(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
During the conversion from difference to differential in the grey polynomial model, the “misplaced replacement” problem will occur. A novel unbiased grey polynomial model, i.e., HUGMP(1, 1, N) is presented to overcome the above drawback. Meanwhile, the parameter estimation of HUGMP(1, 1, N) is directly constructed by the equivalent relation between the parameter estimation and the recurrence relation of the time response function for GMP(1, 1, N) model. The recurrence relation is deduced from the solution of the homogenized differential equations, converted from the whitenization equation of GMP(1, 1, N) model by introducing new variables. The simulated values are directly calculated by the precise direct integration method in order to reduce round-off error and improve fitting accuracy. Moreover, it is proved that the proposed unbiased grey polynomial model possesses not only complete coincidence of simulation to non-homogeneous exponential sequence with polynomial time terms, but also multiple transformation consistency. At last, the results of applications verify the effectiveness of the proposed model by comparing with other conventional models.