Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

Yang Yang; Dingyu Xue

doi:10.1109/JAS.2017.7510355

Volume 4 Issue 4

Oct. 2017

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2017 > 4(4): 724-733

Yang Yang and Dingyu Xue, "Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus," IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 724-733, Oct. 2017. doi: 10.1109/JAS.2017.7510355

Citation:

Yang Yang and Dingyu Xue, "Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus," IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 724-733, Oct. 2017. doi: 10.1109/JAS.2017.7510355

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Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

doi: 10.1109/JAS.2017.7510355

Yang Yang^{1, 2
,},
Dingyu Xue^{1
,
,}

1.
College of Information Science and Engineering, Northeastern University, Shenyang 110004, China
2.
College of Engineering, Bohai University, Jinzhou 121013, China

Funds:

the National Natural Science Foundation of China 61174145

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Abstract

Abstract

The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model (GM) depends on the preprocessing of the original data, the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1, 1) and improve the accuracy of predictor. The state space model of optimally modified GM(1, 1) predictor is given and genetic algorithm (GA) is used to find the smallest relative error during the modeling step. Furthermore, the fractional form of continuous GM(1, 1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.
- Fourier series,
- fractional-order accumulation,
- genetic algorithm (GA),
- grey model (GM)

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References(35)

References

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Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

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