Stereological estimation based on isotropic slices through fixed points

Stereological estimators of length and surface area based on measurements in an isotropic slice through a fixed point are described. Measurements of three-dimensional angles are not needed. The estimators depend only on distance measurements. The variance of the length estimator is studied in some detail. Applications to particle analysis and second-order stereology are discussed.     

Stereological determination of curvature distributions of spatial fibre systems

Under the assumption of homogeneity and isotropy, this paper solves the problem of determining spatial curvature distributions of fibre processes from curvatures of projection curves from thin sections. As an example, a sample of dislocation lines in a hot-rolled Fe-Ni alloy is discussed.     

Stereological estimation of tubular length

Very efficient and unbiased principles exist for estimating the total three‐dimensional (3D), two‐dimensional and zero‐dimensional amounts of arbitrary structure in 3D space. The total one‐dimensional length of real structure, in the ordinary sense, is an abstraction from the point of view of integral geometry. All stereological estimators of ‘tubular length’ are thus approximations. In addition, they are riddled by biases due to several types of artificial edges and other practical problems. This paper discusses several of these and proposes practical solutions of minimal biases.     

Second-order integral sliding-mode control with experimental application

In the present study, a second-order sliding-mode controller is proposed for single-input single-output (SISO) uncertain real systems. The proposed controller successively overcomes the variations caused by the uncertainties and external load disturbances although an approximate model of the system is used in the design procedure. An integral type sliding surface is used and the stability and robustness properties of the proposed controller are proved by means of Lyapunov stability theorem. The chattering phenomenon is significantly reduced adopting the switching gain with the known parameters of the system. Thus, the proposed controller is suitable for long-term application to the real systems. The performance of the proposed control scheme is validated by a real system experiments and the results are compared with the similar controllers presented in the literature.     

积分切换面自适应滑模控制及其在并联机器人中的应用

针对交流伺服电机作为驱动装置的2-DOF并联机器人,设计出一种带有积分切换面的自适应滑模控制器。首先,带有积分运算切换面的变结构控制器使系统具有对未知参数变化和外部干扰不敏感的特性。其次,通过设计一种自适应律,实现对系统不确定量的在线辨识估计,以辨识结果实时调整控制器参数,以削弱系统抖动,提高了控制系统的实用性。仿真结果表明所设计控制器抗干扰能力强,能较好地实现2-DOF并联机器人各支路的运动控制,具有较好的稳定性和鲁棒性能。     

Precision of area estimation: a numerical study

After listing some general formulae for sampling in n-dimensional space, the author considers the one-dimensional case: the estimation of the length of a line segment by counting the number of points that happen to fall within the segment. If the points are equidistantly located, the variance of the estimate is a strictly periodic function of the length of the segment. This systematic sample has a higher efficiency than simple and stratified random samples of the same intensity. With some modifications, the results carry over to the two-dimensional case: the estimation of the area of a plane figure by counting the number of sample points falling inside the figure. However, the strict periodicity of the variance in the one-dimensional systematic case is replaced by a ‘Zitterbewegung’. The magnitude of this oscillation is seen to be very different for figures of different shapes. Some results are presented also for the estimation of areas by line transects, and for the estimation of volumes by aid of lattices of points in R³, and R⁴. Some comments are also given on the practical implications of the results for sampling in the plane.     

Unbiased volume estimation with coaxial sections: an application to the human bladder

A problem of current medical interest is how to estimate the volume of an object from coaxial sections. Such images can be produced in ultrasound scanning, when the planar scan sections all emanate from a common axis. Two unbiased volume estimators for this sampling regime, previously published without derivation, are derived and presented here in some detail. The estimators are based on an ancient theorem of Pappus of Alexandria (c. ad 320). One of the estimators was used to estimate the volume of urine in the bladder of six human volunteers. The case example was attractive because the corresponding volumes could be voided and directly measured after the scanning session, thus confirming the unbiasedness of the estimator used. Sample size guidelines are also given.     

