Measurement uncertainty evaluation of optical multi-sensor-measurements

Optical coordinate metrology facilitates the set-up of in-line applications for quality inspection in shop floor for a variety of products. Yet, for situations with high requirements it is not possible to fulfill all demands by devices based on a single measurement principle. To enable high measurement rates and as well as precise and contact-less data acquisition, a combination of subsystems with different principles and properties has to be implemented. To assure the fitness of an optical multi-sensor-measurement system combining a shadow system and a light-section system for the in-line inspection of concave extruding profiles, an experimental measurement uncertainty analysis has been performed. To this aim, a prototype is set-up and the effect of typical environmental influences like dust, object’s vibrations, the illuminations’ pitch error or extraneous light, is examined. Subsequently, the measurement system is evaluated under shop floor conditions and the results are analyzed.     

Standard uncertainty evaluation in image-based measurements

The present paper is devoted to address the use and evaluation of measures coming from digital images in an industrial context. Starting from a discussion about the importance and role of this class of measurements, the authors show the architecture of an image-based measurement system and introduce the important issue of the related uncertainty then coming to investigate models and methods for evaluating it.

After presenting an original method for evaluating the uncertainty of images deriving measurements, some examples of practical interest are introduced and evaluated leading the reader to the understanding of related problems. The paper is also enriched by the presence of an introductive section discussing a bibliography of the state of the art in the field.     

A simple numerical procedure for estimating nonlinear uncertainty propagation

Accurately determining the effect of the propagation of uncertainty in nonlinear applications can be awkward and difficult. The Monte Carlo approach requires statistically significant numbers of function evaluations (typically 10⁵ or more) and analytical methods are intractable for all but the simplest cases. This paper derives and demonstrates a method to estimate the propagation of uncertainty in nonlinear cases by representing the function in a piecewise fashion with straight line segments. The probability density function of the result can be calculated from the transformation of the line segments. The mean and confidence intervals of the result can then be calculated from the probability density function. For the special case of a normal distribution in the independent variable, calculation of the mean and confidence intervals requires evaluation of only the error function (erf). A simple example is presented to demonstrate the technique. Variations on the basic approach are presented and discussed.     

An MCMC algorithm based on GUM Supplement 1 for uncertainty evaluation

This paper describes a simple Markov chain Monte Carlo algorithm for evaluating measurement uncertainty according to Bayesian principles. The algorithm has two phases, the first coinciding with the Monte Carlo method described in GUM Supplement 1 (GUMS1), the second a simple Metropolis–Hastings algorithm. The second phase can be regarded as a post-processing add-on to the GUMS1 calculation and can be used whenever a GUMS1 approach is adopted. The algorithm allows users freedom to choose their preferred prior distribution for the measurand, rather than that implicitly assigned in the GUMS1 approach, thereby avoiding some of the problems that can arise when applying GUMS1 to certain types of measurement model. The post-processing can be implemented in a few lines of software, so that many of the practical difficulties in implementing Bayesian approaches to measurement uncertainty evaluation are largely removed.     

Comparison of GUM and Monte Carlo methods for evaluating measurement uncertainty of perspiration measurement systems

Measurement uncertainty is an important parameter to express measurement results including means and reliability. The uncertainty analysis of the biomedical measurement system needs to be established. A perspiration measurement system composed of several sensors was developed. We aim to estimate the measurement uncertainty of this system with several uncertainty sources, including airflow rate, air density, and inlet and outlet absolute humidity. Measurement uncertainty was evaluated and compared by the Guide to the expression of the uncertainty in measurement (GUM) method and Monte Carlo simulation. The standard uncertainty for the perspiration measurement system was 6.81 × 10⁻⁶ kg/s and the uncertainty percentage <10%. The major source of the uncertainty was airflow rate, and inlet and outlet absolute humidity. The Monte Carlo simulation could be executed easily with available spreadsheet software programs of the Microsoft Excel. GUM and Monte Carlo simulation did not differ in measurement uncertainty with precision to two decimal places. However, the sensitivity coefficient derived by GUM provided useful information to improve measurement performance, which was not evaluated with the Monte Carlo simulation method.     

