摘要
根据矩阵理论推导非等间距GM（1,1）模型参数的矩阵形式,研究了压缩变换和初始点变化下非等间距GM（1,1）模型参数性质及其对模型精度的影响;在相对误差平方和最小的准则下,分别对初始条件和初始点进行优化,给出参数优化公式,发现两种优化方法是等价的;基于新信息优先原理,通过引入加权系数λ,综合考虑新旧信息变化规律,以加权求和的1-AGO序列作为初始条件,提出了全信息初始条件优化的非等间距GM（1,1）模型.最后,通过实例分析表明,本文提出的优化模型在拟合精度和预测精度上均有明显改善,表明优化的初始条件能充分提取新旧数据的有效信息,进一步提升建模效果.
According to the matrix theory, the simplified matrix forms of parameters in the unequal interval GM（1, 1） model is put forward, the properties and the effect on the modelling precision of the unequal interval GM（1, 1） model are studied under the contractive transformation and optimization of the initial point, respectively. Under the algorithm of minimizing the square sum of the relative error between the original series and the forecasting sequences, the optimizing formula of parameters are put out with the optimization of the initial condition and the initial point, respectively. Subsequently, it can be found that the two optimized approaches can obtain the similar accuracy of prediction. Then, the weighting coefficient of A is introduced to reflect the patterns of the new and old information in the 1-AGO sequence. And the unequal interval GM（1, 1） based on perfect information is proposed with the optimized initial condition. Eventually, examples show that, the precision of simulation and prediction can both be improved by the novel model, and the modeling accuracy can be further enhanced by employing the optimized initial condition with the extraction of the effective information in the new and old series.
作者
丁松
党耀国
徐宁
冯宇
DING Song;DANG Yaoguo;XU Ning;FENG Yu(College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;College of Management Science and Engineering, Nanjing Audit University, Nanjing 211815, China)
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2018年第6期1575-1585,共11页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(71371098,71771119,71701101)
南京航空航天大学博士学位论文创新与创优基金(BCXJ16-09)
江苏省高校自然科学研究项目(16KJD120001)
江苏省社科基金重点研究项目(16GLA001)~~
关键词
非等间距
GM(1
1)模型
初始条件
初始点
优化
unequal interval
GM（1
1） model
initial condition
initial value
optimization
