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中文摘要：
推导基于原序列和一阶生成序列的扩展GM（1，M）模型无偏解法，并给出灰色模型的最大预测时间尺度计算式。新建立的模型具有数值稳定、建模客观以及无偏性的特点。应用实例表明，对于小湾水电站高边坡工程，无偏扩展GM（1，M）预测精度及可靠性均优于无偏GM（1，1）和扩展GM（1，M）。
英文摘要：
An unbiased estimation method based on original series and accumulated series for extended grey model （E-GM） is developed, and the formula is proposed for calculating maximum predictable time scale of grey model. Unbiased extended GM （UE-GM） has the characteristics of numerical stability, modeling objectivity and unbiased property. The steep slope engineering of Xiaowan Hydropower Station is studied as a case. The results show that the UE-GM （1, M） model is better than the U-GM （1, 1 ） and the E-GM （1, M） models in precision and reliability.
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