基于先验信息的供水管网阻力系数识别
Pipe resistance coefficient identification of water distribution system based on prior information

供水管网阻力系数识别是指通过调整管网水力模型中管道阻力系数，使模型计算值与监测值相符的过程。由于实际中监测点数量有限，管网阻力系数识别为欠定的优化问题。现行方法通常采用管道分组这一参数化方法将欠定问题转换为超定，应用遗传算法或其它随机搜索算法求解。提出了基于先验信息的供水管网阻力系数识别算法，所提出算法根据管道管材、管龄等先验信息对管道阻力系数进行估计，并将估计值作为伪观测值引入目标函数将欠定优化问题转换为超定，采用高斯-牛顿算法进行求解。与现有方法相比，所提出算法避免了管道分组不唯一的问题；再者，推导了供水管网阻力系数雅克比矩阵解析式用于搜索向量构造，提高了参数识别计算效率。采用小型管网阐明了雅克比矩阵计算及搜索向量构造，利用大型管网验证了算法的实用性。
Pipe resistance coefficients (PRCs) identification of water distribution systems (WDSs) is a process of adjusting the PRCs in hydraulic model of WDSs to make its predictions consisting with measurements. Because the number of monitoring sensors is limited in practice, the identification of PRCs of WDSs is an under-determined optimization problem. Existing methods tend to use a parametric method of pipe grouping to convert the under-determined problem to over-determined, and then solve it using GA or other stochastic searching algorithms. This paper presents a prior information based algorithm for PRCs identification of WDSs. In the proposed method, the PRCs are estimated previously according to prior information of pipe material and pipe-age, and then used as pseudo observations introduced into objective function to convert the under-determined optimization problem to over-determined one, and the Gauss Newton algorithm is utilized to solve it. Compared to existing method, the proposed algorithm avoids the non-uniqueness problem of pipe grouping; in addition, the analytic formula of Jacobian matrix of PRC is deduced for searching vector construction, which improves the calculation efficiency of parameter identification. A simple network was used to illustrate the calculation of Jacobian matrix and the construction of search vector, and a larger network was utilized to validate the practicability of the method.