基于隐式微分/代数方程的多体系统动力学设计灵敏度分析方法

基于一般性的积分型目标函数、隐式相容初始条件及终止时刻表达式,系统建立了含设计参数的用隐式微分／代数方程表达的多体系统动力学设计灵敏度分析的直接微分方法和伴随变量方法．为降低目标函数及其对设计变量导数的计算复杂性。将其积分形式的计算转化为微分形式．所得到的结果可方便地应用于高效的间接最优化设计方法．最后通过采用绝对坐标建模的平面两连杆机械臂模型对该方法进行了验证．     

平面隐式曲线的Hermite 插值逼近

隐式曲线在医学图像处理、地理信息系统、数值场可视化等领域中有着重要应用。 在分析点采样和曲线逼近理论的基础上,提出一种运用Hermite 插值方法逼近平面隐式曲线的 算法。首先将曲线绘制区域网格化,在网格单元各边中通过线性插值计算曲线采样点;其次通 过计算采样点精简前后构成的曲线段之间产生的误差优化采样点;最后通过Hermite 插值法逼 近隐函数曲线。实验表明,通过该算法绘制出的曲线在采样点数量较少的情况下,其光滑度和 准确度仍较高。     

用变向线控制变向来绘制隐函数曲线——正负法数控绘图(Ⅱ)

数控绘图技术从五十年代末期诞生至今,二十余年来产生了不少绘图方法,然而这些方法都只能直接产生一些基本曲线,显函数曲线和参数曲线。本文给出隐函数曲线高精度直接数控绘制的方法,也可用以计算隐函数方程所包围的面积、弧长和极点等。     

基于OpenCL的自动微分并行实现及其应用

针对如光束平差这样的大规模优化问题,实现基于OpenCL的并行化自动微分。采用更有效的反向计算模式,实现对多参数函数的导数计算。在OpenCL框架下,主机端完成C/C++形式的函数构建以及基于拓扑排序的计算序列生成,设备端按照计算序列完成函数值以及导数的并行计算。测试结果表明,将实现的自动微分应用于光束平差的雅可比矩阵计算后,相比于采用OpenMP的Ceres Solver,运行速度提高了约3.6倍。     

微分压缩因子及其在热力学偏导数数值计算上的应用

压缩因子Z在定量地表示实际气体的P-V-T关系上特别有用。对于热力学偏导数则可以用一种与Z有关的函数,即微分压缩因子表示各种热力学偏导数关系。其定义如下:各种热力学偏导数可用Bridgman表(表1)以Z_P和Z_T项等来表示。例如:和一、Z_P,Z_T的计算从Bridgman表出发来计算热力学偏导函数首先要算出Z_P或Z_T来,Z_P和Z_T可以类似     

基于微分平滑滤波的特征点跟踪

光流跟踪作为一种重要的二维运动估计技术,在运动目标检测和跟踪中有着重要的作用.L-K光流跟踪算法是一种利用Newton-Raphson梯度下降法进行图像匹配的算法,所以离散图像的偏导数的计算显得尤为重要.由于数字图像离散的方格结构导致在计算各阶偏导数时产生较大的误差.利用微分平滑滤波的方法先利用一个连续的基础函数模拟离...     

一种估计深度相机位姿精度的闭式算法

针对深度相机,提出了估计位姿变换精度的闭式解算法.相对位姿由6自由度向量T=[x,y,z,α,β,γ]表示,计算该向量的协方差矩阵来表征相对位姿精度.定义3维点对到相对位姿的隐式函数,利用隐式定理计算该隐式函数相对于点对集合的偏导数,从而根据隐式函数变化趋势和深度相机测量误差来计算协方差矩阵.该方法要求3维点对匹配准确无误,所以本文同时提出在给定相对位姿情况下匹配3维点对算法,该算法充分利用深度相机可以同时返回深度信息和灰度信息的特点.最后在随机生成数据和真实数据上验证了相对位姿精度估计算法的有效性.     

基于微分/代数方程的多体系统动力学设计灵敏度分析的伴随变量方法

基于多体系统动力学微分/代数方程数学模型和通用积分形式的目标函数,建立了多体系统动力学设计灵敏度分析的伴随变量方法,避免了复杂的设计灵敏度计算,对于设计变量较多的多体系统灵敏度分析具有较高的计算效率.文中给出了通用公式以及具体的计算过程和验证方法,并将目标函数及其导数积分形式的计算转化为微分方程的初值问题,进一步提高了计算效率和精度.文末通过一曲柄-滑块机构算例对算法的有效性进行了验证.     

