引入修正因子的非等时距时变参数灰色预测模型及应用

Correcting factor of gray with prediction model unequal interval time-varying parameters

边坡系统是一类典型的复杂灰色系统,由于其位移监测数据离散程度较高,因此应用经典灰色预测模型往往会出现预测值偏差较大的情况。本文针对经典灰色预测模型GM(1,1)的不足,依据灰色系统理论信息处理原则,在灰色预测模型中引入Legendre时变参数,建立了非等时距时变参数边坡位移的灰色预测模型,并在计算过程中引入修正因子修正预测结果,根据后验方差比C的大小确定修正因子λ的取值,从而确定引入修正因子后边坡位移预测的整体最优化值,提高预测精度。此位移预测模型充分考虑了预测系统的时变性和灰色性,降低了预测系统的整体预测误差。由于文中预测实例的监测数据及测试时间间隔均有较大离散性,因此应用此模型进行预测较为合理。实例计算表明:预测模型可以较好的模拟已测数据并对边坡位移的短、中期变化有较为理想的预测效果。

Slope system is a sort of typical complex gray system, applying classical gray prediction model will engender large error in predicted value due to the high discrete degree of monitored displacement. Based on the classical gray model GM（1, 1）, according to the principle of manegement to information of the gray system theory, introducing Legendre time-varying parameters into the gray prediction model, the gray prediction model of unequal interval for slope displacement was established. During the solution, a correcting factor was introduced to predicted results. The value of correcting factor was confirmed according to the posterior square ratio c, consequeutly confirming the whole optimum value of slope displacement prediction and increasing prediction precision. In the model, both time-varying and gray property were adequately considered, so the whole prediction error was reduced. The prediction model was reasonable in the case, because the monitoring data and test time interval of prediction example were of high discreteness. The case study shows that the prediction model can preferably simulate test data and the prediction results of slope displacement in the short-term and middle-term.