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1

A new approach to nonlinear modelling of dynamic systems based on fuzzy rules

Bartczuk Ł., Przybył A., Cpałka K.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 3

603--621

EN

For many practical weakly nonlinear systems we have their approximated linear model. Its parameters are known or can be determined by one of typical identification procedures. The model obtained using these methods well describes the main features of the system’s dynamics. However, usually it has a low accuracy, which can be a result of the omission of many secondary phenomena in its description. In this paper we propose a new approach to the modelling of weakly nonlinear dynamic systems. In this approach we assume that the model of the weakly nonlinear system is composed of two parts: a linear term and a separate nonlinear correction term. The elements of the correction term are described by fuzzy rules which are designed in such a way as to minimize the inaccuracy resulting from the use of an approximate linear model. This gives us very rich possibilities for exploring and interpreting the operation of the modelled system. An important advantage of the proposed approach is a set of new interpretability criteria of the knowledge represented by fuzzy rules. Taking them into account in the process of automatic model selection allows us to reach a compromise between the accuracy of modelling and the readability of fuzzy rules.

2

Modelowanie kartograficzne z wykorzystaniem neurorozmytych automatów komórkowych

Olszewski R.

Archiwum Fotogrametrii, Kartografii i Teledetekcji

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2003

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Vol. 13a

171--180

PL

Mapa jako środek przekazu informacji chorologicznej, tj. informacji o rozmieszczeniu obiektów i zjawisk w przestrzeni geograficznej, podlega ograniczeniom wynikającym z zakresu pojemności informacyjnej. W procesie przekazu kartograficznego istnieje zatem konieczność celowego uogólnienia informacji źródłowej realizowanego poprzez generali-zację. Jednym ze sposobów generalizacji jest agregacja danych przestrzennych. Istnieje wiele algorytmicznych metod agregacji, większość z nich związana jest z generalizacją danych zapisanych w formacie wektorowym. Dla danych źródłowych w postaci rastrowej wymaga to pracochłonnej wstępnej konwersji formatu raster → wektor oraz wynikowej konwersji wektor → raster. Autor podjął próbę zastosowania bezpośredniej agregacji obiektów powierzchniowych na obrazach rastrowych. Przeprowadzone badania wskazują na celowość zastosowania metod tzw. sztucznej inteligencji obliczeniowej, jako metody kartograficznego modelowania tak zdefiniowanych danych źródłowych. W artykule omówiono trzy wybrane metody sztucznej inteligencji obliczeniowej (automaty komórkowe, sztuczne sieci neuronowe i systemy wnioskowania rozmytego) oraz ich zastosowanie w procesie generalizacji kartograficznej.

EN

Investigations which have been performed by the author justify utilisation of methods of the, so-called, artificial intelligence, as a complex method of cartographic modelling of source data. Of the many existing methods for area aggregation a majority concern maps in vector format. The author investigated some approaches to direct aggregation of area objects in raster maps. This includes cellular automata, neural networks and fuzzy inference systems. The essence of cellular automata is the ability to create complex, global patterns and spatial behaviour, based on simple rules of changes of local range and on knowledge concerning individual cells. Therefore a model of the cartographic generalization process, combining the nature of quantitative generalization of the content and the form with the nature of qualitative generalization, may be developed based on the theory of non-linear cellular automata.

3

A new approach of virtual finite element experimentation as a means for modeling advanced machining processes

Hassan A.I., Kosmol J.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2001

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z. 15

143-148

EN

Despite the large number of models of advanced machining processes, such as abrasive waterjet machining (AWJM), which have been developed so far, there still has been confusion about the nature by which workpiece surfaces are eroded. The finite element method (FEM) could provide both qualitative and quantitative means in order to explain the AWJ erosion process. This paper presents an attempt to model the AWJM process using the powerful tool of the finite element method. The main objective is to develop an FE model which would enable to predict the depth of cut without any cutting experiments. In the new model, interaction of the abrasive particle with the workpiece material is traced at small time increments. The model accurately predicts the depth of cut as a result of AWJ impact and the FE results are in good agreement with experimental results.

PL

Nowe podejście do nieliniowego modelowania obróbki strumieniem wodnościernym (AWJM) metodą elementów skończonych jest przedmiotem referatu. To podejście uwzględnia ruch cząstki ścierniwa od momentu opuszczenia dyszy mieszającej aż do odbicia się od powierzchni przedmiotu obrabianego po wykonaniu pracy skrawania z bardzo małym krokiem czasowym rzędu 0,01 μs. Badania symulacyjne pozwoliły na śledzenie zagłębiania się cząstki ścierniwa w materiale przedmiotu. Wykazały że wzrost ciśnienia cieczy zwiększa głębokość penetracji cząstki ścierniwa a tym samym i głębokość cięcia strumieniem cieczy. Bardzo istotny jest także wniosek o niezwykle krótkim czasie procesu odkształcania się warstwy wierzchniej pod działaniem cząstki ścierniwa, który nie przekracza 0,5 μs. Można więc sądzić, że opracowany model elementów skończonych dokładniej symuluje wzajemne oddziaływania warstwy wierzchniej przedmiotu obrabianego i cząstki ścierniwa.

4

Non-linear time series modelling in financial economics

Chappell D.

Management

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2000

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Vol. 4, no 1

85-100

EN

In this paper we give a summary of some of the non-linear time series modeIs. We present and discuss the properties of the random walk model, ARCH (auto-regressive conditional heteroscedasticity) and GARCH (generalised ARCH) classes of models, threshold auto-regressive models, smooth transition autoregressive models, bilinear models and others. We give examples of modelling chosen economic and financial phenomena and we offer modelling strategy based on flow chart.

5

Dynamic Neural Networks for Process Modelling in Fault Detection and Isolation Systems

Korbicz J., Patan K., Obuchowicz A.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 3

519-546

EN

A fault diagnosis scheme for unknown nonlinear dynamic systems with modules of residual generation and residual evaluation is considered. Main emphasis is placed upon designing a bank of neural networks with dynamic neurons that model a system diagnosed at normal and faulty operating points.To improve the quality of neural modelling, two optimization problems are included in the construction of such dynamic networks: searching for an optimal network architecture and the network training algorithm. To find a good solution, the effective well-known cascade-correlation algorithm is adapted here. The residuals generated by a bank of neural models are then evaluated by means of pattern classification. To illustrate the effectiveness of our approach, two applications are presented: a neural model of Narendra's system and a fault detection and identification system for the two-tank process.

6

Nonregular nonlinear sector modelling

Piegat A.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 3

611-632

EN

Fuzzy modeIs realize human-like modelling schemes. However, a human being can create in his mind relatively simple modeIs of real systems with maximum two inputs. The reason is that human models are based on rectangular lattice partitions of the input spaces. Such a partition enables us to understand the modelled system, which is a great advantage of fuzzy modelling. Despite this, the rectangular lattice partition makes modelling of systems with large numbers of inputs and those realizing complicated inputs/output mappings impossible or very difficult. The paper puts forward a self-organizing and self-tuning method for modelling nonlinear systems. It is based on a nonrectangular partition of the input space. The conclusions of rules can be here linear or nonlinear. For the latter, a special delinearization function (SDL) is proposed. It makes it possible to decrease considerably the number of rules, which results in efficient modelling. Also, the amount of measurement information from the system needed to learn a model can be decreased considerably.