蒙特卡罗法评定圆度测量不确定度

形位误差测量的复杂性和测量结果评定的多样性,使形位误差的不确定度评定较为困难。因此,探索一种准确、高效的形位误差测量不确定度评定方法具有实际的意义。目前,主要根据《测量不确定度评定指南》进行形位误差不确定度评定,评定过程需要计算出误差模型中的传递系数。当误差模型复杂或者参数之间存在非线性时,评定结果准确性差。为解决该问题,在分析形位误差测量不确定度评定方法和评定原理之后,提出了采用蒙特卡罗法评定形位误差测量不确定度。该方法利用计算机产生伪随机数来模拟圆度误差的实际测量值,将其代入误差模型中,构成圆度误差的概率分布,并求出其期望值和方差,从而得出圆度误差和测量不确定度。试验数据显示,蒙特卡罗法评定圆度不确定度结果可靠、高效快捷,为几何量测量领域、误差分析与数据处理领域提供了新的方法,值得推广和应用。     

基于MATLAB的直线度测量不确定度评定程序设计

形位误差测量不确定度评定由于其测量的复杂性和测量结果评定的多样性,导致在实际测量结果中形位误差测量的不确定度评定成了难题;尤其是测量点较多,测量数据难以处理,处理结果的准确性难以保证;为此,根据直线度测量不确定度的评定过程对其进行了评定程序的设计,在程序命令的提示下,输入测量值便可得到直线度误差,输入单点测量不确定度便可得到直线度测量不确定度;该程序根据测量不确定度常用的GUM法和蒙特卡罗法思想进行设计,可得到两种不同的评定结果,不受测量点的多少、测量数据的复杂程度等因素影响;通过数据验证,程序可靠准确,为直线度测量不确定度评定提供了便捷、高效的数据处理方法;通过测量数据验证,该程序准确可靠,具有一定的实际应用价值和推广意义。     

高频电磁镜面板平面度测量的不确定度评定

针对某部队高频电磁镜面TEM室的镜面板平面度误差测量与评定任务,从测量仪器的选择、测量误差的评定等方面解决镜面板平面度测量不确定度的评定问题。与传统的平面度误差测量不确定度评定方案不同,重点针对高频电磁镜面TEM室的超大镜面板平面度进行不确定度评定。测量方法采用相对测量法,从测量便利性方面选择合像水平仪,误差评定选择最小二乘法,基于MATLAB融入蒙特卡罗方法对其进行平面度误差评定,评定结果为4μm,解决了高频电磁镜面板的平面度误差评定问题,保证了高频电磁信号的高保真传递,实现了大型TEM喇叭、D-dot等电磁传感器的精确校准。     

圆柱度误差评定中规范不确定度计算方法的研究

针对目前误差评定结果往往只提供测量不确定度的情况,根据新一代产品几何规范(GPS)不确定度体系,研究了圆柱度误差评定时规范不确定度的计算方法。基于最小区域法提出了圆柱度误差评定的数学模型,用改进粒子群算法得到圆柱度误差值,并通过研究影响规范不确定度每一个元素的传播系数及相关系数推导出了规范不确定度的详细计算公式,且以此为基础开发了圆柱度误差评定的图形界面。经实例验证,该方法可以在新一代GPS体系下准确、直观、方便地评定圆柱度误差。     

基于贝叶斯理论的ATS测量不确定度评定

从自动测试系统(ATS)的组成机理出发,提出一种ATS测量不确定度评定方法;其基本过程是首先基于测量信号路径,建立相应的测量链;其次,计算各个传递单元的不确定度,静态测量、动态测量分别选用贝叶斯信息融合法和贝叶斯预测法进行评定;最后,利用蒙特卡罗(MC)法计算各链的合成不确定度;通过某ATS中具体的测量链作为实例,重点分析了动态测量不确定度评定过程中遇到的不同情况及解决办法;实验表明,较其它常用评定方法,该法评定ATS静态测量得到的结果更接近理论值,不确定度变化小,评定动态测量得到结果更符合ATS动态特性且精确度高.     

基于Crystal Ball软件对测量不确定度的评定

本文首先介绍了测量不确定度的概念,接着阐述了测量不确定度在实验室检测过程中的作用,然后介绍了测量不确定度的方法和步骤,本文介绍了使用Crystal Ball利用蒙特卡罗方法在测量不确定度的应用的步骤,通过软件的使用可以解决在测试实际工作中评定测量不确定度遇到的困难。     

基于MATLAB的平面线轮廓度误差评定

为准确快速评定线轮廓度误差,提出了一种基于分割逼近法与MATLAB相结合的用于计算平面线轮廓度误差的新方法,该方法符合最小条件原理;它根据平面线轮廓度误差的定义建立了误差评定的数学模型,采用分割逼近法快速求取测点到理论曲线轮廓的最小距离,通过坐标变换实现被测轮廓与理论轮廓位置的匹配,消除因位置偏差引起的线轮廓度评定的不精确问题.阐述了平面线轮廓度误差评定的步骤;实验结果表明该方法能够快速获得较好的误差评定结果.     

