Minimum zone evaluation of conicity error using minimum potential energy algorithms

Huang, Pei-Hsing; Lee, Ji-Chun

doi:10.1016/j.precisioneng.2010.03.008

Cited by 11 publications

(5 citation statements)

References 16 publications

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“…The Broyden-Fletcher-Goldfarb-Shanno Algorithm (BFGS) [49,126,136,144] is one of the most famous quasi-Newton algorithms for unconstrained optimization. Moving away from deterministic algorithms, intelligence-oriented algorithms (Genetic algorithms, Swarm algorithms) [97,173,179,180] with their simplicity are another way to search the solution of extreme problems with many local minima. An optimization toolbox has been implemented in Matlab software for solving complex optimization problems.…”

Section: Least Squares Methods (Lsm)mentioning

confidence: 99%

Modelling and traceability for computationally-intensive precision engineering and metrology

et al. 2018

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In contrast to measurements of the dimensions of machined parts realized by machine tools and characterized by CMMs, software results are not fully traceable and certified. Indeed, a computer is not a perfect machine and binary encoding of real numbers leads to rounding of successive intermediate calculations that may lead to globally false results. This is the case for poor implementations and poorly conditioned algorithms. Therefore, accurate geometric modelling and implementations will be detailed. Based on the works of National Metrology Institutes, the problem of software traceability will also be discussed. Some prospects for this complex task will finally be suggested.

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Section: Least Squares Methods (Lsm)mentioning

confidence: 99%

Modelling and traceability for computationally-intensive precision engineering and metrology

et al. 2018

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“…Chatterjee and Roth 7 adopted a simplex search method for the vertices to achieve an optimum for Chebyshev fitting. Huang and Lee 21 implemented the form error evaluation using the minimum potential energy algorithm, which is stimulated by the techniques in mechanics. The calculated results of MZE by the PDIP method is equivalent to the results obtained by Chatterjee and Roth 7 and can obtain a little better result for Cone 2 in the study by Huang and Lee.…”

Section: Numerical Validationmentioning

confidence: 99%

“…The calculated results of MZE by the PDIP method is equivalent to the results obtained by Chatterjee and Roth 7 and can obtain a little better result for Cone 2 in the study by Huang and Lee. 21 As far as the authors know, there are no publications concerning the quantitative evaluation of form errors of cones in the sense of MCE and MIE yet, thus comparison cannot be undertaken for them. The results shown in Table 3 are to be verified and compared for the readers in the future.…”

Section: Numerical Validationmentioning

confidence: 99%

Evaluating the form errors of spheres, cylinders and cones using the primal–dual interior point method

Zhang

Jiang

Forbes

et al. 2013

Proceedings of the Institution of Mechanical Engineers, Part B:

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In precision metrology, the form errors between the measured data and reference nominal surfaces are usually evaluated in four approaches: least squares elements, minimum zone elements, maximum inscribed elements and minimum circumscribed elements. The calculation of minimum zone element, maximum inscribed element and minimum circumscribed element is not smoothly differentiable, thus very difficult to be solved. In this article, a unified method is presented to evaluate the form errors of spheres, cylinders and cones in the sense of minimum zone element, maximum inscribed element and minimum circumscribed element. The primal–dual interior point method is adopted to solve this non-linearly constrained optimisation problem. The solution is recursively updated by arc search until the Karush–Kuhn–Tucker conditions are satisfied. Some benchmark data are employed to demonstrate the validity and superiority of this method. Numerical experiments show that this optimisation algorithm is computationally efficient and its global convergence can be guaranteed.

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“…On the contrary, evolutionary algorithms are able to search the variable space more amply, but normally have a slower convergence rate. Recently, Huang and Lee evaluated the conicity error using minimum potential energy algorithms [21], which are very elaborate.…”

Section: Review Of Related Workmentioning

confidence: 99%

Minimum zone evaluation of the form errors of quadric surfaces

Zhang

Jiang

Scott

2011

Precision Engineering

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a b s t r a c tQuadric surfaces commonly exist in natural objects and artificial components. It is widely needed to evaluate the form quality of a measured data set, but the commonly used least squares method will lead to over-estimation and its results are not consistent with the definitions in ISO standards. In this paper a shape recognition approach is presented to determine the surface type and shape parameters from the general implicit quadratic function. Then a self-adaptive differential evolution algorithm is utilized to perform minimum zone evaluation for generic quadrics. The maximal orthogonal distance from the data points to the associated surface is taken as the target to be optimized. Finally experimental examples are presented to verify the developed algorithm.

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Minimum zone evaluation of conicity error using minimum potential energy algorithms

Cited by 11 publications

References 16 publications

Modelling and traceability for computationally-intensive precision engineering and metrology

Modelling and traceability for computationally-intensive precision engineering and metrology

Evaluating the form errors of spheres, cylinders and cones using the primal–dual interior point method

Minimum zone evaluation of the form errors of quadric surfaces

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