误差模型

Comprehensively making use of the basic theory, such as Space Analytic Geometry, Gear Meshing Engagement Theory, Method of Mathematical Calculation, Theory for Error Analyzing and Data Processing, the author has established the mathematical models of the new method, which has included the analytic mathematical model for precision orientation, the mathematical model for the ball's diameter and the measuring diameter, the mathematical model about the ball's centre, the calculation model for tooth alignment diviations and the model for tooth alignment error evaluation.

本文综合应用空间解析几何学、啮合原理、计算方法、误差理论与数据处理等有关基础理论，推导建立了新方法的数学模型，包括：确定定位关系的解析法数学模型，测球直径与测量半径的数学模型，测球球心的数学模型，齿向偏差的计算模型以及齿向误差的评定数学模型等。

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

A new calculation model is established using the simulating curves presented by Standing and Katz. The coefficients of the correlation are determined by fitting to the data of Standing and Katz Z-factor chart. The results of the two models are compared, the conclusion can be drawn that the error of LXF model is smaller than that of DAK model.

利用两种模型对不同拟对比温度和拟对比压力组合条件下的天然气偏差系数进行了拟合计算，与理论图版值的误差对比显示，在高温高压条件下LXF模型的拟合结果更优，特别是随着拟对比压力的增加，LXF模型的误差不断减小，因此，该模型更适用于高压和超高压条件下天然气偏差系数的工程计算。

Secondly, the analytic expressions of the error band boundary line for the s model of line segment are deduced, the parameter equations of the error band boundary are gotten.

考虑实用性和合理性，将线元看成离散点的集合，将线的不确定性看成点的不确定性的聚合体，将线元的位置不确定性模型看成以各点误差椭圆的长半轴E为半径的误差圆的聚合体，建立了以线元上任意点处的误差椭圆的长半轴E为带宽的线元不确定性ε模型。

Theoretically, the error model of maximum direction is more rigorous for describing error of transition curve lines.

给出了以缓和曲线法方向的中误差表示误差带宽的εσ模型，以及以最大方向误差表示带宽的εm模型的计算方法。

Phase velocity error caused by position error of microtremor observation array is computed under different conditions such as two different dispersive phase velocity models of Rayleigh wave, three kinds of radius, 19 kinds of observation position mode and 6 types of position error.

为研究地脉动观测台阵中观测点之间的定位误差带来的影响，计算了在两种瑞利波频散模型、3种不同的圆周半径以及19种观测位置等多种情况下由6种定位误差引起的瑞利波相速度相对误差，结果表明：由于圆周上观测点数目有限，在不存在定位误差时，相速度误差也是存在的，随观测点位置的不同，相速度相对误差存在差异，其最大值约为最小值的3倍。

In this paper the effects of scanning truncation error, scanning position error, random amplitude and phase error, and multiple-reflection error in near-field antenna measurement are analyzed; error equations and the uncertainty of measurement are obtained through computer simulation; compensated techniques for reducing the effects of measurement errors in near-field antenna measurement are presented and the formula and arithmetic of phaseless near-field techniques are derived.

本文从解析法和数值仿真两个角度深入分析口面天线近场测量中扫描面截断误差、扫描面位置误差、随机幅相误差、多次反射误差等误差源对天线远场特性测量精度的影响，一方面从理论上给出相应的误差方程，另一方面建立误差分析模型，通过计算机模拟，得到不同误差条件下测量结果的不确定度，并介绍了减小这些误差的修正方法，推导无相位近场测量的公式和算法。

The following conclusions have been made in this paper.(1) Based on CO_2 flux data of eddy covariance, variation characteristics of gross primary productivity in four flux observation stations were studied, which are an alpine meadow, an alpine shrub meadow, a swamp alpine meadow and a steppe alpine meadow at Dongxiong. The results show that photosynthetic capacity of the alpine meadow is the highest, and the annual total GPP is 652.2g C/m~2. Daily-differencing approach is used to analyze the random error of CO_2 fluxes measurements. The results show that the distribution of random error follows more closely follows a double-exponential, rather than a normal distribution, capturing the high peak and thick tail, and the random error varies with environment variables, which violates the assumptions for the ordinary least squares fitting with normality and homoscedasticity, consequently, we introduce maximum likelihood method for parameter optimization.

本文主要在以下几个方面开展工作并获得了一些认知和结论：(1)通过分析样带区域内高寒草甸、高寒灌丛、沼泽化湿地和草原化高寒草甸四个通量观测站点草地生态系统总初级生产力变化特征，研究结果表明HBBT矮嵩草草甸生态系统植被光合作用能力较强，年GPP总量为652.2 gC/m~2，明显高于其他三种生态系统；通过利用"单塔日变化法"获得四站点通量观测数据随机误差，结果表明通量观测随机误差概率分布呈现尖峰厚尾的特征，与正态分布相比，更服从双边指数分布，进一步分析表明通量观测随机误差随环境变量(风速、温度和光合有效辐射)的变化而变化，这违背了普通最小二乘法进行生态过程模型参数优化正态分布且误差同质的假设，因此本研究中引入最大似然法进行生态过程模型参数优化。

Differing from the feed-back error compensation method, the selflearning error pre-compensation method offered by the paper is based on both ANN and time series technique to obtain the error pre-compensating curve using the non-linear ANN pre-compensation model. Because of the self-learning character of the ANN, this new type of precompensation model can be self-adjusted.

与常规的反馈补偿方法不同，本文提出的自学习误差预测补偿方法，将时间序列预测与神经网络的自学习自适应优化建模技术相结合，利用神经网络非线性预测模型产生误差预补偿函数，并利用神经网络的自学习特性对所建预测模型进行修正，所以这种新型的误差补偿方法能够获得更高的误差补偿精度和控制速度，简单实用，适于推广，具有生产应用价值。

First, we consider nonholonomic chained systems with modeling error, in this section,based on back-stepping , using the so-called adding a integrator , state-scaling technique , we design discontinuous feedback law,such that the trival solution of the closed-loop systems global strong stable; Second,we consider high-order nonholonomic chained systems with modeling errors and external disturbances, in this section,using input/state-scaling and integrator backstepping methods , we design discontinuous feedback law and give out the switching strategy, such that the closed-loop systems global /C-exponential stable; Finally, we consider a class of more general power chained form systems with particular drift-terms, in this section , using Lyapunov method, we design time-varying feedback law , such that the closed -loop systems p—exponential stable.

第一部分考虑的模型为带有模型误差的高阶非完整链系统，我们运用加幂积分器、State-scaling技巧以及基于Back-stepping方法构造出不连续反馈律，从而使得所讨论系统的闭环系统的平凡解全局强稳定；第二部分考虑的模型为带有模型误差的不确定高阶非完整链系统，这一部分我们运用input／state scaling和integrator backstepping方法构造出不连续反馈律，并给出切换策略，使得所对应的闭环系统全局κ-指数稳定；第三部分考虑的系统是形式更为一般的且带有特殊形式漂移项的幂链系统，利用Lyapunov函数方法，设计出时变反馈律，从而使得相应的闭环系统ρ-指数稳定。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失