基于MATLAB和VB的平面度、圆度、球度形状误差评定的软件设计

形状误差是实际形状相对其理想形状的偏差,关系着工件的质量,针对平面度、圆度、球度等不同的形状误差,先后出现了许多新的算法.采用计算简便、运算速度快、广泛应用于各种形状误差的评定的最小二乘法;运用MATLAB语言编写误差的计算程序,在Visual Basic环境下开发了软件系统的用户界面程序,同时编写VB与MATLAB之间的接口程序,完成这两种软件之间的调用.通过与现有最小区域法的计算结果相比较验证程序的正确性,便于在工程实际中推广应用.     

专用短程通信设备载波频率及最大发射功率测量不确定度分析

为使专用短程通信设备相关参数测量结果更加准确可靠,测量水平与质量得到提高,根据JJF1059.1-2012测量不确定度评定与表示,对测量不确定度评定的方法进行分析;以专用短程通信设备载波频率及最大发射功率的测量为实例,详述了误差来源分析、数学模型建立、不确定度分量合成、扩展不确定度计算等评定过程;通过本方法而得到的测量不确定度,对专用短程通信设备相关参数测量结果的质量有了比较可靠的保证,并可用于指导组建测试系统、配置测试设备、分析测试结果等。     

测量不确定度评定应基于误差理论

《测量不确定度指南》(GUM)因免用真值、不涉及误差等原因,曾导致一些学者将不确定度与误差对立起来,捋清测量不确定度评定与误差理论的关系,仍是当前值得论述的问题。本文从测量不确定度与真值和测量误差、测量不确定度评定方法与误差分类、测量不确定度评定与概率分布、合成不确定度与误差合成理论这几方面论述了二者间的重要关系,并根据误差理论发展情况,指出GUM应予扩展应用的若干问题。     

蒙特卡洛法在发动机推力测量不确定度评估中的应用

现行对发动机试验推力测量不确定度的评估一直采用GUM法,存在输入量和输出量概率分布假设以及非线性模型近似等问题,有一定的局限性;以发动机推力矢量测量为例,文中简述了压电式推力矢量测量的数学模型,运用GUM法对推力矢量参数的不确定度评估,同时分析了蒙特卡洛法的原理、具体评估过程和适用性,编制了软件,并将不确定度评估结果与GUM法评估结果进行对比;对比结果表明,在发动机试验推力矢量参数的不确定度评估过程中,蒙特卡洛法相比GUM法更为适用.     

A general approach for the machining quality evaluation of S-shaped specimen based on POS-SQP algorithm and Monte Carlo method

In S-shaped specimens which are frequently used to reflect the machining ability of machine tools, the surface error refers to the distance between the points on the actual machining surface to their relevant points on the design surface. The proper measurement of this error is crucial for evaluating the machining quality of S-shaped specimens. During the process of error measurement, improper registration between the measurement coordinate system and the design coordinate system, as well as neglected uncertainty remain the main obstacles for the quality evaluation of S-shaped specimens. This study proposes a general method for the high-precision machining quality evaluation of S-shaped specimens that overcomes both problems. By applying the non-uniform rational B-spline (NURBS) surface molding technology, the surface of S-shaped specimen was reconstructed. Based on the minimum area principle and the particle swarm optimization-sequential quadratic programming (POS-SQP) algorithm, a surface error model of S-shaped specimen was developed. This model minimizes the maximum distance of the transacted measurement points to the design surface. It can be used to obtain the optimal registration matrix of the measurement coordinate system, with minimal surface error of S-shaped specimen. Additional common algorithms were also adopted to search the optimal registration matrix for comparison. Accounting for the random characteristics of basic parameters and the nonlinearity of surface error model, an uncertainty model of the surface error of S-shaped specimen was established based on the Monte Carlo method. This could obtain the actual tolerance zone of the surface error, according to which, the allowable tolerance zone of the surface error was optimized and a defined evaluation result of machining quality of S-shaped specimen was obtained. Then, a general approach for the evaluation of the machining quality of S-shaped specimen was developed based on POS-SQP algorithm and Monte Carlo method. This approach was implemented in a case study though a series of experiments. The experimental results identified the proposed approach as effective in improving the measurement quality and the evaluation of the machining quality of S-shaped specimens can thus be performed within an allowable tolerance zone.     

