An immune evolutionary algorithm for sphericity error evaluation

This study proposes an intelligent algorithm that combines a modified cuckoo search (MCS) algorithm with an adaptive fuzzy logic controller (MCSF) to evaluate minimum zone sphericity with high speed and accuracy. To accelerate the convergence of the iteration procedure, the proposed MCS algorithm introduces an optimized initial solutions distribution model and a modified biased/selective mechanism to the original cuckoo search. Moreover, an adaptive fuzzy logic controller is designed to ensure global search ability in the early stage of the search process and strong convergence performance in the later stage of iteration. This is achieved by adaptively adjusting the control coefficient α of step size and the probability pa of discovering an invasive cuckoo’s egg in MCS. Simulation and comparison results indicate that the proposed method achieves excellent convergence behavior and reaches the global optima faster than conventional heuristic methods. The MCSF method runs 60 iterations in ~0.4 s, and its results for the standard deviation of sphericity are 1/8–1/2 of those of the conventional heuristic methods. The proposed method can easily be extended to evaluate minimum zone roundness, cylindricity, and straightness.

Section: Examples and Discussionmentioning

confidence: 99%

Section: Minimum Zone Sphericity (Mzs)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimum zone sphericity evaluation based on a modified cuckoo search algorithm with fuzzy logic

Huang

Jiang

Chao

et al. 2018

“…Fan and Lee [28] cast the problem of MZS error evaluation into the problem of minimum potential energy of a simulated mechanical system and proposed a search algorithm for the optimal MZS solution around the LSS solution. Wen and Song [29] proposed an immune evolutionary algorithm for the MZS error. Huang et al [30] computed the MZS error using a search algorithm with diverse search directions and adaptive step sizes.…”

Section: A Simple Unified Branch-and-bound Algorithm For Minimum Zone...mentioning

confidence: 99%

A simple unified branch-and-bound algorithm for minimum zone circularity and sphericity errors

Zheng

2020

This paper presents a simple branch-and-bound (B&B) algorithm to compute the minimum zone circularity/sphericity error, which is formulated as the problem of finding the centers of two concentric circles/spheres that contain given points between them and have minimal difference in their radii. For any square domain of the center, a lower bound on the minimal radius difference attainable over the domain is proposed, and this monotonically increases as the domain is divided into square subdomains. Along with the branching operation, a domain will become infinitely small and provide only a center of concentric circles/spheres such that its lower bound is equal to the radius difference. Using such a lower bound, therefore, the B&B algorithm guarantees the computing of the exact circularity/sphericity error and it is proven that the accuracy of the computed result can be easily specified by the termination tolerance of the algorithm as needed. In addition, the algorithm is very efficient and easy to implement.

“…Chen et al [3] constructed three mathematical models to evaluate the minimum circumscribed sphere, the maximum inscribed sphere, and the minimum zone sphere by directly resolving the simultaneous linear algebraic equations. Wen et al [5] proposed an immune evolutionary algorithm by imitating the defence process of the immune system and the ideas of mutation in evolutionary biology. Samuel et al [6] developed algorithms based on computational geometric techniques, which are characterized by the use of the limacoids as assessment features to be considered for evaluating the sphericity error using form data.…”

Section: Introductionmentioning

confidence: 99%

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

Liu¹,

Xu²,

Zhang³

et al. 2015

As one of the Geometrical Product Specifications that are widely applied in industrial manufacturing and measurement, sphericity error can synthetically scale a 3D structure and reflects the machining quality of a spherical workpiece. Following increasing demands in the high motion performance of spherical parts, sphericity error is becoming an indispensable component in the evaluation of form error. However, the evaluation of sphericity error is still considered to be a complex mathematical issue, and the related research studies on the development of available models are lacking. In this paper, an intersecting chord method is first proposed to solve the minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error. This new modelling method leverages chord relationships to replace the characteristic points, thereby significantly reducing the computational complexity and improving the computational efficiency. Using the intersecting chords to generate a virtual centre, the reference sphere in two concentric spheres is simplified as a space intersecting structure. The position of the virtual centre on the space intersecting structure is determined by characteristic chords, which may reduce the deviation between the virtual centre and the centre of the reference sphere. In addition,two experiments are used to verify the effectiveness of the proposed method with real datasets from the Cartesian coordinates. The results indicate that the estimated errors are in perfect agreement with those of the published methods. Meanwhile, the computational efficiency is improved. For the evaluation of the sphericity error, the use of high performance computing is a remarkable change.