Bayesian Modelling of Fluid Flow in PipelinesSite maintained by Jonathan Rougier. Please contact me if you would like further details. Statistics GroupDepartment of Mathematical Sciences University of Durham South Road Durham DH1 3LE England Tel: +44 (0) 191 374 2361 Fax: +44 (0) 191 374 7388 |
We introduce uncertainty into the traditionally deterministic analysis of transient fluid behaviour in pipelines (the water-hammer equations). We are able to represent our beliefs about the fluid as a probabilistic assessment of pressure and flow at vertices along the pipeline, and to propagate these beliefs forward in time. This allows us to perform a more informative off-line analysis of particular operational events (such as rapid valve closure). We can also use our approach for on-line monitoring, e.g. for leak-detection. |
On this page you will find information about the following:
You can also download a copy of our paper A Bayesian Analysis of Fluid Flow in Pipelines as a postscript file or a pdf file, from which the outlines below are taken. A version of this paper will be appearing in the Journal of the Royal Statistical Society, Series C, in 2001.
We generalise the simple state vector in two ways. First, we augment it with an extra set of quantities denoting the pipeline coefficient (crudely, the local friction effect) between each of the vertices. Therefore the state vector consists of pressures, flows and friction coefficients. These friction coefficients may or may not evolve through time: it is up to the engineer to determine this. Second, we do not treat the state vector as known, but as unknown, with a given mean and variance. Naturally if some quantities are known then their variances can be zero.
The purpose of our analysis is to allow us to evolve not just the state vector, but, more generally, the mean and the variance of the state vector, through time according to the boundary conditions. Therefore uncertainty about the state vector at time t-1 will feed through to uncertainty about the state vector at time t. This propagation of uncertainty is done entirely in accordance with the physics of fluid flow in pipelines. An interesting implication is the existence of `waves' of uncertainty that can traverse the pipeline in much the same way as a pressure wave.
Our stochastic approach offers the following important advantages.
The role of the simulator as likelihood function paves the way for a fully Bayesian analysis of leak detection, in which it is possible for experts to incorporate detailed beliefs about the `leakiness' of the pipeline, and derive probabilistic descriptions of the leak (in terms of location, size and time of occurrence) if a leak is thought to have occurred.
Page last updated 11.09.00.