An algebraic approach for robust fault detection of input-output elastodynamic distributed parameter systems

This paper deals with the problem of designing a robust fault detection methodology for a class of input-output, uncertain dynamical distributed parameter systems, namely mechanical elastodynamic systems, which are representative of a whole class of problems related to on-line health monitoring of mechanical and civil engineering structures. The proposed approach does not require full state measurements and is robust to measuring, modeling and numerical errors, thanks to a time varying detection threshold. In order to avoid the problems associated with classical discretization techniques for distributed parameter systems, which can lead to numerical errors difficult to bound a priori, and thus higher thresholds, a suitable structure-preserving algebraic approach, called Cell Method, will be employed. This method consists in writing the equations of a distributed parameter system directly in discrete form, avoiding the usual discretization process and leading to a symplectic, that is energy preserving, numerical scheme.