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中文摘要：
基于GM（1,1）幂模型的模拟误差分析,本文提出了无偏GM（1,1）幂模型及其参数优化方法。从理论上证明了无偏GM（1,1）幂模型对传统GM（1,1）幂模型及其本身的时间响应函数所表达的曲线进行模拟和预测具有重合性,其参数优化方法可以准确识别原始数据所蕴含的参数特性,完全消除了GM（1,1）幂模型自身固有的偏差。其建模过程避免了传统方法由差分方程向微分方程的跳跃导致的误差,应用范围覆盖了无偏GM（1,1）模型和离散灰色模型。数值模拟和实例分析表明,无偏GM（1,1）幂模型使得传统模型的模拟与预测精度得到了显著的改善。
英文摘要：
Based on the analysis of inherent errors in traditional GM（1,1） power model,this paper puts forward Unbiased GM（1,1） power model.It is theoretically proved that the complete coincidence of the prediction and simulation to the original data of its time response curve generated form has achieved.The unbiased model presented in this paper has completely eliminated the inherent simulant error of the traditional model,but also avoided the jumping errors from the differential equation to differential equation in traditional grey modeling.The application of this model covers unbiased GM（1,1） model and gray discrete model.Numerical simulation and case analysis shows that the simulation and prediction accuracy in traditional modeling has been significantlg improved by unbiased GM（1,1） power model.
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