A formulation for fault detection in stochastic continuous-time dynamical systems

Abstract

In this work, a general formulation for fault detection in stochastic continuous-time dynamical systems is presented. This formulation is based on the definition of a pre-Hilbert space that approximates the corresponding likelihood ratio, so that orthogonal projection techniques associated with the statistics of the involved stochastic processes can be applied. The general setting gathers different existing schemes within the same framework. In the second part, the paper addresses a comparative analysis of the two fundamental existing schemes for fault detection in continuous-time stochastic dynamical systems. Such schemes prove to be efficient when dealing with specific types of fault functions; on the other hand, they show very different performance sensitivities when dealing with new fault profiles and system noise. This study suggests the use of a combined scheme, supervised by a high-level decision rule set.

Keywords:

• fault diagnosis
• continuous-time dynamical systems
• stochastic processes
• pre-Hilbert space

2000 AMS Subject Classifications :

• 34F05
• 60G35
• 60H10
• 62L10

Acknowledgements

This work was partially supported by project MTM2007-62064 of the Plan Nacional de I+D+i, MEyC, Spain, and by project CCG07-UPM/000-3278 of the Universidad Politécnica de Madrid (UPM) and CAM, Spain.