改进的等维灰数递补模型预测边界确定方法  

A prediction boundary determination method of the equal-dimension gray filling model based on law of error propagation

作　　者：郝珈纬 张安兵[1,2] 王贺封 焦旭[1,2] 张玉杰 

机构地区：[1]河北工程大学资源学院,河北邯郸056038 [2]河北省煤炭资源综合开发与利用协同创新中心,河北邯郸056038

出　　处：《测绘科学》2017年第10期45-49,共5页Science of Surveying and Mapping

基　　金：河北省自然科学基金项目(D2015402134);河北省教育厅科学研究项目(YQ2012012;QN2014184)

摘　　要：针对当前利用灰色预测模型进行地表沉降预测研究更多注重模型本身探讨而较少涉及预测值合理范围以及预测值时间响应函数的还原方法的情况,该文提出了一种改进的等维灰数递补模型预测边界的确定方法,采用了误差传播定律对预测值范围进行界定,并尝试利用中值近似处理代替累减生成建立预测值的时间响应函数;最后,结合工程实例给出了预测值上下边界,探讨了模型在误差允许范围内的预测步长,并对比分析了改进的等维灰数递补模型、原始的等维灰数递补模型和GM(1,1)模型。结果发现:改进的等维灰数递补模型具有较好的拟合效果与预测精度。Aiming at the problem that the existing surface subsidence prediction study by using the gray model more focuses on the model itself, with little to the reasonable range of gray model＇s prediction value and the reduction method of the time response function, an improved equal-dimension gray filling model method was proposed to determine the prediction boundary, and based on the law of error propaga- tion theory. The range of prediction was defined, then the prediction value time response function was built by using median approximate algorithm instead of inverse accumulated generating operation. Finally, the top and bottom ranges of prediction value were provided, and the model predictive time length was dis- cussed with the range of allowable error by an engineering case. Through comparative analysis of the im- proved equal-dimension gray filling model, equal-dimension gray filling model and GM（1, 1）model, the result indicated that the fitting effect and prediction accuracy of the improved equal-dimension gray filling model were better.

关 键 词：等维灰数递补模型 GM(1 1)模型 误差传播定律 沉降预测 灰色边界 预测步长 

分 类 号：P208[天文地球—地图制图学与地理信息工程]