逻辑函数高阶布尔c-偏导数求解的算法实现

针对已有方法在求解布尔c-偏导数时只能解决小规模电路的问题,提出一种基于变量操作运算的大函数高阶布尔c-偏导数求解算法.首先将高阶布尔c-偏导数求解运算转化为逻辑函数的展开运算;然后根据乘积项是否包含需要展开的变量将函数分解成需要展开和不需要展开的二部分,进一步提高算法的速度.文中算法用C语言编程实现,并用MCNC测试电路进行了测试,结果表明,该算法能快速实现大函数高阶c-偏导数的求解;其效率与函数拆分的结果有关,但对输入变量的数量不敏感.     

非齐次隐马尔可夫因子模型期望最大化算法

潜变量模型在刻画因子之间的相互关系以及因子与观测变量之间的关联性时具有重要作用。在实际应用中,观测数据往往呈现出时序变异、多峰、偏态等特性,因此将经典的潜变量模型延伸到非齐次隐马尔可夫潜变量模型,并且为避免对完全数据的积分计算,将期望最大化（expectation-maximization,EM）算法引入到似然函数的计算上;采用Akaike信息准则和Bayes信息准则选择合适的模型,提出了相应的统计计算和检验方法,有效解决了隐马尔可夫模型中的最大估算似然函数问题;最后选择心理．健康数据进行了实验,实验结果表明该方法是有效的。     

Improved semi-analytic sensitivity analysis combined with a higher order approximation scheme in the framework of adjoint variable method

In the design sensitivity analysis, the adjoint variable method has been widely used for the sensitivity calculation. The adjoint variable method can reduce computation time and save computer resources because it can provide the sensitivity values only at the positions in which designers are willing to obtain. However, exact analytical differentiation with respect to the design variables is commonly employed in adjoint variable method. Although the exact derivative assures the accurate sensitivity, it is cumbersome to take differentiation in an exact manner for every given type of finite element. Therefore, in the present study, a new improved semi-analytic design sensitivity method is proposed in the framework of adjoint variable method. Recently, a numerical inaccuracy trouble in the traditional semi-analytic method has been settled by the rigid body mode separation technique and high order approximation scheme. Combining the adjoint variable method with improved semi-analytic design sensitivity scheme, the design sensitivity value can be calculated accurately and efficiently. Through numerical examples, the efficiency and accuracy of the proposed semi-analytic sensitivity scheme in the adjoint variable method are demonstrated.     

Fractional differentiation and non-Pareto multiobjective optimization for image thresholding

Various techniques have previously been proposed for single-stage thresholding of images to separate objects from the background. Although these global or local thresholding techniques have proven effective on particular types of images, none of them is able to produce consistently good results on a wide range of existing images. Here, a new image histogram thresholding method, called TDFD, based on digital fractional differentiation is presented for gray-level image thresholding. The proposed method exploits the properties of the digital fractional differentiation and is based on the assumption that the pixel appearance probabilities in the image are related. To select the best fractional differentiation order that corresponds to the best threshold, a new algorithm based on non-Pareto multiobjective optimization is presented. A new geometric regularity criterion is also proposed to select the best thresholded image. In order to illustrate the efficiency of our method, a comparison was performed with five competing methods: the Otsu method, the Kapur method, EM algorithm based method, valley emphasis method, and two-dimensional Tsallis entropy based method. With respect to the mode of visualization, object size and image contrast, the experimental results show that the segmentation method based on fractional differentiation is more robust than the other methods.     

Piecewise fractional Legendre functions for nonlinear fractional optimal control problems with ABC fractional derivative and non-smooth solutions

In this study, to solve fractional problems with non-smooth solutions (which include some terms in the form of piecewise or fractional powers), a new category of basis functions called the orthonormal piecewise fractional Legendre functions is introduced. The upper bound of the error of the series expansion of these functions is obtained. Two explicit formulas for computing the Riemann–Liouville and Atangana–Baleanu fractional integrals of these functions are derived. A direct method based on these functions and their fractional integral is proposed to solve a family of optimal control problems involving the ABC fractional differentiation whose solutions are non-smooth in the above expressed forms. By the proposed technique, solving the original fractional problem turns into solving an equivalent system of algebraic equations. The established method accuracy is studied by solving some examples.     

