# State-Based Fault Diagnosis of Finite-State Vector Discrete-Event Systems via Integer Linear Programming

## TL;DR

This paper introduces a method using integer linear programming to verify and diagnose faults in discrete-event systems with limited sensor data.

## Contribution

A novel state-based approach for K-diagnosability verification and fault diagnosis in Vector DES using integer linear programming.

## Key findings

- A necessary and sufficient condition for K-diagnosability is established using integer linear programming.
- Three types of predicates are used to partition outputs for fault detection in Vector DES.
- Online diagnosis is achieved by solving integer linear programming problems based on sensor outputs.

## Abstract

This paper presents a state-based method to address the verification of K-diagnosability and fault diagnosis of a finite-state vector discrete-event system (Vector DES) with partially observable state outputs due to limited sensors. Vector DES models consist of an arithmetic additive structure in both the state space and state transition function. This work offers a necessary and sufficient condition for verifying the K-diagnosability of a finite-state Vector DES based on state sensor outputs, employing integer linear programming and the mathematical representation of a Vector DES. Predicates are employed to diagnose faults in a Vector DES online. Specifically, we use three different kinds of predicates to divide system state outputs into different subsets, and the fault occurrence in a system is detected by checking a subset of outputs. Online diagnosis is achieved via solving integer linear programming problems. The conclusions obtained in this work are explained by means of several examples.