一种马尔可夫的非等间距多点灰色预测模型

Non-equidistant multi-point gray prediction model based on Markov

针对非等间距单点灰色预测模型在处理多点变形预测时,没有考虑点与点之间的关联性和它们之间的相互影响,而且容易受建模数据随机扰动性影响这一问题,该文提出了一种基于马尔可夫的非等间距多点灰色预测模型。首先,结合某基坑的变形实测数据,建立非等间距多点灰色预测模型和非等间距单点灰色预测模型,通过两种模型预测结果对比验证非等间距多点灰色预测模型在处理多点变形预测问题上的优越性;然后运用马尔可夫模型建立状态转移概率矩阵对预测结果进行修正;最后建立基于马尔可夫的非等间距多点灰色预测模型。结果表明,基于马尔可夫的非等间距多点灰色预测模型的拟合及预测精度更高,适应性更强,更符合实际变形情况,具有实际参考价值。

Aiming at the feature that the non-equidistant single-point gray prediction model does not consider the correlation between points and points and its mutual influence as well as be easily affected by random perturbation of modeling data when dealing with multi-point deformation prediction problem,the paper proposes a non-equidistant multi-point gray prediction model based on Markov.Firstly,combining with the deformation data of foundation pit to build non-equidistant multi-point gray prediction model and non-equidistant single-point gray prediction model,by comparing the forecast results of two models,it can verify the superiority of non-equidistant multi-point gray prediction model on dealing with multi-point deformation prediction problem;then to correct the prediction results by establishing the state transition probability matrix based on Markov;finally,a non-equidistant multi-point gray prediction model based on Markov is established.The results showed that the fitting and prediction accuracy of non-equidistant multipoint gray prediction model was higher,which more adaptable,more in line with actual deformation,with practical reference value.