起重机n阶伸缩臂架稳定性的递推公式及数值解法

基于纵横弯曲理论建立了n阶伸缩臂阶梯柱的微分方程组,并利用数学归纳法推导出n阶阶梯柱压杆稳定性的递推公式。针对递推公式中的超越方程,结合结构受力特征,列写补充方程,使用Levenberg-Marquardt数值最优化算法求解了具有n个未知数的超越方程组。利用此算法求解出的长度系数与GB/T3811—2008中的结果和ANSYS 17.0结果进行对比,结果表明,此算法的精度优于其他算法的精度,并且长度系数具有一定的非线性,因此在实用过程中,小范围内的线性插值是可行的。对于大截面的阶梯柱,使用线性插值计算,临界力的误差较大。     

Stereology for anisotropic cells: Application to growth cartilage*

A number of either new or recently available stereological methods are described for estimating volume, surface area and number of anisotropic cells. The methods are illustrated with direct reference to the epiphyseal growth plate. Different estimates of a given quantity are obtained by applying alternative methods to the same set of sections, in order to compare the relative merits of the methods. For instance, the surface area of the cells is estimated via the Dimroth–Watson model (which gives a measure of the degree of anisotropy in addition to the surface area estimate) and from vertical sections using cycloid test systems. Cell number is estimated by traditional unfolding methods and by the new disector method. Also, volume-weighted mean cell volume is estimated from vertical sections via point-sampled intercepts using two different kinds of rulers to classify intercept lengths. Finally, nested design statistics is applied to a set of data from twelve animals in order to compare the relative impacts of biological and stereological (sampling) variations on the observed coefficient of error of a group mean estimate. The preferred methods are listed in the final section.     

Estimating the length of a bounded curve in three dimensions using total vertical projections

A new method is proposed to estimate the total length of a bounded, isolated linear feature in three dimensions from ‘total vertical projections’, obtained by rotating the curve about a fixed axis (arbitrarily called ‘vertical’) and projecting it onto a fixed vertical plane. No sections are required. Properly stained and embedded neuron dendrites, mycelial trees, fluorescent cytoskeletal filaments within a cell, etc., are candidate specimens for the method, especially in combination with the new devices for non-invasive three-dimensional microscopy. It is necessary that the specimen curve is rigid (i.e. of constant shape), that its length density is not too high (so that overlapping effects are not important) and that the embedding medium is fairly transparent. Given these requirements, the method can be very accurate and convenient to use, as is exemplified here.     

High voltage electron microscopy of wet whole cells. Effect of different wet cell preparation methods on visibility of structures

Dimensional measurements have been made on a small number of tracings of low magnification scanning electron micrographs of trabecular bone sections, using the Quantimet Image Analysing Computer, with a view to expressing the properties of the local bone pattern in a quantitative manner. Measurements of the orthogonally projected length of the boundary profile of the interface between bone and marrow were made as a function of the direction of projection, and these showed that the majority of the patterns were distinctly anisotropic. A formula is proposed for calculating the mean widths of the trabecular bands as they appear on the surfaces of the sections, from the mean area of bone and the boundary profile length. As the validity of this formula is not theoretically evident, the results have been compared with direct experimental measurements, and found to agree very well. The mean intercept lengths in the bone and in the marrow spaces have been calculated as a function of direction across the section. The polar diagrams of these lengths are found to have the shapes of ellipses, to an unexpected degree of accuracy. This makes it possible to express the departure from isotropy of the pattern by a single number, for instance by the ratio of the axes of the ellipse. The essential limitations of the methods used in these experiments are briefly discussed, in particular the impossibility of finding the exact symmetry properties of the surface patterns by experiments of this type.     

Electron backscattered diffraction as a tool to quantify subgrains in deformed calcite

In this work, we investigated processing methods to obtain subgrain sizes from electron backscattered diffraction data using samples of experimentally deformed calcite (CaCO₃) polycrystals. The domain boundary hierarchy method, based on area measurements of domains enclosed by boundaries larger than a given misorientation angle, was applied to these calcite samples and was found to be limited by: (i) topological problems; (ii) undersampling of large grains; and (iii) artefacts caused by nonindexing. We tested two alternative methods that may reduce the problems: (i) the measured linear intercept hierarchy method, based on measurements of linear intercept between boundaries having larger misorientations than a given minimum angle; and (ii) the calculated linear intercept hierarchy method, based on the total length of boundaries having misorientations larger than a given minimum angle. The measured linear intercept hierarchy method was found to produce results more representative for the microstructure than the calculated linear intercept hierarchy method, because the calculated linear intercept hierarchy method has a significant uncertainty related to the grid‐based nature of the measurements. Preliminary results on calcite suggest that the measured linear intercept hierarchy method is related, in a complex way, to deformation conditions such as stress, strain and temperature as well as to the characteristics of subgrain rotation and grain boundary migration processes.     

