A novel time-power based grey model for nonlinear time series forecasting

Abstract

To deal with various nonlinear issues in real applications, a novel time-power based grey model is put forward. However, in the original form of this model, the time-power parameter α normally equals to an integer, and then the analytical expression of the time response function will be obtained. Otherwise, if the parameter α equals to a non-integer, one cannot obtain the concrete time response function for future estimations. This situation may significantly restrict the applications of this grey model. To address such drawbacks, an optimized version is designed in this work. In the proposed model, a simplified solution to the differential equation is derived by using the definite integral technique. Furthermore, for improving accuracy, the time-power parameter α is optimized by utilizing the Particle Swarm Optimization algorithm based on the model parameter packages. Subsequently, the efficacy and practicality of this simplified function have been verified by numerical simulations and experimental studies. Moreover, the method of probability density prediction is employed for verifying the reliability and stability of the proposed model for the first time when predicting the settlement of the soft-clay subgrade on an expressway. The demonstration cases illustrate that the quantitative improvements over forecasts of the proposed model are even more pronounced with a level accuracy of 2.29% and 1.19% MAPE values in the fitted and predicted periods, respectively, which can significantly increase the predicting accuracy by more than 10% with respect to the other benchmarks. Therefore, the new proposed model not only has greater application fields and prospects but also achieves higher and more reliable predicting accuracy with the optimal α under the support of the Particle Swarm Optimization algorithm, compared with the competing models.