Unbiased Grey Polynomial Model Based on Precise Direct Integration Method (Journal of Nonlinear Modeling and Analysis, 2024)
During the conversion from difference to differential in the greypolynomial model, the “misplaced replacement” problem will occur. A novelunbiased 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 forGMP(1, 1, $N$) model. The recurrence relation is deduced from the solutionof the homogenized differential equations, converted from the whitenizationequation of GMP(1, 1, $N$) model by introducing new variables. The simulatedvalues are directly calculated by the precise direct integration method in order to reduce round-off error and improve fitting accuracy. Moreover, it isproved that the proposed unbiased grey polynomial model possesses not onlycomplete coincidence of simulation to non-homogeneous exponential sequencewith polynomial time terms, but also multiple transformation consistency. Atlast, the results of applications verify the effectiveness of the proposed modelby comparing with other conventional models.