Non-Equidistant GM(1,1) Models Based on Fractional-Order Reverse Accumulation and the Application

ZENG Liang

doi:10.21656/1000-0887.380252

Volume 39 Issue 7

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ZENG Liang. Non-Equidistant GM(1,1) Models Based on Fractional-Order Reverse Accumulation and the Application[J]. Applied Mathematics and Mechanics, 2018, 39(7): 841-854. doi: 10.21656/1000-0887.380252

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Non-Equidistant GM(1,1) Models Based on Fractional-Order Reverse Accumulation and the Application

doi: 10.21656/1000-0887.380252

ZENG Liang

Department of Basic Courses, Guangdong Polytechnic College, Zhaoqing, Guangdong 526100, P.R.China

Funds: The National Natural Science Foundation of China(61472089)

Received Date: 2017-09-07
Rev Recd Date: 2017-11-09
Publish Date: 2018-07-15

Abstract

Abstract

For the prediction of non-equidistant decreasing series, a non-equidistant GM(1,1) model based on the 1st-order reverse accumulation was constructed, and the least square solutions of the model parameters and the discrete time response functions applicable to prediction were given. In order to further improve the prediction accuracy, a fractional-order reverse accumulation non-equidistant GM(1,1) model was proposed. With the objective of minimizing the average relative error of simulation, a nonlinear programming model was established to obtain the optimal order. Finally, numerical simulation and an example of the prediction of the fatigue strength of Ti alloy were given to verify the validity and practicability of the proposed model.
- grey prediction model,
- reverse accumulation,
- non-equidistant,
- GOM(1,1) model,
- fractional order

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References(22)

References

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