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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。
The construction of background values is a key factor that affects the accuracy and adaptability of the weighted non-equidistant GM (1,1) prediction model. In this paper, the traditional weighted non-equidistant GM (1,1) model is optimized by constructing a new background value by means of an integral function method. The optimized model is adapted to both high-growth exponential and low-exponential exponential sequences and improves the traditional model Prediction accuracy and adaptability. However, the optimized model is still susceptible to random disturbance of the modeling data. The Markov model has the advantage of weakening the random perturbation of the modeling data. Based on this, the optimized weighted non-equidistant GM (1,1) model and Markov theory are organically combined to construct an optimized weighted non-equidistant Markov-GM (1,1) prediction model. Finally, combined with the measured deformation data of the second phase project of Xiushan Lake, the model of metabolism was used to predict and verify. The results show that the fitting and prediction accuracy of the optimized weighted non-equidistant Markov-GM (1,1) prediction model are better than those of the traditional weighted non-equidistant GM (1,1) prediction model. The applicability of the new prediction model Stronger, with practical reference value.