水下机械手运动学逆解的一种优化解法

本文给出一种运用约束最优化的变尺度法求解Schilling水下机械手运动学逆解的方法。这种方法不仅具有牛顿方法的快速性和理想的总体收敛性,通过迭代求取H阵,不仔在奇异性问题,运用惩罚函数法选取步长,保证了从任意点进行搜索,同时有效地处理了约束的存在。这种方法较其它优化算法和搜索法有明显的快速性,在PⅡ550微机上的求解实验证明此算法完全可以用在此机械手运动学的实时求解中。

一种基于优化算法的机械手运动学逆解

本文给出一种基于优化算法的机械手运动学逆解的方法 ,这种优化方法基于信赖域方法 ,,具有超线性的收敛速率 .这种方法不仅具有牛顿方法的快速收敛性 ,又具有理想的总体收敛性 .这种方法较 CCD& BFS有明显的优点 ,可以在一般的 PC机上实现实时求解 .在 P II40 0上仅需不到 10 ms就可以求得最优解 .

Bézier曲线间最近距离的计算方法

针对Bzier曲线间最近距离计算问题,提出一种简捷、可靠的计算方法.该方法以Bernstein多项式算术运算为工具,建立Bzier曲线间最近距离的计算模型;然后充分利用Bzier曲面的凸包性质和de Casteljau分割算法进行求解.该方法几何意义明确,能有效地避免迭代初始值的选择和非线性方程组的求解,并可进一步推广应用于计算Bzier曲线/曲面间的最近距离.实验结果表明,该方法简捷、可靠且容易实现,与Newton-Raphson方法的融合可进一步提高该方法的运行速度.

精密复杂曲面重构与多轴数控加工刀位规划策略

数控加工作为现代制造中的标志性加工技术，在航空航天、运载工具、动力装备等领域的精密复杂型面加工中占据着主导地位。随着国内高速数控加工中心及高档数控机床等硬件设备的日趋成熟和普及，围绕高速数控加工的一些深层次问题便逐步显现出来，这突出表现在数控机床的高速加工特性与传统加工方法之间的矛盾。本文将主要围绕复杂型面高速数控加工中的两大关键技术：曲面造型技术与刀位规划策略，展开论述，着重解决其中的一些关键科学问题，以期为复杂型面的高速数控加工提供新的技术支持。 1. 以罐车曲面重构为例，详细论述了从不完整散乱数据到曲面精确重构的整个过程，着重解决了自由曲面重构理论在实际应用中遇到的一些问题。针对不完整散乱数据，提出一种散乱数据的有序化处理方法，同时给出了面向NURBS的数据自动参数化策略，用于构造罐车的系列截面轮廓线。然后以曲面蒙皮操作为基础实现罐车曲面的快速重构。最后利用参数曲面的离散表达，完成罐车容积的快速检定并借以验证罐车曲面重建的精确性。 2. 以Bézier曲线/曲面为基础，运用多元Bernstein多项式算术运算，将点到复杂曲线/曲面最近点的计算转化为Bernstein多项式方程的求解，进而基于Bernstein基函数的线性精度性质，给出一种新的最近点计算模型。然后通过de Casteljau快速分割算法和二叉/四叉树递归分解的搜索策略寻找最近点。该方法可以有效避免繁琐的迭代计算和对初始值的选择，并从计算效率入手，对其加以改进，成功实现了分割算法与Newton-Raphson方法的融合。再利用B样条曲线/曲面与Bézier曲线/曲面之间成熟的转换算法，将所提出的方法进一步推广到应用更为广泛的B样条曲线/曲面。 3. 通过对刀具轨迹有效性的分析，将刀具轨迹规划分为曲面上曲线族的选择和有效合理排布方式的设计两个方面，为刀具轨迹规划提供了新的设计思路。并以此为基础，对最优刀具轨迹的定义进行了重新阐述，指出今后刀具轨迹规划的研究必须综合考虑轨迹的几何、刀具的运动以及机床的动力学特性。 4. 针对数控加工中心高速加工特性，提出一种等参数螺旋轨迹生成方法。该方法以减少抬刀和路径转接为目的，并综合考虑刀具轨迹几何与运动力学性能，特别适合自由曲面的高速数控加工。同时，在刀具路径的链接、误差分析等方面，也提出了一些颇具特色的方法，从而避免了传统偏置轨迹繁琐的自交干涉检测，能够有效抑制刀具负载的波动，减小刀具的磨损。 5. 在正确重建网格模型拓扑关系的基础上，从离散微分几何学这一新的角度入手，给出了一种新的三角网格曲面微分几何特性分析方法，进而以参数曲面上曲线偏置方法为基础，结合三角网格曲面的拓扑结构和局部区域的精确拟合，建立了网格曲面上的曲线偏置模型，并将计算最近点的方法进一步推广用来计算曲面上的偏置点，从而避免了繁琐的迭代计算。以此为基础，对网格模型的边界轮廓进行等残留偏置，给出了网格曲面上的等残留刀具轨迹生成方法。可进一步利用螺旋线连接各条轨迹，生成更为光滑刀具路径。

