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中文摘要：
针对NGM（1,1,k）的基本形式与白化微分方程的跳跃性关系,尝试对NGM（1,1,k）模型进行优化.首先对白化微分方程积分,得到新的NGM（1,1,k）参数估计基本形式,通过定义其中的前置与后置背景值,分析误差产生的几何原因,进而推导背景值计算公式;然后利用误差平方和构建期望函数,求解时间响应函数中的最优常数表达式;总结优化后的NGM（1,1,k）模型的建模步骤,并证明该模型具有非齐次白指数重合性;最后,通过两个算例将优化模型与经典模型进行对比,取得了良好的效果,进而验证了所提出模型的有效性和实用性.
英文摘要：
According to the jumping relation between the basic form and the whitenization differential equation in NGM（1, 1, k）, the model is optimized. Firstly, the whitenization differential equation is integrated in the interval [k- 1, k]to obtain the new parameter estimation basic form of NGM（1, 1, k）. The front and before background value are defined and the precise calculation formulas are derived. The causes of error are also analyzed in the geometric relationship. Then the desirability function is built based on the sum of the error square, to determine the optimal constant value in the time response function. The optimized modeling steps of NGM（1, 1, k） are summarized, and it is proved that the model has a non-homogeneous white exponential superposition. Finally, the optimization model and the classical model are contrasted by two examples, the good results obtained show the effectiveness and practicality of the proposed optimization model.
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