Efficient Inverse Transient Analysis in Series Pipe Systems

Measurement of the changes in heads initiated by a valve closure are used to calibrate the friction factors in a hydraulic system consisting of a series-connected pipeline and a downstream valve joining two reservoirs. The calibration is performed by minimizing the inverse least-squares problem representing the difference between the measured and predicted transient response in the network. The hydraulic transient is modeled using the method of characteristics. Unlike previous approaches, the sensitivity information required for the minimization or error is obtained by direct differentiation of the method of characteristic equations and the valve equation with respect to the friction factors. The sensitivity of the calibration results to the amount of data included in the analysis, the initial friction factor estimates, and modeling and simulated measurement errors is discussed.