基于马尔科夫优化的灰色GM (1,1) 沉降预测模型及应用

针对灰色GM(1,1)模型在对随机波动较大的沉降数据序列进行预测时存在的不足,本文结合灰色理论模型和马尔科夫链理论,建立了一种基于马尔科夫修正的新维GM(1,1)沉降预测模型。首先,考虑监测数据的时效性,通过在原始数据列中不断补充新的沉降监测数据,采用新陈代谢的方法建立了新维GM(1,1)模型；随后采用马尔科夫链理论对新维GM(1,1)模型进行优化,根据模型预测时产生的相对误差范围对其进行状态区间划分,并构建了相应的状态转移概率矩阵,得到了基于马尔科夫优化的新维GM(1,1)预测模型；将本文中的模型应用于福州火车站南广场深基坑周边建筑物地表沉降预测中,并对不同模型的预测效果进行对比分析,结果表明：基于马尔科夫优化的灰色GM(1,1)模型的预测精度较传统灰色GM(1,1)模型有明显提高,验证了本文所提出的优化模型在基坑沉降分析与预测中的合理性。

An Optimizated GM (1,1) grey prediction Model based on Markov Chain and Its Appication

Aiming at the shortcomings of the grey GM(1,1) model in predicting the settlement data with large random fluctuations, an optimized model was proposed combined the grey theory model and Markov chain theory in this paper. Firstly, considering the timeliness of monitoring data, an improved GM(1,1) model was established by adding newest monitoring data to the original data column; And then, the Markov chain theory was applied to GM. (1,1) model and the state interval is divided according to the relative error range. The GM(1,1) model optimized based on Markov Chain is obtained by constructing the corresponding state transition probability matrix. All models proposed in this paper are applied to the prediction of ground settlement of buildings around a deep foundation pit of south square in Fuzhou railway station, and the prediction results of different models are compared and analyzed. The results show that the prediction accuracy of GM(1,1) model optimized based on Markov Chain is higher than that of the traditional grey GM(1,1) model, which verifies the rationality of the optimizated model for analysis and prediction of foundation pit settlement.