The problem of analyzing errors in measuring systems

Summary In the operation of a linear measuring system with its elements subjected to various random external disturbances which produce in the elements additional static errors, transmitted to the output of the system together with the basic errors of the elements, a total static error is produced at the output. The latter error is the one which determines the accuracy of the measuring system under given conditions.If in experimental work the required variable is measured several times by means of a measuring system, whose elements are subjected to various random external disturbances, a statistical analysis of the measurement results may produce a certain compensation of the static measurement errors of this variable.     

一种ABS齿圈参数检测系统误差校正方法研究

为了纠正ABS齿圈参数检测系统装夹机构旋转时轴承晃动等因素带来的误差,运用最小二乘法曲线拟合原理及空间三维直角坐标系仿射变换方法进行了误差校正。首先,对该方法进行理论分析,推导出系统坐标变换矩阵公式;其次,根据误差校正方法建立了数学模型,推导出变换后坐标计算公式,将测量坐标系中各参数代入变换公式,并计算出轮廓数据变换后坐标;最后,运用Matlab对模型进行了仿真实验。实验结果表明:校正后参数值与实际参数值之间偏差小于1 μm。解决了实际测量过程中各种误差带来的影响,提高了检测系统的测量精度。     

A methodology for determining complex permittivity of construction materials based on transmission-only coherent,wide-bandwidth free-space measurements

An integrated methodology for determining the unique combination of complex permittivity based on measured transmission coefficient and time difference of arrival (TDOA) information in free-space measurements is proposed. The methodology consists of an estimation procedure of the real part of complex permittivity based on TDOA, and a root-searching procedure based on parametric system identification (SI) together with an error sum of squares (SSE) criterion. Generally, non-unique combinations of dielectric constant and loss factor are encountered when lossy or low-loss materials are measured and the proposed methodology is aimed at the determination of unique combinations of dielectric constant and loss factor for such materials. The proposed methodology is validated by measurements of several materials with known dielectric properties. The estimated complex permittivity values for Teflon, Lexan, Bakelite, and concrete are in good agreement with those reported in the literature. The method has potential for in-situ measurement of dielectric properties for construction materials. Applicability and limitations of the methodology are discussed.     

多边法位姿测量系统中跟踪方式对测量精度的影响研究

为了精确测量大尺寸位姿,建立了一种由7台激光跟踪干涉仪组成的大尺寸位姿测量装置。根据测量各反射镜的激光跟踪干涉仪数量的不同,采用322和331两种跟踪方式对位姿测量精度的影响进行仿真实验,从而发现被测点位置与基站构成平面的距离相关,由坐标解算公式推导被测点坐标值与测量基站之间的相对位置与测量误差间的误差模型,通过分析x、y、z 方向上误差对距离变化的敏感程度,发现z方向距离变化引起的误差最为敏感。当被测点与测量基站的距离由1300.8mm减小到0mm时,测量误差由2.2μm增大到2626.1μm。实际姿态测量结果表明:当采用一种跟踪方式时可以避免被测点与测站点平面过近,有利于提高系统测量精度,所提出的误差模型可为多边法位姿测量系统的优化布局提供一种量化的理论分析方法。     

Measurement System Analysis: The Usual Metrics Can Be Noninformative

It is important to be able to demonstrate that a measurement process is adequate for the application. Measurement system analysis is a methodology for doing this. The approach is to separate the total variation of a set of measurements into components. The variation among devices being tested is separated from the measurement error. The total measurement error is often separated into several components. Two basic types of metrics utilize the variance component estimates to conclude whether the measurement process is adequate or not. One type of metric compares the measurement error to the variation among tested devices or, equivalently, to the total variation. The other compares the measurement error to the width of the test limits or the product specifications. This paper describes a situation that is becoming increasingly common in testing consumer electronic devices. The situation, called “alignment,” is not actually a “test” in the usual sense, and presents a challenge in using the standard metrics to determine the adequacy of a measurement process. The problem is described and several potential solutions are presented although an ideal solution is yet to be identified.     

A novel method of determining the permittivity of liquids

A novel method to measure the permittivity of liquids is used in a microwave gauging system, developed for the detection of liquid levels in tanks. The system is described as a frequency stepped continuous wave (FSCW) radar for precision liquid level detection. Usually a radar system is only employed to find the surface of the liquid. With the microwave measurement system described here, one can detect a second level that may be the tank bottom or an impurity level, for example. To monitor the permittivity of the liquid with the same measurement system, a novel algorithm is derived. Measured uncertainties of ±0.2 mm have been achieved for the multilevel range detection performed in the frequency range from 2 to 3 GHz. From these measured data, the error of the calculated permittivity was about 2%. By using this technique to determine the permittivity of the liquid, it is possible to reduce the complexity of the measurement system     

