Parameter Identification in Pipeline Networks: Transient-Based Expectation-Maximization Approach for Systems Containing Unknown Boundary Conditions

Abstract

The simulation of hydraulic transients within fluid line networks is important for many applications (for example, water hammer analysis within distribution networks). However, in many instances, modeling efforts are impeded by the fact that the pipeline parameters are either unknown or can vary significantly from their assumed design values. Consequently, research efforts have focused on the development of parameter identification techniques, mapping from measured transient data to pipeline parameter estimates. A limitation of previous works has been the need for systems to have all boundary conditions either measured or known (e.g., transient pressure measurements or reservoir boundary conditions). This paper aims to relax this requirement and presents a parameter identification method for fluid line networks based on transient-state measurements of the hydraulic state variables of pressure and flow, in the presence of unmeasured and unknown boundary conditions. Utilizing a Laplace-domain admittance matrix representation of the system, the contribution to the hydraulic system dynamics from the measured and unmeasured state variables (i.e., boundary conditions) is made explicit. This model is then used as the basis for the development of a parameter estimation methodology based on the expectation-maximization (EM) algorithm. The importance of the EM approach is that it provides a framework for parameter estimation in the presence of unmeasured state variables by effectively integrating out the influence of the unmeasured variables. Numerical examples demonstrate the utility of this method for a network with a range of pipeline models.