Zastosowania sztucznych sieci neuronowych w mechanice i inżynierii

• Autorzy: Lefik M.

Warianty tytułu

EN

Applications of artificial neural networks in mechanics and in engineering

• Języki publikacji: PL

Abstrakty

PL

W prezentowanej pracy można wyróżnić dwa podstawowe obszary tematyczne. Pierwszy z nich to użycie sieci neuronowych warstwowych do modelowania konstytutywnego oraz do identyfikacji parametrycznej, drugi to konstruowanie programów eksperckich przy użyciu sieci typu IAC i baz danych. Pierwsze trzy rozdziały pracy mają charakter rozdziałów wstępnych. Zdefiniowano w nich terminologię oraz opisano narzędzia numeryczne, użyte w dalszej części rozprawy. Kolejne pięć rozdziałów zawiera przykłady zastosowań sztucznych sieci neuronowych w mechanice i w inżynierii. W rozdziale pierwszym przedstawiono krótko genezę i zarys rozwoju historycznego sztucznych sieci neuronowych, opisano elementy budowy operatora neuropodobnego oraz proces transmisji sygnału wejściowego przez sztuczną sieć neuronową. Jak wiadomo, sztuczne sieci neuronowe mogą być analizowane przy użyciu wielu różnych formalizmów matematycznych. W dalszej części rozdziału pierwszego przedstawiono sieć neuronową warstwową jako interpretację graficzną i algorytmiczną wzorów aproksymacyjnych dla funkcji, funkcjonału i operatora. W rozdziale drugim przedstawiono praktyczne metody doboru parametrów sieci neuronowej. Rozpatrzono zagadnienie uczenia nadzorowanego. Przedstawiono metodę największego spadku oraz wynikający z niej algorytm wstecznej propagacji błędu dla doboru wag synaptycznych i biasów w SSN. W dalszej części rozdziału przedstawiono sposób obliczania pochodnej sygnału wyjściowego sieci względem składowych sygnału wejściowego. Przedstawiono zarys analizy jakości wytrenowania SSN. W końcowej części rozdziału autor formułuje "algorytm wielokrotnych startów" służący do oceny prawidłowości działania sieci bez użycia zbioru testującego. Rozdział trzeci poświęcony jest w całości sieciom rekurencyjnym. Przedstawione są sieci typu Hopfielda-Tanka i sieci typu IAC (wzajemna interakcja i konkurencja). W rozdziale czwartym przedstawiono przykład zastosowania sztucznych sieci neuronowych do identyfikacji parametrycznej teoretycznego modelu zachowania mechanicznego kompozytu włóknistego, pod działaniem obciążenia cyklicznego. Sieć neuronową wytrenowano tak, że fragmenty wykresu uzyskanego przy zastosowaniu modelu matematycznego - zostały stowarzyszone z wartościami parametrów, dla których zostały wykreślone. Dzięki temu, prezentacja wykresu eksperymentalnego na wejściu sieci pozwala otrzymać wartości parametrów, dla których, w ramach przyjętego modelu, można otrzymać realistyczny opis zjawiska. W rozdziale piątym przedstawiono metodę bezpośrednią opisu związku konstytutywnego przy pomocy sieci neuronowej. Skupiono uwagę na reprezentacji przyrostowej związku konstytutywnego. Metodę aproksymacji opracowano tak, aby możliwe było przybliżanie funkcji wielowartościowych przy jej pomocy. Uznano, że miarodajnym kryterium poprawności reprezentacji jest zdolność sieci do samodzielnego symulowania zachowania mechanicznego ośrodka dla zadanego programu obciążenia. Rozdział szósty poświęcony jest w całości rozwinięciu zasadniczych tez zarysowanych w rozdziale piątym. Przedstawiono sposób wpisania reprezentacji neuronowej związku konstytutywnego do programu metody elementów skończonych. Zamieszczono dwa przykłady. Pierwszy przedstawia aproksymację danych doświadczalnych opisujących histerezę sorpcji w materiale porowatym przy pomocy SSN, a następnie zastosowanie tego opisu w modelu numerycznym suszenia i zwilżania przegrody budowlanej, rozwiązanym programem MES. Drugi przykład to rozszerzenie modelu cewki nadprzewodzącej, przedstawionego w rozdziale poprzednim, na zadanie dwuwymiarowe. W rozdziale siódmym skupiono uwagę na zastosowaniach SSN do modelowania efektywnych własności kompozytów. Efektywny związek konstytutywny aproksymowany przez sztuczną sieć neuronową jest tu zdefiniowany numerycznie na podstawie skończonej liczby przykładów, bez konieczności przyjmowania założeń "a priori" dotyczących jego postaci. Przedstawiono różne metody gromadzenia danych konstytutywnych koniecznych do treningu sieci: metoda bezpośrednia, metoda samouczącego się programu MES oraz koncepcja zastosowania sieci Hopfielda-Tanka do generacji uśrednionych stanów naprężeń. Przedstawiona w tym rozdziale metoda identyfikacji bezpośredniej parametrów efektywnych związków konstytutywnych pozwala na aproksymację zależności funkcyjnej charakterystyk efektywnych od opisu mikrostruktury. Zależność taka jest trudna do uzyskania w ramach klasycznej teorii homogenizacji. Rozdział ósmy pracy poświęcony jest budowie programów eksperckich opartych nie na regułach wnioskowania, ale na opisach sytuacyjnych zgromadzonych jako przykłady w bazie danych. Do tego celu służy sieć IAC, która użyta jest jako "inteligentna powłoka" nad bazą danych. Przedstawiono dwa przykłady takich zastosowań. Porównano sprawność "inteligentnej bazy danych" z rozwiązaniem tych samych zadań przy użyciu sieci warstwowej.

