Gray model with fractional order and its application to settlement prediction

The traditional settlement prediction models based on the gray theory are all of integer orders, and there are defects that are discontinuous and have large differences from the measured data. In this paper, an improved gray model, which uses fractional derivatives to replace the integer ones, is suggested. The biggest difference between this model and the traditional model is the increased recognition of fractional orders. First, combined with the gray theory, the ordinary differential equation with no input is obtained. Then, an input term is introduced to the equation, and the ordinary differential equation is transformed to obtain a differential equation with a fractional order. Finally, the model is compared with the measured data, and the error is calculated with the traditional gray theory settlement prediction model. The results show that the settlement prediction model established in this paper can provide better prediction for the foundation settlement.