Fault Isolation for Large Scale Discrete-Time Systems Based on Implicit Set Representation

Abstract

To detect faults in a system we can adopt an observer, designed for the healthy system, and monitor the discrepancy between actual and expected behaviour of the residual (difference between the system output and its estimate). To isolate faults, we can compute the invariant sets associated with each fault, and their projection in the residual space (limit set): faults can be isolated if the associated limit sets are separated when a (constant) test input is applied. However, the explicit computation of limit sets can be hard even for low-dimensional systems. As a main contribution, we show that, by adopting an implicit representation of limit sets, very efficient procedures can be used to solve the problem, based on convex quadratic programming or linear programming. Simulations show that the approach is effective in solving even large dimensional problems, which makes it suitable for largescale networked systems.

Active Fault Isolation for Multimode Fault Systems Based on a Set Separation Indicator

“…Consider the following uncertain multimode fault systems with potential fault models [ 16 , 21 , 29 , 30 , 31 , 32 , 33 ]: where is the n -dimensional state vector and n is assumed to be relatively large, e.g., ; is the auxiliary input vector for fault isolation; is the unknown process disturbance vector; is the unknown measurement disturbance vector; is the measurement output vector. The matrices have appropriate dimensions.…”

“…Assumption 1 ensures the existence of an observer and a controller, which provides the necessary conditions for an observer-based active fault diagnosis [ 24 , 29 , 38 ]. Assumption 2 is a classical assumption in fault isolation studies [ 7 , 29 , 30 , 31 ]. Assumptions 1 and 2 are given so that one can focus only on addressing the fault isolation problem.…”

“…Recently, an easy-to-implement AFD method was proposed in [ 29 , 30 ] and this method promised to address the above problems. In order to facilitate the explanation of the construction idea, the studies in [ 29 , 30 ] specifically addressed the issue of active fault isolation (AFI) for AFD based on the assumption of a periodical diagnosis or certain performance-triggered diagnosis. Later, such AFI method was extended to deal with an integrated fault-tolerant predictive control problem in [ 31 ].…”

“…Later, such AFI method was extended to deal with an integrated fault-tolerant predictive control problem in [ 31 ]. Note that the main strategy of AFI in [ 29 , 30 , 31 ] consisted in employing the vertex of the input constraint set as the design reference for the constant auxiliary inputs and further adopting the implicit set representation of the residual steady-state set to design hyperplanes that separated the healthy and faulty residual limit sets. In the offline design phase, the constant auxiliary input and associated separation hyperplanes could be determined by solving linear constrained quadratic programming problems.…”

“…(i) Instead of using the residual steady-state limit sets to design separation hyperplanes to distinguish different fault modes as in [ 29 , 30 , 31 ], this paper advocates the construction of approximate residual transient-state reachable sets and transient-state separation hyperplanes to exploit features in the evolution of different system dynamics. This design method avoids the need to wait for the system to be driven to a steady state by an auxiliary excitation before making a diagnostic decision and therefore helps to achieve fast fault isolation.…”