A Novel Kernel Regularized Nonlinear GMC(1, n) Model and Its Application

The GM(1, n) model with convolution integral (GMC(1, n)) is an effective grey multivariate prediction model with correct solutions. However, the GMC(1, n) model is still linear, which limited its applicability. In order to improve the GMC(1, n) model to be able to deal with the nonlinear relationship between the system input series and output series, a novel nonlinear GMC(1, n) model has been proposed using the kernel method, which is called the kernel regularized nonlinear GMC(1, n) model, abbreviated as KRNGMC(1, n). The KRNGMC(1, n) is represented based on the GMC(1, n) model with a nonlinear function of the input series instead of the linear combination of the input series in the GMC(1, n), by introducing a nonlinear mapping. The kernel function which satisfies the Mercer's conditions has been used in the parameter estimation by solving the regularized optimization problem and the solution of the KRNGMC(1, n) model. The numerical experiment of predicting the condensate gas well production has been carried out, of which the results indicate that the KRNGMC(1, n) is capable to describe the nonlinear relationship between the system input series and output series, and is also accurate to predict the condensate gas production, while the accuracy of GMC(1, n) is not acceptable.