EN

Applications of artificial neural networks in mechanics and in engineering Two kinds of artificial neural networks are mainly addressed in this book. These are: ANNs with hidden layers trained using error back propagation method and an Interactive Activation and Competition ANN. Three initial chapters are introductive while in the five other chapters different applications of the ANN in Mechanics and in Engineering are presented and illustrated with examples. In the first chapter a short historical review of the development of ANN is presented. Author introduces then a formal definition of a neural-like operator and describes its structural elements. The formalism of transmission of an input signal through the neural network is also presented. The aim of this chapter is an interpretation of a classical neural network with hidden layers as a universal approximator of a function, of a functional or of an operator. In the second chapter author reviews some fundamental algorithms that allow finding proper parameters of the ANN with hidden layers. Problem of correct design of the ANN is discussed and some methods of construction of a rational ANN are suggested. Third chapter is devoted to a theory and analysis of recurrent neural networks. The attention is focused on Hopfield-Tank ANN, IAC ANN and on cellular neural net. The fourth chapter presents an example of the use of the ANN with hidden layers for parameter identification of a theoretical model of mechanical behaviour of a fibrous composite under transversal cyclic loading. A set of parameters of a generalised elasto-plastic model is identified to ensure the best accordance between two families of graphs of stress: that predicted by the theory and the experimental one. The adaptation of the theoretical model to obtain a better description of the experimental data is described and the application of the ANN technique for parameter identification is presented. An interpretation of the nature of mechanical processes that govern the considered experiment is proposed and confirmed by the analysis of identified parameters. In the fifth chapter the artificial neural network with two hidden layers is trained to approximate directly a mechanical constitutive relationships for a superconducting cable under transverse cyclic loading. The training is performed using the same, as in the previous chapter, set of experimental data. The behaviour of the cable is strongly non-linear. Irreversible phenomena result with complicated loops of hysteresis. The performance of the ANN, which is applied as a tool for storage interpolation and interpretation of experimental data, is investigated, both from numerical, and from physical viewpoints. The representation of the complex experimental data via ANN is very convenient as a definition of constitutive material relationships for finite element method. The incremental representation of constitutive law is chosen as a suitable form that can be approximated with ANN and used in FE code. Exemplification of the use of the ANN as a constitutive procedure in a FE code is presented in the sixth chapter. First example is the use of ANN inside the hydro-thermo-mechanical FE program HAMTRA to handle a constitutive dependence of sorption on relative humidity in the pores of the porous medium. The second example consists of a 2D continuation of the analysis of the superconducting strand. In the seventh chapter the ANN is used for approximation of the effective constitutive law for composite materials. First, neural network is used as an approximator of the functional dependence of values of components of the effective constitutive matrix on mechanical properties of the components of the cell of periodicity. This dependence is known from examples furnished by direct application of the homogenisation procedure for the exemplary cells. Next, the attention is focused on application of a so-called "self-learning" finite element procedure to modelling an effective behaviour of composites. Third method bases on the simultaneous use of Hopfield-Tank neural network to generate statically admissible stress fields and the ANN with hidden layers to associate them with a corresponding, known state of deformation. It should be highlighted that the above methods can be used in numerical modelling of nonlinear material behaviour with hysteresis. Concept of an application of a neural network of the Interactive Activation and Competition (IAC) type as a basic structure of an expert program that operates not on the rules but on the data collected in a data base - is presented in the eights chapter. Two examples are analysed: an intelligent database containing technical description of building objects and the second - IAC network as a tool for energy auditor. These expert programs joint two functions: collect technical data describing some building objects and allows us to obtain some "opinions" concerning their technical and thermal state. The only source of knowledge, the expert program needs, is a sufficiently rich set of examples. The similar functionality can be obtained with a use of ANN with hidden layer. It is concluded, however, that the IAC network is more advantageous in the role of an "intelligent shell" over a database.

Słowa kluczowe

PL

sieci neuronowe; zastosowanie sieci neuronowych; modelowanie konstytutywne; identyfikacja parametryczna; programy eksperckie

EN

neural networks; constitutive modelling; parametric identification; expert program

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka
• Rocznik: 2005
• Tom: Z. 341
• Strony: 3--258
• Opis fizyczny: Bibliogr. 348 poz.

Twórcy

autor

Lefik M.

• Katedra Geotechniki i Budowli Inżynierskich, Wydział Budownictwa, Architektury i Inżynierii Środowiska, Politechnika Łódzka,

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