灰色GMP(1,1,N)模型及其在冰凌灾害风险预测中的应用  

Grey GMP(1,1,N)model and its application in risk prediction of ice-jam disaster

作　　者：罗党[1] 韦保磊 LUO Dang;WEI Baolei(School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450046, Chin)

机构地区：[1]华北水利水电大学数学与信息科学学院,郑州450046

出　　处：《系统工程理论与实践》2017年第11期2929-2937,共9页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71271086;71503080);河南省高等学校重点科研项目(18A630030)~~

摘　　要：在加权最小二乘框架下构建了含时间多项式项的灰色GMP(1,1,N)模型,该模型既适用于小样本单调序列又适用于波动序列,论证了均方误差最小准则、均方相对误差最小准则与平均绝对百分误差最小准则下的GM(1,1)、NGM(1,1,k)和GM(1,1,t~α)模型均是GMP(1,1,N)模型的特殊形式,将GMP(1,1,N)模型应用于黄河宁蒙河段冰凌灾害风险预测,结果表明2015-2016年的风险预测结果符合实际情况,模型能够识别风险波动变化规律.为不同准则下灰色预测新模型的构建提供了新思路,具有重要的理论意义和工程应用前景.A weighted least square grey GMP（1,1,N） model with time polynomial term is proposed, which is suitable for both monotonic sequences and oscillatory sequences with small sample data. GM（1,1） models, NGM（1,1,k） models and GM（1,1,t~） models under least mean square error criterion, least mean square relative error criterion and least mean absolute percentage error criterion are all proved to be special cases of GMP（1,1,N） model. Finally, GMP（1,1,N） model is applied to predicting the ice-jam disaster risk in Ningxia-Inner Mongolia reach. The result shows that the fluctuation of risk value sequence can be extracted, and the forecasting risk value between 2015 and 2016 accords to facts, which is valuable in theory and practice.

关 键 词：灰色GMP(1 1 N)模型 加权最小二乘法 矩阵分析 冰凌灾害 风险预测 

分 类 号：N941.5[自然科学总论—系统科学]