scholarly journals Rejection sampling for Bayesian uncertainty evaluation using the Monte Carlo techniques of GUM-S1

Metrologia ◽  
2021 ◽  
Author(s):  
Manuel Marschall ◽  
Gerd Wuebbeler ◽  
Clemens Elster
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Prior Information ◽  
Uncertainty Evaluation ◽  
Rejection Sampling ◽  
Nonlinear Functions ◽  
Software Support ◽  
Gaussian Distributions ◽  
Monte Carlo Techniques ◽  
Non Gaussian

Abstract Supplement 1 to the GUM (GUM-S1) extends the GUM uncertainty framework to nonlinear functions and non-Gaussian distributions. For this purpose, it employs a Monte Carlo method that yields a probability density function for the measurand. This Monte Carlo method has been successfully applied in numerous applications throughout metrology. However, considerable criticism has been raised against the type A uncertainty evaluation of GUM-S1. Most of the criticism could be addressed by including prior information about the measurand which, however, is beyond the scope of GUM-S1. We propose an alternative Monte Carlo method that will allow prior information about the measurand to be included. The proposed method is based on a Bayesian uncertainty evaluation and applies a simple rejection sampling approach using the Monte Carlo techniques of GUM-S1. The range of applicability of the approach is explored theoretically and in terms of examples. The results are promising, leading us to conclude that many metrological applications could benefit from this approach. Software support is provided to ease its implementation.

Evaluation of Measurement Uncertainties for Pneumatic Multi-Hole Probes Using a Monte Carlo Method

2016 ◽  
Author(s):  
Magnus Hölle ◽  
Christian Bartsch ◽  
Peter Jeschke
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Compressible Flows ◽  
Uncertainty Evaluation ◽  
Calibration Data ◽  
Input Quantity ◽  
Parameter Evaluation ◽  
Polynomial Curve ◽  
Different Types ◽  
Measurement Uncertainties

The subject of this paper is a statistical method for the accurate evaluation of the uncertainties for pneumatic multi-hole probe measurements. The method can be applied to different types of evaluation algorithms and is suitable for steady flowfield measurements in compressible flows. The evaluation of uncertainties is performed by a Monte Carlo method (MCM), which is based on the statistical law of large numbers. Each input quantity, including calibration and measurement quantities, is randomly varied on the basis of its corresponding probability density function (PDF) and propagated through the deterministic parameter evaluation algorithm. Other than linear Taylor series based uncertainty evaluation methods, MCM features several advantages. On the one hand, MCM does not suffer from lower-order expansion errors and can therefore reproduce nonlinearity effects. On the other hand, different types of PDFs can be assumed for the input quantities and the corresponding coverage intervals can be calculated for any coverage probability. To demonstrate the uncertainty evaluation, a calibration and subsequent measurements in the wake of an airfoil with a 5-hole probe are performed. MCM is applied to different parameter evaluation algorithms. It is found that the MCM approach presented cannot be applied to polynomial curve fits, if the differences between the calibration data and the polynomial curve fits are of the same order of magnitude compared to the calibration uncertainty. Since this method has not yet been used for the evaluation of measurement uncertainties for pneumatic multi-hole probes, the aim of the paper is to present a highly accurate and easy-to-implement uncertainty evaluation method.

A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system

Metrologia ◽  
2007 ◽  
Vol 44 (5) ◽  
pp. 319-326 ◽  
Author(s):  
T J Esward ◽  
A de Ginestous ◽  
P M Harris ◽  
I D Hill ◽  
S G R Salim ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Distributed Computing ◽  
Computing System ◽  
Uncertainty Evaluation

scholarly journals Monte Carlo method to machine tool uncertainty evaluation

2017 ◽  
Vol 13 ◽  
pp. 585-592 ◽  
Author(s):  
S. Aguado ◽  
P. Pérez ◽  
J.A. Albajez ◽  
J. Velázquez ◽  
J. Santolaria
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Machine Tool ◽  
Uncertainty Evaluation

21305 Uncertainty Evaluation Method for Flatness Using Monte Carlo Method with Pseudo Flat

2010 ◽  
Vol 2010.16 (0) ◽  
pp. 447-448
Author(s):  
Shinichi Naito ◽  
Zenichi Miyagi ◽  
Youichi Bitou ◽  
Kensei Ehara
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Evaluation Method ◽  
Uncertainty Evaluation

Uncertainty Evaluation in Distance Measurement by CMM Based on Monte Carlo Method

2013 ◽  
Vol 684 ◽  
pp. 429-433 ◽  
Author(s):  
Hong Li Li ◽  
Xiao Huai Chen ◽  
Hong Tao Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Evaluation Process ◽  
Mathematic Model ◽  
Distance Measurement ◽  
Uncertainty Evaluation ◽  
Measured Quantity ◽  
Complete Uncertainty ◽  
End Distance ◽  
Influence Measurement

There is presented a complete uncertainty evaluation process of end distance measurement by CMM. To begin with, the major sources of uncertainty, which would influence measurement result, are found out after analyzing, then, the general mathematic model of end distance measurement is established. Furthermore, Monte Carlo method (MCM) is used, and the uncertainty of the measured quantity is obtained. The complete results are given out, so the value of CMM is enhanced. Moreover, seen from the evaluation example, the results of uncertainty evaluation obtained from MCM method and from GUM method are compared, the comparison result indicates that the mathematic model is feasible, and using MCM method to evaluate uncertainty is easy and efficient, having practical value.

Uncertainty Evaluation by Monte Carlo Method

MAPAN ◽  
2019 ◽  
Vol 34 (3) ◽  
pp. 295-298
Author(s):  
P. Rachakonda ◽  
V. Ramnath ◽  
V. S. Pandey
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Uncertainty Evaluation

scholarly journals Uncertainty Analysis of a Test Bed for Calibrating Voltage Transformers vs. Temperature

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4472 ◽  
Author(s):  
Mingotti ◽  
Peretto ◽  
Tinarelli ◽  
Ghaderi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Uncertainty Analysis ◽  
Random Effects ◽  
Evaluation Method ◽  
Uncertainty Evaluation ◽  
Test Bed ◽  
Uncertainty Sources ◽  
The Monte Carlo Method

The paper addresses the evaluation of the uncertainty sources of a test bed system for calibrating voltage transformers vs. temperature. In particular, the Monte Carlo method has been applied in order to evaluate the effects of the uncertainty sources in two different conditions: by using the nominal accuracy specifications of the elements which compose the setup, or by exploiting the results of their metrological characterization. In addition, the influence of random effects on the system accuracy has been quantified and evaluated. From the results, it emerges that the choice of the uncertainty evaluation method affects the overall study. As a matter of fact, the use of a metrological characterization or of accuracy specifications provided by the manufacturers provides respectively an accuracy of 0.1 and 0.5 for the overall measurement setup.

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