Multi Criteria Calibration of Pipelines under Unsteady Flows

Partial differential equations of continuity and momentum govern the transient flows in pressurized
pipes. These equations are numerically analyzed using the method of characteristics that consists of
some important uncertainties such as friction loss modeling and wave speed. This work introduces a
calibration methodology to estimate precisely the uncertain parameters and, consequently, the
numerical modeling results. For this purpose, a transient state is generated by closing the downstream
end valve. A numerical model for transient analysis in the pipe is also developed. In that model, four
correction coefficients are considered to be calibrated including; pipe roughness, local and convective
accelerations in the unsteady friction loss model and wave speed. Afterward, a non linear
programming is developed in which the correction coefficients are decision variables. The objective
function is defined as the summation of squares of differences of the observed and calculated
pressures at the valve location. The problem is then solved using a simple genetic algorithm, and the
uncertainties are finally calibrated to the best conditions. The capability of the method is investigated
by solving a well-known experimental pipeline. The approach is found easy to use and results are
satisfactory.