Uncertainty Quantification for Damping in Transient Pressure Oscillations

Abstract

The uncertainty of a model to determine the damping of pressure head oscillations following a sudden valve closure in a simple piping system in a pressurized closed conduit is quantified using Bayesian inference. The joint probability density of the model parameter is estimated based on experimental results published in the literature as well as experiments performed at the University of South Carolina. A Markov chain of the posterior joint distribution of the model parameters is calculated and used to predict the pressure head oscillations. The prediction is performed in a probabilistic fashion, estimating an interval of pressures as a function of time rather than estimating a single point by a traditional regression analysis. The 95% high posterior density of the damping ratio ranges from 1% to 6%. The probabilistic model also correctly predicts the experimental damping ratios when compared with experimental data.