改进的灰色—马尔科夫模型及其在沉降预测中的应用研究

Study on the improved Gray-Markov model and its application in settlement prediction

针对传统的灰色GM(1,1)模型对沉降预测的局限性,本文在传统灰色预测模型的基础上对观测数据进行平滑处理,并分析比较对数函数平滑和含参线性函数平滑后预测的效果。将改进的灰色模型预测值与观测值的残差值用于马尔科夫的状态划分,构造状态转移概率矩阵,建立改进的灰色—马尔科夫模型。文中结合大坝沉降的实测数据,用此模型进行建模。结果表明,基于含参线性函数平滑后的灰色—马尔科夫模型的预测效果最好。

Focusing on the limitations of the traditional grey GM（ 1,1） model for the settlement prediction,the original data is smoothed based on the traditional grey prediction model,the results of logarithmic function smoothing and parametric linear function smoothing are compared and anlyzed. The improved grey model prediction value and residuals of observations are used for state division of Markov process and construction of the state transition probability matrix,so as to establish the improved Grey-Markov model.According to the surveying data of a dam settlement,the results show that the our improved Grey-Markov model with parameters based on the smoothed linear function is the best prediction model.