基于扰动观测器的卫星姿态控制系统自适应有限时间容错控制

针对具有状态时变时滞、系统不确定性、可建模扰动、运行噪声和执行器故障的卫星姿态控制系统,提出一种基于扰动观测器的自适应有限时间复合主动容错控制策略。针对可建模扰动设计扰动观测器,然后基于扰动估计误差设计了主动容错控制器。该时滞依赖控制器包含反馈控制项、扰动补偿项和快速自适应故障补偿项。提出的容错控制策略不仅保证闭环系统动态方程的有限时间有界性,而且保证闭环测量输出对于系统不确定性、运行噪声、执行器故障等的鲁棒性。给出控制器增益限制矩阵存在的充分条件及其线性矩阵不等式形式,进而给出仿真算例。仿真结果表明,基于扰动观测器方法,设计的自适应有限时间容错控制器能够快速估计可建模扰动,进而有效地实现系统的闭环容错控制。相较于基于非复合的自适应有限容错控制器,提出的方法对于状态变量的估计均方根误差分别降低了28.9%、4.7%和36.0%;对于可建模扰动估计的均方根误差降低了38.8%。仿真验证了所提方法的有效性。     

用于C60纳米分子振动分析的碳-碳键合单元及坐标变换

C60是一种纳米分子,具有许多非常重要的物理化学性质,采用Raman光谱可以测得它的分子振动特征,正是这种振动特征可以明显地表征出它的分子结构和原子键合关系。本文基于分子力学的基本分析原理,给出一种用于描述碳-碳共价键在小位移情形下力能关系的计算单元,称为碳-碳键合单元,重点讨论该单元在实际建模过程中的坐标变换问题,将所建立的碳-碳键合单元用于C60纳米分子的振动分析,分别给出了C60纳米分子的Ag(1)、Ag(2)、Hg(1)三个特征振型和频率,并与群论的分析结果、Raman光谱实验结果进行比较,证明了所提出分析方法的正确性和实用性。     

随机并行梯度下降图像匹配方法

基于灰度的图像匹配方法具有匹配精度高等优点, 但在实时性方面还存在不足。本文提出一种基于随机并行梯度下降优化算法的快速图像匹配方法,该方法同时对匹配图像间所有的变形参数施加相互统计独立的随机扰动, 然后计算扰动前后待匹配图像间性能评价函数的改变量, 并用这一改变量对变形参数进行更新, 进行迭代运算, 最终实现快速的最优变形参数估计及图像匹配。将SPGD匹配方法用于对仿真和真实的图像序列中的目标进行跟踪,均证明了该匹配方法能进行正常匹配, 匹配精度和最小二乘方法相当, 但速度要较最小二乘匹配方法快。     

一种改进的基于SINS/GNSS的水平重力扰动测量方法

针对水平重力扰动的动态测量问题,提出了一种改进的基于SINS/GNSS的水平重力扰动测量方法。首先,基于SINS/GNSS重力矢量直接求差模型,考虑Kalman滤波增益引起的传递函数零极点的改变,建立了包含系统时间延迟的直接求差模型,得到水平重力扰动求解值与真实值间的函数关系;然后给出简化重力扰动模型下修正后的水平重力扰动测量表达式;最后,用EGM2008模拟的一段水平重力扰动数据对改进模型进行仿真验证。仿真结果表明改进的直接求差模型测量的水平重力扰动相对于EGM2008模型误差不超过7mGal。     

高压气体状态方程的计算机模拟

在解决某些特殊条件下的力学问题时,有时需要知道几十万大气压下的高压气体状态方程。这种高压状态方程难以用实验方法得到。从分子间相互作用势出发采用近似的统计模型导出理论状态方程是一种可行的办法。例如,在计算凝聚炸药爆轰产物性质时所用过的LJD状态方程(基于Lennard-Jones和Devonshire笼子模型的状态方程)就是其中之一。为了考察它与实际符合的程度,以便在更广的范围内使用这种类型的状态方程,本文采用Monte Carlo方法对高压气体的行为进行了直接的计算机模拟,将计算的等温线与LJD模型的结果进行了比较。     

