Uncertainty determination for CMMs by Monte Carlo simulation integrating feature form deviations

Kruth, Jean‐Pierre; Gestel, Nick Van; Bleys, Philip; Welkenhuyzen, Frank

doi:10.1016/j.cirp.2009.03.028

Cited by 51 publications

(35 citation statements)

References 7 publications

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“…Weckenmann et al [16,17]; Kruth et al [18]), in particular when the sample size is small, which may be a typical situation if uncertainty cost has to be opti-mized. Because sampling strategy is most often determined by the operator, it is the main leverage to control uncertainty as well.…”

Section: Evaluating Geometric Deviationmentioning

confidence: 99%

Optimal inspection strategy planning for geometric tolerance verification

Moroni

Petrò

2014

Precision Engineering

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Two features characterize a good inspection system: it is accurate, and compared to the manufacturing cost, it is not expensive. Unfortunately, few measuring systems posses both these characteristics, i.e. low uncertainty comes with a cost. But also high uncertainty comes with a cost, because measuring systems with high uncertainty tend to generate more inspection errors, which come with a cost.In the case of geometric inspection, the geometric deviation is evaluated from a cloud of points sampled on a part. Therefore, not only the measuring device has to be selected, but also the sampling strategy has to be planned, i.e. the sampling point cloud size and where points should be located on the feature to inspect have to be decided. When the measuring device is already available, as it often happens in geometric measurement, where most instruments are flexible, an unwise strategy planning can be the largest uncertainty contributor.In this work, a model for the evaluation of the overall inspection cost is proposed. The optimization of the model can lead to an optimal inspection strategy in economic sense. However, the model itself is based on uncertainty evaluation, in order to assess the impact of measurement error on inspection cost. Therefore, two methodologies for evaluating the uncertainty will be proposed. These methodologies will be focused on the evaluation of the contribution of * Correspondig Author. Tel +39 02 23998530. Fax +39 02 23998585.Email addresses: giovanni.moroni@polimi.it (Giovanni Moroni), stefano.petro@polimi.it (Stefano Petrò) Preprint submitted to Elsevier January 9, 2015 the sampling strategy to the uncertainty. Finally, few case studies dealing with the inspection planning for a Coordinate Measuring Machine will be proposed.

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Section: Evaluating Geometric Deviationmentioning

confidence: 99%

Optimal inspection strategy planning for geometric tolerance verification

Moroni

Petrò

2014

Precision Engineering

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“…The value of a is selected equal to 2, so that the Lyapunov exponent number is less than 2 [25] Figure 6 presents the behavior of the ICMIC one-dimensional map. It can be considered as the inverse of the Chebyshev map function.…”

Section: Icmic Mapmentioning

confidence: 99%

“…Its sigma value is obtained from the instruments Maximum Permissible Error (MPE) [9][10] Type 2 instead simulates the contribution due to the part to part variability, including the instrument. Points generated by the second type represent a more realistic situation since an inspected part always contains some feature deviation from the nominal geometry [25]. Geometries will be generated both as full geometries and half geometries (e.g.…”

Section: Implementation and Performance Comparisonmentioning

confidence: 99%

Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries

2016

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Fitting algorithms play an important role in the whole measuring cycle in order to derive a measurement result. They involve associating substitute geometry to a point cloud obtained by an instrument. This situation is more difficult in the case of non-linear geometry fitting since iterative method should be used. This article addresses this problem. Three geometries are selected as relevant case studies: circle, sphere and cylinder. This selection is based on their frequent use in real applications; for example, cylinder is a relevant geometry of an assembly feature such as pin-hole relationship, and spherical geometry is often found as reference geometry in high precision artifacts and mechanisms.In this article, the use of Chaos optimization (CO) to improve the initial solution to feed the iterative Levenberg-Marquardt (LM) algorithm to fit non-linear geometries is considered. A previous paper has shown the performance of this combination in improving the fitting of both complete and incomplete geometries. This article focuses on the comparison of the efficiency of different one-dimensional maps of CO. This study shows that, in general, logistic-map function provides the best solution compared to other types of one-dimensional functions. Finally, case studies on hemispheres and industrial cylinders fitting are presented.

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“…Some of the existing studies on measurement uncertainty evaluation are based on historical experience, experts' opinion, and prior data and fail to take the real time measurement data into account [4,5]. Some of the studies are based on the information of measured samples and fail to take the historical information of the measurement system into account [6,7].…”

Section: Introductionmentioning

confidence: 99%

Analysis and Comparison of Bayesian Methods for Measurement Uncertainty Evaluation

Cheng

Chen

et al. 2018

Mathematical Problems in Engineering

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Based on the Bayesian principle, the modern uncertainty evaluation methods can fully integrate prior and current sample information, determine the prior distribution according to historical information, and deduce the posterior distribution by integrating prior distribution and the current sample data with the Bayesian model. As such, it is possible to evaluate uncertainty, updating in real time the uncertainty of the measuring instrument according to regular measurement, and timely reflect the latest information on the accuracy of the measurement system. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The maximum entropy principle and the hill-climbing search optimization algorithm are introduced to determine the prior distribution probability density function and the sample information likelihood function. The probability density function of posterior distribution is obtained by the Bayesian formula to achieve the optimization estimation of uncertainty. Three methods of measurement uncertainty evaluation based on Bayesian analysis are introduced: the noninformative prior, the conjugate prior, and the maximum entropy prior distribution. The advantages and limitations of each method are discussed.

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Uncertainty determination for CMMs by Monte Carlo simulation integrating feature form deviations

Cited by 51 publications

References 7 publications

Optimal inspection strategy planning for geometric tolerance verification

Optimal inspection strategy planning for geometric tolerance verification

Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries

Analysis and Comparison of Bayesian Methods for Measurement Uncertainty Evaluation

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