A simple method for the digital determination of the photoelastic fringe order

A new and simple approach to the digital determination of a photoelastic fringe order using two different loads is proposed. The relationships between the intensity values of light and the isochromatic fringe orders generated from two different loads are derived. The scheme used for the automated determination of the total fringe orders of a full-field photoelastic fringe pattern is described. The usefulness of this method is demonstrated using two isochromatic fringe patterns under two different loads. Extra filters are not needed in the proposed method as in the case of the two-wavelength method.     

基于多模型分段拟合的光纤陀螺温度误差补偿方法

传统光纤陀螺温度误差采用单一模型进行建模与补偿,存在模型适配性较差的问题。考虑到光纤陀螺在不同温度区间的温度特性存在明显差异,为提高光纤陀螺温度误差补偿精度,提出了基于多模型分段拟合的光纤陀螺温度误差补偿方法。设计了-15⁵0℃区间内温度实验,在大量实测数据分析基础上,将陀螺温度特性按照低、中、高三个温度区间,分别建立三种不同阶次的温度误差模型。采用分段拟合的方法进行误差建模,并利用所建模型对光纤陀螺进行了温度误差补偿。实测数据表明,提出方法能够有效改善光纤陀螺的温度漂移,补偿后漂移标准差减少66.67%。     

一种新的加速度计温度误差补偿方法

惯性导航系统实际工作时,环境温度变化会导致IMU的惯性器件加速度计的工作温度变化,其零偏和标度因子因此也会发生变化,最终影响惯性导航系统的初始对准和导航精度.通过两级温度控制,在水平和垂直位置对加速度计进行定点升温试验,利用最小二乘法建立起了加速度计的温度补偿模型.在自然升温和降温过程中,进行加速度计的温度补偿,验证了模型的准确性和重复性.     

Development and assessment of a single-image fringe projection method for dynamic applications

A single-image fringe projection profiling method suitable for dynamic applications was developed by combining an accurate camera calibration procedure and improved phase extraction procedures. The improved phase extraction process used a modified Hilbert transform with Laplacian pyramid algorithms to improve measurement accuracy. The camera calibration method used an accurate pinhole camera model and pixel-by-pixel calibration of the phase-height relationship. Numerical simulations and controlled baseline experiments were performed to quantify key error sources in the measurement process and verify the accuracy of the approach. Results from numerical simulations indicate that the resulting phase error can be reduced to less than 0.02 radians provided that parameters such as fringe spacing, random measured intensity noise, fringe contrast and frequency of spatial intensity noise are carefully controlled. Experimental results show that the effects of random temporal and spatial noise in typical CCD cameras for single fringe images limits the accuracy of the method to 0.04 radians in most applications. Quantitative results from application of the fringe projection method are in very good agreement with numerical predictions, demonstrating that it is possible to design both a fringe projection system and a measurement process to achieve a prespecified accuracy and resolution in the point-to-point measurement of the spatial (X, Y, Z) positions.     

一种光纤陀螺温度误差分段补偿新方法（英文）

分析了光纤陀螺的温度特性,设计了大范围的温度测试,研究了不同温度和温度变化率对光纤陀螺输出的影响,研究了光纤陀螺在不同温度范围内的温度特性。为了提高温度误差补偿精度,根据陀螺温度特性将温度分为低、中、高三个区间,分别利用人工神经网络进行误差建模,提出了一种多模型分段拟合的新方法。根据建立的模型进行温度误差补偿,补偿结果表明,建立的模型能有效地减小了光纤陀螺的温度漂移,精度提高了一个量级。     

基于粒子群优化算法的光纤陀螺温度误差分段补偿方法

针对光纤陀螺的温度误差单一模型补偿方法适配性较差的问题,提出一种基于粒子群优化(PSO)算法的光纤陀螺温度误差分段补偿方法。此方法基于分段建模补偿的思想,在建模时加入温度和温度变化率影响因子,并引入PSO算法极值寻优,得到最优补偿函数。为了验证此方法的补偿效果,设计了?15℃~50℃区间内光纤陀螺温度实验,分别利用所提方法和传统方法对其温度误差进行补偿。试验结果表明,使用所提方法能够极大地降低温度误差,与传统算法相比,在保证补偿后陀螺零偏稳定性一致的前提下陀螺零偏均值降低了一个数量级,并且具有实时补偿性。     

