Calibration of Parameters with Dynamic Effects in Pipe Network Simulation Using the Inverse Transient Analysis in the Frequency Domain

Abstract

Transient flows naturally occur in piping systems due to operation exigencies. It is, therefore, essential to analyze water distribution networks under transient flow conditions in an attempt to enhance their reliability. The accuracy of such an analysis highly depends on such input parameters as pipe wall roughness, wave speed, and unsteady friction loss coefficients. As these parameters vary from system to system and in different flow conditions, they cannot be definitively determined in practice. Generally, the parameters are determined by engineering judgments and trial-and-error estimations. For complex pipe networks, this can be very burdensome and time-consuming. Moreover, there are great numbers of dynamic parameters in water supply networks and their interactions are so complicated that it is extremely difficult to explicitly determine the role of each one in the system responses observed. This calls for mathematical simulation models to predict systems responses accurately. In this study, an inverse transient analysis model is introduced for the calibration of input parameters. A reverse method based on a series of measurements and computations was used for the solution of the calibration problem and efforts were made to reduce the value of the objective function by finding the optimum solution. However, the model introduced in this work differs from other similar ones in that inverse transient analysis models are often used in the time-domain while the current work uses the transfer matrix method to analyze the system in the frequency-domain. The frequency analysis of a pipe network not only provides a deep insight into the system performance but also speeds up the simulation and optimization computations. Finally, the model is applied to a lab-scale pipe network from the Technical University of Lisbon as a reference model. The parameters with dynamic effects are calibrated and compared with available data obtained from massive experimental observations and numerical trial-and-errors in the time domain. Results indicate not only that the model is adequately simple and faster than its counterpart model in the time domain but that it is capable of successfully calibrating the network with results in good agreement with observed data.