To obtain the accurate evaluation of minimum zone sphericity, this paper investigates a method in Cartesian coordinates using cuckoo search (CS) algorithm. In this method, an appropriate space is set as the search zone according to the solution obtained which is based on least square criteria. The aim of search is to find the best candidate position infinitely approximating the ideal reference center of minimum zone sphere. In order to improve the search efficiency, two essential parameters in CS, namely the control coefficient α of step size and the probability pa of discovering an invasive cuckoo's egg are set to 0.618 (value of golden ratio) and 0.05 (common value of statistical significance), respectively. The updating of the candidate points is carried out by Levy flights and biased/selective random walk mechanisms. Levy flights mechanism can ensure the real global optimum is not missed, biased/selective random walk mechanism guarantee the diversity of search direction and adaptability of search step size. During the updating, the new solution can be kept when it is better than the old one. In each search iteration, the position which corresponds to the smallest sphericity is regarded as the present optimum solution. When the iteration terminal condition is satisfied, the optimum position and corresponding sphericity are output as evaluation results. The validness of the proposed CS algorithm was tested by an application example, the results indicate that the proposed method has the advantage of excellent convergence and high efficiency, which is suitable for the hith-precision evaluation of minimum zone sphericity efficiently.
In order to solve boundary effect for non-closed circular profile with conventional Gaussian filter, two modified Gaussian filters based on odd and even functions are put forward. By extending original profile data on the boundary effect area, the sampling information on the boundary effect area of non-closed circular profile can be used fully, and then open-loop Gaussian filter is used for filtering. The validity of two designed filters was tested by numerical simulation and experiment. The results demonstrate that the modified Gaussian filter based on even function is more effective to reduce boundary effect than that based on odd function.
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