# Guaranteed Fault Detection and Isolation for Switched Affine Models

## TL;DR

This paper develops a computationally efficient, optimization-based framework for guaranteed fault detection and isolation in switched affine systems, including measures for detection delay and practical implementation strategies.

## Contribution

It introduces novel optimization formulations for model invalidation and T-distinguishability, a distinguishability index, and an efficient FDI scheme with delay bounds and adaptive features.

## Key findings

- Proposed optimization-based methods outperform previous formulations.
- Introduced a distinguishability index for practical fault detection horizon.
- Demonstrated effectiveness on HVAC system models with multiple faults.

## Abstract

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.