Improved GM (1, 1) model prediction method based on trapezoidal formula

Abstract

The invention discloses an improved GM (1, 1) model prediction method based on a trapezoidal formula, comprising the following steps: 1, selecting a raw data sequence adopted by a prediction model according to a prediction target, wherein the original data sequence is a set of non-negative data sequences; 2, performing an accumulation process on the original data sequence to generate a cumulativesequence; 3, constructing a quadratic interpolation polynomial, building a trapezoidal formula construction background value based on the quadratic interpolation, and using the least-square method tofind parameters a, u; 4, based on the solved parameters a, u, establishing a time response sequence X<^(1)>[(k+1)] to restore the predicted value X<^(0)>[(k+1)] of an initial point, wherein the predicted value is a predicted value sequence of the original data sequence; and 5, according to the predicted values of the original data sequence solved in the previous step, performing error check to determine the prediction accuracy of a GM (1,1) model. The method of the invention can effectively adapt to various types of data changes and effectively improve the prediction accuracy of the model.

Description

technical field [0001] The invention relates to the technical field of prediction, in particular to an improved GM(1,1) model prediction method based on trapezoidal formula. Background technique [0002] As a clean mode of transportation, waterway transportation has been paid more and more attention. Accurate prediction of waterway transportation volume is of great significance for the construction of ports and waterways. Traditional prediction methods include: BP neural network, regression prediction, and analytic hierarchy process etc. These methods need to correctly select the influencing factors of port throughput, while GM(1, 1) does not need to consider the influencing factors, which avoids the reduction of prediction accuracy caused by improper selection of influencing factors. [0003] The classic GM(1,1) model forecast proposed by Professor Deng Julong, in which the background value function structure is quite different from the actual value. Through research, it is...

AI Technical Summary

Problems solved by technology

[0007] However, there is a problem in the above-mentioned method, the Runge phenomenon will appear in high-order interpolation, the present invention uses quadratic interpolation and improves the trapezoidal formula for this problem, it is found through experiments that this method has higher prediction accuracy for instances with faster data growth

Images