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Back Propagation Learning Algorithm

Neural Networks. MLP for System Modeling. f (.). f (.). f (.). Back Propagation Learning Algorithm. Forward propagation. Set the weights Calculate output. Backward propagation. Calculate error Calculate gradient vector Update the weights. Neural Networks. MLP for System Modeling.

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Back Propagation Learning Algorithm

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  1. Neural Networks MLP for System Modeling f(.) f(.) f(.) Back Propagation Learning Algorithm Forwardpropagation • Set the weights • Calculate output Backwardpropagation • Calculate error • Calculate gradient vector • Update the weights

  2. Neural Networks MLP for System Modeling f(.) f(.) f(.) Feedforward Network Input Output Neuron Layer Neuron Layer

  3. Neural Networks MLP for System Modeling Feedforward Network

  4. Neural Networks MLP for System Modeling Output Input Neuron Layer Neuron Layer Output Input Neuron Layer Neuron Layer Recurrent Networks External Recurrence Time Delay Element Internal Recurrence Time Delay Element Time Delay Element

  5. Neural Networks MLP for System Modeling Dynamic System Output Input Dynamic System System parameter Input-output data vector

  6. Neural Networks MLP for System Modeling Dynamic Model Output Input Dynamic Model weights bias input-output data vector

  7. Neural Networks MLP for System Modeling . . . . . . . . . . . . Neural Network Dynamic Model Feedforward : system output : model output,estimate of system output

  8. Neural Networks MLP for System Modeling . . . . . . . . . . . . Neural Network Dynamic Model Recurrent

  9. Neural Networks MLP for System Modeling ..... T D L ..... Tapped Delay Line (TDL) Unit 1 Unit 2 Unit 3 Unit n

  10. Neural Networks MLP for System Modeling . . . . . . Implementation Output Input Dynamic System feedforward external recurrence T D L T D L

  11. Neural Networks MLP for System Modeling Example Single Tank System A : cross-sectional area of the tank a : cross-sectional area of the pipe Learning Data Generation Save data to workspace Area of operation

  12. Neural Networks MLP for System Modeling Example Data size : 201 from 200 seconds of simulation Feedforward Network External Recurrent Network

  13. Neural Networks MLP for System Modeling Homework 4 • A neural network with 2 inputs and 2 hidden neurons seems not to be good enough to model the Single Tank System. Now, design a neural network with 4 inputs and 4 hidden neurons to model the system. Use bias in all neurons and take all a = 1. Delta of 2–2–1 network • Be sure to obtain decreasing errors. • Submit the hardcopy and softcopy of the m-file. 4–4–1 Network

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