Evaluation of minimum zone sphericity by combining single-space contraction strategy with multi-directional adaptive search algorithm

Huang, Jingzhi; Jiang, Lin; Zheng, Huixin; Xie, Mingzuo; Tan, Jiubin

doi:10.1016/j.precisioneng.2018.09.008

Cited by 9 publications

(20 citation statements)

References 18 publications

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“…However, the convergence rate decreases with the increase of the number of iterations. Figure 5(b) shows that distance decreases one order of magnitude per ~10 iterations using the method in [29]. Ii is clear that a faster and better convergence characteristic is achieved using the proposed BSOM.…”

Section: Verification With Datasets From Literaturementioning

confidence: 88%

“…In order to reduce the search range, the method proposed in the literature [29] is used to determine the initial search area and generate original candidate points. The initial search area is divided into two sections based on the average distance D.…”

Section: Bidirectional Search Of Unequal Probability and Offset Searc...mentioning

confidence: 99%

“…Step 1: Determine the initial search area and obtain the compressed zone using the method in [29]; Step 2: Generate solution candidate points randomly in the compressed zone; Step 3: Select the best point by comparing the MZR;…”

Section: Evaluation Procedures Of Mzr Based On Bsommentioning

confidence: 99%

“…Therefore, a proper offset is vital for the search mechanism. According to our previous work [29], the forward search probability P 1 = 0. Therefore, the coefficient b = 0.6 is determined considering the solution accuracy and efficiency.…”

Section: Determination Of Bsom Parametersmentioning

confidence: 99%

“…The standard deviation is less than 5.3777 × 10 −9 mm. Especially, compared with SSCS&MDAS [29], BSOM has superior performance and greatly reduces the running time when the number of data sets is large.…”

Section: Verification With Datasets From Literaturementioning

confidence: 99%

See 4 more Smart Citations

Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

Huang¹,

Chao²,

Jiang³

et al. 2019

Meas. Sci. Technol.

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This paper reports an improved method that integrates a bidirectional search of unequal probability and an offset movement mechanism (BSOM) to evaluate the minimum zone roundness (MZR) with high speed and accuracy. The centre and roundness of a least-squares circle are first solved to construct an original search zone, and the initial candidate points of the minimum zone circle centre are configured. A bidirectional search of unequal probability that considers the subsequent points either toward or away from the current best candidate point is designed to enhance the global search ability. Considering the candidate points at different located positions have different effects on convergence characteristics, the search area is divided into two sections based on the average distance between the current best candidate point and the other candidate points, and different forward and backward search probabilities are configured. An adaptive offset movement mechanism is integrated to generate new candidate points for the next generation. The effectiveness of the proposed method is experimentally verified using datasets from previous studies. The configurations of BSOM parameters and influence of the distribution and number of data points on evaluation accuracy and efficiency are analyzed. The experimental examples and comparison results demonstrate the excellent convergence performance of the proposed method, which reaches the global optimum faster than previous methods. Across six different datasets, only 0.0095 s–0.0282 s is required when the average distance D ⩽ 1.0 × 10−7 mm as the iteration convergence condition, and the standard deviation of the MZR is less than 5.3777 × 10−9 mm, while the search parameters are set as P1 = 0.6, P2 = 0.95, and b = 0.6. The proposed approach is expected to be suitable for on-line evaluation of roundness error.

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Section: Verification With Datasets From Literaturementioning

confidence: 88%

Section: Bidirectional Search Of Unequal Probability and Offset Searc...mentioning

confidence: 99%

Section: Evaluation Procedures Of Mzr Based On Bsommentioning

confidence: 99%

Section: Determination Of Bsom Parametersmentioning

confidence: 99%

Section: Verification With Datasets From Literaturementioning

confidence: 99%

See 3 more Smart Citations

Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

Huang¹,

Chao²,

Jiang³

et al. 2019

Meas. Sci. Technol.

Self Cite

View full text Add to dashboard Cite

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Improved sphericity error evaluation combining a heuristic search algorithm with the feature points model

Huang

Jiang

Chao

et al. 2019

Review of Scientific Instruments

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This paper describes a high-speed method of evaluating sphericity errors using a heuristic search algorithm combined with a feature points model (HSA–FPM). First, the sphere center and sphericity of the least-squares sphere are calculated to establish the initial candidate points of the sphere center. An iterative search procedure is then conducted based on the specified heuristic search algorithm and sphericity evaluation criterion, and the current globally optimal sphere center O is obtained under certain termination conditions. To determine the decisive feature points and construct a sphericity evaluation model, the distances di between the sphere center O and all sampling points are calculated and sorted. The modified sphere centers are then determined using the corresponding feature points model. As an application example, the Nelder–Mead algorithm is combined with the feature points model. Experimental results demonstrate that the proposed method achieves the exact sphericity solution with relatively few iterations, requiring only ∼0.01 s for the whole evaluation procedure. This corresponds to an improvement in evaluation efficiency of ∼26%–61% over previous methods. The proposed HSA–FPM method is in complete agreement with several well-known evaluation criteria and is quite suitable for real-time measurements and evaluations of sphericity errors.

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

Zheng

2020

Meas. Sci. Technol.

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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.

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Evaluation of minimum zone sphericity by combining single-space contraction strategy with multi-directional adaptive search algorithm

Cited by 9 publications

References 18 publications

Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

Improved sphericity error evaluation combining a heuristic search algorithm with the feature points model

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

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