Laplace-domain analysis of fluid line networks with applications to time-domain simulation and system parameter identification.

Abstract

Networks of closed conduits containing pressurised fluid flow occur in many different instances throughout the natural and man made world. The dynamics of such networks are dependent not only on the complex interactions between the fluid body and the conduit material within each fluid line, but also on the coupling between different lines as they influence each other through their common junctions. The forward modelling (time-domain simulation), and inverse modelling (system parameter identification) of such systems is of great interest to many different research fields. An alternative approach to time-domain descriptions of fluid line networks is the Laplace-domain representation of these systems. A long standing limitation of these methods is that the frameworks for constructing Laplace-domain models have not been suitable for pipeline networks of an arbitrary topology. The objective of this thesis is to fundamentally extend the existing theory for Laplace-domain descriptions of hydraulic networks and explore the applications of this theory to forward and inverse modelling. The extensions are undertaken by the use of graph theory concepts to construct network admittance matrices based on the Laplace-domain solutions of the fundamental pipeline dynamics. This framework is extended to incorporate a very broad class of hydraulic elements. Through the use of the numerical inverse Laplace transform, the proposed theory forms the basis for an accurate and computationally efficient hydraulic network time-domain simulation methodology. The compact analytic nature of the network admittance matrix representation facilitates the development of two successful and statistically based parameter identification methodologies, one based on an oblique filtering approach combined with maximum likelihood estimation, and the other based on the expectation-maximisation algorithm.