A fuzzy logic controller with multilayer neutral network whose synaptic weights represent the fuzzy knowledge base and its application to the highly nonlinear systems is presented in this work. The scaling factors of the input variables, membership functions and the rule sets are optimized by the use of the multiobjective genetic algorithms. The fuzzy network structure is specified by a combination of the mixed Takagi-Sugeno's and Mamdani's fuzzy reasoning. The mixed, Binary-Real-Integer, optimal coding is utilized to construct the chromosomes, which define the same of necessary prevai;ling parameters for the conception of the desired controller. This new controller stands out by a non-standard gain, which varies lineary with the fazzy inputs. Under certain conditions, it becomes similar to the conventional PID controller with non-linearly variable coefficients. Computer simulation indicates that the designed fuzzy controller is satisfactory in control of a nonlinear system "Inverted Pendulum".
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Feedforward neural networks are usually used for functions approximation [1]. This feature of such a class of networks is explained in the paper by Cybenko [2]. In literature we can find many different application of neural networks as universal approximators [3], [4]. It seems that one of the most interesting application (not trivial at all example) of neural networks is the reconstruction of attractors of chaotic time series. The analysis of time series is mainly based on the embedding theorem by Takens, [5]. The commonly used algorithm for neural networks learning, called the backpropagation algorithm [6], is a gradient descent method for searching a minimum of a function. This kind of algorithm for nonconvex function (like the learning error function of feedforward neural networks) often stops in a local minimum. Even various modifications of this algorithm [9] still cannot avoid local minimal points. Up to now, in practice, the only way to try to find a near global optimum solution is to perform computations several times with different starting initial weights values and to choose the best solution. In this work we propose a new global optimization algorithm for neural networks learning - one that allows to find a global minimum of the learning error, at least theoretically. The algorithm is based on dynamic programming [10], [11], namely the learning of multilayer neural networks is considered as a special case of a multistage optimal control problem [12]. In such a case layers ale treated as stages while weights as controls. The problem of optimal weight adjustment is converted into a problem of optimal control. The multistage optimal control problem can be solved in various ways, as, e.g., by the application of dynamic programming [13]. Within the backpropagation framework, weights ale tuned layer-by-layer as well as step-by-step to minimize the learning error. Meanwhile, in the new algorithm for each layer starting from the output layer, a return function is connstructed first, and then this function is minimized wit h respect to weights. This procedure is performed stage-by-stage, that is layer-by-layer.
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W pracy ukazano możliwość zastosowania sztucznych sieci neuronowych (SSN) jako alternatywy dla typowych modeli matematycznych. Jest to narzędzie za pomocą, którego można w szybki oraz dokładny sposób przewidzieć i zaprognozować wiele zmiennych parametrów. Cechy sieci neuronowych sprawiają, że możliwa jest analiza zjawisk charakteryzujących się nieliniowością oraz aproksymacja funkcji wielu zmiennych. Przedstawiono przykłady zastosowania SSN do modelowania wybranych zjawisk i procesów w inżynierii środowiska.
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In this paper the possibilities of using artifical neural networks (ANN) as an alternative to conventional methematical models are displayed. It is a tool which can be a quick and accurate way to predict and forecast the number of variables. Features of neural networks (make) it possible to analyze the phenomena that characterize the nonlinearity and approximation of functions of several variables. Examples of application of ANN for modeling of selected phenomena and processes in environmental engineering are presented.
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W artykule przedstawiono lokalizację obciążenia wywołującego uplastycznienie w konstrukcji belkowej na podstawie zmian charakterystyk dynamicznych. Porównując charakterystyki dynamiczne konstrukcji wyjściowej z pomierzonymi na konstrukcji obciążonej dodatkowym, znanym obciążeniem kontrolnym, otrzymano informacje pozwalające zlokalizować obciążenie.
EN
The paper presents the localization of the load casing yielding in a beam structure on the basis of changes of dynamic parameters. The comparison of dynamic characteristics of investigated structure and the structure loaded with an additional, known load gives the information necessary to the identification of the load casing yielding.
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