Verhulst优化模型在基础沉降预测中的应用

摘要

Due to the low accuracy of the traditional grey Verhulst model in the foundation settlement prediction, the paper puts forward the optimized discrete grey Verhulst model and the grey Verhulst model of background val-ue and initial optimization.Using discretization thought for reference,a grey discrete Verhulst model was con-structed by reciprocal generation of the original data sequence.The grey discrete Verhulst model realizes changes from continuous form to discrete form,and eliminates jumping errors from the differential equation to the differ-ence equation.The grey Verhulst model of background value and initial optimization were established by using the reciprocal transformation and the optimization model without constraint to acquire the parameters of the back-ground value and initial value.The predicted results show that compared with the traditional Verhulst model by engineering examples,the proposed models possess much higher prediction precision.So the suitable model can be selected from the two optimization models to predict the settlement of similar projects.%由于传统的灰色Verhulst模型在基础的沉降预测中精度较低，提出优化的灰色离散Verhulst模型和背景值初值优化的灰色Verhulst模型。优化的灰色离散Verhulst模型是采用离散化思维对原数据序列进行倒数变换创建，完成了从连续的形式向离散的形式变化，减少了传统Verhulst模型建模过程中从微分方程到差分方程带来的误差。背景值初值优化的灰色Verhulst模型是采用变换倒数和优化的约束模型来求解背景值参数与初值参数而建立的。经过工程实例中优化模型与传统的Verhulst模型的对比，由预测结果可以得出2种优化模型具备更高的预测精度的结论，因此在沉降分析中可从这2种优化的模型中选取合适的模型对类似工程沉降进行预测。