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Highlights A novel grey Richards model GERM(1,1, ) is proposed. The optimal nonlinear terms and background value of the novel model are determined by Genetic algorithm. The comparative study shows that the new model is superior to the other seven benchmark models. The predict the daily number of new confirmed cases of COVID-19 of four regions are projected.

Objective: and accurate prediction of clean energy can supply an important reference for governments to formulate social and economic development policies. This paper begins with the logistic equation which is the whitening equation of the Verhulst model, introduces the Riccati equation with constant coefficients to optimize the whitening equation, and establishes a grey prediction model (CCRGM(1,1)) based on the Riccati equation. This model organically combines the characteristics of the grey model, and flexibly improves the modelling precision. Furthermore, the nonlinear term is optimized by the simulated annealing algorithm. To illustrate the validation of the new model, two kinds of clean energy consumption in the actual area are selected as the research objects. Compared with six other grey prediction models, CCRGM(1,1) model has the highest accuracy in simulation and prediction. Finally, this model is used to predict the nuclear and hydroelectricity energy consumption in North America from 2019 to 2028. The results predict that nuclear energy consumption will keep rising in the next decade, while hydroelectricity energy consumption will rise to a peak and subsequently fall back, which offers important information for the governments of North America to formulate energy measures.

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Image filtering can change or enhance an image by emphasizing or removing certain features of the image. An image is a system in which some information is known and some information is unknown. Grey system theory is an important method for dealing with this kind of system, and grey correlation analysis and grey prediction modeling are important components of this method. In this paper, a fractional grey prediction model based on a filtering algorithm by combining a grey correlation model and a fractional prediction model is proposed. In this model, first, noise points are identified by comparing the grey correlation and the threshold value of each pixel in the filter window, and then, through the resolution coefficient of the important factor in image processing, a variety of grey correlation methods are compared. Second, the image noise points are used as the original sequence by the filter pane. The grey level of the middle point is predicted by the values of the surrounding pixel points combined with the fractional prediction model, replacing the original noise value to effectively eliminate the noise. Finally, an empirical analysis shows that the PSNR and MSE of the new model are approximately 27 and 140, respectively; these values are better than those of the comparison models and achieve good processing effects.