分数阶反向累加NHGM(1,1,k)模型及其应用研究

灰色预测模型的模拟序列是齐次指数序列,而实际应用中大量存在着近似非齐次指数序列,为了解决这个问题,在已有研究的基础上,提出了一阶反向累加NHGM(1,1,k)模型和分数阶反向累加NHGM(1,1,k)模型.分析了两种模型的扰动界,并对一阶反向累加NHGM(1,1,k)模型和分数阶反向累加NHGM(1,1,k)模型的计算公式进行了推导,给出了两类模型适用于小样本建模的原因.由于充分利用了系统的新信息,分数阶反向累加NHGM(1,1,k)模型的预测精度更高,实例分析发现其解的稳定性更好.最后,将分数阶反向累加NHGM(1,1,k)模型运用在具有多个研制阶段的某型号武器装备可靠度的预测上,取得了较高的预测精度.

Research on fractional order reverse accumulative NHGM(1, 1, k) model and its application

The simulation sequence of grey forecasting model is homogeneous exponential sequence. However, there exist a large number of the approximate inhomogeneous sequences in the practical application. The first order reverse accumulative NHGM(1, 1, k) (FTORA-NHGM(1, 1, k)) model and fractional order reverse accumulative NHGM(1, 1, k) (FORA-NHGM(1, 1, k)) model were proposed on the basis of previous research. The perturbation bounds of the two models were analyzed, and the calculation formulas of the FTORA-NHGM(1, 1, k) model and FORA-NHGM(1, 1, k) model were derived. The reason that the two models were suitable for small samples was given. The FORA-NHGM(1, 1, k) model has higher prediction accuracy because it takes full advantage of the new information of the system. It was found that the solution of the FORA-NHGM(1, 1, k) model has higher stability through the instance analysis. Finally, the FORA-NHGM(1, 1, k) model was used in the prediction of the reliability degree of a certain type of weapon with multiple development phase, and higher prediction was achieved.