改进的Verhulst沉降预测模型及其参数估计方法

为提高软土路基沉降预测灰色Verhulst模型的预测精度,首先从沉降初始实测值修正和增加时间指数项两个方面对灰色Verhulst模型的离散时间响应式进行了改进;然后基于最小二乘原理,利用差分进化算法对改进的灰色Verhulst模型时间响应式进行直接地优化估计,避免了灰色Verhulst模型常规估计方法中因背景值选取问题而导致的计算误差.实例计算结果表明,改进的灰色Verhulst模型较原模型具有更好的灵活性和适应性,比Gompertz模型、Logistic模型、Bertalanffy模型、Weibull模型及原灰色Verhulst模型这几种沉降预测模型具有更高的预测精度,可供工程设计参考.

Improved verhulst model of settlement prediction and its parameter estimation method

To improve prediction accuracy of the gray Verhulst model of soft soil roadbed settlement,the improvement has been proposed for the discrete-time response formula,which are the amendment to the initial value of measured settlement and the addition of time exponent.Then,based on the least square principle,the method using Differential Evolution algorithm to optimize the improved discrete-time response formula directly was given to avoid the calculation deviations due to selection of background value while using traditional estimation method.The results show that,compared with the original gray Verhulst model,the improved gray Verhulst model is more flexible and adaptive.Furthermore,the improved gray Verhulst model has higher prediction accuracy than other types of settlement prediction model：the Gompertz model,the Logistic model,the Bertalanffy model and the Webull model.Therefore,it is applicable in engineering design.