| Grey model is an important method for time series prediction with small samples.With the relatively simple prediction process and high prediction performance,it has attracted the attention of many scholars.At present,with the development of grey prediction theory,scholars put forward lots of novel grey models.However,most of these models lack adaptive ability,so they always fail to achieve high prediction performance when dealing with the prediction tasks in different scenarios Secondly,the current grey model has the problem of insufficient prediction performance for the data of complex nonlinear features.In order to ease the above problems,the main research contents of this thesis are as follows1.An adaptive grey model fusing with neural ordinary differential equations is presented.Combining a novel neural network to improve the whitening equation of grey model,the adaptive grey model is able to define a suitable grey model for samples with different characteristics.The model has a flexible differential equation,so it can be applied to many prediction tasks with different distribution characteristics.The grey model is trained by the given sample data,the parameters of the grey model are updated by back propagation to find the optimal model structure,and then the model is solved by the numerical solution of differential equations.2.A multikernel nonhomogeneous grey model with high nonlinear time series prediction ability is proposed.Kernel method is a kind of method that can deal with nonlinear features effectively,but the single kernel method has some limitations.In order to solve this problem,the multikernel learning algorithm of center alignment is combined to express the heterogeneous nonlinear features by using multiple kernel functions,and the weights of different kernel matrices are obtained by optimizing the center alignment values of different kernel matrices to generate more sufficient kernel matrices.Finally,the multikernel learning method is introduced into the nonhomogeneous grey model,and the centered alignment multikernel nonhomogeneous grey model is established to further improve the prediction accuracy of the model for nonlinear data. |
