Improvement And Application Of GM(1,1) Forecasting Model In Urban Water Consumption

With the development of social economy, the modern social productivity has been greatly improved. Scientific prediction has gradually replaced the prediction of superstition and experience and developed into a branch of prediction subject, whose appearance is adapt to the needs of development of modern economy.The traditional forecasting method is a forecasting method that was researched by people according to the characteristics and rules of the system. However, These prediction models are aimed at the problems of the "big data" and the "clear system information". With regard to the uncertain problems of the "little data" and "poor information", the research scholars put forward the gray forecasting model. The gray forecasting model uses the few data and has simple principle and can be used in the inspection examination. However, its predictive ability has certain limitations and its long-term prediction accuracy is low.In order to avoid the limitation of the gray prediction model, people try to combine it with other models to form a combined forecasting model. The combined models can actualize the mutual complementation of the functions and advantages among different models so that it can avoid the limitations of a single model, enhance the ability of forecasting and increase the prediction accuracy.The main research work of this paper is as follows:In the first part of the paper, the basic theories, the main concepts and the basic principles of the gray system are expounded, and the basic principles are analyzed and proved in detail;In the second part of the paper, this paper introduces the basic model of the gray system, namely GM(1,1). The design idea of the model is expounded and the modeling principle is proved in detail.In the third part of the paper, it introduces the MSR-GM(1,1) prediction model. The combination forecasting model is formed by the combination of the prediction model and the multiple linear regression model. First, the gray correlation degree would be used to select the independent variables, which serves as a set of prediction independent variables with a large gray correlation degree to the dependent variable. Second, in order to further simplify the model, using stepwise regression theory, we make a further selection to the selected set of prediction independent variables so that we can select the more accurate correlation factor as the final independent variable set. Then, we can establish regression model according to the selected set of independent variables. At the same time, we can establish()GM1,1 prediction model and forecast it respectively according to the selected set of independent variables. We can calculate predictive value of the dependent variable. by means of pluging the predicted generation into the established regression model.Finally, the evaluation is carried on theMSR-GM(1,1) prediction model which were established. The combined forecasting model would be used to predict the water consumption of a city, and the results show that the combination model has high prediction accuracy, which proves the rationality of the model.In the fourth part of the paper, it describes the GM(1,1)-MA prediction model, which is the combination of the gray prediction model and the time series model. First, the gray prediction model would be used to carry a reasonable and medium-term prediction on the system in question. Second, with regard to error sequence produced by prediction, we should select the proper smooth period M and establish reasonable and simple sliding smooth model,which would be used to smooth, analyze and predict the error series and to correct the residual error of prediction model so that we can obtain a combination forecasting model with a higher accuracy. Finally, the effectiveness of the combined forecasting model would be verified by an example. The results show that the prediction accuracy of the combined forecasting model is higher than that of any single model.In the fifth part of the paper, we use the MSR-GM(1,1) prediction model and the MSR-GM(1,1) prediction model to simulate and predict the water consumption of a city respectively. The result shows that the prediction accuracy of the combined forecasting model is higher than that of any single model. Besides, it has a greater reference value.