时变参数预测模型及其在沉降预测中的应用

A NEW PREDICTION MODEL WITH TIME - DEPENDENT PARAMETERS USED FOR SETTLEMENT PREDICTION

在灰色GM(1.1)模型的基础上,建立了非等时距的时变参数灰色预测模型。模型参数假定是时间的连续函数,并表示成多项式形式,根据前期已有的信息,采用最小二乘法确定参数多项式中的待定系数,可得参数的预测公式,然后根据参数预测公式来建立响应的预测公式,即时变参数预测模型。最后将此模型应用于沉降预测,实例计算表明时变参数预测模型有望提高沉降的预测精度。

On the basis of the grey model GM (1, 1), a new grey prediction model with time - dependent parameters is established . The parameters of model, which can be expressed in polynomial expression, is assumed to be a continous function of time. The undetermined coefficients of polynomial expression can be solved by the principle of least square method based on the previous informations, hance, the prediction formulae of parameters can be obtained. Then according to the prediction tormulae of parameters to establish the prediction formulae of response, it is the prediction model with time - dependent parameters. Finally, it is applied to the settlement prediction. The calculated results of an example show that the prediction model with time - dependent parameters can enhance the prediction accuracy of the settlement.