Generating multi-section silicon steel sheet cutting patterns in the manufacturing industry of electric generators

Circular and sectorial blanks are often cut from silicon steel sheet to make stators and rotors of electric generators. This paper presents an algorithm to generate optimal multi-section cutting patterns for the blanks. A cutting pattern includes one or more sections, each of which consists of strips of the same direction and length. Blanks in a strip are of the same size. The algorithm employs dynamic programming to generate cutting patterns, and linear programming to determine the cutting scheme. Cutting stock data from a factory that produces electric generators are analyzed, and the results indicate that the algorithm is efficient in improving material usage.     

Estimation of surface area from vertical sections

‘Vertical’ sections are plane sections longitudinal to a fixed (but arbitrary) axial direction. Examples are sections of a cylinder parallel to the central axis; and sections of a flat slab normal to the plane of the slab. Vertical sections of any object can be generated by placing the object on a table and taking sections perpendicular to the plane of the table. The standard methods of stereology assume isotropic random sections, and are not applicable to this kind of biased sampling. However, by using specially designed test systems, one can obtain an unbiased estimate of surface area. General principles of stereology for vertical sections are outlined. No assumptions are necessary about the shape or orientation distribution of the structure. Vertical section stereology is valid on the same terms as standard stereological methods for isotropic random sections. The range of structural quantities that can be estimated from vertical sections includes V_v, N_v, S_v and the volume-weighted mean particle volume v?_v, but not L_v. There is complete freedom to choose the vertical axis direction, which makes the sampling procedure simple and ‘natural’. Practical sampling procedures for implementation of the ideas are described, and illustrated by examples.     

Stereology of single objects

Systematic stacks of Cavalieri type, spatial grids, vertical sections and projections, etc., are recent sampling tools for the stereology of single objects, namely of isolated objects that can be orientated and scanned at will in a prescribed way. The increasing use of modern noninvasive scanning devices is facing potential users with the challenge of encompassing the necessary knowledge to implement 'good' stereology. The present paper presents a coherent set of recent stereological methods for single objects in a historical perspective, emphasizing the fact that all relevant techniques — old and new — emanate from a common, relatively small set of basic principles.     

Estimation of subcellular organelle volume from ultrathin sections through centrioles with a discretized version of the vertical rotator

A method for the fast and efficient estimation of the volume (but not surface area) of subcellular organelles is presented. It consists of a rotator/coaxial-section approach based on the Pappus theorem and represents a discretized version of the vertical rotator where, instead of measuring intercept lengths, the points in distance classes are counted. Centrioles serve as a unique reference 'double-point' with constant size allowing unbiased cell selection from the whole population with equal probability and without the disector application. The sandwich-like method of sample preparation allows comparison of control and experimental cases with the same errors caused by overlapping and overprojection. Test experiments demonstrated that the vertical discretized rotator was an efficient and precise tool for the estimation of volume and that a few independent sections of unknown thickness were sufficient for the quantification of one experimental point.     

A simple algorithm to measure the volume-weighted and number-weighted mean volume of particles

An algorithm is presented which offers an alternative approach for measuring volume- and number-weighted mean volume and standard deviation of particles. Using a computer-assisted manual method the following intermediate steps are performed automatically: generation of linear probes emanating from the sampling point of the object and intersecting the profile periphery, measurement of their lengths, and measurement of the area of the transect required for estimating the standard deviation of the volume-weighted mean volume. By first tracing manually the outline of the periphery of the object with a cursor, on a magnetic tablet or on an image acquired into the computer with a video camera, the location of all pixels of the periphery is registered and the area of the transect is measured concurrently. The computer is informed of the coordinates of the selection point in the uniform random (UR) sampling grid by clicking the cursor. All ensuing operations are automatic. In the case of isotropic UR (IUR) sections the algorithm traces a series of uniform systematic random linear probes between the sampling point and the object profile periphery emanating from this selection point, radiating at angular intervals of 29–30° to the periphery. In the case of vertical sections, similar lines are generated at intervals where the sine of the angle changes by a value of 0·33. The volume-weighted mean volume of the object is estimated from the average of all the products , where l represents the length of each individual random linear probe. As the periphery is traced, the algorithm can automatically determine the area of the cross-section of the object, from which the standard deviation of the volume-weighted mean volume can be calculated. Some elements of the above algorithm are also used for the measurement of the number-weighted mean volume. The latter procedure is facilitated using an acoustic vertical depth monitor attached to the microscope. The impact of truncation (‘lost caps’) on the precision of the measurements is discussed. The algorithm is of particular use in light microscopy for measuring cell nuclei by direct visual inspection of the microscopic field using a side-arm mirror assembly interfaced with a magnetic tablet.     

