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在加权最小二乘框架下构建了含时间多项式项的灰色GMP(1,1,N)模型,该模型既适用于小样本单调序列又适用于波动序列,论证了均方误差最小准则、均方相对误差最小准则与平均绝对百分误差最小准则下的GM(1,1)、NGM(1,1,k)和GM(1,1,t~α)模型均是GMP(1,1,N)模型的特殊形式,将GMP(1,1,N)模型应用于黄河宁蒙河段冰凌灾害风险预测,结果表明2015-2016年的风险预测结果符合实际情况,模型能够识别风险波动变化规律.为不同准则下灰色预测新模型的构建提供了新思路,具有重要的理论意义和工程应用前景.
A gray GMP (1,1, N) model with time polynomial is constructed under the weighted least squares framework. This model is not only suitable for small sample monotone series but also for fluctuating series. The minimum mean square error criterion is proved. The GM (1,1), NGM (1,1k) and GM (1,1, t-α) models with the minimum relative error criterion and the minimum absolute mean absolute error criterion are both GMP (1,1, N ) Model, the GMP (1,1, N) model was applied to predict the ice disaster risk in the Ningxia-Menghe section of the Yellow River. The results show that the risk prediction results from 2015 to 2016 are in line with the actual situation and the model can identify the variation of risk fluctuations. It provides a new idea for the construction of a new gray prediction model under different criteria, which has important theoretical significance and engineering application prospects.