中文摘要：

针对GM（1,1）模型易受建模数据随机扰动影响,且模型稳定性较差的问题,该文提出了基于马尔科夫（Markov）理论的GM（1,1）预测优化模型。首先,通过最小二乘原理选取GM（1,1）模型的最优初值,利用指数函数法构造新的背景值,同时利用正化残差序列法进一步修正残差。然后,将优化的GM（1,1）模型和马尔科夫理论有机结合,进一步对优化的GM（1,1）模型进行改进,构建了优化的灰色马尔科夫预测模型。最后,以某建筑物的变形实测数据为基础,进行了传统GM（1,1）预测模型、优化的GM（1,1）预测模型和优化的灰色马尔科夫预测模型的实例计算比较,结果表明：优化的灰色马尔科夫预测模型的拟合精度和预测精度优于传统GM（1,1）预测模型和优化的GM（1,1）预测模型,且适用性更强,稳定性更好。

英文摘要：

The original values,conformation of background values and correction of residual errors perform important factors to the precision and stability of gray GM（1,1）model.In this paper,the optimal initial values were selected by the least square principle,and new background values were created by exponential function and the residual sequence was corrected by normalized residual sequence method.Although the forecasting precision of optimized GM（1,1）mode was improved,it was still affected by random fluctuation of data easily,and the stability of it was still unsatisfactory.Markov model can reduce the fluctuation of data forecasting and improve the stability of forecasting the model.Based on above,combing the optimized GM（1,1）model and Markov theory,the optimized gray Markov forecasting model was proposed.At last,the effectivity of traditional GM（1,1）model,optimized GM（1,1）model and optimized gray Markov model were compared based on practical data of some buildings.The result showed that the fitting and forecasting accuracy of the optimized gray Markov model was better than that of traditional GM（1,1）model and optimized GM（1,1）model,which improved the applicability and stability.