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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,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,建立了无需设定初始值约束的优化模型,并以南水北调工程沉降监测实例验证了模型预测精度,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 unsystematic nature of the modeling mechanism of the classical Verhulst model and the unscientific setting of initial values, the optimal estimation formulas of the improved model and the model parameters of the gray derivative are given. The calculation formula of virtual initial value is deduced by using the sum of the sum of the original data and the residual sum of squares of the fitting value as the constraint criterion. The optimization model without any initial value constraint is established. The model is verified by the settlement monitoring example of South-to-North Water Diversion Project Forecast accuracy, and provide a reasonable solution for mid-long term forecasting modeling of settlement monitoring.