Measurement System Analysis in a Production Environment with Multiple Test Parameters

The purpose of measurement system analysis (MSA) is to separate the variation among devices being measured from the error in the measurement system. The total measurement system error can be further decomposed into variance components associated with the measurement equipment and repeatability. An analysis of variance approach based on a variance component model is used to model the variables of interest. Once estimated, the variance components are used to compute various metrics, which quantify the adequacy of the measurement system for the application in which it is used. Confidence intervals computed on the variance components and metrics indicate the amount of precision in the estimates. The MSA is typically conducted on a single measurement variable with a single measurement instance. The aim of this paper is to extend the univariate single-instance case to a common manufacturing test scenario where multiple parameters are tested on each device with a sequence of tests, which may include retest and test and repair steps. The methods presented are illustrated with examples from an industrial application.     

座底式长基线水声跟踪系统校阵方法研究

为了解决座底式长基线水声跟踪系统的高效校阵问题,结合工程项目实际提出一种智能化分组并行校阵方法。该方法利用水下基阵布阵施工时获得的水声及差分全球定位系统(Differential Global Positioning System,DGPS)测量数据为基准,在校阵试验中采用多个水下基阵分组并行校阵的快捷方式,根据自动反馈的测量数据进行校阵误差收敛测量,当满足事先设定的校准误差后,获得水下基阵的精确位置信息,同时完成多个水下基阵的阵型校准。最后,在某水域采用跑船试验的方式进行验证。长基线系统测量的船只航行轨迹与DGPS轨迹重合性好,证明该方法具有智能化程度高、测量精度高、测阵效率及经济性好等优点,具有较高的军事及民用价值。     

光纤直流大电流传感器非线性机理及校准技术

非线性误差是干涉型数字闭环光纤电流传感器超大电流测量的主要误差源之一。借助琼斯矩阵方法,推导了光纤1/4波片不理想条件下传感器输出与被测电流的理论关系,确定了1/4波片的方位角和相位延迟误差是造成光纤电流传感器超大电流测量非线性的主要原因之一。仿真结果表明:在5~300kA范围内,方位角误差小于4.53°,相位延迟误差小于9.05°,可保证传感器的测量误差小于0.2%。搭建了光纤直流大电流传感器校准系统,提出了分段线性插值补偿方法校准光纤电流传感器的非线性误差。测试结果表明:非线性补偿后传感器的测量误差由最大的0.6%降低到0.1%以内,证明了非线性补偿方法的有效性。     

基于三坐标测量机的滚珠丝杠副螺距误差测量

滚珠丝杠副螺距误差测量采用比较测量原理.结合三坐标测量机重复定位精度高、适合测量复杂型面特点,找出了一种在三坐标测量机上测量滚珠丝杠副螺距误差的方法和理论依据,总结了测量中的注意事项和这种测量方法的局限性.     

汽轮机变工况下调节级压力预测模型及应用

为监视汽轮机通流部分的健康状况和进行故障早期诊断,以汽轮机变工况计算为理论基础,基于弗留格尔公式和Weierstrass逼近定理,建立了调节级压力的多元回归模型。根据某660MW间接空冷机组大修后的运行数据对模型进行回归分析和验证,结果表明：模型具有很高的拟合度,自变量对因变量影响显著;稳态工况时,预测结果与实测值趋势一致,相对误差约为1.2%,实现了变工况下调节级压力软测量。将模型应用于电厂分布式控制系统中,建立了汽轮机通流部分故障的预警系统。     

Impact and Assessment of Measurement Systems that Meet the 4:1 Rule

This article considers the impact of a measurement system that meets the 4:1 rule. Probabilities of accepting a bad part and rejecting a good part are evaluated. A simulation study calculates the increased estimates of the population standard deviation when the measurement error is ignored, where both non‐trending and trending populations are considered. Also, the impact of sample size is evaluated on estimates and upper confidence bounds of the measurement system standard deviation that are used to assess the 4:1 rule capability; both measurement systems from a single and multiple sources of variation are explored. Copyright © 2014 John Wiley & Sons, Ltd.     

Quality assessment of biometric systems: a comprehensive perspective based on accuracy and performance measurement

Despite the efforts of the international biometric community, the measurement of the accuracy of a biometric system is far from being completely investigated and, eventually, standardized. This paper presents a critical analysis of the accuracy and performance measurement of a biometric system. Current approaches to the problem and procedural error have been described and criticized. Finally, a methodology for the measurement of the accuracy of biometric systems with nonsymmetric matching function will be proposed and discussed.     

Performance characteristics of a composite multivariate quality control system.