A non-linear seales method for strongly non-linear oscillators

A non-linear seales method is presented for the analysis of strongly non-linear oseillators of the form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbdiqb-Hha4zaadaGaey4kaSIa% am4zaiaacIcacqWF4baEcaGGPaGae8xpa0JaeqyTduMaamOzaiaacI% cacqWF4baEcqWFSaalcuWF4baEgaGaaiaabMcaaaa!4FEC!\[\ddot x + g(x) = \varepsilon f(x,\dot x{\text{)}}\], where g(x) is an arbitrary non-linear function of the displacement x. We assumed that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbdiab-Hha4jaacIcacqWF0baD% cqWFSaalcqaH1oqzcaGGPaGaeyypa0Jae8hEaG3aaSbaaSqaaiaaic% daaeqaaOGaaiikaiabe67a4jaacYcacqaH3oaAcaGGPaGaey4kaSYa% aabmaeaacqaH1oqzdaahaaWcbeqaaiaad6gaaaaabaGaamOBaiabg2% da9iaaigdaaeaacaWGTbGaeyOeI0IaaGymaaqdcqGHris5aOGae8hE% aG3aaSbaaSqaaiab-5gaUbqabaGccaGGOaGaeqOVdGNaaiykaiabgU% caRiaad+eacaGGOaGaeqyTdu2aaWbaaSqabeaacaWGTbaaaOGaaiyk% aaaa!67B9!\[x(t,\varepsilon ) = x_0 (\xi ,\eta ) + \sum\nolimits_{n = 1}^{m - 1} {\varepsilon ^n } x_n (\xi ) + O(\varepsilon ^m )\], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabsgacqaH+oaEcaGGVaGaaeizaiaadshacqGH9aqpdaaeWaqa% aiabew7aLnaaCaaaleqabaGaamOBaaaaaeaacaWGUbGaeyypa0JaaG% ymaaqaaiaad2gaa0GaeyyeIuoakiaadkfadaWgaaWcbaGaamOBaaqa% baGccaGGOaGaeqOVdGNaaiykaaaa!4FFC!\[{\text{d}}\xi /{\text{d}}t = \sum\nolimits_{n = 1}^m {\varepsilon ^n } R_n (\xi )\], % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabsgacqaH3oaAcaGGVaGaaeizaiaadshacqGH9aqpdaaeWaqa% aiabew7aLnaaCaaaleqabaGaamOBaaaaaeaacaWGUbGaeyypa0JaaG% imaaqaaiaad2gaa0GaeyyeIuoakiaadofadaWgaaWcbaGaamOBaaqa% baGccaGGOaGaeqOVdGNaaiilaiabeE7aOjaacMcaaaa!5241!\[{\text{d}}\eta /{\text{d}}t = \sum\nolimits_{n = 0}^m {\varepsilon ^n } S_n (\xi ,\eta )\], and R _n,S _nare to be determined in the course of the analysis. This method is suitable for the systems with even non-linearities as well as with odd non-linearities. It can be viewed as a generalization of the two-variable expansion procedure. Using the present method we obtained a modified Krylov-Bogoliubov method. Four numerical examples are presented which served to demonstrate the effectiveness of the present method.     

自适应卡尔曼滤波在惯性测量组合误差补偿中的应用

惯性元件误差是捷联惯导系统的主要误差源，必须在导航过程中加以补偿。根据机动目标跟踪理论和惯性测量组合动态模型，分别建立状态方程和观测方程，利用机动频率自适应的算法进行卡尔曼滤波，以此达到惯性测量组合动态误差和随机误差补偿的目的。仿真结果说明该方法可行有效，优于传统的误差补偿算法，能较好地提高系统导航精度。     

A perturbation method for certain non-linear oscillators

We present a perturbation method for the analysis of single degree of freedom non-linear oscillation phenomena governed by an equation of motion containing a parameter ? which need not be small. The approach is to define a new parameter α = α(?) in such a way that asymptotic solutions in power series in α converge more quickly than do the standard perturbation expansions in power series in ?. Phenomena considered are free vibration of strongly non-linear conservative oscillators and steady state response of strongly non-linear oscillators subject to weak harmonic excitation.     

A direct method for non-linear normal modes

This paper presents a direct method for locating normal modes in certain holonomic, scleronomous, conservative non-linear two degree of freedom dynamical systems. The method does not require that the system studied be close to a linear system.     

