Fault Detection in Distributed Parameter Systems
This project of research addresses the topic of "Fault Detection" (FD) in "Distributed Parameter Systems" (DPS), extending ideas from "Lumped Parameter linear/nonlinear Systems" (LPS) theory to a class of Infinite Dimensional Systems (IDS). In contrast to the most common FD schemes for DPS which are based on certain kind of Early Model Reduction, this project considers a novel methodology for the FD design, avoiding an Early Lumping and discrete approximation of the dierential operators involved in PDE models.
The FD scheme proposed is a Model-based structure (Observer based method) designed by a Lyapunov's Stability analysis and Convex Optimization. The design procedure keeps the innite dimensional nature of the DPS models in every stage of the design, due to it does not attempt to reconstruct the solution of these systems, as common methods do. On the contrary, this proposed methodology allows to capture the system characteristics by means of the construction of parametric operators in spaces of nite dimension, which satisfy necessary stability conditions and suitable ltering properties.
One of the main problems in the model-based FD design addressed by this research is to develop robust schemes with a suitable level conservatism before system's uncertainties (error approximation due to modelling as well as measurements). For Observer-based FD methods, the level conservatism is established by the design of "residual generators" with "detection thresholds". The methodology of design proposed explores how the construction of parametric operators and its optimisation conducts to FD schemes with non-conservative thresholds. For the operator representation, optimisation over positive polynomials by Sum-of-Squares (SOS) and Moment approaches are considered. In addition, using the same tools mentioned, FD schemes based on Adaptive Observers are investigated for PDE models with nonlinear dynamics.
- Alessandro Astolfi
- Thomas Parisini