Construction of accumulative time-delay nonlinear ATNDGM(1, N) model and its application

YE Lili, XIE Naiming, LUO Dang

Systems Engineering - Theory & Practice ›› 2021, Vol. 41 ›› Issue (9) : 2414-2427.

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Systems Engineering - Theory & Practice ›› 2021, Vol. 41 ›› Issue (9) : 2414-2427. DOI: 10.12011/SETP2020-0028

Construction of accumulative time-delay nonlinear ATNDGM(1, N) model and its application

  • YE Lili1, XIE Naiming1, LUO Dang2
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Abstract

As to the problem of prediction modelling for multivariable time-delay and nonlinear systems, a new multivariable grey prediction model, called the accumulative time-delay nonlinear multivariable discrete grey model (ATNDGM(1, N)), is proposed by adding time-delay driving term and power exponent, and its parameters calculation method is given. The accumulative time-delay grey incidence model is put forward to determine the driving factors and time-delay parameters, and the relationship between the time-delay period and the time-delay weight is discussed. In addition, the optimal power exponent is determined by particle swarm optimization. It is proved to be that the DGM(1, N)、DGPM(1, N) and ATDGM(1, N) models are all the special cases of ATNDGM(1, N) model, and the affections of multiplication transformation caused to this model is studied. The numerical examples are carried out to assess the modeling feasibility in comparison with other models. Finally, the ATNDGM(1, N) model is employed to predict the agricultural output value in Henan Province. The results show that this model has high fitting and forecasting accuracy, which can effectively deal with the prediction problem of small sample multivariable systems with time-delay and nonlinear characteristics.

Key words

grey ATNDGM(1, N) model / accumulative effect / time-delay / nonlinearity / agricultural output value

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YE Lili , XIE Naiming , LUO Dang. Construction of accumulative time-delay nonlinear ATNDGM(1, N) model and its application. Systems Engineering - Theory & Practice, 2021, 41(9): 2414-2427 https://doi.org/10.12011/SETP2020-0028

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Funding

National Natural Science Foundation of China (71671090, 51979106); Qinglan Project for Excellent Youth or Middle-Aged Academic Leaders in Jiangsu Province of China
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