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.     

基于多项式混沌展开的非线性系统试验不确定度评定方法

非线性系统试验结果的不确定性分析表征了试验结果的分散性。提出一种基于多项式混沌展开的非线性系统试验不确定度评定方法,通过Ishigami测试模型将该评定方法与国家标准《用蒙特卡罗法评定测量不确定度》中规定的方法进行了比较,结果表明,提出的方法拥有更高的精度及效率。以座椅安全带固定点试验为例,采用多项式混沌展开法建立试验的代理模型,实现了安全带固定点试验的测量不确定度的评定。针对样本数不足的问题,分别采用改进的双曲线截断技术以及基于多项式混沌展开模型的Sobol灵敏度分析对模型简化,结果表明,提出的两种简化方法均能明显降低模型对样本的需求。研究结果表明,提出的多项式混沌展开及其简化方法可广泛用于各种产品试验的不确定度评定中。     

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。     

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.     

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.     

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.     

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.     

国标高效液相色谱法测定黄曲霉毒素的不确定度评定

依据GB/T18979-2003《食品中黄曲霉毒素的测定-免疫亲和层洗净化高效液相色谱法和荧光光度法》中的HPLC法,对花生中黄曲霉毒素测量的不确定度进行分析评定,对样品的制备、标准溶液的配制及检测等影响因素进行分析,确定各分量的分布类型,并进行分步计算和整体合成。     

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.     

Estimating uncertainty of measurements for cavitation detection in a centrifugal pump

Measurement of noise and vibration signal in audible frequency range to detect cavitation in centrifugal pumps is rather unknown technique. There were already some studies performed on this technique and they showed quite good results. Due to many factors that influence the quality of the measurement, an uncertainty analysis should be performed. This paper deals with estimation of a measurement uncertainty for different kinds of measurement ways to detect the cavitation in a centrifugal pump with noise and vibration signal in audible frequency range from 20 Hz to 20 kHz. Especially the measurement uncertainties for cavitation detection in broad frequency range and at a discrete frequency were analyzed. Results showed that this technique is reliable despite many possible influences on uncertainty.     

Estimation of the measurement uncertainty in the anisotropy test

The evaluation of the sheet metal drawability in mechanical shaping processes depends on a large number of analysis, among which the anisotropy evaluation. Nowadays, there is no Brazilian test laboratory accredited by the Metrology, Quality and Technology National Institute (INMETRO) to perform this analysis. So, the object of the present work is to establish a procedure for the estimation of the measurement uncertainty in the plastic anisotropy ratio of sheet metals, in accordance to the Guide to the Expression of Uncertainty in Measurement (GUM), aiming at the accreditation of this test in the Physical Metallurgy Laboratory. As results, we present the calculations performed and the uncertainty form proposed, and an analysis of which sources contributed the most for the uncertainty in the execution of a test. Finally, we propose improvement actions aiming at the reduction of the calculated uncertainty and the adequacy of the Measurement System for the desired application.