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

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.