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J4  2010, Vol. 44 Issue (7): 1368-1372    DOI: 10.3785/j.issn.1008-973X.2010.07.024
自动化技术     
基于函数cot (xα)变换及背景值优化的灰色建模
戴文战1, 熊伟1, 杨爱萍2
1. 浙江理工大学 自动化研究所,浙江 杭州 310018; 2. 浙江财经学院 外国语学院,浙江 杭州 310018
Grey modeling based on cot (xα) transformation
and background value optimization
DAI Wen-zhan1, XIONG Wei1, YANG Ai-ping2
1. Department of Automatic Control, Zhejiang SciTech University, Hangzhou 310018, China; 2. School of Foreign
 Language, Zhejiang University of Finance and Economics, Hangzhou 310018, China
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摘要:

灰色模型的精度很大程度上取决于待建模序列的光滑度,满足级比条件是灰色建模的前提.针对因陡变而不满足灰色建模条件的离散序列x(k),从理论上证明了经f(x)=cot (xα)变换且在满足0.212 5≤f(x)≤π/2的条件下,序列F(k)=f(x(k))能够满足非畸形灰色模型建模级比条件,对光滑度的改善程度较现有的其他变换更有效.根据非负序列的一次累加生成单调递增序列,提出一种背景值优化重构的方法,利用矩形面积加梯形面积之和,实现背景值重构时正负误差相抵消,使重构后的背景值更加趋近于真值,进一步提高了模型精度.提出基于函数cot (xα)变换及背景值优化的灰色建模步骤,通过实例验证了本方法的有效性.

Abstract:

 The precision of grey model greatly depends on the smooth degree of discretetime sequence, and the need of stepwise ratio of discrete sequence must be met. A method of grey modeling based on cot (xα)(α>0) transformation and its background value optimization was proposed in case that original discretetime sequence can not meet the condition for grey modeling. The discretetime sequence F(k)=f(x(k)) transformed by f(x)=cot (xα) can meet the requirements of grey modeling under the condition of 0.212 5≤f(x)≤π/2, and the smooth degree of F(k) was greatly improved compared with other transformation functions. Then the background value was rebuilt based on the monotonic rise of accumulated generating sequence. The sum of the rectangle area and the trapezium area was used to realize that the negative error was balanced off by the positive error. The rebuilt background value was more close to the practical value, and the model accuracy was improved. Finally, the step of grey modeling was given, and the application results showed that it is effective.

出版日期: 2010-07-01
:  N 941.5  
基金资助:

国家”863”高技术研究发展计划资助项目(2009AA04Z139);教育部高等学校博士学科点专项基金资助项目(20070338002).

作者简介: 戴文战(1958—),男,浙江台州人,教授,博导,从事过程建模与控制、多目标决策、灰色系统建模等研究.E-mail: dwzhan@zstu.edu.cn
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引用本文:

戴文战, 熊伟, 杨爱萍. 基于函数cot (xα)变换及背景值优化的灰色建模[J]. J4, 2010, 44(7): 1368-1372.

DAI Wen-Zhan, XIONG Wei, YANG Ai-Ping. Grey modeling based on cot (xα) transformation
and background value optimization. J4, 2010, 44(7): 1368-1372.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2010.07.024        http://www.zjujournals.com/eng/CN/Y2010/V44/I7/1368

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