非线性连续神经网络的鲁棒性分析

对一类连接矩阵为对角稳定的非线性连续神经网络系统，基于Ｌｙａｐｕｎｏｖ函数法，我们分别研究具有固定和扰动平衡点的扰动系统的渐近稳定性，对于这类系统，我们具体给出了保持该系统稳定的各优动项的界，此外，在扰动系统平衡点存在的分析中还首次引入Ｎｅｗｔｏｎ－Ｋａｎｔｏｒｏｖｉｃｈ方法，给出扰动系统平衡点的迭代解法及其与名义系统平衡点的误差估计，这里的结果对具体网络的设计具有重要的指导作用。     

考虑毛细作用微梁剥离的实验和力学模型

毛细力诱发的粘附现象在自然界和工农业生产中广泛存在，例如微机电系统、微纳米自组装、油气驱替等．本文系统研究了两根微梁的毛细粘附行为，包括梁剥离过程中液桥的形貌以及剥离力-位移变化规律．试验发现，微梁在毛细力作用下的剥离部分经历了液膜粘附和液滴粘附两个阶段．考虑两个阶段的液桥形状特征，分别建立系统的能量泛函，采用变分原理推导了考虑毛细力的微梁剥离的非线性微分方程和边界条件．基于Matlab 编程求解方程，得到了剥离力-位移曲线，理论计算与试验结果具有很好的一致性．另外，参数研究表明，接触角和表面张力系数对液膜粘附的微梁剥离影响显著，而对液滴粘附的剥离影响较小；微梁刚度对两个阶段的剥离都有明显影响．本文的试验结果和理论分析对于实际工程中微结构的定量设计具有一定参考价值．     

以扰动重力为边值条件确定外部扰动重力场

惯性导航系统的精确导航离不开地球重力场信息的支持,然而目前利用扰动重力求解地球外部空间扰动重力场的研究相对较少。针对地球外部空间扰动重力场求解问题,推导了以实际地形面为边界面的利用扰动重力与格林积分公式推求外部扰动重力三分量的公式,给出了利用扰动重力与豪汀积分公式计算扰动重力三分量的表达式。通过数值实验对格林积分法、豪汀积分法与点质量模型法进行了对比分析,结果表明:三种方法均可以在3 km处以优于2 mGal的精度逼近扰动重力三分量。所提出的方法对于地球外部扰动重力场的确定具有一定的借鉴与参考意义。     

基于小波神经网络的高精度惯导重力扰动补偿方法

重力扰动矢量(空间同一点实际重力与正常重力之差,包括垂线偏差和重力异常两部分)一直是惯性导航系统的重要误差源之一。针对重力扰动误差精确补偿问题,推导并建立了考虑重力扰动的惯导误差方程,并提出了基于小波神经网络的重力扰动补偿方法。通过仿真验证了小波神经网络的重力扰动补偿方法对惯导导航精度的提高效果。24 h仿真结果表明:所提出的重力扰动补偿方法能有效减小惯导导航系统误差,经重力扰动矢量补偿后,速度误差最大能减小约0.2 m/s,降低约30%,位置误差最大能减小约3000 m,降低约25%。     

空间机械臂关节轨迹跟踪的自适应反演滑模控制

讨论了载体位置、姿态均不受控制情况下,具有外部扰动与参数不确定的自由漂浮空间机械臂系统关节空间轨迹跟踪的控制问题.结合系统动量、动量矩守恒关系及拉格朗日方法,建立了自由漂浮空间机械臂的系统动力学方程.针对外部扰动与参数不确定的情况,提出一种自适应反演滑模控制方案.此控制方案无需要求系统动力学方程关于惯性参数呈线性函数关系;同时,它可保证系统具有全局意义下的渐近稳定性.数值仿真结果证实了该控制方案可有效地消除外部扰动与参数不确定对系统的影响,控制空间机械臂系统各关节按关节空间内的期望轨迹进行运动.     

