UNIVERSITAT POLITÈCNICA DE CATALUNYA Programa de doctorat: Tecnologies avançades de la producció Qualitative Modelling of Complex Systems by Means of Fuzzy Inductive Reasoning. Variable Selection and Search Space Reduction. Josep Maria Mirats Tur Directors: Rafael Huber François E. Cellier (Univ. Politècnica de Catalunya) (Univ. of Arizona) Barcelona, Novembre 2001
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UNIVERSITAT POLITÈCNICA DE CATALUNYA Programa de doctorat: Tecnologies avançades de la producció Qualitative Modelling of Complex Systems by Means of Fuzzy.
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UNIVERSITAT POLITÈCNICA DE CATALUNYAPrograma de doctorat: Tecnologies avançades de la producció
Qualitative Modelling of Complex Systems by Means of Fuzzy Inductive Reasoning. Variable Selection and
Search Space Reduction.
Josep Maria Mirats Tur
Directors:
Rafael Huber François E. Cellier
(Univ. Politècnica de Catalunya) (Univ. of Arizona)
Barcelona, Novembre 2001
Context and motivation
• To model and simulate the output or outputs of a system in order to control it
• To solve the modelling and simulation problem we can use Deductive and/or Inductive modelling approaches
Context and motivation
• Unfortunately FIR, in its previous state, could not deal with large-scale systems
•FIR, is a modelling and simulation methodology capable of generating an input-output model
•It qualitatively learns the behaviour of a system from its real past data. Interesting for ill-defined systems
Objectives
• Problem: To obtain a qualitative model of a (ill-defined) system with a large number of measurable variables
• Objective: To reduce the FIR model search space in order to solve the aforementioned problem
Index of subjects
• About the Fuzzy Inductive Reasoning methodology
• Main lines of research in the dissertation
• Developed methods– Sub-optimal mask search algorithm– Method based on spectral coherence functions– Subsystem decomposition methods
• Applications
• Conclusions and future work
About the FIR methodology
Fuzzification Module
(recoding)
Qualitative Modelling Engine
Defuzzification Module
(regeneration)
Qualitativedata
Qualitativepredictions
Qualitative Simulation Engine
Model(mask + behaviour)
FIR
Quantitativepredictions
Prediction error
4.22.58.61.0
3.14.12.31.4
2.51.14.07.2
1.84.31.02.1321 yxxx
real-valued trajectories from the system variables
42.2
33.1
27.5
98.7
y
About the FIR methodologyThe Qualitative modelling engine
Conclusions•Since the FIR modelling engine is of exponential complexity, new techniques had to be devised that would reduce the number of masks to be visited•This can be accomplished either by reducing the number of ‘-1’ elements in the mask candidate matrix, or by decomposing the system into subsystems.•The so enhanced FIR toolbox can now easily cope with large-scale systems comprising of dozens if not hundreds of variables.•The new tools were built in a modular fashion so that they can be combined to form a variety of search-space reduction algorithms.
Main contributionsReducing FIR model search space
• New sub-optimal mask search algorithm
• Spectral coherence functions based method
• Subsystem decomposition:• Using Fuzzy Reconstruction Analysis
– Re-implementation of the FRA module
• Using FIR to find the structure of a system
• Using statistical techniques
Other resultsFIR methodology
• Improvement to the FIR simulation engine - Corrected five-neighbours prediction formula
• New use of the unreconstructed variance methodology
• The concept of variable acceptability, ‘envelopes’• A variable similarity measure based on a modified
Hr value
Future research
•More thorough validation of the search-space reduction algorithms
•Investigate alternative algorithms to include time in the analysis
•Parameters intrinsic to the sub-optimal search algorithm and the energy method
•Is a subsystem decomposition preferable to a whole model?
•Parameters intrinsic to FIR
UNIVERSITAT POLITÈCNICA DE CATALUNYAPrograma de doctorat: Tecnologies avançades de la producció
Qualitative Modelling of Complex Systems by Means of Fuzzy Inductive Reasoning. Variable Selection and
Search Space Reduction.
Josep Maria Mirats Tur
Directors:
Rafael Huber François E. Cellier
(Univ. Politècnica de Catalunya) (Univ. of Arizona)
Barcelona, Novembre 2001
About the FIR methodologyQualitative Simulation Engine