FaultDetectionTools.jl
The FaultDetectionTools.jl
package (or shortlyFDITools
) is a collection of Julia functions for the analysis and solution of fault detection and isolation (FDI) problems and model detection problems. The functions of this collection rely on the DescriptorSystems package [2], whose underlying computational functions are based on the MatrixPencils.jl
[3] and MatrixEquations.jl
[4] packages.
The implemented functions are based on the computational procedures described in Chapters 5, 6 and 7 of the book:
Andreas Varga, "Solving Fault Diagnosis Problems, Linear Synthesis Techniques", vol. 84 of Studies in Systems, Decision and Control, Springer International Publishing, 2017.
This book describes the mathematical background of solving synthesis problems of fault detection and model detection filters and gives detailed descriptions of the underlying synthesis procedures.
The targeted functionality parallels the functionality of the MATLAB collection of tools FDITOOLS
, whose User's Guide of the version V1.0 is provided in the file fditoolsdoc.pdf
. Supplementary information on the targeted functionality is also available on arXiv in the documentation of the companion MATLAB FDITOOLS
collection.
The available functions in the current version of the FaultDetectionTools.jl
package are:
Building FDI related objects
FDIModel
Fault detection and isolation synthesis model.FDFilter
Fault detection filter object.FDIFilter
Fault detection and isolation filter object.FDFilterIF
Fault detection filter internal form object.FDIFilterIF
Fault detection and isolation filter internal form object.fdimodset
Setup of synthesis models for solving fault detection and isolation problems.fdIFeval
Evaluation of the internal forms of fault detection and isolation filters.
Analysis of FDI synthesis models
fdigenspec
Generation of achievable FDI specifications.fdichkspec
Feasibility analysis of a set of FDI specifications.
Solving FDI problems
efdsyn
Exact synthesis of fault detection filters.efdisyn
Exact synthesis of fault detection and isolation filters.afdsyn
Approximate synthesis of fault detection filters.afdisyn
Approximate synthesis of fault detection and isolation filters.emmsyn
Exact model-matching based synthesis of fault detection filters.ammsyn
Approximate model-matching based synthesis of fault detection filters.
Performance evaluation of FDI filters
fditspec
Computation of the weak or strong structure matrix.fdisspec
Computation of the strong structure matrix.fdiscond
Computation of the fault detection sensitivity condition.fdif2ngap
Computation of the fault-to-noise gap.fdimmperf
Computation of the model-matching performace.
Building model detection related objects
MDModel
Model detection component synthesis model.MDMModel
Model detection multiple synthesis model.mdmodset
Setup of multiple synthesis models for solving model detection problems.MDFilter
Model detection filter object.MDFilterIF
Model detection filter internal form object.mdIFeval
Evaluation of the internal forms of model detection filters.
Analysis of model detection synthesis models
mdgenspec
Generation of achievable model detection specifications.mddist
Computation of distances between component models.mddist2c
Computation of pairwise distances between two sets of component models.
Solving model detection problems
emdsyn
Exact synthesis of model detection filters.amdsyn
Approximate synthesis of model detection filters.
Performance evaluation of model detection filters
mdspec
Computation of the weak structure matrix.mdsspec
Computation of the strong structure matrix.mdperf
Computation of the distance-matching performace.mdmatch
Computation of the distance-matching performace to a component model.mdgap
Computation of the noise gaps.
Computational utilities
fdhinfminus
Evaluation of theH∞-
index of the transfer function matrix of a descriptor system model.fdhinfmax
Evaluation of the maximum of column norm of the transfer function matrix of a descriptor system model.fditspec_
Computation of the weak or strong structure matrix of a descriptor system model.fdisspec_
Computation of the strong structure matrix of a descriptor system model.fdiscond_
Computation of the column-gains sensitivity condition of the transfer function matrix of a descriptor system model.
Release Notes
Main developer
License: MIT (expat)
References
[1] A. Varga, Solving Fault Diagnosis Problems – Linear Synthesis Techniques, Vol. 84 of Studies in Systems, Decision and Control, Springer International Publishing, 2017.
[2] A. Varga, DescriptorSystems.jl: Manipulation of generalized state-space (descriptor) system representations. Zenodo: https://doi.org/10.5281/zenodo.5148319.
[3] A. Varga, MatrixPencils.jl: Matrix pencil manipulation using Julia. Zenodo: https://doi.org/10.5281/zenodo.3894503.
[4] A. Varga, MatrixEquations.jl: Solution of Lyapunov, Sylvester and Riccati matrix equations using Julia. Zenodo: https://doi.org/10.5281/zenodo.3556867.