带弹序的弹幕武器立靶密集度测试

提出一种基于4个线阵TDI-CCD相机组成的三空间靶面结构对多弹丸着靶参数进行测试,以解决弹幕武器等高射速武器多弹丸同时着靶时的立靶密集度测试难题。测试时,2个CCD相机在空中交汇形成与预定弹道方向垂直的立靶靶面I;靶面II和靶面III分别由1个CCD相机的探测面形成,并分别与靶面I在竖直方向和水平方向上成一定夹角。根据三靶面的空间几何结构、飞行弹丸在4个线阵CCD相机上的成像时间和成像角度,分析了单发弹丸的着靶坐标、飞行速度和穿靶角度。根据多弹丸在三靶面间的成像位置关系以及弹丸飞行速度约束,推导出多发弹丸着靶时的时空散布参数,如弹序、弹丸存速和着靶坐标。仿真和实际试验验证显示测试的多靶面间目标匹配率达到100%。提出的测试方法有效地解决了多发弹丸同时着靶时出现的假目标问题并克服了单CCD立靶测试参数单一等缺点。     

基于线结构光的三维垂线位移测量方法

垂线测量法是观测大坝变形位移的一种简便而有效的方法,在实际大坝变形监测中得到广泛应用。 针对现有垂线坐标 仪大多只能测量垂线二维位移且结构复杂的问题,本文提出了一种基于线结构光的三维垂线测量方法。 基于垂线测量中垂线 方向不变,利用线结构光测量原理实现垂线三维位移测量。 首先,本文采用线结构光测量获取垂线二维位移,然后基于垂线上 固定标志点的成像光线和垂线相交于一点的事实,综合垂线二维测量结果和通过相机内参数恢复的固定标志点成像光线方程, 实现垂线三维位移测量。 实验结果表明,本方法在水平面内 Y 方向上的位移测量精度为±0. 1 mm,在水平面内 X 方向和竖直 Z 方向上的位移测量精度达到±0. 05 mm,测量范围为 0~ 80 mm。 相较目前垂线位移测量方法,本文方法垂线位移测量精度和测 量范围更高,且测量结构简单。     

Stereological analysis and modelling of gradient structures

Gradient structures are inhomogeneous along a particular gradient direction but homogeneous perpendicular to that direction. Consequently, structural parameters such as volume fraction or surface area density are local characteristics which depend on the 'vertical' coordinate with respect to the 'vertical' gradient axis.
Analogously, models for gradient structures have model parameters depending on the vertical coordinate z . For example, a Voronoi tessellation with a gradient is generated by a gradient point process with a local intensity which is a function of z . Similarly, a gradient germ grain model is obtained from a gradient point process where the grain size distribution may also depend on z . For a gradient Boolean model, local volume fraction V_V ( z ) and local surface area density S_V ( z ) can be calculated from the model parameters.
Stereological methods for gradient structures are based on vertical sections parallel to the gradient direction. Estimation of V_V ( z ), S_V ( z ) and local length density L_V ( z ) is done by lineal analysis using horizontal test lines with vertical coordinate z . Similarly, lineal analysis is used to estimate local mean cell volume of gradient tessellations. For the estimation of local particle number density and size in the spirit of the Wicksell problem the use of kernel methods and distributional assumptions is required.     

Stereological estimation of the volume-weighted mean volume of arbitrary particles observed on random sections*

A stereological estimator of the weighted mean volume of particles of arbitrary shape is described. This unbiased estimator is based on simple point-sampling of linear intercept lengths. The complete absence of shape assumptions effectively breaks the long-standing ‘convexity-barrier’: the only requirement here is that individual particles can be unambiguously identified by their profiles on random sections. Practical details of the simple estimation procedure and an example with very irregular particles are reported. Finally, an estimator of the variance of the weighted distribution of particle volume is discussed. This estimator is also valid for particles of arbitrary shape. For any mixture of ellipsoids (spheres, oblates, prolates and triaxial ellipsoids) the estimator is reduced to a simple function of measurements of diameters in the section plane.     

