The Optimization Method Research On Grey MGM (1, M) And Verhulst Model

Grey prediction model is an important part of grey system theory. It is to research the greyMGM(1,m) model and Verhulst model. The characteristics, the background value optimizationmethod and the time response-type optimization method are studied on the grey MGM(1,m) modeland Verhulst model under equal and non-equal space. Main results are as follows:(1) MGM (1, m) model and its optimization method are studied. Corresponding multiplytransformation is made for the original data series of MGM(1, m) model. The effect of multipletransformations on parameters characteristics of the model is analyzed, and the changes of simulationand prediction values and the relative errors of the model after multiple transformations are discussed.Starting from its error source of structural formula for the background value, the paper usesnon-homogeneous exponential functions to fit the accumulated sequences and establishes aMGM(1,m) model of background value optimazation in order to improve the simulation andprediction accuracy of the traditional MGM(1,m) model.(2) The optimization method on the non-equidistance MGM(1,m) model is studied. The modelmechanism of the non-equidistance MGM(1,m) model is researched to establish the model for thenon-equidistance original data sequences obtained from the actual work (such as materialsengineering, physics, remote sensing mapping and professional), simulate and predict these originaldata sequences. The characteristics of non-equidistant MGM(1,m) model is discussed under theoriginal sequence made by multiply transformation. The calculation formula of parameter vector,simulation and prediction values and the relative errors of the non-equidistant MGM(1,m) modelafter multiple transformations are derived by using the operation nature about matrix.The changes ofparameter vector,simulation and prediction values and the relative errors after multipletransformations are compared,which lays the theoretical foundation for the non-equidistanceMGM(1,m) model. In addition, this paper researches the building method of background value on thenon-equidistant MGM(1,m) model and uses the functions with non-homogeneous exponential law tofit the accumulated sequences for every variable to optimize background value of non-equidistantMGM(1,m) model to establish optimization model.(3) The optimization method on the grey Verhulst model is studied. With regard to thepreprocessing of original grey modeling data, the parameters characteristics of the grey Verhulstmodel under multiple transform is studied. For the optimization problem of the time responsefunction,the parametercof time response function is determined using the least-squares method inthe Verhulst model, and the time response function optimization Verhulst model is established. Finally,this paper researches the problem of background value optimization of the model. With regardto the optimization problem of the background value, the paper uses the Logistic function to fit theaccumulated sequence,solves three parameters in Logistic function, gets the optimal formula ofbackground value of grey Verhulst model through a series of mathematical derivation, and constructsthe optimal grey Verhulst model after analyzing background value error of traditional grey Verhulstmodel.(4) The optimization method on the non-equidistance grey Verhulst model is studied. Thecharacteristics of the non-equidistance grey Verhulst model under the case of being multiplied by thenumber changing for the modeling data sequence are researched. The time responsive of thenon-equidistant grey Verhulst model is optimized to establish the corresponding optimization model.The background value optimization of the non-equal spacing grey Verhulst model is researched. Theoptimization method research of non-equidistant grey Verhulst model is a promotion for the equallyspaced case.