可控结构半弹道式再入飞行器的跟踪及充满空间的模型集设计

由于再入过程中结构变化的未知以及流场等不确定因素的影响, 可变结构半弹道式再入飞行器(Semi-ballistic reentry vehicle, SBRV)的模式及其变化方式通常也是未知的. 本文在分析可控结构SBRV再入运动特征以及模式特征的基础上, 提出了充满模式空间的模型集, 新模型集根据Hicknell准则设计, 该模型集与Monte Carlo法生成的模型集相比不但具有更高的可信度和精度, 而且对机动的反应更灵敏. 理论分析和仿真结果证明了这种充满空间的模型集对于该机动跟踪问题的合理性与有效性.     

Error measures for fuzzy linear regression: Monte Carlo simulation approach

The focus of this study is to use Monte Carlo method in fuzzy linear regression. The purpose of the study is to figure out the appropriate error measures for the estimation of fuzzy linear regression model parameters with Monte Carlo method. Since model parameters are estimated without any mathematical programming or heavy fuzzy arithmetic operations in fuzzy linear regression with Monte Carlo method. In the literature, only two error measures (E₁ and E₂) are available for the estimation of fuzzy linear regression model parameters. Additionally, accuracy of available error measures under the Monte Carlo procedure has not been evaluated. In this article, mean square error, mean percentage error, mean absolute percentage error, and symmetric mean absolute percentage error are proposed for the estimation of fuzzy linear regression model parameters with Monte Carlo method. Moreover, estimation accuracies of existing and proposed error measures are explored. Error measures are compared to each other in terms of estimation accuracy; hence, this study demonstrates that the best error measures to estimate fuzzy linear regression model parameters with Monte Carlo method are proved to be E₁, E₂, and the mean square error. One the other hand, the worst one can be given as the mean percentage error. These results would be useful to enrich the studies that have already focused on fuzzy linear regression models.     

Numerical and visual evaluation of hydrological and environmental models using the Monte Carlo analysis toolbox

The detailed evaluation of mathematical models and the consideration of uncertainty in the modeling of hydrological and environmental systems are of increasing importance, and are sometimes even demanded by decision makers. At the same time, the growing complexity of models to represent real-world systems makes it more and more difficult to understand model behavior, sensitivities and uncertainties. The Monte Carlo Analysis Toolbox (MCAT) is a Matlab library of visual and numerical analysis tools for the evaluation of hydrological and environmental models. Input to the MCAT is the result of a Monte Carlo or population evolution based sampling of the parameter space of the model structure under investigation. The MCAT can be used off-line, i.e. it does not have to be connected to the evaluated model, and can thus be used for any model for which an appropriate sampling can be performed. The MCAT contains tools for the evaluation of performance, identifiability, sensitivity, predictive uncertainty and also allows for the testing of hypotheses with respect to the model structure used. In addition to research applications, the MCAT can be used as a teaching tool in courses that include the use of mathematical models.     

Mean field variational Bayesian inference for nonparametric regression with measurement error

A fast mean field variational Bayes (MFVB) approach to nonparametric regression when the predictors are subject to classical measurement error is investigated. It is shown that the use of such technology to the measurement error setting achieves reasonable accuracy. In tandem with the methodological development, a customized Markov chain Monte Carlo method is developed to facilitate the evaluation of accuracy of the MFVB method.     

Decision theoretic approach to real-time robust identification

A decision-theoretic approach to the estimation of unknown parameters from a linear discrete-time dynamic measurement model in the presence of disturbance uncertainty is considered. The unknown disturbance statistics are characterized by a certain class of distributions to which the real disturbance distribution is confined. Using game theory and the asymptotic estimation error covariance matrix as the criteria of how good an estimator is, the stochastic gradient-type algorithm is shown to be optimal in the min-max sense. Since the optimal solution is not tractable in practice, several suboptimal procedures are derived on the basis of suitable approximations. The convergence of the derived algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the algorithms.     

Estimating the uncertainty of modeled carbon sequestration: The GreenCert™ system

The GreenCert? system was developed to help farm and ranch owners to quantify, standardize, pool and market CO₂ emissions offset (sequestration) credits derived from improved rangeland or cropland management. It combines a user-friendly interface with the CENTURY biogeochemical model, a GIS database of soil and climate parameters, and a Monte Carlo-based uncertainty estimation methodology. This paper focuses on uncertainty treatment, discussing sources of error, parameter distributions, and the Monte Carlo randomization approach, culminating in a sensitivity analysis of model parameters.Idealized crop and grazing scenarios were used to evaluate the uncertainty of modeled soil organic carbon stocks and stock changes stemming from variability in site and management parameters. Normalized sensitivity coefficients and an integrated index for relative sensitivity of the model to the ensemble of the tested variables indicate that environmental factors are the most important in determining the actual size of the soil carbon stock, but that management is a much more important determinant of short- to medium-term carbon fluxes. GreenCert? uses the patented C-LOCK^® approach to efficiently limit uncertainty in the most critical phase of the modelling process by maximizing the use of available management information, and quantifies the remaining uncertainty in an unbiased fashion using Monte Carlo parameter randomization.