灰色预测模型初始条件求解的优化解法The optimization method for solving gray prediction model initial condition
周一帆,鲁铁定,王奉伟,吴定邦
摘要(Abstract):
针对GM(1,1)模型初始条件的选择最优化问题,提出一种新的最优初始条件求解算法,即把对最优初始条件选择问题转化为求最优的C值,通过两个算例分析表明,文中的算法与文献[4]的FGM(1,1)模型相比,在达到同等精度的条件下,运行效率更高,算法更简单直观,更有利于程序实现,验证了文中提出的算法的有效性和可行性。
关键词(KeyWords): 灰色理论;GM(1,1)模型;FGM(1,1)模型;最优C值
基金项目(Foundation): 国家自然科学基金项目(41204003,41374007,41464001);; 江西省科技落地计划项目(KJLD12077);; 江西省教育厅科技项目(GJJ13457);; 中国博士后基金项目(2012M511962);; 江西省中青年教师发展计划访问学者专项(2012-132);; 江西省远航工程计划项目(2013-132)
作者(Author): 周一帆,鲁铁定,王奉伟,吴定邦
DOI: 10.16251/j.cnki.1009-2307.2017.09.002
参考文献(References):
- [1]党耀国,王俊杰,康文芳.灰色预测技术研究进展综述[J].上海电机学院学报,2015(1):1-7,18.(DANG Yaoguo,WANG Junjie,KANG Wenfang.Survey of gray prediction model reserch[J].Journal of Shanghai Dianji University,2015(1):1-7,18.)
- [2]党耀国,刘思峰,刘斌.以x(1)(n)为初始条件的GM模型[J].中国管理科学,2005(1):133-136.(DANG Yaoguo,LIU Sifeng,LIU Bin.The GM models that x(1)(n)be taken as initial value[J].Chinese Journal of Management Science,2005(1):133-136.)
- [3]袁德宝,崔希民,高宁.同时利用x(1)(1)和x(1)(n)为GM(1,1)建模初始条件的预测方法研究[J].大地测量与地球动力学,2013(3):79-82.(YUAN Debao,CUI Ximin,GAO Ning.A forecast method combining x(1)(1)with x(1)(n)as initial value of GM(1,1)model[J].Journal of Geodesy and Geodynamics,2013(3):79-82.)
- [4]王康,周世健.初始条件改进全概括灰色预测模型研究[J].测绘科学,2014,39(12):29-32.(WANG Kang,ZHOU Shijian.Study on grey prediction model of summarizing all the intial condition improvements[J].Science of Surveying and Mapping,2014,39(12):29-32.)
- [5]李大军,孙旭红,汤拥军.PGM(1,1)灰色预测模型及其应用[J].华东地质学院学报,2002(1):40-43.(LI Dajun,SUN Xuhong,TANG Yongjun.PGM(1,1)Grey prediction model and its application[J].Journal of East China Geological Institute,2002(1):40-43.)
- [6]徐进军,王海成,白中洁.反向累加灰色模型的建立及其在沉降预测中的应用[J].测绘信息与工程,2012(1):1-3,29.(XU Jinjun,WANG Haicheng,BAI Zhongjie.Establish of grey model based on reverse accumulation and its application to subsidence prediction[J].Journal Geomatics,2012(1):1-3,29.)
- [7]邓聚龙.灰色系统理论教程[M].武汉:华中理工大学出版社,1990.(DENG Julong.Grey system theory tutorial[M].Wuhan:Huazhong University of Science Press,1990.)
- [8]王奉伟,周世健,周清,等.三重加权变形监测预测模型及应用[J].测绘科学,2016,41(4):10-14.(WANG Fengwei,ZHOU Shijian,ZHOU Qing,et al.Application of development weighted treble in TPGM(1,1)model[J].Science of Surveying and Mapping,2016,41(4):10-14.)
- [9]武汉大学测绘学院测量平差学科组.误差理论与测量平差基础[M].武汉:武汉大学出版社,2003.(School of Geodesy and Geomatics’Surveying Adjustment Discipline Groups.Error theory and surverying adjustment basis[M].Wuhan:Wuhan University Press,2003.)
- [10]邢治宇,蔡勇斌.灰预测中值迭代调整法之研究[C]//灰色系统理论与应用论文集.[出版地不详]:[出版者不详],2000:305-308.(XING Zhiyu,CAI Yongbin.A study on the method of grey prediction by mean iteration adjustment[C]//Grey System Theory and Application Essays.[S.l.]:[s.n.],2000:305-308.)
- [11]张智星,MATLAB程序设计与应用[M].北京:清华大学出版社,2002.(ZHANG Zhixing.MATLAB program design and application[M].Beijing:Tsinghua University Press,2002.)