Abstract
In this study, we propose a new gray model called “normalized beta function gray model”. Its main idea is to use the normalized beta function to optimize the linear gray action quantity into a nonlinear form. It is worth mentioning that when solving the nonlinear parameters of the newly proposed model, we construct a nonlinear optimization problem with constraints by taking the mean square error of the model as the objective function, and find the optimal solution under the given precision by using the simulated annealing algorithm. We use the new gray model to predict gasoline consumption and PM2.5 concentration, compared with the other three gray models, the proposed gray model reduces the mean absolute percentage error to 2.99% and 32.75%, respectively, which is 88.67% and 60.25% lower than the maximum value of mean absolute percentage error of four gray models. We also apply the newly proposed gray model to the simulation studies, which shows excellent prediction ability.
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