摘要
针对经典Verhulst模型背景值建模机理的不严密和初始值设定的不科学性,该文给出了灰导数改进模型及模型参数的最优估计式。采用原始数据一次累加与其拟合值的残差平方和最小作为约束准则,推导出虚拟初始值的计算公式,建立了无须设定初始值约束的优化模型。以南水北调工程沉降监测实例,比较了在3种背景值构造方法和两种初始值约束条件下的预测精度。结果表明,该文提出的初始值优化模型与灰导数法构造背景值,所得残差的平方和最小,从而验证了优化模型的可行性,为沉降监测中长期预报建模提供了合理的解决方案。
In view of the background value modeling mechanism of classical Verhulst model is imprecise and the initial value setting is not scientific, the improved grey derivative model and the optimal model parameters estimation were studied in this paper. Using 1-AGO and its minimum residual sum of squares of the fitting value as a constraint criterion, the calculation formula of virtual initial value was deduced and the optimization model without setting the initial value constraint was established. Taking the settlement monitoring for South-to-North Water Diversion as an example, the prediction accuracy of constraint conditions by three background value construction methods with two initial value were compared. The results showed that the residual sum of squares by the proposed method is the smallest, which verified the feasibility of the optimization model and provided a reasonable solution for the long-term subsidence monitoring prediction modeling.
出处
《测绘科学》
CSCD
北大核心
2017年第6期82-86,共5页
Science of Surveying and Mapping
基金
河北省"三三三人才工程"资助项目(20130618)
关键词
VERHULST模型
沉降监测
初始值优化
背景值
Verhulst model
subsidence monitoring
optimization of initial value
background value
