Calibration using inverse transient analysis

The measured changes in heads and pressures caused by a transient event, such as a valve closure, can be used to calibrate the friction factors in a hydraulic system. The calibration is performed by formulating an inverse transient problem in a non-linear least squares manner. The minimization is done by the Levenberg-Marquardt method. Transient behaviour is simulated using the method of characteristics, with the head and flow at each section being solved for independently of the heads and flows at other sections for the same time step. Differentiation of these direct equations, with respect to the friction factors, provides the sensitivity information needed for the minimization.