基于保凸保单调的分段幂函数在水位流量关系曲线拟合中的应用

Application of Subsection Power Function in Fitting of Stage-discharge Relation Curve Based on Convexity and Monotonicity Preserving

文章构建一类保凸保单调的分段幂函数,它可以满足水位流量关系曲线的保单调不反曲要求,同时可以有效解决水位流量关系常规模型率定时中高水、低水无法兼顾的问题。然后将此新水位流量关系模型用于水位流量关系曲线的自动优化率定,并采用差分进化算法求解该模型,实例表明该模型可以很好地拟合水位流量关系曲线,比常用的常规水位流量关系模型拟合效果更佳,避免了人工率定的任意性并降低了人工操作的复杂性。

In this paper, a subsection power function based on convexity and monotonicity preserving is established, which can not only meet the convexity and monotonicity preserving requirements of stagedischarge relation curve but also effectively solve the problems of considering both middle-high and lower water levels in conventional model calibration of stage-discharge relation curve. Then, use the new model for automatic calibration of stage-discharge relation curve and solve the model by differential evolution algorithm. It is showed that the new model can fit the stage-discharge relation curve better than conventional model, which avoids randomicity of artificial calibration and simplifies the complexity of manual operation.