基于Logistic曲线和Gompertz曲线的最优组合沉降预测模型及其应用

Optimal Combinational Predictive Model of Settlement Based on Logistic Curve and Gompertz Curve and Its Application

地基的全过程沉降量与时间呈S形曲线关系,可用Logistic模型和Gompertz模型较好地描述。根据Logistic曲线和Gompertz曲线的共性和个性,引用最优加权组合建模理论,以组合模型的对数误差平方和最小为目标函数来确定最优的加权系数,建立了最优加权几何平均组合沉降预测模型。通过工程实例,验证了该最优组合沉降预测模型的可行性。对比计算结果表明,最优组合沉降预测模型的精度不仅比Logistic模型和Gompertz模型的预测精度要高,而且可靠性也优于各个单一预测的模型,是地基沉降观测资料的一种有效分析方法。

The settlement-time relation of foundation during the whole process of construction and operation can be described by a sigmoid or S-shaped curve, which can be modeled by the Logistic model and the Gompertz model. According to the general character and individual character of both Logistic curve and Gompertz curve, using the optimal weight combined modeling theory and the target function of the least square sum of the logarithnfic en,or, a kind of optimal weight geometric average combinational predictive model is estabished. A practical example is u^d to validate the feasibility of the predictive model. Comparative calculation result shows that, not only the predictive precision of the optimal combinational predictive model is better than that of the Logistic model and Gompertz model, but the dependability of the combinational model is superior to each single model. It provides an effective analysis method for the inspected data of the settlement of foundation.