基于 Markov 理论的加权非等距GM（1，1）预测优化模型

摘要

The structure method of background value in the weighted non‐equidistance GM(1 ,1) prediction model has an important influence on the precision and adaptability of the model .This paper optimizes the traditional weighted non‐equidistance GM (1 ,1) model which creates a new background by divisions of function method .The optimized model is suited to build the weighted non‐equidistance GM (1 ,1) model for both high grow th index series and low grow th index series .It improves the precision and adaptability of the traditional model .But the optimized model is still affected by random fluctuation of modeling data easily .Markov model has the advantage of reduce the fluctuation of forecasting the modeling data .Based on above ,this paper combines the optimized weighted non‐equidistance GM (1 ,1) model and Markov theory ,producing the optimized weighted non‐equidistance Markov‐GM (1 ,1) prediction model .Finally , with data of the deformation monitoring of the second phase of Xiushan Lake project , the metabolism computing model is used to predict . The results show that the optimized weighted non‐equidistance Markov‐GM (1 ,1) prediction model of the accuracy is better than the traditional weighted non‐equidistance GM (1 ,1) prediction model ,and new prediction model performs with better applicability ,which has practical reference value .%背景值的构造方法是影响加权非等距GM （1，1）预测模型的精度和适应性的关键因素。文中通过等分函数法构造新的背景值对传统的加权非等距GM （1，1）模型进行优化，优化后的模型使其同时适应于高增长指数序列和低增长指数序列，提高传统模型的预测精度和适应性能力。但是优化后的模型依然易受建模数据随机扰动影响。马尔科夫（Markov）模型具有削弱建模数据的随机扰动性的优势。基于此，将优化的加权非等距GM （1，1）模型和Markov理论有机结合，构建优化的加权非等距Markov‐GM （1，1）预测模型。最后，结合秀山湖二期工程的变形实测数据，运用新陈代谢的计算模式进行预测验证。结果表明：优化的加权非等距Markov‐GM （1，1）预测模型的拟合和预测精度都优于传统的加权非等距GM （1，1）预测模型，新的预测模型的适用性更强，具有实际的参考价值。