Wavelet method applied to specific adhesion of elastic solids via molecular bonds

We propose a wavelet method to analyze the stochastic-elastic problem of specific adhesion between two elastic solids via ligand-receptor bond clusters, which is governed by a nonlinear integro-differential equation with a singular Cauchy kernel to describe the mean-field coupling between deformation of elastic materials and stochastic behavior of the molecular bonds. To solve this problem, Galerkin method based on a wavelet approximation scheme is adopted, and special treatment which transforms the singular Cauchy kernel into a smooth one has been proposed to avoid the cumbersome calculation of singular integrals. Numerical results demonstrate that the method is fully capable of solving the specific adhesion problems with complex nonlinear and singular equations. Based on the proposed method, investigations are performed to reveal the relation between steady-state pulling force and mean surface separation under different stress concentration indexes, which is crucial for assembling the overall constitutive relations for multicellular tumor spheroids and polymer-matrix microcomposites.     

Specific adhesion of a soft elastic body on a wavy surface

This paper aims at developing a stochastic-elastic model of a soft elastic body adhering on a wavy surface via a patch of molecular bonds. The elastic deformation of the system is modeled by using continuum contact mechanics, while the stochastic behavior of adhesive bonds is modeled by using Bell's type of exponential bond association/dissociation rates. It is found that for sufficiently small adhesion patch size or stress concentration index, the adhesion strength is insensitive to the wavelength but decreases with the amplitude of surface undulation, and that for large adhesion patch size or stress concentration index, there exist optimal values of the surface wavelength and amplitude for maximum adhesion strength.     

A closed model of fluctuating particle motion in a turbulent flow

Random particle motion in a turbulent and molecular velocity fluctuation field is considered. Using a spectral representation of the carrier-phase Eulerian velocity fluctuation correlations, a closed system of integral equations for calculating the carrier-phase velocity correlation along the particle trajectory and the particle Lagrangian velocity fluctuation correlation is obtained. Based on this system, the fluctuations of the particle parameters are analyzed. In the limiting case of a passive admixture, an estimate is found for the ratio of the integral Lagrangian and Eulerian time scales and the Kolmogorov constant for the Lagrangian structure function of the carrier-phase velocity fluctuations.     

A study on the measurement of mean velocity and its convergence in molecular dynamics simulations

In many particle‐based simulations, measurement of local mean flow velocity and other continuum‐based properties are of utmost importance. Macroscopic quantities, such as mean flow velocity, temperature, and density, can be estimated by averaging the corresponding microscopic behavior of the particles. The two main subjects that should be considered in the averaging over the particles in a specific problem are spatial and temporal behaviors of them. In this paper, we study the latter. Because of the chaotic nature of the collisions among the molecules and consequently their random path, extracted macroscopic values fluctuate about their average values causing statistical errors. In this paper, an averaging method called SAM‐Modified‐CAM (SMC) will be proposed for the measurement of mean velocity that reduces statistical errors in its calculation. This proposal is based on the study conducted here on the implementations of two common averaging methods, sample‐averaged measurement (SAM) and cumulative average measurement (CAM) in molecular dynamics. In addition, convergence of mean flow velocity measurement is thoroughly discussed, and a convergence criterion is proposed for this purpose. Implementation of the proposed method in different test cases has approved its reliable performance. Copyright © 2010 John Wiley & Sons, Ltd.     

Towards gigantic RVE sizes for 3D stochastic fibrous networks

The size of representative volume element (RVE) for 3D stochastic fibrous media is investigated. A statistical RVE size determination method is applied to a specific model of random microstructure: Poisson fibers. The definition of RVE size is related to the concept of integral range. What happens in microstructures exhibiting an infinite integral range? Computational homogenization for thermal and elastic properties is performed through finite elements, over hundreds of realizations of the stochastic microstructural model, using uniform and mixed boundary conditions. The generated data undergoes statistical treatment, from which gigantic RVE sizes emerge. The method used for determining RVE sizes was found to be operational, even for pathological media, i.e., with infinite integral range, interconnected percolating porous phase and infinite contrast of properties.     

无限长圆柱体中广义电磁热弹耦合问题研究

基于L-S广义热弹性理论,研究了处于磁场中无限长理想圆柱导体在边界受热冲击作用时的电磁热弹耦合问题.建立了广义电磁热弹耦合的有限元方程,为避免积分变换方法求解带来的精度丟失.采用将有限元方程直接在时间域求解的方法,得到了圆柱体中的温度、位移、应力、感应磁场和感应电场的分布规律,反映了热的波动性及电磁热弹的耦合效应.结果表明,将有限元方程直接在时间域求解,可以获得各物理量的准确分布.得到温度在热波波前处的阶跃,准确地反应热波的波动效应.     

