In April 2016 Manchester eScholar was replaced by the University of Manchester’s new Research Information Management System, Pure. In the autumn the University’s research outputs will be available to search and browse via a new Research Portal. Until then the University’s full publication record can be accessed via a temporary portal and the old eScholar content is available to search and browse via this archive.

Related resources

Search for item elsewhere

University researcher(s)

Academic department(s)

OPTIMAL MEASUREMENT LOCATIONS FOR PARAMETER ESTIMATION OF DISTRIBUTED PARAMETER SYSTEMS

Alana, Jorge Enrique

[Thesis]. Manchester, UK: The University of Manchester; 2011.

Access to files

FULL-TEXT.PDF (pdf)

Abstract

Identifying the parameters with the largest influence on the predicted outputs of a model revealswhich parameters need to be known more precisely to reduce the overall uncertainty on themodel output. A large improvement of such models would result when uncertainties in the keymodel parameters are reduced. To achieve this, new experiments could be very helpful,especially if the measurements are taken at the spatio-temporal locations that allow estimate the parameters in an optimal way. After evaluating the methodologies available for optimal sensor location, a few observations were drawn. The method based on the Gram determinant evolution can report results not according to what should be expected. This method is strongly dependent of the sensitivity coefficients behaviour. The approach based on the maximum angle between subspaces, in some cases, produced more that one optimal solution. It was observed that this method depends on the magnitude of outputs values and report the measurement positions where the outputs reached their extrema values. The D-optimal design method produces number and locations of the optimal measurements and it depends strongly of the sensitivity coefficients, but mostly of their behaviours. In general it was observed that the measurements should be taken at the locations where the extrema values (sensitivity coefficients, POD modes and/or outputs values) are reached. Further improvements can be obtained when a reduced model of the system is employed. This is computationally less expensive and the best estimation of the parameter is obtained, even with experimental data contaminated with noise. A new approach to calculate the time coefficients belonging to an empirical approximator based on the POD-modes derived from experimental data is introduced. Additionally, an artificial neural network can be used to calculate the derivatives but only for systems without complex nonlinear behaviour. The latter two approximations are very valuable and useful especially if the model of the system is unknown.