Modelleerimine ja Juhtimine Tehisnärvivõrgudega

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Modelleerimine ja Juhtimine Tehisnärvivõrgudega ---------------------------------------------- Identification and Control with artificial neural networks Eduard Petlenkov, Eduard Petlenkov, 2013

Artificial neuron Input vector: Vector of weight coeffitients: Weighted sum Nonlinear element Input vector: Vector of weight coeffitients: Weighted sum: Eduard Petlenkov, 2013

Biological neuron and biological neural networks Eduard Petlenkov, 2013

Sigmoid functions are having an "S" shape (sigmoid curve) Activation functions (1) OUT=f(NET) Sigmoid functions are having an "S" shape (sigmoid curve) 1 Logistic function 2 Hyperbolic tangent Eduard Petlenkov, 2013

Types of artificial neural networks Feedforward Feedback internal feedback external feedback Structure: inputs etalon Supervised learning Selflearning (unsupervised) Training/ learning: inputs Training criteria Eduard Petlenkov, 2013

Interpritation of results How to use artificial neural networks Network Data preprocessing Interpritation of results Inputs Outputs Eduard Petlenkov, 2013

Feedforward neural networks and multilayer perceptron Feedforward networks are networks in which an output of a neuron can be connected only with an input of a next layer neuron. - Input layer - Output layer - Hidden layer - Weighting coefficients, where is the number of the neuron’s input “from each to each” - neuron’s number in the layer - number of the layer Eduard Petlenkov, 2013

Mathematical function of a two-layer perceptron - Activation function of the hiddent layer neurons; - Activation function of the output layer neurons. Eduard Petlenkov, 2013