Uncertainty Analysis of Optimal Dynamic Linear System Models

Linear time invariant system models are insufficient for physical systems which have deterministic or stochastic time varying parameters. These parameters can be important to system performance, as in the case of a vehicle suspension, or safety, as in the case of a structural health monitoring problem. Time varying models are difficult to uniquely identify because they can have many parameters. For deterministic systems, researchers often assume input bases of variation or assume the bandwidth of variation. For stochastic systems, researchers often assume the correlation structure of the system parameters and the input. This thesis presents the novel application of matrix calculus methods which allow an analyst to choose the assumed portions of a system model’s structure in order to find unknown system coefficients uniquely. These structured system identification methods are used to provide solutions for the time varying impulse response, or the novel solution for input-time variation of example systems. Traditional optimal and adaptive identification methods are also reproduced by this framework. Consistent methods are derived to evaluate the coherence and variance for any structured system model. The results presented in this thesis allow novel and traditional identification methods to be analyzed in a common structured identification framework. Traditional and novel model structures are compared using a suspension and structural health monitoring problem to show where novel methods improve prediction error and improve the understanding of model variance terms. Future work is expected to find additional useful model structures and solution methods based on this framework