离散化

In this paper, the maximum likelihood algorithm with process and measurement noise for nonlinear continuous-discrete system given by Jategaonkar and Plaetschke is improved in two aspects: 1 to avoid the disadvantages of sensitivities computation by common finite-difference method, in which the perturbation sizes should be selected optionally, an improved finite-difference method with best perturbations, is presented. 2 to improve the numerical stability of Jategaonkar's algorithm, maximum likelihood algorithm with fast triangular square-root decomposition filter is given.

摘要对Jategaonkar等人给出的同时计及过程及观测噪声的非线性连续-离散系统的极大似然算法从两个方面进行了改进：1给出了计算灵敏度的最佳摄动有限差分算法，避免了普通有限差分法计算灵敏度矩阵时需人为选择参数摄动量大小而带来的缺点；2给出了具有快速三角化平方根滤波的极大似然算法，提高了原算法的数值稳定性。

Using truncated cone, circular and triangular models to simulate the contact surface, the thermal contact resistance is calculated based on unstructured Delaunay triangulation gird solution and finite element method.

分别采用截锥体、圆弧形和三角形模型来模拟实际物体的接触面，利用DELAUNAY三角形非结构化网格离散温度场，并使用有限元法数值计算接触热阻。

The local averaging method is used to discretize the random field, correlated random variables are transformed to a set of uncorrelated normalized random variables, combining viscoelastic stochastic finite element method with H-L algorithm, the reliability of solid propellant grain is studied with different random parameters.

为了讨论各类随机因素对药柱结构可靠性的影响，采用局部平均法离散参数随机场，并通过相关结构分解成归一化的独立随机变量，将可靠度指标算法和粘弹性随机有限元法相结合，进行了固体推进剂药柱的结构可靠性分析。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

Chapter 3, Analyse the focal point and the difficult point of the unit visualization of discrete element method.

第四章主要对离散元等值线，云图的可视化方法进行了分析说明。

It adopts Reynolds time-average N-S equation and k-s turbulence model to calculate the inner 3-D viscid turbulence flow of hydraulic turbine. In the unstructured grid, the governing equations are discredited with Finite Volume Method based on Finite Element Method. And the pressure correction method is proposed in numerical calculations.

然后采用基于雷诺时均N-S方程与标准k-ε湍流模型来计算水轮机三维粘性湍流场，在非结构化网格中，采用基于有限元的有限体积法对方程进行离散，用压力校正法进行数值求解。

The computational complexity has been reduced about 5 times over against the original one. Moreover, the interpolation and quantization processing of CW is more reasonable; 2. A secondary power normalization algorithm is proposed in this dissertation. This normalization algorithm ensures that the energy sum of SEW and REW is 1. So, the energy ratio of SEW and REW can be achieved only by using SEW energy. This ratio is applied in REW quantization and CW composition; 3. For more efficient quantization for Slowly Evolving Waveform magnitude, Rapidly Evolving Waveform magnitude and power parameters, firstly, by applying the Equivalent Rectangular Bandwidth theory, classifiable multi-codebooks method, analysis-by-synthesis approach and so on, a predictive AbS multi-codebooks SEW magnitude quantization scheme is proposed. In the scheme, pitch information is exploited to determine which codebook is searched; secondly, for REW magnitude quantization, this dissertation proposed a DCT-matrix multi-codebooks quantization scheme. The classification in muti-codebooks is based on pitch and quantized SEW power. The multi-codebooks structure may offer more the information in quantization and solve the problem of the bit requirement limits in quantization by consuming some extra storage space; Furthermore, for the switch quantization of CW gain, a new classified parameter is proposed.

本文的主要贡献体现为如下几方面：一、为了减少WI模型的计算复杂度，提出了基于快速傅立叶变换、三次B样条插值和周期延拓技术的特征波形(Characteristic Waveform，CW)表示和对齐的快速算法，与原方法相比，计算量下降到原方法的1/5，同时也使得CW在插值和量化时更合理；二、为了严格保证SEW与REW的能量和为1，提出了一种特征波形的二次功率归一化算法，仅需要SEW能量就可以算出二者的能量比，并可应用到后续的REW的分类量化和CW合成中；三、为了对慢渐变波形(Slowly Evolving Waveform，SEW)幅度、快渐变波形(Rapidly Evolving Waveform，REW)幅度和特征波形功率进行有效量化，本文首先采用临界频带理论、分析合成技术、感觉加权技术以及预测式矢量量化技术，提出了一种基于基音周期分类的SEW分析合成预测式多码书量化方法；其次，本文根据基音和量化后SEW的功率信息对REW幅度进行分类，提出了一种基于离散余弦变换的REW矩阵多码书量化方法。

The method in this paper abandon thisreinitialization step by discreting the convection terms in governing equations usingspecial schemes borrowed from conservational law equations.

通过对控制方程中输运项离散方法的特殊处理，本文的方法屏弃了这个重新初始化步骤。

In this paper, a moving-boundary problem occurring under the acidifying was discussed, which was transformed into a coupled problem of an initial-boundary value problem of nonlinear parabolic equation and an initial value problem of differential equation.

建立了油气层酸化过程中的动边界模型，经Landau变换后，将所求问题转化为定边界上的非线性抛物型方程初边值问题和常微方程的初值问题的耦合问题，并给出了耦合问题的全离散格式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。