Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

Effects of rare earth element lanthanum on the microstructure of copper matrix diamond tool materials

Effects of rare earth element La on the microstructure of Cumatrix diamond tools were researched under the conditions of variousmaterials components and the process parameters in order to improvematerials properties. SEM, XPS and X-ray were used to investigate thefracture section, microstructure and the element valence inmaterials. The Results shown that the combination of rare earthelement La and transition element Ti is advantageous to the bondingstate Between diamond particles and matrix, so it can improve thematerials properties. Suitable sintering temperature is 790 deg. C.

Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.

Finite Element Analysis of Push-Out Test of SiC Fiber Reinforced Titanium Matrix Composites

Based on the interphase layer model and the spring layer model, an improved interface model was developed to evaluate the interfacial shear strength of Titanium matrix composites(TMCs) and to analyze the effects of various parameters on the interfacial properties. The results showed that the improved interface model is more suitable for calculating the interfacial properties of SiC fiber reinforced titanium matrix composites. The interfacial shear strength of SiC/Timetal-834 predicted is 500 MPa. In addition, in order to better understand the interfacial properties of composites, some push out phenomenon were analyzed.

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

基于共旋坐标法的几何非线性裂纹梁单元

现有有限元软件模拟裂纹结构主要采用指派裂纹的实体和壳单元,但缺少梁单元。因此,在弹性梁单元的曲率函数中引入Dirac-δ函数表征局部损伤的曲率变化,得到位移分布函数;推导出应变矩阵和单元刚度矩阵,提出了裂纹梁单元。基于共旋坐标法理论进一步发展了考虑裂纹损伤的几何非线性裂纹梁单元,给出了单元的具体算法及流程。利用课题组开发的有限元求解框架,在程序中实现了裂纹梁单元及共旋列式裂纹梁单元。经过典型算例,对比分析了裂纹位置、裂纹深度及外荷载对裂纹梁弯曲性能的影响。结果表明:该单元能够准确描述裂纹结构的挠度变化,同时与现有模拟裂纹结构弯曲变形的单元相比,提出的裂纹梁和共旋列式裂纹梁在精度分别提高了约1%和4%,并且能够退化成无损伤的梁单元和几何非线性梁单元。

NORMALIZED ELEMENT NODE TOPOLOGICAL MATRIX OF FINITE ELEMENT MESHES

On the basis of concept of element node topological analysis, the normalized element node topological matrices for finite element meshes are presented in the paper, including 3-node and 6-node triangular element, 4-node and 8-node quadrilateral element, 8-node and 20-node hexahedral element. It is beneficial to further analyzing topological characteristics of finite element models and automatic generation of meshes

机械专业研究生课程思创融合探索与实践

在研究生课程中开展课程思政与创新教育,是在研究生阶段实施立德树人、培养创新能力的重要途径。结合机械专业研究生阶段的课程特点,构建思创融合的研究生课程思政目标。挖掘知识点与思政元素、创新理念的关系,建立专业课程知识与思创新元素的映射矩阵,并探索教学过程中的渗透方法,采用课程思创目标达成度评价反馈优化思创元素映射矩阵与思创渗透方法,促使研究生为我国新兴产业发展而奋斗,树立自主创新、尊重创新与知识产权的意识,为研究生课程的课程思创融合教学改革提供参考。

基于对抗自编码填补网络的MIMO雷达故障阵元缺失数据重构

多输入多输出(Multiple In Multiple Out,MIMO)雷达的阵元故障会导致其协方差矩阵出现整行整列数据缺失,从而降低其角度估计性能。为此,提出一种对抗自编码填补网络(Adversarial Autoencoder Imputation Network,AAEIN)来重构故障阵元的缺失数据。该网络由负责重构缺失数据的自动编码(Autoencoder,AE)网络和负责分辨数据来源的鉴别器组成。在二者的对抗训练中,AE网络的重构能力和鉴别器的分辨能力不断得到提升,直至两者收敛。为避免网络训练过程中参数量大和计算复杂度高的问题,文中结合MIMO雷达协方差矩阵的Hermitian特性,使用协方差矩阵上三角部分构建数据集用于网络训练。仿真结果表明,文中方法可以有效地重构故障阵元的缺失数据且具有较高的重构精度。

考虑剪切变形的欧拉梁单元一致质量矩阵

为明确考虑剪切变形的欧拉梁单元一致质量矩阵推导方法,以形函数为基础,基于虚功原理,区分伸缩、扭转以及是否考虑剪切变形的弯曲受力状态,给出了欧拉梁单元一致质量矩阵表达式。研究表明:不考虑剪切变形时,欧拉梁受弯状态的一致质量分析中一般不计单元上微元体水平方向的惯性力,此时仅需弯曲变形引发的竖向位移形函数即可;考虑剪切变形时,则需计入水平方向的惯性力,且同时需要完整的竖向位移形函数和纯弯曲转角位移形函数;对于变截面欧拉梁单元,其一致质量矩阵表达式过于复杂,可在等截面梁的基础上,根据元素位置对矩阵元素匹配左右端或平均截面面积及截面极惯性矩近似给出实用的质量矩阵表达式;考虑剪切变形时,欧拉梁的刚度矩阵亦可经竖向位移和纯弯曲转角位移形函数计算得到,这一过程与使用纯弯曲竖向位移和纯剪切竖向位移形函数的过程在本质上是一致的。