Direct descent curvature optimal control with a modification algorithm and its application to nonlinear process

This paper presents a direct descent second order or direct descent curvature algorithm with some modifications for the optimal control computations. This algorithm is compared with Hamiltonian methods in the literature. The proposed algorithm has generated numerically robust solutions with respect to conjugate points. The weighting matrix updating scheme was developed to improve the second-order optimal control algorithm, tested the performance of the algorithm, and shown on the benchmark and industrial process. The time-varying optimal feedback (TVOFB) gains are also generated along the trajectory as byproducts. If the trajectory deviates from the optimal trajectory for any reason (i.e., changing of system parameters, step disturbance into the plant, changing of initial conditions), it is held on the optimal trajectory by means of the optimal feedback. Simulations have been given for controlling the Van der Pol and bioreactor system, which are nonlinear benchmark systems.     

A novel linear tracking integrator with integral compensation and its application

A novel linear tracking integrator (LTI) with integral compensation is proposed for efficient integral estimation from a contaminated measurement with a constant or time-varying bias. The limitation of finite-time convergent integral observer (FTCIO) in ruling out the integral drift is firstly revealed via describing function method. Subsequently, by the utilization of integral action in the feedback path, a simple but effective linear tracking integrator is established to provide a practical solution in achieving a drift-free integral estimate. The highlight is that the proposed LTI can simultaneously give the accurate integral and tracking estimates from a noisy measurement without relying on the condition of observability. In addition, frequency-domain analysis of LTI is investigated to give a viable guideline of parameter tuning. Illustrative simulations and comparison with Kalman filter are included to demonstrate the superiority of LTI in accomplishing precise integral tracking in the presence of constant or time-varying bias. Finally, the effectiveness of LTI is also confirmed by an application on autopilot design for aircraft.     

利用光纤曲率传感器重建三维曲面结构

为了实现对弯曲结构的三维空间数据的测量与重建,建立了光纤曲率传感器的准分布式测量系统。对该系统中传感器的布置方式、空间弯曲曲率和扭转角的测量及三维结构重建方法进行了研究。首先,将光纤曲率传感器绕成环形,布置在柔性基底的两个对称表面,组成准分布式测量系统。根据线性叠加原理,同时测量出结构的弯曲和扭转变形。使用光纤曲率传感器提供的弯曲和扭转信息,采用微分几何的方法,建立由曲线切线和曲率确定的运动坐标系,在运动坐标系中根据空间结构的扭转角确定密切平面。然后,在密切平面中进行曲线的弯曲计算和运动坐标系的变换分析,并进行拟合过程的公式推导。最后,对该方法进行了试算验证,并利用准分布式测量系统对两支点间距为500 mm的简支梁进行了结构重建。结果显示,在相邻两检测点进行20点插值时,简支梁曲线的最大偏差为1.1 mm,表明设计的系统和重建方法能够较高精度地实现曲面结构的三维重建。     

Stereological estimation of surface area and barrier thickness of fish gills in vertical sections

Previous morphometric methods for estimation of the volume of components, surface area and thickness of the diffusion barrier in fish gills have taken advantage of the highly ordered structure of these organs for sampling and surface area estimations, whereas the thickness of the diffusion barrier has been measured orthogonally on perpendicularly sectioned material at subjectively selected sites. Although intuitively logical, these procedures do not have a demonstrated mathematical basis, do not involve random sampling and measurement techniques, and are not applicable to the gills of all fish. The present stereological methods apply the principles of surface area estimation in vertical uniform random sections to the gills of the Brazilian teleost Arapaima gigas. The tissue was taken from the entire gill apparatus of the right‐hand or left‐hand side (selected at random) of the fish by systematic random sampling and embedded in glycol methacrylate for light microscopy. Arches from the other side were embedded in Epoxy resin. Reference volume was estimated by the Cavalieri method in the same vertical sections that were used for surface density and volume density measurements. The harmonic mean barrier thickness of the water‐blood diffusion barrier was calculated from measurements taken along randomly selected orientation lines that were sine‐weighted relative to the vertical axis. The values thus obtained for the anatomical diffusion factor (surface area divided by barrier thickness) compare favourably with those obtained for other sluggish fish using existing methods.     

