数学处理

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

Bayesian network is considered the strongest foun...

贝叶斯网络被认为是数学基础最强的不确定性处理理论。

In the development process of simulation model, the paper models the container terminal logistic system from the aspects of the whole design, vessel scheduling management and frontward loading and unloading work.

其次，论文以排队网络理论，对集装箱码头的一些稳态指标作了数学描述，最后利用事件调度法对集装箱码头这一离散系统的船舶到、离港的排队模型进行事件处理。

Especially, applying the estimation of map-aiding matching to modify Kalman Filter, the precision of error in the road is obtained in the field of road, so it can satisfy demand of VMS.(3) For the moving vehicles in a city, DGPS is so often affected by obstructing that DGPS signals are intermitted. The paper establishs mathematical model of DGPS/DR.

本文建立了组合导航系统的数学模型，提出了对观测量进行误差补偿的迭代扩展卡尔曼滤波算法，通过该算法将DGPS和DR系统集成起来，进行综合数据处理，从而可以连续不断地为行驶在街道上的车辆提供精确的定位服务。

The particle size distribution fractal was introduced into powders' flowability testing, through used the mathematical model which utilize the geometry properties of the particle, and propitious to the digital micrographic image analysis method. It was gained the fractal dimensions, discussed the relationship between the powders' flowability denotation parameters and powders' PSDF, and also made a primary research about the action effect of flow addition reagent magnesium stearate.

本文中在颗粒流动性测试时引入粒度分布分形维数，通过采用利用颗粒几何特征，便于采用数字显微和用像处理计算粉体粒度分布分形维数值的数学模型，得到粉体粒度分布分形维数值，探讨颗粒流动性表征参数与粉体粗度分布分形维数值间的关系；并就流动助剂硬脂酸镁对粉体流动性能的改进与粉体粒度分布分形维数值关系进行了初步探讨。

At the same time, artificial neural network was adopted to put forward a new thoughtfulness and effective method for evaluating mineral resources synthetically, which can break through restrictions of statistical models on synthetical assessment of mineral resources. Shooting at nodi and pivotal problems in GIS-based mineral resources assessment, the integration of assessing methods of mineral resources, GIS technology and artificial neural network were emphasized.

以计算机可视化技术便捷、直观的展现出矿产资源综合评价的全过程；利用GIS强大的数据管理和空间分析功能，有效的解决了多源、多类型、多属性地质数据的处理和分析问题；利用人工神经网络技术突破了统计数学模型对矿产资源综合评价及成矿预测的约束和限制，为矿产资源综合评价提供了一种新思路和有效的方法。

As a result, for feed-forward NN model this paper first proposes the concepts of"attractor"and"attraction region","fake attractor"and"fake attraction region", and norm of describing"attraction region". Further this paper presents a mathematics method of calculating feed-forward NN"attraction region", it solves the overelaborate job of checking NN fault-tolerance performance by testing all detecting samples, so to test fault-tolerance performance using theoretic characteristic norm is an important break. In accordance with feed-forward NN low fault-tolerance and difficult to satisfy practical application, according to practical application theory, this paper presents an actual method of enhancing NN fault-tolerance performance, builds the mechanism of reconstructing NN model based on combining NN and fuzzy process, reforms NN "fake attractor"and"fake attraction region"to enhance NN fault-tolerance performance greatly.

为此，本文首先给出了前馈NN模型的&吸引子&和&吸引域&，&伪吸引子&和&伪吸引域&的定义，以及描述吸引域的指标，在此基础上提出了一种计算前馈NN模型&吸引域&大小的数学计算方法，该方法提出解决了目前依靠对检测样本的测试工作来检验NN容错性的繁琐工作，而用具理论意义的性能指标来检验，这是一个重要的突破；针对前馈NN容错性较低以致难于满足实用的缺点，根据NN实用稳定性理论，提出了一种提高其容错性的实用方法，建立了基于NN与模糊处理相结合的NN模型重构机制，重构NN&伪吸引子&和&伪吸引域&来大大地提高NN的容错性。

However, such tidal overheight is often ignored in the current regional numerical simulation due to intensive computational requirement. Only the mean sea level is used as the fixed seaward boundary, which may wrongly predict the groundwater table position. Therefore, we aim to determine an equivalent seaward boundary through numerical modeling. The equivalent seaward boundary takes into account the tide-induced overheight effects.

然而，由于潮汐动边界处理的复杂性而导致巨大的计算量，在现有的区域地下水数学模型中，潮汐引起的海平面波动通常被忽略，仅仅以平均海平面高度作为模型的海岸边界条件，其预测出的地下水水位位置与实际情况可能会有一定的误差。

The method utilizes petrographical information obtained from two-dimensional thin sections to stochastically reconstruct the 3D model of a stone sample by the theories and techniques of image processing and mathematic morphology.This paper compares quantitatively the reconstructed microstructures...

这种方法利用从二维薄片取得的岩相学图象信息，用图象处理理论技术和数学形态学的方法生成了岩石的三维模型，对重建的三维微观结构和实际砂岩的表面细微结构进行了定量比较，比较显示，这种重建方法得到的三维模型孔隙率与原始图象基本一致，其水平面/纵切面/横切面上的颗粒长径分布与实际岩石有较好的相关性。

The non-structure grid is used for complex irregular boundary processing. An efficient algorithm PISO is used for the model and it can correct the bias of the mesh, so it can reduce iterative times. The flow pattern, energy dissipation ratio and velocity field are obtained.

根据不同的运行工况，利用计算流体力学软件FLUENT对无压隧洞洞内消能工的水流流态进行了二维简化数学模型的数值模拟，在求解过程中采用混合结构网格来处理复杂的边界形状；采用了效率较高PISO算法进行计算，在计算过程中进行了相邻校正和偏斜校正，减少了达到收敛所需的迭代次数。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。