We present the results of an evaluation of the performance characteristics of a composite multivariate quality control (CMQC) system that incorporates quality control rules for univariate, multivariate, and correlation conditions. The CMQC system evaluated is designed to help analysts detect unacceptable trends and systematic error in one or more variables, unacceptable random error in one or more variables, and unacceptable changes in the correlation structure of any pair of variables. It is also designed to be tolerant of missing data, to allow analysts to reject as few as one or as many as all variables in a run, and to provide analysts with control statistics and graphics that logically relate to sources of analytical error. We show that the various components of the CMQC system have adequate statistical power to detect systematic errors, random errors, and correlation changes under the conditions likely to be encountered with multivariate analytical measurement systems: (1) a single variable with increased systematic or random error; (2) all variables or a subgroup of variables affected by a common problem that increases systematic or random error; and (3) missing data for one or more variables in a run. We also show that the power of the multivariate component of the CMQC system to detect systematic and random errors is higher than the power of an alternative multivariate test criterion.     

Optimization of instrument calibration

An optimal (minimum-error) instruments calibration technique based on the method of least squares and on correction with comparable argument and function errors is described. Expressions are derived for calculating linear regression coefficients and calibration errors. The process of calibration when the instrument signals are nonlinear functions of the measured parameter and when the measurement error is different at different points of the measurement range is discussed. Calibration of an instrument operating in an automatic control system for maximum factory benefit is cited as an example.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 26–28, October, 1993.     

融合加权SVD改进算法的工业机器人运动学标定

针对环境或人为因素引入的测量粗差对测量坐标系和机器人基坐标系的转换存在较大影响的问题,对奇异值分解(SVD)算法进行了改进,并将其应用于机器人运动学标定中。以ABB-IRB2600型机器人为研究对象,建立修正型D-H(MD-H)运动学模型和误差模型;通过激光跟踪仪测量得到机器人末端靶球位置坐标,在SVD算法中,根据补偿前位置误差大小对测量数据重新分配权重,转换测量坐标系和机器人基坐标系;使用Levenberg-Marquart(L-M)算法进行了误差参数辨识,并在Matlab中对机器人25个运动学参数进行了仿真补偿。仿真和实验结果表明,加权SVD算法稳定性更优,能够减小测量粗差影响,经标定后机器人的平均绝对误差降低了65.10%,均方根误差降低了65.85%,其绝对定位精度得到了明显提高。     

A variable selection procedure for X-ray diffraction phase analysis

The X-ray diffraction method has been widely used for qualitative and quantitative phase abundance analysis of crystalline materials. We propose the use of partial least squares when building the calibration model for a quantitative phase analysis based on X-ray diffraction spectra. We also propose a variable selection procedure to reduce the measurement points in terms of angles as an alternative to using the whole pattern. The proposed method is based on the variable importance in projection derived from the partial least squares and it considers some practical issues regarding the angle measurement. The method was particularly applied to the simultaneous determination of weight fractions of some iron oxides. It was found that the number of measurement points can be reduced to 30 percent of the total number of points with a small sacrifice in prediction error.     

Validation and error estimation of computational models

This paper develops a Bayesian methodology for assessing the confidence in model prediction by comparing the model output with experimental data when both are stochastic. The prior distribution of the response is first computed, which is then updated based on experimental observation using Bayesian analysis to compute a validation metric. A model error estimation methodology is then developed to include model form error, discretization error, stochastic analysis error (UQ error), input data error and output measurement error. Sensitivity of the validation metric to various error components and model parameters is discussed. A numerical example is presented to illustrate the proposed methodology.     

连续变孔径法单模光纤模场直径（MFD）测量的数据处理

分析了连续变孔径法单模光纤秆径测量的数据处理方法,误差源及其对测量结果的影响。计算结果表明,用分段多项式最小二乘法拟合计算ＭＦＤ,可以取得满意的计算精度。文中给出了测量系统总的误差估计。     

基于线激光传感器的工件尺寸测量系统的误差补偿方法

提出了一种基于线激光传感器的工件尺寸测量系统的误差补偿方法,利用坐标系投影和图像处理技术进行误差补偿。设定传感器坐标系OM-XMYMZM和设备坐标系O-XYZ,分析坐标轴夹角φ、δ、γ对工件尺寸坐标值X、Y、Z的误差,建立了基于φ、δ、γ在XOY、YOZ、XOZ平面上的投影角α、β、θ的误差补偿模型。利用图像处理技术测得α、β、θ,计算经过误差补偿的工件尺寸坐标值X′、Y′、Z′。对尺寸100mm×100mm×10mm的长方体工件进行测量实验,分别测量了长度、宽度、圆心距、圆直径、圆线距、台阶高度。测量结果表明:经误差补偿后的工件尺寸测量误差在40μm以内,优于未补偿前的520μm;均方根误差低于40μm,优于未补偿前的580μm。其中,圆心距误差补偿效果最显著,测量误差减小了560μm;圆直径误差补偿效果最不明显,测量误差减小了10μm。