A two-stage procedure for determining the number of trials in the application of a Monte Carlo method for uncertainty evaluation

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.

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

Metrologia ◽

10.1088/0026-1394/44/5/008 ◽

2007 ◽

Vol 44 (5) ◽

pp. 319-326 ◽

Cited By ~ 19

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

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Monte Carlo Optimization of Two-Stage Cascade R134A Refrigeration System With Flash Chamber

Volume 3: 28th Computers and Information in Engineering Conference, Parts A and B ◽

10.1115/detc2008-49063 ◽

2008 ◽

Author(s):

Yousef M. Abdel-Rahim

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Pressure Ratio ◽

Volume Ratio ◽

Heat Rate ◽

Cycle Performance ◽

Specific Work ◽

Refrigeration System ◽

Two Stage ◽

Monte Carlo Optimization

Present paper studies the optimal characteristics of the two-stage cascade R134A refrigeration system with flash and mixing chambers over its operating ranges of all cycle controlling parameters. The COP, total heat rate in Qin, total work rate in Win and second law efficiency ηII are used as cycle performance parameters. Compared to the practically-limited other rate-based optimization methods and to other experimentally-optimized specific cases of cycle parameters, the application of Monte Carlo method has proved to be very effective for optimizing the cycle performance in its global sense over all cycle controlling parameters. Correlations relating performance and cycle controlling parameters are presented and discussed. Study shows that COP of the cycle can reach a value of 8 at intermediate pressure P2 of about 200 kPa, and a maximum value of 9.92 at about 370 kPa and 720 kPa, beyond which COP goes as low as 4.2. P2 alone has no significant effect on Qin, Win and ηII unless values of other controlling parameters are specified. Values of Qin, Win and ηII can reach as high as 94 kW, 23 kW and 0.85 and as low as 6.8 kW, 1.1 kW and 0.57 respectively depending on other cycle parameters. Neither pressure ratio nor volume ratio of the HP compressor has any effect on Qin, Win or ηII. However, the ratio of inlet to exit temperatures of the condenser has the greatest effect on both ηII and the volumetric specific work of the HP compressor, which is about double the value of the volumetric specific work of the LP compressor. Study shows an almost linear relationship between the two mass flow rates in the upper and lower loops of the cycle, where its value in the lower LP loop is about 75% that in the upper HP loop. Findings of the present work as well as the elaborate application of Monte Carlo method to real cycles can greatly open the way for reducing the trade-off design methods currently used in developing such systems as well as direct the useful experimentations and assessment of such designed systems.

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Monte Carlo method to machine tool uncertainty evaluation

Procedia Manufacturing ◽

10.1016/j.promfg.2017.09.105 ◽

2017 ◽

Vol 13 ◽

pp. 585-592 ◽

Cited By ~ 1

Author(s):

S. Aguado ◽

P. Pérez ◽

J.A. Albajez ◽

J. Velázquez ◽

J. Santolaria

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Machine Tool ◽

Uncertainty Evaluation

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

The Proceedings of Conference of Kanto Branch ◽

10.1299/jsmekanto.2010.16.447 ◽

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

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.684.429 ◽

2013 ◽

Vol 684 ◽

pp. 429-433 ◽

Cited By ~ 1

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.

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