自学习式GPS车辆自主导航仪的研究

提出一种用GPS接收机通过自学习方式进行车辆自主导航和引导的方法。该方法首先对GPS接收机接收的定位信息通过回归算法进行线性化处理，然后以线性相关系数判断为准则对路径信息进行分段，再将这些线性相关的分段直线信息进行压缩和记录就形成了可以自主导航的路径信息。在导航过程中，利用这些线性相关的分段直线信息，通过矢量夹角计算和矢量方向判断的方法可以预测出前方路径的行驶方向，从而完成自主导航。这种由自学习方式获取的导航路径信息具有很高的导航精度和方向判别性。     

Computerized method to determine crystal orientations from Kikuchi patterns

A computerized method for determining crystal orientations from Kikuchi line patterns is described. The method is rapid and easy to use. When the Bravais lattice is known, the user need only specify a reference direction and the coordinates of the origin and of two points on each of six Kikuchi lines (three pairs). The programs yield the hkl indices of the Kikuchi lines, the beam direction, and the rotation matrix relating the crystal to a chosen reference frame. This rotation matrix can be used for various purposes, e.g., to specify an angle of rotation around a chosen axis or to calculate the misorientation between any two crystals.     

A linear air bearing stage with active magnetic preloads for ultraprecise straight motion

In this paper, we propose a linear motion stage designed with magnetically preloaded air bearings. The magnetic actuators for preloading air bearings were combined with permanent magnets and coils to adjust the air bearing clearance by actively controlling the magnetic force. The system was designed to achieve a simplified configuration of air bearing stage while providing ultraprecise straight motion by actively compensating for the motion errors. The porous aerostatic bearings and magnetic preload actuators were designed and analyzed numerically for a single-axis prototype linear stage driven by a coreless linear motor. A magnetic circuit model was derived for the magnetic actuators. The static stiffness and load capacity of the air bearing stage in the vertical (magnetically preloaded) direction were experimentally measured and compared with the results from the numerical analysis. Motion control laws for three degrees of freedom (i.e., vertical, pitch, and roll motions) were obtained with a high linearity and independence for each axis. The active compensation of three motion errors, the vertical, pitch and roll motion errors were performed through curve-fitting the three errors measured with combination of capacitive gap sensors and a laser interferometer. The errors were reduced from 1.09 to 0.11 μm for the vertical straightness error, from 9.42 to 0.18 arcsec for the pitch motion, and from 2.42 to 0.18 arcsec for the roll motion as level of measured repeatability.     

Stereological estimation using vertical sections in a complex tissue

A method designed for stereological estimation in a very complex tissue using vertical sections is presented. In some tissues, the random rotation of the tissue for vertical sections may obscure recognition of the anatomical structures of interest. The present method overcomes this problem by generating sections with both a particular orientation, 'mapping sections', and ordinary random vertical sections usable for the required observations. A map describing the positions of the vertical sections is produced to make the complex reference space recognizable. The method is illustrated by estimating the number and size of neurones in the dorsal raphe nucleus of the human brainstem with its dense packing of roughly 100 nuclei within a volume less than 50 cm³.     

Quantification and visualization of anisotropy in trabecular bone

A number of methods for measuring anisotropy in trabecular bone using high‐resolution X‐ray computed tomography exist, which give different answers but have not been compared in detail. In this study, we examine the mean‐intercept length (MIL), star volume distribution (SVD) and star length distribution (SLD) methods, their algorithmic implementation for three‐dimensional (3D) data, and how their results relate to each other. A uniform ordered sampling scheme for determining which orientations to sample during analysis enhances the reproducibility of anisotropy and principal component direction determinations, with no evident introduction of biasing. This scheme also facilitates the creation of a 3D rose diagram that can be used to gain additional insights from the data. The directed secant algorithm that is frequently used for traversing pixel and voxel grids for these calculations is prone to bias unless a previously unreported normalization is used. This normalization ameliorates the bias present when using cubic voxels, and also permits calculations on data sets in which the slice spacing is not equal to the pixel spacing. Overall, the three methods for quantification of anisotropy give broadly similar results, but there are systematic divergences that can be traced to their differences in data and processing, and which may impact on their relative utility in estimating mechanical properties. Although discussed in the context of computed tomography of trabecular bone, the methods described here may be applied to any 3D data set from which fabric information is desired.     

Unbiased estimation of capillary length from vertical slices*

Previous stereological approaches to estimate feature length include isotropic sections, which tend to be inefficient for highly anisotropic structures such as skeletal muscle capillaries, and semiparametric model-based methods, which require transverse and longitudinal sections only, but are biased to a variable, unknown degree. The recent method of vertical slices combines the advantages of both approaches, namely it is unbiased, efficient and convenient. This study illustrates for the first time how to apply the vertical slices method in biology by direct light microscopy and intersection counting with a properly orientated cycloid test system. Neither image processing nor confocal microscopy are used. The purpose of the study was to estimate capillary length in the left ventricle of rat heart. Beyond this, a novel histochemical method enables the staining of the venular capillary region in red and the arteriolar capillary region in blue, and hence estimates their separate lengths. The vertical slices method to estimate feature length seems to be a promising approach for biology.