Output behavior equivalence and simultaneous subspace identification of systems and faults

TL;DR

This paper presents a subspace method for identifying systems with additive faults without requiring nominal data, introduces output behavior equivalence, and estimates fault matrices explaining the data with minimal dimension.

Contribution

It introduces a novel subspace approach for simultaneous system identification and fault reconstruction without nominal data or fault class assumptions.

Findings

Standard PI-MOESP can recover system matrices under mild fault assumptions

Output behavior equivalence characterizes systems with identical output sets

Method estimates fault matrices with minimal dimension explaining the data

Abstract

We address the problem of identifying a system subject to additive faults, while simultaneously reconstructing the fault signal via subspace methods. We do not require nominal data for the identification, neither do we impose any assumption on the class of faults, e.g., sensor or actuator faults. We show that, under mild assumptions on the fault signal, standard PI-MOESP can recover the system matrices associated to the input-output subsystem. Then we introduce the concept of output behavior equivalence, which characterizes systems with the same output behavior set, and present a method to establish this equivalence from system matrices. Finally, we show how to estimate from data the complete set of fault matrices for which there exist a fault signal with minimal dimension that explains the data.