  This paper considers the problem of fault detection and isolation (FDI) for
switched affine models. We first study the model invalidation problem and its
application to guaranteed fault detection. Novel and intuitive
optimization-based formulations are proposed for model invalidation and
T-distinguishability problems, which we demonstrate to be computationally more
efficient than an earlier formulation that required a complicated change of
variables. Moreover, we introduce a distinguishability index as a measure of
separation between the system and fault models, which offers a practical method
for finding the smallest receding time horizon that is required for fault
detection, and for finding potential design recommendations for ensuring
T-distinguishability. Then, we extend our fault detection guarantees to the
problem of fault isolation with multiple fault models, i.e., the identification
of the type and location of faults, by introducing the concept of
I-isolability. An efficient way to implement the FDI scheme is also proposed,
whose run-time does not grow with the number of fault models that are
considered. Moreover, we derive bounds on detection and isolation delays and
present an adaptive scheme for reducing isolation delays. Finally, the
effectiveness of the proposed method is illustrated using several examples,
including an HVAC system model with multiple faults.