直动从动件盘形凸轮廓线曲率半径的确定

直动从动件盘形凸轮机构的基本尺寸确定后,根据从动件的运动情况,在画出其轮廓线之前,可以彩和图解法较方便地确定出凸轮廓线的曲率半径,并介绍了这种方法的原理和作图过程。     

Finite difference spectral moment estimation for profiles the effect of sample spacing and quantization error

The mean square slope m₂ and curvature m₄ of surface profiles are characteristics that depend upon the frequency content of the roughness. Together with the mean square profile height m₀ they determine the microgeometrical behaviour of contacting rough surfaces. It is shown that in the absence of quantization error, the error due to finite sample spacing in estimating these spectral moments for a sinusoid is negligible when more than 8 points per cycle are used. In the presence of quantization error, large potential overestimates of m₂ and m₄ can occur. The error decreases initially with increased sample spacing and then increases. The severity of the distortion is shown to increase as the peak-to-peak range of the sine wave decreases relative to the full range of the a/d converter used in the digitization process.     

混粉电火花加工在模具制造中的应用

通过对混粉电火花加工工艺与传统模具制造工艺的比较，从混粉电火花加工工艺的机理、表面特性、影响因素等各方面来阐述，混粉电火花加工是生产高精度、高寿命、效率的模具的最有效的工艺之一。     

消谱线弯曲长波红外成像光谱仪设计

为了实现遥感目标的长波红外高光谱成像,有效消除平面光栅产生的谱线弯曲,设计了离轴透镜消谱线弯曲长波红外平面光栅成像光谱仪。分别计算了平面光栅和离轴透镜产生的谱线弯曲,分析了谱线弯曲随相关参量的变化关系,并基于此设计了消谱线弯曲的初始结构。通过优化设计得到的光学系统的通光孔径为100mm,F数为2,光谱分辨率为20nm,空间分辨率为150μrad,冷光阑效率为100%,成像质量接近衍射极限,系统谱线弯曲由原有的180μm以上变为14.3μm以内。该项设计获得了具有普适性的消谱线弯曲公式,证明了离轴透镜具备校正谱线弯曲的特殊功能。最后的设计结果表明,在满足系统成像质量要求且不增加系统复杂度的前提下,采用离轴透镜的平面光栅光谱仪的系统谱线弯曲小于探测器像元尺寸的1/2,满足使用要求。     

Pull-in analysis of an electrostatically actuated nano-cantilever beam with nonlinearity in curvature and inertia

In this paper, the nonlinear behavior of electrostatically actuated carbon nanotubes (CNTs) is investigated based on a comprehensive model with nonlinearity in curvature, inertia and electrostatic force. The aim of this study is to show when the nonlinear formulation needs to be taken into account and when the linear formulation can simulate the system behavior accurately. The model comprises a cantilevered CNT suspended over a fixed electrode plate from which a DC potential difference is imposed. A relatively large gap between the CNT and the ground plate is considered. The versatile Galerkin method is employed to reduce the nonlinear integro-differential equations of motion to a set of nonlinear ordinary differential equations in time, and then, the reduced equations are solved by direct numerical integration. Dynamic response of the system before and beyond the pull-in voltages and effect of gap to length ratio of the CNT are studied. It is shown that in a large gap to length ratio, when the applied voltage is close to the corresponding pull-in voltage the nonlinear terms have a profound role in the dynamic behavior of the system. Eventually, the contribution of nonlinear terms are examined and it is found that the nonlinear inertia and curvature terms have softening and hardening effects, respectively, whereas the hardening effect of the nonlinear curvature has a major contribution.     

A theoretical study on the application of asymmetric rolling for the estimation of friction

In this work, a method for the estimation of friction coefficient is proposed based on the asymmetric rolling operation. Asymmetry is produced by operating the lower and upper rolls at different speeds. A slab method based computer code is developed for estimating the curvature of the rolled sheet under asymmetric rolling conditions. Strain-hardening behavior of the material has been incorporated and Wanheim and Bay's friction model is employed. The developed code is used for solving the inverse problem of estimating the coefficient of friction by measuring the curvature of the rolled sheet under known operating conditions. The simulations show a good potential of the method.