基于加权最小二乘法的供水管网节点流量校核

管网水力模型是实现供水系统现代化管理的重要工具,要使水力模型能比较准确地反映管网真实运行状态,达到预期使用目的,其中的参数需要校核。将管网节点流量校核作为优化问题,采用加权最小二乘法逐步迭代求解,与已有研究相比,采用矩阵分析法推导供水管网雅克比矩阵解析式,引入水量分配矩阵聚合节点流量,将欠定问题转化为超定,提高了校核的计算效率和结果的可靠性。采用简单管网阐明了雅克比矩阵的计算、节点流量的聚合及梯度向量的构造,利用实际管网验证了方法的实用性。

Nodal demand calibration of water distribution system using the weighted least squares method

Hydraulic model of water distribution systems (WDSs) is an essential tool to realize modernization management of WDSs. To make the model capable of reflecting the system''s behavior with reasonable accuracy and achieving intended purposes, the parameters in it should be calibrated. The nodal demand calibration of WDS models is formulated as a nonlinear optimization problem, which is then solved iteratively using weighted least squares method. Comparing to previous studies, the proposed method deduces the analytical solution of Jacobian matrix of WDSs based on matrix analysis method, and translates the under-determined problem to over-determined by aggregating the nodal demand using demand allocation matrix, such that the computational efficiency and the reliability of calibration results were improved. A simple network is used to illustrate the computation of Jacobian matrix, the construction of gradient vectors and the aggregation of nodal demand. The practicability of the method is further validated by a real network.