Identifying traction–separation behavior of self-adhesive polymeric films from in situ digital images under T-peeling

In this paper procedures are developed to identify traction–separation curves from digital images of the deformed flexible films during peeling. T-peel tests were performed for self-adhesive polymeric films. High quality photographs of the deformed shape within and outside the zone of adhesive interaction were made in situ by the digital light microscope. The deformed line is approximated by a power series with coefficients computed by minimizing a least squares functional. Two approaches to identify the traction–separation curve for the given deformation line are proposed. The first one is based on the energy integral of the non-linear theory of rods and allows the direct evaluation of the adhesion force potential. The second one utilizes the complementary energy type variational equation and the Ritz method to compute the adhesion force. The accuracy of both approaches is analyzed with respect to different approximations for the deformed line and the force of interaction. The obtained traction vs. axial coordinate and the traction–separation curves provide several properties of the adhesive system including the maximum adhesion force, the length of the adhesive zone and the equilibrium position, where the adhesive force is zero while the separation is positive.     

One-dimensional statistical models

The properties of one-dimensional statistical systems are studied. A consistent comparison of the values of the binary correlation function obtained from the configuration integral and from Bogolyubov chain equations in various approximations is presented. The results obtained here are discussed briefly.The existing methods for studying the behavior of real statistical systems are usually based on perturbation theory, and the presence of small parameters characterizing the proximity of the system to an ideal system is assumed. Strongly interacting systems do not permit the isolation of small parameters; therefore, there are no effective methods for studying them at present. In this connection, it appears to be of interest to turn to one-dimensional systems which enable the investigation to be advanced much further and, in particular, permit a consideration of the case of strong interaction. Comparison of the exact results with approximate results obtained by methods for decomposing chains of recurrence equations for correlation functions [1] may be regarded as a qualitative criterion of the accuracy of the latter.Configuration integrals for one-dimensional statistical systems were first obtained in reference [2]. Papers have recently appeared in which one-dimensional models are studied by methods of the theory of stochastic processes [3–6].     

Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method

Dynamic stress intensity factors (DSIFs) are important fracture parameters in understanding and predicting dynamic fracture behavior of a cracked body. To evaluate DSIFs for both homogeneous and non-homogeneous materials, the interaction integral (conservation integral) originally proposed to evaluate SIFs for a static homogeneous medium is extended to incorporate dynamic effects and material non-homogeneity, and is implemented in conjunction with the finite element method (FEM). The technique is implemented and verified using benchmark problems. Then, various homogeneous and non-homogeneous cracked bodies under dynamic loading are employed to investigate dynamic fracture behavior such as the variation of DSIFs for different material property profiles, the relation between initiation time and the domain size (for integral evaluation), and the contribution of each distinct term in the interaction integral.     

A solution to the thermo-elastic interface crack branching in dissimilar anisotropic bi-material media

An interface crack or delamination may often branch out of the interface in a laminated composite due to thermal stresses developing around the delamination/crack tip when the media is exposed to heat flow induced by environmental events such as a sudden short-duration fire. In this paper, the thermo-elastic problem of interface crack branching in dissimilar anisotropic bi-media is studied by using the theory of Stroh’s dislocation formalism, extended to thermo-elasticity in matrix notation. Based on the complex variable method and the analytical continuation principle, the thermo-elastic interface crack/delamination problem is examined and a general solution in compact form is derived for dissimilar anisotropic bi-media. A set of Green’s functions is proposed for the dislocations (conventional dislocation and thermal dislocation/heat vortex) in anisotropic bi-media. These functions may be more suitable than those which have appeared in the literature on addressing thermo-elastic interface crack branching in dissimilar anisotropic bi-materials. Using the contour integral method, a closed form solution to the interaction between the dislocations and the interface crack is obtained. Within the scope of linear fracture mechanics, the thermo-elastic problem of interface crack branching is then solved by modelling the branched portion as a continuous distribution of dislocations. The influence of thermal loading and thermal properties on the branching behavior is examined, and criteria for predicting interface crack branching are suggested, based on the extensive numerical results from the study of various cases.