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

大别山硬玉石英岩带中的水

The Dabie Mountains is a collisional orogenic belt between the North China and Yantze Continental plates. It is the eastern elongation of the Tongbai and Qingling orogen, and is truncated at its east end by the Tan-Lu fault. Jadeite-quartzite belt occurs in the eastern margin of UHPMB from the Dabie Mountains. Geochemical features indicate that the protoliths of the jadeite-quartzite and associated eclogite to be supracrustal rocks. The occurrence of micro-inclusions of coesite in jadeite and garnet confirmed that the continental crust can be subducted to great depth (8 0-100km) and then exhumed rapidly with its UHP mineral signature fairly preserved. Therefore, study of UHP jadeite-quartzite provides important information on subduction of continental crustal rocks and their exhumation histories, as well as the dynamics of plate tectonic processes at convergent margins. The purpose of this paper is to investigate the presence of hydrous component in the jadeite-quartzite belt, significant natural variations in the hydrous component content of UHP minerals and to discuss the role of water in petrology, geochemistry and micro-tectonic. On the basis of our previous studies, some new geological evidences have been found in the jadeite-quartzite belt by researches on petrography, mineralogy, micro-tectonic, hydrous component content of UHP minerals and combined with the study on rheology of materials using microprob, ER, TEM. By research and analysis of these phenomenona, the results obtained are as follows: 1. The existence of fluid during ultra-high pressure metamorphic process. Jadeites, omphacite, garnet, rutile, coesite and quartz from the jadeite-quartzite belt have been investigated by Fourier transform infrared spectrometer and TEM. Results show that all of these minerals contain trace amount of water which occur as hydroxyl and free-water in these minerals. The two-type hydrous components in UHP minerals are indicated stable in the mantle-depth. The results demonstrated that these ultra-high pressure metamorphic minerals, which were derived from continental crust protoliths, they could bring water into the mantle depth during the ultra-high pressure metamorphism. The clusters of water molecules within garnet are very important evidence of the existence of fluid during ultra-high pressure metamorphic process. It indicated that the metamorphic system was not "dry"during the ultra-high pressure stage. 2.The distribution of hydrous component in UHP minerals of jadeite-quartzite. The systematic distribution of hydrous components in UHP minerals are a strong indication that water in these minerals, are controlled by some factors and that the observed variations are not of a random nature. The distribution and concentration of hydrous component is not only correlated with composition of minerals, but also a function of geological environment. Therefore, the hydrous component in the minerals can not only take important part in the UHP metamorphic fluid during subduction of continental crustal rocks, but also their hydroxyl transported water molecules with decreasing pressure during their exhumation. And these water molecules can not only promote the deformation of jadeite through hydrolytic weakening, but also may be the part of the retrograde metamorphic fluid. 3.The role of water in the deformed UHP minerals. The jadeite, omphacite, garnet are strong elongated deformation in the jadeite-quartzite from the Dabie Mountains. They are (1) they are developed strong plastic deformation; (2) developed dislocation loop, dislocation wall; (3) the existence of clusters of water molecular in the garnet; and (4) the evolution of micero-tectonic from clusters of water molecular-dislocation loop in omphacite. That indicated that the water weakening controlled the mechanism of deformed minerals. Because the data presented here are not only the existence of clusters of water molecular in the garnet, but also developed strong elongation, high density of dislocation and high aspect ratios, adding microprobe data demonstrate the studied garnet crystals no compositional zoning. Therefore, this indicates that the diffusion process of the grain boundary mobility did not