A Novel Fractional-order Discrete Grey Model with Initial Condition Optimization and Its Application

Abstract

Estimating the optimal order of fractional accumulating operator and the optimal initial value are two inherent problems in studies of fractional grey models. To find the optimal order of fractional accumulating operator, numerical iteration algorithm is applied in this paper. It is used in applications compared with the other two existing optimization algorithm (genetic algorithm and particle swarm optimization algorithm), which proves that the numerical iteration algorithm is simpler than the other two algorithms and has the same accuracy. At the same time, this paper proposes a numerical method to find the optimal initial condition and gives a proof. And based on methods mentioned previously, a novel fractional-order grey discrete model with initial value optimization is proposed. In order to test the new model, per capita power consumption in southern Jiangsu province is employed. Results show that the new fractional-order discrete grey model proposed in this paper is better than the competitive grey model in predicting and fitting periods.