Modified grey model predictor design using optimal fractional-order accumulation calculus

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 U+0028 GM U+0029 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 U+0028 1, 1 U+0029 and improve the accuracy of predictor. The state space model of optimally modified GM U+0028 1, 1 U+0029 predictor is given and genetic algorithm U+0028 GA U+0029 is used to find the smallest relative error during the modeling step. Furthermore, the fractional form of continuous GM U+0028 1, 1 U+0029 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.

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