基于比力差分测量的加速度计温度误差补偿方法

针对温度变化引起的惯导系统中石英挠性加速度计测量误差,提出了一种基于比力差分测量的加速度计温度误差补偿方法。首先,建立包含温变速率影响的温度误差模型,利用标定惯导系统加速度计参数时的温度作为标定参数温度基准。其次,借助不带转台的温箱对惯导系统进行全温测试,通过同一方位前后时间段加速度计输出的差分消除未知的比力真值,只保留由于温度改变引起的标度因数与零偏变化,通过多位置观测对这两项参数进行最小二乘拟合估计,获得对应温度系数。该方法不需要温箱具备高精度定位基准,能够实现全温范围与快速变温工作条件下温度误差的精确建模。试验结果表明,应用该补偿方法可使加速度计测量精度在全温范围内保持在10μg量级。     

基于数字图像处理技术的惯导航向误差解算技术

船载经纬仪是航天测量船专用光学测量设备,其重要功能就是通过测星校航向,并以此为基准对惯性导航设备进行校准.描述了经纬仪测星原理并分析了其易受天气因素影响的缺点,通过对上述问题的深入研究提出了一种新型的基于数字图像处理技术的测星方法.该方法通过采集经纬仪测星时的视频图像,并根据星体位置解算航向误差,极大程度提高了经纬仪测星能力,弥补其功能上的缺陷.通过对传统测星法、人工判读法和数字判读法的优缺点、误差分析和实际应用效果的比对,对该方法进行了准确的评估,得出了其数据精度高、满足任务需求、有效弥补经纬仪功能缺陷并提高测量船整体测控精度的结论,具有其独特的优势和利用价值,值得在测量船以及其它动态测量单元中普及和推广.     

含高阶余项的非线性动力系统数值计算法

建立了一种求解非线性动力系统高精度数值计算的新方法,重构了等价的非线性动力系统方程,该方程考虑了非线性函数的任意高阶项,并给出了该方程的Duhamel积分表达式,在时间步长内用Newton-Raphson法进行数值迭代求解,该方法能连续满足微分方程而不只是在离散的步长端点满足方程,从而打破了传统的Euler型有限差分法。计算实例表明,该方法计算精度高于传统的Runge-Kutta,Newmark-β和Wilson-θ等方法。     

A perturbation-incremental method for strongly non-linear non-autonomous oscillators

A perturbation-incremental method is extended for the analysis of strongly non-linear non-autonomous oscillators of the form , where g(x) and are arbitrary non-linear functions of their arguments, and ε can take arbitrary values. Limit cycles of the oscillators can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at period-doubling bifurcation along a frequency-response curve is made simple by the present method. Subsequent continuation of an emanating branch is also discussed.     

A spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulation

Discrete particle simulation is a well‐established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions. Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost. Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications. The spectral projection method consists of a discrete Fourier‐transform of the particle locations. The Fourier‐transformed particle number density and momentum fields can then be used to compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid. The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright © 2008 John Wiley & Sons, Ltd.     

A consistent closure method for non-linear random vibration

—A closure method is proposed for calculating moments of the state vector of a non-linear system satisfying an Itô stochastic differential equation. It is based on a finite set of moment equations and a sequence of probabilities converging to the exact distribution of the state vector that is obtained by the minimization of an objective function. Numerical results for one-dimensional diffusion processes show that the proposed closure technique is robust in the sense that resultant moments are satisfactory even when crude approximations are used for the probability of the state vector.     

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

A non-linear method for the calculation of the loss tangent distribution function

A procedure to obtain the tangent distribution function from internal friction peaks in solids is described. The method was applied to simulated data in order to show that the distribution can reproduce accurately the internal friction data in transition region as well as in most of the terminal region. Finally, the procedure is applied to experimental data in glass transition peaks of polystyrene.     

A finite element variational multiscale method for incompressible flows based on the construction of the projection basis functions

In this article, we present a finite element variational multiscale (VMS) method for incompressible flows based on the construction of projection basis functions and compare it with common VMS method, which is defined by a low‐order finite element space L_h on the same grid as X_h for the velocity deformation tensor and a stabilization parameter α. The best algorithmic feature of our method is to construct the projection basis functions at the element level with minimal additional cost to replace the global projection operator. Finally, we give some numerical simulations of the nonlinear flow problems to show good stability and accuracy properties of the method. Copyright © 2011 John Wiley & Sons, Ltd.