Section: New Results

Sensor faults: detectability and distributed Fault Diagnosis. A positive invariance based approach.

Participants : Sorin Olaru [correspondent] , Vasso Reppa [L2S] , Abid Kodakkadan [L2S] , Marios Polycarpou [University of Cyprus] .

The paper [62] introduces the performance analysis of local monitoring modules of a distributed diagnosis scheme tailored to detect multiple sensor faults in a class of nonlinear systems. The local modules monitor the healthy operation of subsets of sensors (local sensor sets). Every module is designed to detect the occurrence of faults in the local sensor sets when some analytical redundancy relations (ARRs) are violated. The set of ARRs is formulated using structured residuals and adaptive thresholds based on a nonlinear observer. In order to characterize the sensitivity of every monitoring module to local sensor faults, we obtain structural fault detectability conditions based on adaptive thresholds, and strong fault detectability conditions based on ultimate robust positively invariant sets. These conditions correspond to explicit relationships between the local sensor faults, the worst-case bounds on modeling uncertainties and the design parameters of the local monitoring module.

In a recent paper [44] , we considered the abnormal functioning of sensors (measurement channels) deployed for monitoring and control of discrete linear time invariant systems affected by additive uncertainties. The main objective was to analyze the sensor fault detectability via a robust positive invariance based technique. The analysis relies on the categorization of detectable faults and leads to certain conditions for guaranteed nondetectability, guaranteed detectability and implicit detectability.

As a support to this line of research, in the paper [73] we presented a methodology for computing robust positively invariant sets for linear, discrete time-invariant systems that are affected by additive disturbances, with the particularity that these disturbances are subject to state-dependent bounds. The proposed methodology requires less restrictive assumptions compared to similar established techniques, while it provides the framework for determining the state-dependent (parameterized) ultimate bounds for several classes of disturbances. The added value of the proposed approach is illustrated by an optimization-based problem for detecting the mode of functioning of a switching system.