Expression of uncertainty in fuzzy scales based measurements

Fuzzy scales were introduced as a transition between weak scales and strong scales. Preceding studies on fuzzy scales considered only ideal exact measurement without any consideration of uncertainty. The goal of this paper is to present a general approach for the management of uncertainty within the context of fuzzy scale based measurements. After a short reminder on fuzzy scales, a method to define a probability density function or a possibility function on indications given by a fuzzy scale based measurement is exposed. Finally, a method based on the evidence theory is applied to build simultaneously a probability density function and an associated possibility function.     

Using historical results obtained in the tensile tests for Type A evaluation of uncertainty

The specification of mechanical properties is essential for adequate choice of material, as well as for design and manufacturing of components and products. The main limitations in estimating uncertainty in testing are related to specimens destruction, sample size and existence of a wide range of influences quantities that are hard to quantify. This paper shows that it is possible to make use of historical data to minimize the effects of these limitations. A case study applied to the tensile test is presented, showing that Type A evaluation of uncertainty obtained from multiple homogeneous samples is more appropriate for the estimation of measurement uncertainty. And it is also demonstrated that the application of strength standard deviation has higher representativeness than the use of diameter and force standard deviations separately.     

Evaluation of measurement uncertainty using mixed distribution for conducted emission measurements

For evaluation of measurement uncertainty for conducted emission measurements, we propose a new model which uses mixed distribution. Namely, evaluation of probability density function (PDF) for the measurand has been done using a Monte Carlo method and a modified least-squares method. As the Monte Carlo method required numerical calculation of approximate PDF values, pseudorandom number generator (PRNG) was developed for these requirements. For illustration, this work presents mixed distributions of two normal distributions, normal and rectangular distributions, and normal and also triangular distributions in case of conducted emission measurements. The results obtained by the Monte Carlo method and the modified least-squares method are compared to the corresponding results when applying the standard Guide to the Expression of Uncertainty in Measurement (GUM) procedure.     

微波小功率标准装置校准结果的测量不确定度评定

本文介绍了微波小功率标准装置及其校准结果的测量不确定度评定方法,在不同频段详细评定了校准结果的测量不确定度。     

Leap motion controller three dimensional verification and polynomial correction

We propose a leap motion controller (LMC) dimensional verification based on ISO 10360-2:2009 with a coordinated measuring machine (CMM) as the reference framework. A pointer device comprising a thin aluminum cylinder was used to simulate a human finger. This was mounted on the spindle of the CMM to mark known positions over the LMC workspace. Polynomial tendency line corrections were applied to reduce the error in the LMC and CMM framework alignment. One dimension verification results were less than 0.1 mm in the X and Z axes, whereas the Y axis produced unsuitable results. The mean error was 9.6 mm in three-dimensional (3D) verification. Our findings demonstrate the difference between manufacturer quoted accuracy (0.01 mm) to that practically obtainable when the pointer was placed in a known position. LMC needs to add tracking models and position error compensation in applications requiring high accuracy, such as industrial processes or surgical procedure simulations.     

Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation

Evaluating the measurement uncertainty for gears with analytical or experimental methods is usually very time- and cost-consuming. In this paper we therefore present a Monte Carlo based method for evaluating the measurement uncertainty of gear measurements on gear measuring instruments, the VCMM-Gear, which is based on the method of the VCMM for coordinate measuring machines. Necessary extensions of the mathematical model of the measurement process in order to consider the significant uncertainty influences from rotary tables, workpiece clamping and scanning are described. Additionally the statistical reliability of the evaluated measurement uncertainty and the consideration of systematic error contributions to the measurement uncertainty are discussed. Finally the results of some first verification measurements are presented, giving a reliable impression of the capability and suitability of the VCMM-Gear.     

