Wyniki wyszukiwania - BazTech

1

Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

Smoczek J.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 4

749--759

EN

A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.

2

Is the conventional interval arithmetic correct?

Piegat A., Landowski M.

Journal of Theoretical and Applied Computer Science

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2012

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Vol. 6, nr 2

27-44

EN

Interval arithmetic as part of interval mathematics and Granular Computing is unusually important for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic thinking, Computing with Words, grey systems, fuzzy arithmetic and probabilistic arithmetic. However, the mostly used conventional Moore-arithmetic has evident weak-points. These weak-points are well known, but nonetheless it is further on frequently used. The paper presents basic operations of RDM-arithmetic that does not possess faults of Moore-arithmetic. The RDM-arithmetic is based on multi-dimensional approach, the Moore-arithmetic on one-dimensional approach to interval calculations. The paper also presents a testing method, which allows for clear checking whether results of any interval arithmetic are correct or not. The paper contains many examples and illustrations for better understanding of the RDM-arithmetic. In the paper, because of volume limitations only operations of addition and subtraction are discussed. Operations of multiplication and division of intervals will be presented in next publication. Author of the RDM-arithmetic concept is Andrzej Piegat.

3

A Framework for Interval Quantization and Application to Interval Based Algorithms in Digital Signal Processing

Santana F. T., Santana F. L., Guerreiro A. M. G., Dória Neto A. D., Santiago R. H. N.

Fundamenta Informaticae

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2011

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Vol. 112, nr 4

337-363

EN

In this article, we use the interval mathematics and targeted rounding by specific functions to establish a framework for interval quantization. The function approximation FId, that maps x to an interval [x1, x2] such that x1 is the largest floating point number less than or equal to x and x2 is the smallest floating point number greater than or equal to x, is used to establish the sampling interval and the levels of interval quantization. We show that the interval quantization levels (Nj) represent the specific quantization levels (nj ), that are comparable, according to Kulisch- Miranker order and are disjoint two by two. If an interval signal X[n] intercepts a quantization interval level Nj , then the quantized signal will be Xq[n] = Nj. Moreover, for the interval quantization error (E[n] = Xq[n] - X[n]) an estimate is shown due to the quantization step and the number of levels. It is also presented the definition of interval coding, in which the number of required bits depends on the amount of quantization levels. Finally, in an example can be seen that the the interval quantization level represent the classical quantization levels and the interval error represents the classical quantization error.

4

Interval mathematics for analysis of multi-level granularity

Kreinovich V., Alo R.

Archives of Control Sciences

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2002

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Vol. 12, no. 4

323-350

EN

The more complex the problem, the more complex the system necessary for solving this problem. For very complex problems, it is no longer possible to design the corresponding system on a single resolution level, it becomes necessary to have multi-level, multiresolutional systems, with multi-level granulation. When analyzing such systems - e.g., when estimating their performance and/or their intelligence - it is reasonable to use the multi-level character of these systems: first, we analyze the system on the low-resolution level, and then we sharpen the results of the low-resolution analysis by considering higher-resolution representations of the analyzed system. The analysis of the low-resolution level provides us with an approximate value of the desired performance characteristic. In order to make a definite conclusion, we need to know the accuracy of this approximation. In this paper, we describe interval mathematics- a methodology for estimating such accuracy. The resulting interval approach is also extremely important for tessellating the space of search when searching for optimal control. We overview the corresponding theoretical results, and present several case studies.

5

Przedziałowe metody rozwiązywania algebraicznych równań nieliniowych mechaniki konstrukcji

Pownuk A.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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1999

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z. 9

231-236

PL

W pracy przedstawiono przedziałowe metody znajdowania wszystkich pierwiastków algebraicznych równań nieliniowych oraz relacji oparte na matematyce przedziałowej. Przedstawione algorytmy zastosowano do rozwiązywania nieliniowych równań równowagi, problemów stateczności oraz drgań własnych układów prętowych.

EN

In this paper the methods for system of nonlinear algebraic equations and relations based on interval mathematics are presented. Presented algorithms were applied to solve systems of nonlinear equilibrium equations, stability problems and free vibrations of bars.

6

Modelowanie niepewnych parametrów układów mechanicznych metodami matematyki przedziałowej

Pownuk A.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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1999

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z. 9

225-230

PL

W pracy przedstawiono nowe metody modelowania przedziałowych oraz zbiorowych nieokreśloności parametrów w układach mechanicznych. Metody te oparte sana matematyce przedziałowej. Przedstawione algorytmy zastosowano do problemów obliczania przemieszczeń oraz optymalizacji konstrukcji inżynierskich.

EN

In this paper the new methods of modelling interval and sets uncertainties of parameters of mechanical systems are presented. The method are based on interval mathematics. Presented algorithms was applied to calculation displacements and optimization of engineering constructions.