超声振动辅助研磨SiCp/Al材料去除特性的研究

SiCp/Al因具有高强度,低密度,高耐磨性等优点被应用在许多领域,如航空航天,汽车和电子领域等。但SiCp/Al是典型的难加工材料,在研磨过程中极易造成表面损伤,从而影响工件的表面精度和材料去除率。基于金属基复合材料的研磨去除机理,建立有限元仿真模型。仿真模拟超声去除SiCp/Al的表面损伤形式、颗粒的破碎方式与材料去除过程。通过超声振动辅助研磨SiCp/Al实验可知,超声振动能够有效降低表面粗糙度。材料去除率随主轴转速和研磨深度的增加而增大,随进给速度的增加而减小。

埃尔米特梁单元的分块对角与高阶质量矩阵

埃尔米特梁单元常用的集中质量矩阵,是由挠度自由度对应的一致质量矩阵元素通过行求和或节点积分构造.然而,数值结果表明该集中质量矩阵在求解包含自由端的梁振动问题时,会出现频率精度掉阶现象.本文首先从保障质量矩阵最优收敛性的数值积分精度出发,分别针对三次和五次梁单元,发展了质量矩阵的梯度增强节点积分方案.利用梯度增强节点积分方案,可以得到具有分块对角形式的单元质量矩阵,而其组装的整体质量矩阵除边界节点外仍然呈现对角形式.对于两种单元,其分块对角质量矩阵分别具有4阶最优精度和6阶次优精度.再者,将标准一致质量矩阵和具有同阶精度的梯度增强节点积分质量矩阵进行优化组合,建立了具有超收敛特性的高阶质量矩阵.最后,通过数值算例系统验证了三次和五次单元的分块对角与高阶质量矩阵的频率计算精度.

基于有限元仿真的ECT感兴趣区域高分辨率图像重建

感兴趣区域的高分辨率图像重建是电容层析成像(electrical capacitance tomography,ECT)技术的研究热点之一。均匀电极分布的ECT模型仅在重建场域的边界位置具有较高的灵敏度系数,不适用于感兴趣区域成像。为改善感兴趣区域中的灵敏度分布,提高图像分辨率,提出了一种基于有限元仿真ECT感兴趣区域高分辨率图像重建方法,根据保角变换理论优化电极分布。进行了仿真实验,将均匀电极和优化电极分布的灵敏度矩阵代入Tikhonov算法、Landweber算法和ART算法,重建结果表明上述方法可有效提高感兴趣区域的图像重建精度。

龙岩山麻鸭蛋壳质量与元素组成、基质含量和超微结构关系的研究

本试验旨在研究蛋壳元素组成、超微结构和钙化壳基质含量对龙岩山麻鸭蛋壳质量的影响。试验选用300日龄龙岩山麻鸭所产白壳蛋300个,根据蛋壳强度平均分为高、中、低3个试验组,每组5个重复,每个重复20个蛋,测定蛋壳质量、元素组成和超微结构。结果表明:高、中、低蛋壳强度组蛋壳强度分别为(4.67±0.09)kg/cm^(2)、(3.78±0.02)kg/cm^(2)和(2.86±0.03)kg/cm2,组间差异显著(P<0.05);各组间的蛋重、蛋形指数、蛋壳厚和蛋壳重无显著差异(P>0.05)。3组间钙化壳的基质含量差异不显著(P>0.05),各组元素相对含量在蛋壳超微结构的不同层次差异不显著(P>0.05)。对蛋壳超微结构观察发现,与中、低强度蛋壳组相比,高强度蛋壳组横断面致密性更好,乳突顶部连接更紧密;并且各组间的乳突层有效厚度差异显著(P<0.05),高、低蛋壳强度组的乳突间隙差异显著(P<0.05)。综上所述,厚度相似的蛋壳,其蛋壳各层元素相对含量和基质含量对龙岩山麻鸭蛋壳强度无显著影响,蛋壳超微结构致密度对蛋壳质量具有重要作用,其中乳突层有效厚度和乳突间隙是影响蛋壳质量的重要因素。

判定广义严格对角占优矩阵的新条件

仅利用矩阵自身的元素,得到了广义严格对角占优矩阵的几个新的判定条件,扩大了判别范围.给出了数值算例.