Frequency domain analysis of transient flow in pipelines; application of the genetic programming to reduce the linearization errors

The transient flow analyzing by the frequency domain method (FDM) is computationally much faster than the method of characteristic (MOC) in the time domain. The FDM needs no discretization in time and space, but requires the linearization of governing equations and boundary conditions. Hence, the FDM is only valid for small perturbations in which the system’s hydraulics is almost linear. In this study, the linearization errors of the FDM applied to a reservoir-pipe-valve system (RPV) are discussed and by using the Genetic Programming (GP), some correction coefficients are defined to reduce them. By applying the correction coefficient at the opening size of the valve, the first frequency of the frequency domain method is modified. Moreover, the responses at higher-order frequencies are evaluated by some new correction factors obtained by the GP. Solving an illustrative example shows that the error of the system can be significantly reduced by using the applied correction factors.