Metody wnioskowania przybliżonego. Właściwości i zastosowanie

Butkiewicz, B.

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Tytuł artykułu

Metody wnioskowania przybliżonego. Właściwości i zastosowanie

Autorzy

Butkiewicz B.

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Warianty tytułu

Języki publikacji

Abstrakty

Badanie właściwości metod wnioskowania przybliżonego jest trudne ze względu na ich liczbę i różnorodność. Dyskusję ograniczono do uogólnionych metod Mamdaniego, Larsena, Tsukamoto i Takagi-Sugeno. Uogólnienie dotyczy matematycznych operacji dogodnych do interpretacji spójników "and", "or", "also" stosowanych w regułach wnioskowania. Podano warunki konieczne, które powinny spełniać te operacje. Nową klasę operacji spełniających te warunki nazwano operacjami podstawowymi (B-operacjami) dla metod wnioskowania. Klasa ta jest szersza niż klasa norm trójkątnych. Specjalną uwagę poświęcono systemom sterowania. Przedstawiono rezultaty poprzednich badań autora i niektóre z nich uogólniono. Głównymi rezultatami teoretycznymi są twierdzenia o niezależności stanu ustalonego systemu ze sterownikami FPD, FPI, FPID od wyboru operacji wnioskowania, o ile zastosowano normy trójkątne lub B-operacje. Twierdzenia te uogólniono na systemy o wielu wyjściach i wejściach (MIMO). Badano ponadto dynamikę systemów. Pokazano, że odpowiedź skokowa zależy bardzo słabo od operacji wnioskowania dla szerokiej klasy operacji stosowanych do interpretacji "and", "or", "also". Zależy ona również słabo od doboru metody defuzzyfikacji. Wprowadzono nową koncepcję twierdzenia rozmytego. Sformułowano rozmyte twierdzenie o dynamice systemu ze sterownikiem rozmytym. W dalszej części pracy badano wpływ metod wnioskowania na modele rozmyte. Analizowano uogólnione modele typu Mamdaniego, Larsena i Takagi-Sugeno. Zaproponowano modyfikację modelu Takagi-Sugeno usuwającą jego niedokładność w strefach przejściowych, obserwowaną dla funkcji przynależności o kształcie trójkątów. W ostatniej części pracy przedstawiono rozmyto-probabilistyczno-ewidencyjny model procesu uszkodzeń elementu oraz przykład jego zastosowania do estymacji niezawodności kondensatorów. Ponadto podano przykłady przemysłowych zastosowań logiki rozmytej do analizy obrazów w metalurgii, do opisu procesu spiekania proszków żelaza oraz konstrukcji inteligentnego czujnika promieniowania podczerwonego z mikroprocesorem rozmytym.

Investigation of approximate reasoning is difficult, because of the many very different reasoning methods. Thus, discussion is limited here to the generalized Mamdani, Larsen, Tsuka-moto, and Takagi-Sugeno methods. The generalization concerns mathematical operations which are suitable for the interpretation of the connectives "and", "or", "also" in reasoning rules. The necessary conditions for these operations are established. A new class of operations, satisfying these conditions, is called B-operations, basic operations for reasoning methods. This class is larger than triangular norms. Special attention was given to the fuzzy control system. Some results of the author's previous works is presented and some of them are generalized. The main theoretical results are theorems about the non-dependence of the steady state of the system with FPD, FPI, and FPID controllers on the choice of reasoning operations, if triangular norms or B-operations are used. These theorems were generalized for fuzzy multiple input multiple output (FMIMO) systems. Moreover, the dynamics of the systems were investigated. It was shown that system step res-ponse has a very weak dependence on the reasoning operation for large class of operations used for the interpretation of "and", "or", "also". There is also weak dependence of the dynamics on the choice of defuzzification method. A new concept of fuzzy theorem was introduced. A fuzzy theorem of system dynamics with fuzzy controller was formulated. In a further part of the work, the influence of reasoning methods on the fuzzy models was investigated. Generalized Mamdani, Larsen, and Takagi-Sugeno models were considered. A modification of the Takagi--Sugeno model is proposed to remove the defects of model nonaccuracy in intermediate areas if standard triangular shape of membership functions are used. In the last part of the work, a probabilistic-fuzzy-evidence model of failure process of the element is presented and an example of its application for the estimation of reliability of capacitors. Moreover, examples of industrial applications of fuzzy logie to the analysis of camera pictures in metallurgy, to the sintering process of iron powders, and intelligent sensor of infrared radiation with a fuzzy microprocessor are described.

Słowa kluczowe

metoda wnioskowania przybliżonego

Wydawca

Oficyna Wydawnicza Politechniki Warszawskiej

Czasopismo

Prace Naukowe Politechniki Warszawskiej. Elektronika

Rocznik

2001

Tom

z. 132

Strony

3--117

Opis fizyczny

Bibliogr. 198 poz., rys., schem.

Twórcy

autor

Butkiewicz B.

Instytut Systemów Elektronicznych Politechniki Warszawskiej

Bibliografia

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