An improved grey dynamic GM(2, 1) model

Abstract

In recent years, the grey dynamic model GM(2, 1), which is based on the grey system theory has been successfully applied in many prediction fields to solve efficiently the predicted problems of uncertainty systems. However, this model has irrational problem concerning the calculation of initial value and derivative. Therefore, the predicted accuracy of GM(2, 1) is unsatisfying when original data show great randomness. In this paper, the new calculation of initial value and derivative are first proposed to enhance the predicted power according to cubic spline function. The newly generated model is defined as 3spGM(2, 1). To further improve predicted accuracy, the Taylor approximation method is then applied to 3spGM(2, 1). We call the improved version as T-3spGM(2, 1). Finally, the effectiveness of proposed model is validated by using fault data sets of electric product.

Keywords:

• grey dynamic GM(2,1) model
• initial value
• derivative
• cubic spline function
• Taylor approximation method
• optimization method

2000 AMS Subject Classifications :

• 90C90
• 46G05
• 65D10
• 62M10
• 68M15

Acknowledgements

The work was supported by Grants-in-Aid for Scientific Research (No. 6050) of Japan Society for the Promotion of Science.