优化的灰色离散Verhulst模型在基坑沉降预测中的应用

Application of optimized grey discrete Verhulst model in settlement prediction of foundation pit

基于传统的灰色Verhulst模型在基坑沉降预测中精度较低的问题,提出优化的灰色离散Verhulst模型。在基坑沉降监测中,由于有新的监测沉降值不断补充到原始数据序列中,各种因素会带来新的扰动,原来的模型精度降低,为避免由此产生的误差,用新陈代谢方法建立优化灰色离散Verhulst一维、二维新陈代谢模型。将传统Verhulst模型、优化的灰色离散Verhulst模型及优化灰色离散Verhulst一维、二维新陈代谢模型进行比较。研究结果表明:该模型通过采用离散化思维对原数据序列进行倒数变换,从连续形式向离散形式变化,减小了传统Verhulst模型建模过程中从微分方程到差分方程带来的误差;采用新陈代谢方法的优化灰色离散Verhulst模型精度更高,可选用该模型对基坑进行沉降预测。

Considering the low accuracy of the traditional grey Verhulst model in the foundation pit settlement prediction,the optimized discrete grey Verhulst model was put forward. In the settlement monitoring of foundation pit, the newmonitoring settlement data was constantly added to the original data sequence, and all kinds of factors would bring newdisturbance, so the original model accuracy was reduced. In order to avoid the resulting errors, the metabolic method wasused to establish the optimization of one？dimensional and two？dimensional metabolic model of grey discrete Verhulstmodel. The traditional Verhulst model, the optimization of the discrete grey Verhulst model and the optimization of one？dimensional and two？dimensional metabolic model of grey discrete Verhulst model were compared. The results showthat the proposed model is based on the reciprocal transformation of the original data sequence by using discrete thinking,and the change from continuous form to discrete form reduces the error from the differential equation to the differenceequation in the modeling process of the traditional Verhulst model. The optimized grey discrete Verhulst model based onthe metabolic method has higher accuracy, and the model can be used to predict the settlement of the foundation pit.