System identification of nonlinear resonant systems

This dissertation addresses the problem of thermo-acoustic combustion instability modelling using nonlinear system identification. Specifically we are interested in the identification of closed loop limit cycling systems composed of a linear transfer function with a static nonlinearity in feedback.; To begin we address the feasibility of the identification task, in terms of both data quality and dynamical capabilities of the model. Subsequently, we demonstrate that, despite the paucity of information available, a grey-box nonlinear model can be identified. The model correctly predicts the dominant system behavior.; The nonlinear tools of describing functions, bifurcation theory and manifold analysis are used to further refine a low-complexity nonlinear model capable of describing the data and consistent with physical understanding. These tools are also used to better understand the identified model dynamical behavior.; An atypical method for combining multiple experiments is considered. We construct a framework for combining multiple experiment information using bifurcation theory and follow an approach of successive deduction, hypothesis formulation and falsification testing in an attempt to invalidate the model.; Model confidence is quantified in terms of bias and variance properties connecting the model, data and measures. The allows a more informed decision as to the model validity. We formulate a generic definition for the bias confidence, which gives an indication of overparametrization of the model or weak persistence of excitation in the data. We also formulate a generic definition for the variance confidence, which gives an indication of the parameter estimate variability due to different realizations of the underlying noise processes. These involve techniques for empirical estimation of the distribution of the estimated parameters. We reformulate these for dynamical system models by ensuring the correlation properties of the input-output data are preserved.; Finally a multiplicative reference signal is introduced to increase identifiability of the model, at the expense of cyclostationary signals. Using cyclostationary signal analysis we develop the mapping of excitation properties in the scalar non-stationary data to the vector stationary lifted signals. The mapping of identifiability properties in the lifted vector system to the rank properties of the regression matrix is also created.