Research On The Buffer Operators With Parameters And Gm (1, 1) Power Model

With the wider application of Grey forecast theory, there are increasingly many new issues that need to be tackled with this theory. Based on ideas of"questions raising, question analysis, and question solution", this paper focuses on the theories and application of parameter-contained buffer operators and GM(1,1) exponential model. This research aims at improving Grey Systems Theory as well as expanding its application. The study can be concluded as the following parts.1. The smoothness of buffer operator is defined by initiating criterion of improving the smoothness of series as well as analyzing the smoothness of weakening buffer operator and reinforcement buffer operator. The reason of buffer operator to improve the forecast accuracy of shock disturbed system has been revealed in aspects of improving smoothness of series and eliminating shock disturbed factors.2. It is known that function strength cannot be slightly adjusted in traditional buffer operator so that its function effect is hard to co-ordinate. To solve this problem, the variable parameter is introduced in the construction of buffer operators. Such operators can be divided into two categories, exponential buffer operators and weight variable buffer operators. Several practical exponential weakening and reinforcement buffer operators are constructed. In addition, the relation of various kinds of buffer operators has been studied as well as the quantificational relation between parameters and their function strength in exponential buffer operators. Besides, the function strength is measured quantitatively and effectively controlled in weight variable buffer operator to original series. This can perfectly solve the discrepancy of results in quantitative forecast and qualitative analysis in forecast process of shock disturbed system. Based on this, the axiom of"monotony invariance"is put forward to further improve the axiom system of buffer operators.3. The whitenization methods of power exponent in GM(1,1) Power Model is put forward with the solution in whitenized differential method and properties of solution. Based on definition of condition matrix in inverse problem, the issues of possible ill-condition of matrix are studied in the parameter estimation. The main factors affecting the ill-condition of GM(1,1) Power Model are concluded. Based on non-linear optimization methods, the power exponents, interpolation coefficient of background value, and initial condition are optimized. The optimal results are verified in case study to achieve high accuracy in fluctuant series with small sample. In addition, based on the basic definition of GM(1,1) Power Model, five derived models are put forward to perfect the system of Grey Exponential Models.4. Based on the error analysis of GM(1,1) Power Model, unbiased GM(1,1) Power Model is put forward. Furthermore, the unbiasedness of model is proved in theory and in case study. Based on this, the optimization of initial condition in unbiased GM(1,1) Power Model is analyzed separately taking account of given parametersβ1 andβ2. The effectiveness of model is studied in case study.5. The forecast and warning of water discharge rate in 31 provinces and administrative regions are studied by method of weight variable buffer operator and optimized GM(1,1) Power Model, followed by policy analysis.