Improvement Of GM (1,1) Model And Its Application In Bridge Alignment Control

Gray system theory is widely applied for bridge construction control because of its simple operation, requiring less amounts of data and achieving higher accuracy, but it is found that the accuracy of model prediction is unstable in practical application. Through studying the process and mechanism of GM (1,1) model, there are two main factors that affect the accuracy of GM(1,1)model:(1) The smoothness of the sequence data.(2) Gray differential equation established through simulating the analog differential equations is difficult to ensure that approximate fits the equations and differential equations strictly.Aimed at these two problems, this paper made some improvements on GM (1,1) model to reduce the error caused by the model defects. In this thesis, the main research contents include:(1) Preprocessing the original sequence, compressing the amplitude of the data to improve the smoothness through mathematical pan conversion.(2) According to the physical meaning of the Background Value of the traditional model, the Newton interpolation formula is introduced into trapezoidal formula method to simplify the calculation process and improve the fitting precision of the model.(3) The selection of the model boundary conditions will also impact the accuracy of the model, the traditional model took the first observation value in the original sequence as the boundary point, but the newer the observation value is, the more information related to the prediction point it contains. This paper took x (l)=x"(n) as initial value, added the interference factor β(x (1)>=x(n)+β) as initial value to do the research.An exponential function{e-n(i-1)} was fitted, and the traditional model and improved model predictions were compared. The result proved that the improved model prediction accuracy is raised. The application of the improved GM (1,1) model in bridge construction is discussed in this paper. The results also proved the effectiveness and practicality of the improved GM (1,1) model.