A simple recursive scheme for adjusting the contention window size in IEEE 802.11e wireless ad hoc networks

The IEEE 802.11e standard has been introduced recently for providing Quality of Service (QoS) capabilities in the emerging wireless local area networks. This standard introduces a contention window based Enhanced Distributed Channel Access (EDCA) technique that provides a prioritized traffic to guarantee the minimum bandwidth needed for time critical applications. However, the EDCA technique resets the Contention Window (CW) of the mobile station statically after each successful transmission. This static behavior does not adapt to the network state since it reduces the network usage and results in bad performance and poor link utilization whenever the demand for link utilization increases. This paper proposes a new adaptive differentiation technique for IEEE 802.11e Wireless Local Area Networks that takes into account the network state before resetting the contention window. In the new technique, the congestion level of the network is sensed by using previous CW values. Three other enhancement techniques that focus on network adaptation are also discussed. Their main limitations are the high complexity of the implemented algorithms and their slow adaptation to the network state when the channel experiences bursty traffic. The proposed technique is compared to the original differentiation techniques of IEEE 802.11a and IEEE 802.11e standards, as well as to the enhancement schemes. Results show that the proposed adaptive technique outperforms IEEE 802.11e and is comparable to the other enhancement schemes while maintaining relatively low complexity requirements.     

基于分数阶偏微分的图像边缘检测新模型

现有的图像边缘检测方法效果不太理想,得到的图像边缘可能模糊。针对此问题,将分数阶微分理论和现有的Laplacian算子方法相结合应用于图像边缘检测,提出了一种基于分数阶偏微分的图像边缘检测新模型。实验结果表明,相比现有的整数阶微分边缘检测方法,该模型不仅能较好地检测出图像的边缘特征,而且对噪声具有一定的抑制作用,尤其对于纹理细节丰富的图像而言,能够检测出更多的纹理细节信息,是一种比较有效的边缘检测方法。     

Application of Bernoulli matrix method for solving two-dimensional hyperbolic telegraph equations with Dirichlet boundary conditions

The present article is devoted to develop a new approach and methodology to find the approximate solution of second order two-dimensional telegraph equations with the Dirichlet boundary conditions. We first transform the telegraph equations into equivalent partial integro-differential equations (PIDEs) which contain both initial and boundary conditions and therefore can be solved numerically in a more appropriate manner. Operational matrices of integration and differentiation of Bernoulli polynomials together with the completeness of these polynomials are used to reduce the PIDEs into the associated algebraic generalized Sylvester equations which can be solved by an efficient Krylov subspace iterative (i.e., BICGSTAB) method. The efficiency of the proposed method has been confirmed with several test examples and it is clear that the results are acceptable and found to be in good agreement with exact solutions. We have compared the numerical results of the proposed method with radial basis function method and differential quadrature method. Also, the method is simple, efficient and produces very accurate numerical results in considerably small number of basis functions and hence reduces computational effort. Moreover, the technique is easy to apply for multidimensional problems.     

A new variable step size block backward differentiation formula for solving stiff initial value problems

A new block backward differentiation formula of order 4 with variable step size is formulated. By varying a parameter in the formula, different sets of formulae with A-stability property can be generated. At the cost of an additional function evaluation, the accuracy of the method is seen to outperform some existing backward differentiation formula algorithms. The strategy involved in controlling the step size ratio is also described. The problems tested with the method show its efficiency in solving stiff initial value problems.     

自适应事件触发网络化非线性系统滤波器设计

本文针对网络化非线性控制系统设计了基于自适应事件触发方案满足H∞性能的模糊滤波器.第一,提出新的自适应事件触发方案来决定数据包是否需要传输到通信网络中,从而提高网络资源利用率;第二,运用模糊线积分的方法,构建模糊李雅普诺夫泛函,避免求解隶属函数的时间微分;第三,利用Wirtinger不等式及倒凸引理结合的技术,得到滤波...     

采用公钥智能卡加密的数据通信设计

数据加密是保证网络数据通信安全的一种重要技术手段,硬件实现公开密钥功能的智能卡为方便地进行高质量的网络数据加密提供了一种全新的方案。在分析介绍最新智能卡RSA加密功能的基础上,给出了采用该加密方法的网络数据通信的VC编程实现过程。