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Chilekwa, Victor
(2006).
DOI: https://doi.org/10.21954/ou.ro.0000add1
Abstract
A single leak in a duct can be detected, located and sized by measuring the input impedance of the duct and then analytically solving an inverse problem. However, previously applied analytical methods break down when it comes to predicting smaller hole sizes. Results are presented which show that, by treating smaller holes as capillaries and applying appropriate theoretical approximations, accurate predictions of smaller hole sizes are possible.
Extending the analytical methods to a duct containing multiple leaks is non-trivial as the resulting mathematical expressions are highly complex. In this thesis, an alternative approach which uses optimisation methodology to detect, locate and size multiple leaks in a duct is described. The optimisation algorithms are applied to a measurement of the duct’s input impedance but they are able to cope with the presence of multiple leaks. Results are presented which illustrate the success of the optimisation approach in detecting, locating and sizing multiple leaks in a duct.
An objective function incorporating the theoretical input impedance of a model duct and experimental input impedance of the cylindrical pipe under investigation is designed. By studying the behaviour of the objective function and the application of different numerical optimisation methods, it is possible to determine those methods most suitable for investigating leaks. Results are presented showing that the Rosenbrock optimisation algorithm provides predictions of hole sizes and locations which are in good agreement with their actual values. The success of the Rosenbrock optimisation algorithm is attributed to function minimisation techniques incorporating non derivative based search directions and optimisation steps.
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