可行域计算的仿射-区间方法

doi:10.13190/j.jbupt.2015.02.012

北京邮电大学学报 ›› 2015, Vol. 38 ›› Issue (2): 69-73.doi: 10.13190/j.jbupt.2015.02.012

可行域计算的仿射-区间方法

谢永强, 陈建军, 曹鸿钧

西安电子科技大学电子装备结构设计教育部重点实验室, 西安 710071

收稿日期:2014-05-13 出版日期:2015-04-28 发布日期:2015-05-14
作者简介:谢永强(1976—), 男, 讲师, 博士生, E-mail: yqxie@xidian.edu.cn; 陈建军(1951—), 男, 教授, 博士生导师.
基金资助:
国家自然科学基金项目(51175398); 中央高校基本科研业务费专项资金项目(K5051304016)

An Affine-Interval Arithmetic-Based Feasible Region Evaluation Method

XIE Yong-qiang, CHEN Jian-jun, CAO Hong-jun

Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi'an 710071, China

Received:2014-05-13 Online:2015-04-28 Published:2015-05-14

摘要/Abstract

摘要：

提出了一种复杂函数的可行域计算的仿射-区间方法. 首先利用仿射-区间方法对设计域内函数的界限进行分析,并利用分支定界法将该区域分类为可行域、不可行域和不确定域;然后将不确定区域进行细分,并对每个细分后的子区域再进行函数界限分析和分类,直至子区域半径达到设计要求;最后对所有可行域的面(体)积进行统计求和,获得函数的总可行域. 该方法可对非凸函数甚至可行域不连续函数的可行域进行估计. 算例演示了该方法的计算过程,并验证了该方法的有效性.

关键词: 可行域, 仿射算法, 区间算法, 分支定界法

Abstract:

An affine-interval arithmetic-based method for the feasible region evaluation of function or electronic circuits was presented. This method uses affine-interval arithmetic to analyze the bounds of the function, and use branch and bound method divided these intervals into three kinds: accept regions, refuse regions and those of uncertain regions. All the uncertain regions were re-divided and the bounds calculation and classification performed again until the subintervals small enough. The statistics on each of accept regions was performed thereafter to get the sum of the accept regions. The proposed technique guarantees an efficient, reliable and accurate evaluation of the yield, even for non-convex and not simply connected feasible region. The examples presented show the features of the approach.

Key words: feasible region, affine arithmetic, interval arithmetic, branch and bound method

中图分类号:

TP301
O39

谢永强, 陈建军, 曹鸿钧. 可行域计算的仿射-区间方法[J]. 北京邮电大学学报, 2015, 38(2): 69-73.

XIE Yong-qiang, CHEN Jian-jun, CAO Hong-jun. An Affine-Interval Arithmetic-Based Feasible Region Evaluation Method[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2015, 38(2): 69-73.

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可行域计算的仿射-区间方法

An Affine-Interval Arithmetic-Based Feasible Region Evaluation Method

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