土石坝沉降预测中的多变量灰色预测模型

当观测资料的数据量少，而又存在多个相互影响或关联的变量时，常用的灰色预测模型GM(1，1)不能全面考虑多个变量。本文采用自适应MGM(1,n)模型——多变量灰色预测模型，较好地解决了这一问题。MGM(1，n)模型是GM(1，1)模型在，n元多变量情况下的推广，其参数能够反映实际工程或社会系统中多个变量间的相互影响、相互制约的关系。内容包括：建模变量的选择，建立n元微分方程组，求解变量的时间响应函数和模型检验。通过对某土石坝观测资料的计算，表明这一方法是可行和有效的。对比其他几个模型．如GM(1,1)等，MGM(1,n)模型能反映出变量间的相互影响，从而获得较好的预测效果。

Application of grey multi-variable forecasting model for the settlement of earth dam

The general grey model does not work normally when observation data is insufficient and mutual effect or interrelation between variables exists. A self-adapting namely MGM(1,n) model, which is an extension of the GM(1,1) model for n-variable, is introduced to solve the problem. The principle of variable selection, establishment of differential equations for n-variable, deduction of time-response function for solving the variables as well as the statistical tests of the model are give in detatiled. The validity of the method is demonstrated by calculating the observation data of an earth dam. It verifies that the model can reflect the mutual effect between multiple variables and attains the best forecasting.