Optimal sensor placement approaches for the design of inverse experiments by simulation

Abstract

This dissertation serves to present the research conducted on sensor placement optimisation (SPO) using sensitivity analyses of virtual experiments in order to design virtual inverse problems. Two classes of SPO methods are considered namely mode-based and mode-free approaches. The mode-based approaches make use of SIMPLS and SVD to extract useful data by examining the correlation between the target variables (characterising variables) and the sensor measurement variables, while the mode-free approaches eliminate the need of spending the extra time required to extract modes, which ultimately leads to successful sensor placement for solving inverse problems. The aim of the mode-free approach is to maximise the variance explained subject to uniqueness of the information of each sensor. Both approaches aim to maximise the potential of an experimental setup to solve an inverse problem by using the right number of sensors and placing them at the optimal spatial positions. SPO is not only capable of designing an experiment but it is also capable of classifying the well-posed or ill- posed nature of an existing experiment that can be modelled, which saves both time and cost. The approach followed in this study was to design a simple virtual inverse problem for which the well or ill-posedness of the problem can be controlled. Numerous virtual experiments were conducted that varied from well-posed to severely ill-posed to allow for rigorous testing of the various approaches. The e ect of model error and stochastic noise on ability to reliably place sensors is also investigated.