Identifying Parameters And Optimization Method Research Of Several Grey Prediction Models

The grey system theory was born in twentieth Century 80 years, founded by China scholar Professor Deng Julong. It mainly researches "small sample, poor information" uncertain problems, through mining the "part" known information to develop and extract valuable information. In the actual production and life, poor information uncertainty system’s universal existence determines that the new theory has very broad prospects for development. Grey uncertainty prediction is an important field of modern prediction, and successfully applied in many other fields.Grey GM prediction model is one of the main contents of grey system theory, generally refers to the GM(1,1) model and its extended form, mainly including GM(1,1) model, DGM(1,1) model and grey Verhulst model and so on. At present, although the grey GM prediction models have been widely used in many fields of society, economy, science and technology, industry and agriculture, the theory system is still not perfect. Therefore, many experts and scholars who study on gray theory put forward different new ways to further optimize and improve the defects of existing grey GM prediction models from different aspects, to improve the prediction accuracy and extend its scope of application.The simulation and prediction accuracy of grey GM prediction model depends on parameters in the model, so the core goal of most optimization method is to determine the more ideal parameters, in order to achieve the ultimate objective of improving the simulation and prediction precision. According to the problem of the parameters matching and solving of grey GM model and GM direct modeling model, based on the existing theories and methods, this paper does the following five aspects of work:(1) For the GM(1, 1) model is applicable to nearly exponential case, the concept of using minimum sum of error square is proposed to develop new prediction mode. At first, two kinds of simple and quick methods to estimate the development coefficient a are determined directly via approximately estimating the common ratio. Then let the response coefficient c of the time response sequence undetermined, and the simulating formula of the original sequence is obtained by reducing. Again, using four different objective functions to determine the prediction coefficients, and eight kinds of prediction models are constructed through the combination. While adding the original model and other existing four optimization models, a total of thirteen kinds of prediction models are obtained for simulation comparison at the same time. Through example calculation, finding that starting from the angle of average relative error, using the arithmetic mean of the original sequence stepwise to identify the development coefficient and prediction coefficient is the best way to construct the model, and the result can be used as reference in prediction field.(2) For the GM(1, 1) model is applicable to nearly exponential case, the method of combining grey derivative optimization with using the simulated average relative error of the original sequence minimum to estimate forecast coefficient c is proposed to construct a new optimization GM(1,1) model of simplified calculation. The prediction formula()()akcekx-=0? of the model is formally more concise. And the strict index series is theoretically verified that parameter a has white exponential law of coincident property and prediction coefficient c has white coefficient of coincidence property.(3) According to the non-equidistant sequence in non-homogeneous index form, the non-equidistant GM(1, 1) direct model was constructed by the original sequence. And the new non-equidistant GM(1, 1) direct model was established by combining simultaneous optimization of background value and grey derivative with using “average relative error minimum” to determine the response coefficient. Through analyzing the examples, it illustrates the feasibility and effectiveness of the new optimization model.(4) Through the analysis of the traditional grey Verhulst model by using the reciprocal transformation to solve the whitening equation, it is found that the mismatch of the grey differential equation with whitening equation is the root of model errors. The method of directly using the reciprocal transformation sequence of the 1-AGO sequence to establish the grey differential equation that matches with the whitening equation by reciprocal transformation to estimate parameters is proposed. And the methods of optimizing the grey derivative to transform the gray equation and regarding the minimum of average relative error as index to determining the response coefficient are combined to optimize the model. The result shows that the optimization model is simulated and predicted with coincidence to the time response function expressed by the curve.(5) Aiming to the saturated original sequence approximately satisfies Logistic function, the grey Verhulst direct model is constructed by reciprocal generation of the original sequence. And the optimization unbiased grey Verhulst direct model is established by combining simultaneous optimization of background value and grey derivative with using “average relative error minimum” to determine the response coefficient. The result shows that, the model is simulated and predicted with complete coincidence to meet Logistic function curve.