正规矩阵选取半参数灰色模型改进的预测建模  

Improvement of regular matrix selection and its application in predicting and modeling of semiparametric gray model

作　　者：周敏[1,2] 周世健[1,3] 王奉伟[1,2] 

机构地区：[1]东华理工大学测绘工程学院,南昌330013 [2]流域生态与地理环境监测国家测绘地理信息局重点实验室,南昌330013 [3]南昌航空大学,南昌330063

出　　处：《测绘科学》2016年第8期152-155,164,共5页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(41374007);测绘地理信息江西省研究生创新教育基地项目

摘　　要：正规矩阵是对模型误差补偿性的直接表达,时间序列法用一阶差分方程和二阶差分方程计算得到不同的正规矩阵。针对传统GM(1,1)模型没有考虑模型误差,而数据处理过程中所建立的数学模型与客观现实并不一致的问题,该文提出建立顾及模型误差的半参数模型的GM(1,1)模型。对由传统半参数模型得到的正规矩阵采取一阶差分法进行改进,并通过算例证实了改进正规矩阵的半参数模型的GM(1,1)预测精度更高。Normal matrix is the direct expression of the model error compensatory;time series methods take the first-order and second-order differential equation to obtain different normal matrix.Aiming at the problem that traditional GM（1,1）model does not consider the model error,and the mathematical model with the objective reality of the data processing process is not uniform,this paper established the semi parametric model considering model errors of GM（1,1）model.The normal matrix obtained from traditional semi-parametric model was improve by first-order differential,and the numerical example results proved that improved normal matrix＇s semi-parameter model GM（1,1）could get higher prediction accuracy.

关 键 词：模型误差 半参数模型 正规矩阵 GM(1 1) 

分 类 号：P20[天文地球—测绘科学与技术]