[Paper Review] Fault Detection and Isolation Tools (FDITOOLS) User's Guide

Andreas Varga|arXiv (Cornell University)|Mar 24, 2017

Fault Detection and Control Systems12 references3 citations

TL;DR

This paper presents FDITOOLS, a MATLAB-based software toolbox for solving exact and approximate fault detection and isolation (FDI) and model detection problems in linear dynamic systems. It implements synthesis and analysis techniques from Varga's 2017 book, enabling systematic design of FDI filters and model detection filters with performance evaluation via gap metrics, sensitivity, and noise robustness, validated on a lateral aircraft dynamics model with actuator fault scenarios.

ABSTRACT

The Fault Detection and Isolation Tools (FDITOOLS) is a collection of MATLAB functions for the analysis and solution of fault detection and model detection problems. The implemented functions are based on the computational procedures described in the Chapters 5, 6 and 7 of the book: "A. Varga, Solving Fault Diagnosis Problems - Linear Synthesis Techniques, Springer, 2017". This document is the User's Guide for the version V1.0 of FDITOOLS. First, we present the mathematical background for solving several basic exact and approximate synthesis problems of fault detection filters and model detection filters. Then, we give in-depth information on the command syntax of the main analysis and synthesis functions. Several examples illustrate the use of the main functions of FDITOOLS.

Motivation & Objective

• To provide a comprehensive, user-friendly MATLAB toolbox for solving fault detection and isolation (FDI) and model detection problems in linear systems.
• To implement computational procedures from Varga's 2017 book for exact and approximate synthesis of FDI and model detection filters.
• To support performance evaluation of FDI and model detection filters using metrics such as fault sensitivity, noise gaps, and model matching.
• To enable practical application through a case study on lateral aircraft dynamics with actuator loss-of-efficiency faults.
• To facilitate systematic design and analysis of residual generators and evaluation filters for real-time fault monitoring.

Proposed method

• Uses state-space models with additive faults to represent system dynamics under various fault conditions, including loss-of-efficiency (LOE) in actuators.
• Employs the fdimodset and mdmodset functions to construct synthesis models by specifying control, fault, and noise inputs.
• Applies optimization-based synthesis functions such as efdsyn, afdsyn, efdisyn, afdisyn, emmsyn, ammsyn, emdsyn, and amdsyn for exact and approximate FDI and model detection filter design.
• Utilizes performance evaluation functions like fdif2ngap, mdgap, and mdmatch to quantify fault-to-noise gaps and model matching performance.
• Employs Narendra-type evaluation filters with parameters (α=0.9, β=0.1, γ=10) to compute residual evaluation signals θi(t) for fault identification.
• Employs time-domain simulation with step, square, and sinusoidal inputs plus white noise to assess filter performance under realistic conditions.

Experimental results

Research questions

• RQ1 How can exact and approximate fault detection and isolation problems be systematically solved using computational tools in linear systems?
• RQ2 What is the achievable performance of FDI filters in terms of fault sensitivity and noise robustness for a lateral aircraft control system with actuator faults?
• RQ3 How can model detection filters be synthesized to distinguish between multiple physical fault models (e.g., partial or complete actuator failure) with optimal gap performance?
• RQ4 What is the impact of noise on residual evaluation signals, and how can they be processed to reliably detect fault modes?
• RQ5 How do different filter synthesis strategies (exact vs. approximate, minimal vs. non-minimal realization) affect the performance and structure of the residual generator?

Key findings

• The AMDSYN function successfully designed model detection filters for a lateral aircraft model with 9 fault scenarios (including complete actuator failure), achieving a structured performance matrix with zero diagonal entries.
• The model detection performance matrix showed clear separation between residual responses for different fault models, enabling reliable fault identification even under noise.
• The residual evaluation signals θi(t), computed via a Narendra-type filter, exhibited distinct time responses for each fault model, with the correct model identified by the peak response.
• The achieved model detection gap (MDgap) and performance (MDperf) metrics confirmed the robustness and distinguishability of the designed filters across all fault cases.
• The time-domain simulations demonstrated that the filters could reliably detect fault transitions (e.g., from 0% to 50% to 100% actuator degradation) despite input and measurement noise.
• The non-minimal realization with stability degree -1 and poles at -1 yielded stable and well-conditioned filter responses, confirming the effectiveness of the synthesis approach.