Mathematical Model for Evaluating Roundness Errors by Minimum Circumscribed Circle Method

機(jī)譯：最小外接圓法求圓度誤差的數(shù)學(xué)模型

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An unconstrained optimization model is established for assessing roundness errors by the minimum circumscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the minimun circumscribed circle assessment. One example is given to verify the theoretical results presented.

機(jī)譯：建立了基于徑向偏差測(cè)量的最小外接圓法評(píng)估圓度誤差的無約束優(yōu)化模型。對(duì)優(yōu)化模型中目標(biāo)函數(shù)的性質(zhì)進(jìn)行了深入研究。在現(xiàn)代凸函數(shù)理論的基礎(chǔ)上，嚴(yán)格證明目標(biāo)函數(shù)是在二維歐幾里得空間上定義的連續(xù)且不可微的凸函數(shù)。目標(biāo)函數(shù)的最小值是唯一的，并且其任何最小點(diǎn)都必須是其全局最小點(diǎn)。只要是收斂的，任何現(xiàn)有的優(yōu)化算法都可以用于求解目標(biāo)函數(shù)，以便通過最小外接圓評(píng)估獲得所需的圓度誤差。給出了一個(gè)例子來驗(yàn)證所提出的理論結(jié)果。

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《International conference on mechatronics and materials processing》|2011年|380-383|共4頁
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作者
Ping Liu; Hui Yi Miao;
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正文語種
中圖分類工程材料一般性問題;
關(guān)鍵詞
Form error; Roundness; Minimun circumscribed circle; Optimization; Objective function; Convex function;

機(jī)譯：形狀誤差;圓度;最小外接圓;優(yōu)化;目標(biāo)函數(shù);凸函數(shù);

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Mathematical Model for Evaluating Roundness Errors by Minimum Circumscribed Circle Method

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