Propagation of uncertainty in a discrete Fourier transform algorithm

The problem of evaluating the uncertainty that characterises discrete Fourier transform output data is dealt with, using a method based on a ‘white box’ theoretical approach. The main sources of uncertainty (quantization, time jitter, microprocessor finite wordlength) are analysed obtaining equations useful to evaluate the uncertainty in both module and phase output values, for any hardware configuration and for any algorithm operating condition. The theoretical results, verified by both simulation and experimental tests, can be particularly useful for any designer and user of DFT-based instruments, since they allow the measurement configuration to be optimised with respect to the final uncertainty.     

新一代GPS测量不确定度与管理分析

在新一代产品几何技术规范(Next Generation Geometrical Product Specification and Verification,NGGPS)不确定理论基础上,分析各种不确定度之间的关系,重点讨论不确定度管理(Frocedure for Uncertainty Management,PUMA)测量不确定度管理程序所涉及的贡献因素、评定模型和评定关系等关键环节.设计不确定度管理程序,实现贡献因素分析、不确定度自动计算和系统评价,为实现不确定度评定管理的规范统一奠定基础.     

Monte Carlo evaluation of periodic error uncertainty

This paper presents a single analytical expression for the displacement recorded using a polarization-coded, heterodyne interferometer in terms of the various uncertainty contributors, including periodic error and other phase nonlinearities, Abbe error, cosine error, deadpath error, environmental error, interferometer thermal effects, and wavelength stability. The displacement equation is based on the periodic error expression reported by Cosijns et al. Monte Carlo simulation is applied to determine the first and second order periodic error uncertainty. The Monte Carlo simulation is then extended to include the other uncertainty contributors included in the analytical displacement equation.     

The resolution of analogue measuring devices and its associated uncertainty: An investigation with practical recommendations

Despite the popularity of the analogue measuring devices, there is no recognized reference provided comprehensive guidelines for determining their resolution and its associated uncertainty. For filling this gap, this article is introduced as an attempt to explore and investigate all the available works related to this issue. The new terminology “evident space”, “evident resolution”, and “conjunction” were proposed to set a common reference. Two different techniques for determining the analogue resolution were presented and discussed. Several numerical examples were also presented to show different analogue indications and their interpretations. Moreover, reasonable recommendations for determining the resolution uncertainty were suggested depending on the case.     

Measurement uncertainty of adaptive Chirp-z transform

In this paper analysis of measurement uncertainty of Adaptive Chirp-z transform (ACT) algorithm for power frequency measurement is presented. ACT is a new algorithm developed for real time monitoring of power frequency. Every element (hardware and software) of measurement chain is contributing to the total measurement uncertainty. The analysis of passive voltage dividers, analog-to-digital converters, numeric algorithms and processors (word length and type of arithmetic) are also presented. Estimated values of each contributing part of measurement chain are calculated to the final expression of measurement uncertainty.     

Generalized expressions of second and third order for the evaluation of standard measurement uncertainty

The Guide to the Expression of Uncertainty in Measurement (GUM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the measurement function is strongly non-linear the use of this linear approximation may be inadequate and therefore higher order terms from the Taylor series cannot be neglected. The present paper aims to derive generalized expressions of second and third order for the evaluation of the estimate of a measurand and its associated standard uncertainty. A case study is given to illustrate an application of the proposed methods and the results obtained with the GUM method are compared to the corresponding ones when applying the method proposed in GUM Supplement 1.     

Modified uncertainty estimation of antenna factor measurement by standard site method

The standard site method was used to measure antenna factor. Based on calculation of antenna factor uncertainty, ways of more precise estimation of uncertainty, leading to uncertainty reduction, are presented. Using uncertainty standards together with known approaches to radiated emission measurement uncertainty calculation, a model of antenna factor measurement and an equation for calculation of its uncertainty were derived. Possible steps to reduce resultant measurement uncertainty are described, including an analysis of correlation, and acknowledgment of frequency dependence. The uncertainty was calculated in 25 frequency points in the range from 30 MHz to 1000 MHz. Furthermore, various calculations of uncertainty are executed to examine the suggested effects on the uncertainty value.