Efficient inverse transient analysis in series pipe systems

Measurement of the changes in heads initiated by a valve closure are used t o calibrate the friction factors in a hydraulic system consisting of a seri es-connected pipeline and a downstream valve joining two reservoirs. The ca libration is performed by minimizing the inverse least-squares problem repr esenting the difference between the measured and predicted transient respon se in the network. The hydraulic transient is modeled using the method of c haracteristics. Unlike previous approaches, the sensitivity information req uired for the minimization or error is obtained by direct differentiation o f the method of characteristic equations and the valve equation with respec t to the friction factors. The sensitivity of the calibration results to th e amount of data included in the analysis, the initial friction factor esti mates, and modeling and simulated measurement errors is discussed.