Grey Incidence And Grey Forecasting Models With Their Application

Grey system is a kind of uncertainty research method for the problem of “less data and poor information”,and has been successfully applied in many fields.Environmental pollution system is a kind of typical uncertain system,the influence factors of that are numerous and complex,so classical methods are difficult to deal with.In order to promote the development of grey system theory and the environmental pollution analysis,this paper studies the technology of grey modeling,resolving the structure of environmental pollution by using the grey incidence theory,fitting the development trend of environmental pollution by using grey prediction theory.The main research contents and conclusions are as follows:(1)Extended grey incidence distance space,the geometric difference between sequences is represented as the space distance between the vectors and the matrixs.Firstly,defining unitary sequence and multiple sequences,the grey incidence models are classified according to the original data type.Then the geometric characteristic difference between unitary sequences is extracted as a vector based on nearness and similarity,and the grey incidence model based on vector norm is constructed.Based on the grey space grid theory,the geometric characteristic difference between multiple sequences is extracted as a matrix,and the multivariate grey incidence model based on matrix norm is constructed.Finally,the property of the model is studied,and the unity of the two models is verified.(2)A new weighted multivariate grey incidence model is constructed to explore the relationship between the two groups of different variables.Firstly,the multiple sequences are reduced by constraint weights to set up the basis of the analysis between multiple sequences and unitary sequence.Then,the geometric characteristic of the sequence is extracted as a vector,and the degree function of grey incidence is established with the weight as the independent variable.Finally,the optimal weights are solved by nonlinear programming,and the unilateral weighted multivariate grey incidence model is constructed.Based on the same idea researching on the problem of grey incidence between two sets of multivariate sequences under different conditions,the bilateral weighted multivariate grey incidence model is constructed on the basis of dimension reduction in two sets of multivariate sequences.(3)Grey incidence test model.Firstly,the nonlinear characteristics of the grey correlation model is studied to point out that the grey incidence model does not have the condition for direct test.Then,the characteristic difference is extracted from the grey incidence model with correlation coefficient and the generalized grey incidence model,and the unity of the two kinds of methods is verified.Then according to the fluctuation degree of the characteristic difference sequence,the fluctuation coefficient is defined,and combining grey incidence degree the stability test coefficient is constructed to measure the stability of the relationship between the sequences.In the case of the original data for time series,the slope of the line in the least square fitting of the characteristic difference sequence is defined as the tendedcy test coefficient,which is the trend of the variation of the relationship between the sequences.Finally,based on the concept of stability and tendency,three test models are constructed,which is unitary grey incidence test model,matrix type multivariate grey relational model and new weighted multivariate grey incidence model.(4)The optimization of non-homogeneous grey forecasting model and the extension of multivariate non-homogeneous grey forecasting model.Firstly,the unitary non-homogeneous grey forecasting theory is summarized,and the basic form of NGM(1,1,k)is defined.Then the background value of NGM(1,1,k)is optimized by the numerical integration method,and the accurate calculation formula of background value is derived.Through the method of adding parameters to optimize the NGM model,deriving the basic form of NGM(1,1,k)from two aspects of grey derivative and background value,the direct modeling formula of unbiased NGM(1,1,k)is established.Then,the time response function of the NGM model is optimized,and the optimal constant is solved with the least square of the error.Finally,the multivariate non-homogeneous grey forecasting model is studied,and the NGM(1,1,k)is constructed through determining the coefficient ratio of the relevant factors on the effective contribution rate.(5)Research on air pollution in Nanjing by using grey modeling technique.Firstly,air pollution status of Nanjing is analyzed through vertical and horizontal comparison,and we find that Nanjing in the Yangtze River Delta region is a more serious pollution of the city.Then the main sources of air pollution in Nanjing and the main power of air pollution control are analyzed,the main factors that affect the atmospheric environment in Nanjing are summarized as five aspects: industry,agriculture,urban life,transportation and environmental protection.Collecting Nanjing air quality days,PM2.5,PM10,SO2,NO2,CO and other major pollutants annual indicators,and collecting the representative indicators of the main impact factors system,using the grey modeling technique to analyze,we found that the industrial and transportation systems have the greatest impact on the atmospheric environment of Nanjing,and the impact of urban life and agriculture is decreased in turn,environmental pollution control improve the quality of the atmosphere in Nanjing,but governance efficiency needs to be more improved,the development trend of major pollutants has strong uncertainty.