摘要
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.
The simulation sequence of grey forecasting model is homogeneous exponential sequence. How- ever, 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.
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2016年第4期1033-1041,共9页
Systems Engineering-Theory & Practice
基金
欧盟第7研究框架玛丽.居里国际人才引进计划(FP7-PIIF-GA-2013-629051)
国家自然科学基金(71401051)
国家自然科学基金与英国皇家学会国际合作交流项目(71111130211)
国家社会科学基金资助重点项目(12AZD102)~~
关键词
灰色预测
反向累加
分数阶
复杂装备
grey prediction
reverse accumulation
fractional order
complex equipment
