基于函数cot（x^α）变换及背景值优化的灰色建模  

Grey modeling based on cot（x^α） transformationand background value optimization

作　　者：戴文战[1] 熊伟[1] 杨爱萍[2] 

机构地区：[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

出　　处：《浙江大学学报（工学版）》2010年第7期1368-1372,共5页Journal of Zhejiang University：Engineering Science

基　　金：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)

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0.2125≤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.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（x^α）（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（x^α） 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.

关 键 词：灰色模型 光滑度 离散序列 

分 类 号：N941.5[自然科学总论—系统科学] TP301.6[自动化与计算机技术—计算机系统结构]