Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (5): 1009-1018.doi: 10.23919/JSEE.2020.000075

• Systems Engineering • Previous Articles     Next Articles

Fractional derivative multivariable grey model for nonstationary sequence and its application

Yuxiao KANG(), Shuhua MAO*(), Yonghong ZHANG(), Huimin ZHU()   

  • Received:2019-11-05 Online:2020-10-30 Published:2020-10-30
  • Contact: Shuhua MAO E-mail:kangyuxiao@whut.edu.cn;maosh_415@whut.edu.cn;1358167754@qq.com;zhuhuimin@whut.edu.cn
  • About author:KANG Yuxiao was born in 1983. She received her M.S. degree in 2008 from Wuhan University of Technology (WHUT), Wuhan. She is currently pursuing her Ph.D. degree at the School of Science, WHUT. Her research interests are grey system theory and application. E-mail: kangyuxiao@whut.edu.cn|MAO Shuhua was born in 1973. He received his Ph.D. degree in 2011 from Wuhan University of Technology (WHUT), Wuhan. He is now a professor in WHUT. His research interests are prediction modeling and risk assessment of uncertain systems. E-mail: maosh_415@whut.edu.cn|ZHANG Yonghong was born in 1995. He is currently pursuing his M.S. degree of statistics with the Department of Statistics, Wuhan University of Technology. His research interest is grey system. E-mail: 1358167754@qq.com|ZHU Huimin was born in 1979. She received her M.S. degree in 2008 from Wuhan University of Technology (WHUT), Wuhan. She is currently pursuing her Ph.D. degree at the School of Science, WHUT. Her research interests are grey system theory and application. E-mail: zhuhuimin@whut.edu.cn
  • Supported by:
    the National Natural Science Foundation of China(51479151);the National Natural Science Foundation of China(61403288);This work was supported by the National Natural Science Foundation of China (51479151;61403288)

Abstract:

Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC$ \mathit{\boldsymbol{(q, N)}} $ is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization (PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC$ \mathit{\boldsymbol{(q, N)}} $ model is used to predict the municipal solid waste (MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.

Key words: fractional derivative of Caputo type, fractional accumulation generating operation (FAGO), Laplace transform, multivariable grey prediction model, particle swarm optimization (PSO)