Study Of Hydraulic Model Calibration And Leakage Location Of Water Distribution System

The construction and application of water distribution model (WDM) are essentialmeasure and approaches for realizing the modernization management of waterdistribution system (WDS), which are not only useful for improving the waterdispatching and optimizing operations, but also are the basis for conducting researchesof leakage location, water quality simulation and early-warning of emergent pollutionevents. Because the nodal demand and pipe roughness can not be measured directly, theWDM constructed needs to be calibrated based on the measurements of nodal pressureand pipe flow. How to calibrate the WDM with insufficient measurements and toimprove the calibration efficiency are the hot and difficult subjects in the research filedof WDS. This paper focus on the study of pipe roughness calibration, nodal demandcalibration and leakage location of WDSs, and the following achievements have beenobtained:1) The calibration of WDM is a complex nonlinear optimization problem, and itssolving method can be roughly divided into “Gradient-based algorithm” and “Stochasticsearch algorithm”. The calculation of Jacobian matrix is the key to use theGradient-based algorithm for parameter calibration. Currently, perturbation method ismost widely used for calculating Jacobian matrix of WDS, but it is computationalexpensive and low precision. This paper proposes the matrix analysis method to deducethe analytical solution of Jacobian matrix of WDS, including the Jacobian matrix ofnodal pressure and pipe flow to the nodal demand, pipe, and diameter. The derivationcan not only improve the efficiency of parameter calibration, but also facilitate theparameter sensitivity analysis, leakage location, and the optimization placement ofnodal pressure sensor as well as other related research.2) An empirical value based weighted least squares method has been proposed forpipe roughness calibration. Because the number of measurements is less than thenumber of pipes, pipe roughness calibration is an underdetermined problem.Traditionally, the number of unknown quantites is reduced by grouping pipes accordingto their material and age. This paper introduces the empirical value of pipe roughnessinto the objective function as pseudo measurements. This method can take fulladvantage of experience information of pipe roughness and transform theunderdetermined calibration problem to be overdetermined conveniently.3) An inverse-calculation model has been constructed for nodal demand calibration. Considering that translating the nodal demand calibration to optimization problemneeds to solve the hydraulic equations repeatedly, a new inverse-calculation model hasbeen proposed to increase the efficiency of nodal demand calibration. This modelreconstructs the network energy equation and quality equation via decomposingvariables by using the matrix decomposition method. The unknown nodal pressure, pipeflow and nodal demand can be acquired directly by solving this model, which providesa new algorithm for network hydraulic simulation.4) To study the hydraulic characteristics of leakage pipe and simulate the hydraulicstate of leakage WDS, a pipe leakage model has been constructed and verified usingrelated measured data. Leakage can be regarded as abnormal increase of nodal demandand will lead to abnormal change of measurements. This paper uses first-ordersecond-moment method to quantify the normal range of measurements for leakagewarning. Leakage location can be translated to optimization problem, and an objectfunction has been established to minimum the difference between measurements andcalculation value of WDM. The leakage can be located by comparing the objectivefunction residuals via calibrating the nodal demand one by one. On account of the hugecomputation problem when calibrating nodal demand one by one for large pipe network,an weighted least squares regression analysis is conducted to the first order Taylor seriesexpansion of objective function for improving location efficiency.5) Optimization placement of pressure and quality monitoring sensors based onpipe leakage characteristics. Leakage location needs related information supplied bymonitoring sensors, and the optimization placement of pressure and quality monitoringsensors can make the water pressure changes and pollutions to be monitored timely andaccurately. The placement of pressure monitoring sensors is optimized by calculatingthe leakage probability of each node and using K-means cluster method to analyze thewater pressure sensitivity-matrix. Considering the probability of pollution invaded isrelated to the pipe leakage, the leakage probability is introduced to the shortest flowtime matrix as a weight coefficient and the placement of quality monitoring sensors isoptimized by solving the objective function according to the cover set concept.All proposed algorithms in this paper have been written programs in MATLABplatform, and the example networks combined with numerical simulation are used toillustrate the implementation process, to test the convergence speed and to verify thecorrectness and feasibility of the proposed algorithms.