OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
Figure 4 Multi-layer feed forward artificial neural
network
2. Artificial Neural NETWORK MODELING
The multi-layer feed forward ANN of Fig.4 consists three parts: input layer, the hidden layer, and the output
layer. The neurons between the layers are connected by the links having synaptic weights. The error backpropagation
training algorithm is based on weight updates so as to minimize the sum of squared error for -
number of output neurons, given as:
Where
= desired output for the th pattern. The weights of the links are updated as
where is the learning step, is the learning rate and is the momentum constant
In Eq. (3) is the error term, which is given as follows:
where is the number of neurons in the hidden layer.
)
The training process is initialized by assigning small random weight values to all the links. The input-output
patterns are presented one by one and updating the weights each time. The mean square error (MSE) at the end
of each epoch due to all patterns is computed as
Where = number of training patterns.
The training process will be terminated when the specified goal of MSE or maximum number of epochs is
achieved. Before training and validation the total input and output data were normalized for increase accuracy
and speed of the network.
3. Artificial neural network training
The training of ANN for 9 input-output patterns has been carried out using programming in neural network (NN)
toolbox available in MATLAB software. First neural network architecture has been decided. The general
network is supposed to be 4–n–2, which implies four neurons in the input layer, n neurons in the hidden layer
and two neurons in the output layer. In the present study we have 4 neurons in the input layer (corresponding to 4
process inputs, current, wheel speed, pulse on-time, and duty factor), 2 neurons in the output layer
(corresponding to 2 outputs MRR and R a and one hidden layer of 23 neurons was employed. The following
learning factors are used to successfully train the network.
• Learning rate ( ) = 0.05; momentum factor (α) = 0.85;
• Maximum number of epochs = 5000; tolerance for MSE = 0.00001.
The ANN training simulation was carried out using the variable learning rate training procedure “traingdx” of
the MATLAB NN toolbox. This procedure improves the performance of EBPTA by allowing the learning rate to
change based on the complexity of the local error surface. Fig.5 shows the variation of MSE during the training.
In the present study, the desired MSE achieved after 1466 epochs.
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