Affiliations: [a]
Academic Affairs Office of Sanjiang University, Nanjing, Jiangsu, China
| [b] School of Computer Science and Information Engineer, Shanghai Institute of Technology, Shanghai, China
| [c] Department of Information Science and Engineering, Zaozhuang University, Zaozhuang, Shandong, China
| [d] College of Intelligent Education, Jiangsu Normal University, Xuzhou, Jiangsu, China
Correspondence:
[*]
Corresponding author. Liu Caixia, E-mail: cxsqz@126.com.
Abstract: Fractional order grey model is effective in describing the uncertainty of the system. In this paper, we propose a novel variable-order fractional discrete grey model (short for VOFDGM(1,1)) by combining the discrete grey model and variable-order fractional accumulation, which is a more general form of the DGM(1,1). The detailed modeling procedure of the presented model is first systematically studied, in particular, matrix perturbation theory is used to prove the validity in terms of the stability of the model, and then, the model parameters are optimized by the whale optimization algorithm. The accuracy of the proposed model is verified by comparing it with classical models on six data sequences with different forms. Finally, the model is applied to predict the electricity consumption of Beijing and Liaoning Province of China, and the results show that the model has a better prediction performance compared with the other four commonly-used grey models. To the best of our knowledge, this is the first time that the variable-order fractional accumulation is introduced into the discrete grey model, which greatly increases the prediction accuracy of the DGM(1,1) and extends the application range of grey models.
