Transient Frequency Analysis In The Water Distribution Network And Its Application

The water distribution network(WDS)is an important part of the water supply system,and it is of great practical significance to ensure the safe operation of the WDS.This research focuses on transient flow,which is closely related to the safe operation of the water supply network.In traditional research,the simulation of transient flow events in pipelines is performed in the time domain.However,pipeline transients can also be analyzed in the frequency domain if Fourier Transform is applied to the linearized governing equation.The transient flow frequency domain analysis method for simple pipelines is relatively mature,but it is still difficult to perform transient flow frequency domain analysis for complex pipeline networks.The primary goal of this research is to improve the method for frequency domain analysis of transient flows in complex pipe networks.In this paper,through the method of graph theory and using the incidence matrix of the WDS,the frequency domain analysis equation of the transient flow in the WDS is constructed(Eq 2.100 in the text).This equation can not only deal with more complex nodes,but also facilitate the solution of the transient flow frequency domain response function of the pipe network,which provides great convenience for the transient flow frequency domain analysis in the water supply pipe network.Using this frequency domain analysis equation,it is proved that the WDS can be approximated as a linear system with a frequency domain response function.The case study shows that the established theory can accurately simulate the frequency domain response function of the water supply network in the transient flow process,and has obvious advantages in time efficiency compared with the traditional method of characteristic(MOC).This time advantage can be exploited for the following applications of the transient flow frequency domain analysis method.One application is to use this theory to construct a fast estimation method for the head of the WDS during a burst event.Solving the system output according to the system frequency domain input and frequency domain response is the dual problem of the system frequency response extraction.After solving the frequency response of the pipe network system through virtual events,the frequency output of the system can be calculated by estimating the frequency input of the system.By inverting the result to the time domain,the pressure of each place in the pipe network can be obtained.This paper introduces in detail the methods of selecting virtual events,extracting frequency response functions,and estimating system input.And the transient frequency analysis is extended to Laplacian domain.The case study shows that compared with the MOC,the estimation method proposed in this research can achieve an order of magnitude improvement in the efficiency of simulating the burst pressure.The second application is to use deep learning to identify the pipeline leak characteristics of the network in the frequency domain response function of transient flow.The traditional leakage identification method based on the transient flow frequency response greatly depends on the accuracy of the hydraulic model of the pipe network.Using the deep learning method,through the learning of a large number of samples,the deep network can extract the leakage characteristics of the pipeline network in the frequency domain response function under the interference of hydraulic uncertainty.The results of the case analysis show that the accuracy of identification is mainly affected by the accuracy of the transient acoustic speed and the size of leakage.In a network of 149 pipes,for small leaks,the algorithm can narrow down the range of possible leaks to 8 pipes in 90% of cases.The case analysis results also show that thanks to deep learning,the accuracy of leakage identification using the transient flow frequency domain response has been dramatically improved when the hydraulic model of the system is inaccurate.