take place in these garnets. On the basis of above features, we consider that it can only be explained by plastic deformation of the garnets. The clusters of water molecules present in garnet was directly associated with mechanical weakening and inducing in plastic deformation of garnet by glissile dislocations. Investigate of LPO, strain analysis, TEM indicated that these clinopyroxenes developed strong elongation, high aspect ratios, and developed dislocation loop, dislocation wall and free dislocations. These indicated that the deformation mechanism of the clinopyroxenes plastically from the Dabie Mountains is dominant dislocation creep under the condition of the UHP metamorphic conditions. There are some bubbles with dislocation loops attached to them in the omphacite crystal. The bubbles attached to the dislocation loops sometimes form a string of bubble beads and some loops are often connected to one another via a common bubble. The water present in omphacite was directly associated with hydrolitic weakening and inducing in plastic deformation of omphacite by dislocations. The role of water in brittle deformation. Using microscopy, deformation has been identified as plastic deformation and brittle deformation in UHP minerals from the Dabie Mountains. The study of micro-tectonic on these minerals shows that the brittle deformation within UHP minerals was related to local stresses. The brittle deformation is interpreted as being caused by an interaction of high fluid pressure, volume changes. The hydroxyl within UHP minerals transported water molecules with decreasing pressure due to their exhumation. However, under eclogite facies conditions, the litho-static pressure is extreme, but a high fluid pressure will reduce the effective stress and make brittle deformation possible. The role of water in prograde metamorphism. Geochemical research on jadeite-quartzite and associated eclogite show that the protoliths of these rocks are supracrustal rocks. With increasing of temperature and pressure, the chlorite, biotite, muscovite was dehydrous reaction and released hydrous component during the subduction of continental lithosphere. The supracrustal rocks were transformed UHP rocks and formed UHP facies assemblage promotely by water introduction, and was retained in UHP minerals as hydrous component. The water within UHP minerals may be one of the retrograde metamorphic fluids. Petrological research on UHP rocks of jadeite-quartzite belt shows that there was existence of local fluids during early retrograde metamorphism. That are: (1) coronal textures and symplectite around relict UHP minerls crystals formed from UHP minerls by hydration reactions; (2) coronal textures of albite around ruitle; and (3) micro-fractures in jadeite or garnet were filled symplectite of Amp + PI + Mt. That indicated that the reactions of early retrograde metamorphism dependent on fluid introduction. These fluids not only promoted retrograde reaction of UHP minerals, but also were facilitate to diffuse intergranular and promote growth in minerals. Therefore, the hydrous component in the UHP minerals can not only take important part in the UHP metamorphic fluid during subduction of continental crustal rocks, but also their hydroxyl transport water molecules with decreasing pressure and may take part in the retrograde metamorphic fluid during their exhumation. 7. The role of water in geochemistry of UHP jadeite-quartzite. Geochemical research show that there are major, trace and rare earth element geochemical variations in the jadeite-quartzite from the Changpu district of Dabie Mountains, during retrograde metamorphic processes from the jadeite-quartzite--gneiss. The elements such as SiO_2、FeO、Ba、Zr、Ga、La、Ce、PTN Nd% Sm and Eu increase gradually from the jadeite-quartzite to retrograded jadeite-quartzite and to gneiss, whilst TiO_2. Na_2CK Fe2O_3、Rb、Y、Nb、Gd、Tb、Dy、Ho、Er、Tm、Yb decrease gradually. And its fO_2 keep nearly unchanged during early retrograde metamorphism, but decreased obviously during later retrograde metamorphism. These indicate that such changes are not only controlled by element transformation between mineralogical phases, but also closely relative to fluid-rock interaction in the decompression retrograde metamorphic processes.