摘要
为了估计给水系统节点流量和节点水压参数,实时模拟给水系统的运行状态,本文建立了参数估计最小二乘数学模型。该模型是带等式、非负约束的非线性优化问题。利用Wolfe既约梯度法和Rosen投影梯度法求解优化模型,讨论了模型求解步骤,得出了Rosen投影梯度法中投影矩阵的快速计算方法。编制了求解模型的计算机程序,应用于实际给水系统的参数估计,估计的节点水压与实测节点水压的平均误差为1.35m,表明模型及其求解方法是可行的,且Rosen法的速度更快。
In order to simulate the operating state of a water supply system,a least-square mathematic model has been built to estimate node water flow and water pressure head in the water supply system. The model is a nonlinear optimization model with equality and no negative constraints. The Wolfe gradient and the Rosen projection algorithm are used to solve this model. The framework for the model solving has been discussed. A quick method to calculate the Rosen projection matrix has been determined. A program has been developed to solve the model, and is applied to estimate parameters of an actual water supply system. The average difference of node water head between the estimated values and the measured values is 1.35m. This shows that the model and its solving algorithm are feasible. Moreover, we find that the Rosen projection algorithm is quicker than the Wolfe gradient algorithm.
出处
《工程数学学报》
CSCD
北大核心
2009年第5期819-826,共8页
Chinese Journal of Engineering Mathematics
基金
杨州大学自然科学基金(SK0513114)
关键词
给水系统
参数估计
优化模型
既约梯度法
投影梯度法
water supply system
parameter estimate
optimization model
Wolfe gradient
Rosen projection
作者简介
丛海兵（1968年1月生），男，博士，副教授．研究方向：给水排水工程优化与水处理技术．
