导得到多变量有限元列式,并以区间B样条小波尺度函数作为插值函数对两类广义场变量进行离散。此单元的优势在于可以提高广义力的求解精度,因为在传统有限元中,只有一类广义位移场函数,所以广义力通常是通过对位移的求导得到,而多变量单元中,广义位移和广义力都是作为独立变量处理的,避免了求导运算。此外,区间B样条小波是现有小波中数值逼近性能非常好的小波函数,以它作为插值函数可进一步保证求解精度。转换矩阵的应用,可以将无任何明确物理意义的小波系数转换到相应的物理空间,方便了问题的处理。最后,通过数值算例对Euler梁和平面刚架的分析,验证了此单元的正确性和有效性。     

基于小波分析的Timoshenko梁裂缝识别研究

采用等效转动弹簧代替梁内的不扩展横向裂缝,研究Timoshenko裂缝梁的横向振动特性,建立了一种与有限元分析相结合的、基于模态参数的小波分析识别Timoshenko梁内裂缝的方法。以一简支梁为例,通过建立含横向不扩展裂缝的Timoshenko梁的有限元模型,用Lanczos法对结构的模态进行了计算分析,求出了基本振型和转角模态。分别应用mexh小波和db小波为母小波对二者做小波变换,进行多尺度分析,通过小波系数模极大值位置识别出梁内的裂缝。并对识别结果进行对比,发现识别Timoshenko梁裂缝时,基于转角模态小波变换的方法对小波基、尺度的要求较低,变换后的小波系数线更为平滑,奇异性特征更为明显,故运用转角模态小波变换来识别Timoshenko梁裂缝,较之运用基本振型小波变换的方法更为方便、有效。该方法对Timoshenko梁裂缝识别的工程应用具有参考价值。     

插值小波自适应求解层状介质波传问题

利用多尺度插值小波理论,提出一种适合于求解一般边界层状介质波传问题的快速自适应配点算法。将问题放在多尺度插值空间中进行,其插值小波系数与物理空间点一一对应,可简单快速地处理非线性、边界等。使非均匀变化的响应得到自适应压缩存储,改善了计算效率。地震勘探中数值实例显示了方法良好的潜力。     

去噪正则化模型修正方法在桥梁损伤识别中的应用

以传统基于灵敏度分析的有限元模型修正方法为基础,提出一种结合小波去噪过程的正则化模型修正损伤识别方法.为改进模型修正方法损伤识别效果,一方面利用有损结构模态与模态噪声的波形在时频域内的差异,以结构有限元模型为基准,对实测模态差进行小波去噪处理,并利用修正后的模态构造目标函数;一方面采用正则化方法改善反问题求解的非适定性.由于从输入数据和求解过程两方面同时改善了结构损伤识别反问题的求解,因此可以有效抑制实测模态参数中噪声的影响,正确识别结构损伤.以连续梁桥模型为例的损伤识别数值模拟表明,所提出方法在保持识别算法鲁棒性、抑制噪声的同时,可有效提高桥梁结构损伤的识别精度.     

张量积空间中框架的一种新构造

因为非张量积且较实用的高维小波基不多见,常常用低维的小波基作张量积来构造高维小波基。本文中,我们利用算子论的方法,研究了两个Hilbert空间中的框架张量以及张量积空间中框架的关系。将高维空间中的框架表示可以转化为低维空间中的框架张量,同时也可以把高维空间中的向量用低维空间的框架张量来表示。     

Hierarchic finite element bases on unstructured tetrahedral meshes

The problem of constructing hierarchic bases for finite element discretization of the spaces H¹, H ( curl ), H ( div ) and L₂ on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non‐uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements. Copyright © 2003 John Wiley & Sons, Ltd.