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David C. Silverman |
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Training the Back-Propagation Neural Network Once the network is constructed, it has to be trained. As mentioned in the discussion of the back-propagation neural network, the artificial neural network most often applied in corrosion (and elsewhere) has been the back-propagation network. In corrosion applications, it has been used to solve either complex pattern-matching problems or fit relationships among variables for which explicit functions cannot be written. This type of network is shown in this figure) ..
The training algorithm is summarized below. The actual equations
for the algorithm are available in a number of textbooks, for example "Artificial
Intelligence, A Modern Approach", S. J. Russell and P. Novig, Prentice Hall, 1996
and "Neural Networks-Algorithms, Applications, and Programming Techniques", J. A. Freeman
and D. M. Skapura, Addison-Wesley, 1992.
The network learns ("fits" might be an alternative description) a predefined set of input-output pairs known as the training set. The methodology is a two phase cycle consisting of propagation and adaptation. The algorithm is known as the generalized delta rule. A number of variations exist. A set of weights are arbitrarily chosen for each processing element ) .
After the input
is applied to the first layer of network units, the output is propagated to the next layer as
an input to that layer until an output from the network is calculated (output layer).
This output pattern is compared to the desired output. An error is created as the sum of
the squares of the differences between the each calculated and desired output. Nothing
magical exists with respect to the error function. Cubic and fourth power differences have
also been used.
This error is sent backward from the output layer to each computing element that contributed to the output (the next lower hidden layer). But the total error is divided among the computing elements according to their relative contributions to the original output. Once completed, the process is repeated for each layer of computing elements. The weights for each pathway to each computing elements are updated. The network converges toward a state that should enable all training patterns to be coded properly. Back-propagation is a fairly robust form of non-linear regression. As the network trains, the computing elements in the intermediate layer(s) organize themselves so that different computing elements "learn" to recognize different features in the input space. At some point, often at an arbitrarily chosen minimum sum of squares, the training is deemed complete. Another set of input-output patterns, the test set, is then fed to the network to determine how it trained. If the new input contains features that the computing element "recognizes" (that resembles features that it has learned during training), it responds with an active output. If the new input does not contain features that the computing element recognizes (e.g. that does not resemble features that it has learned during training), its response is inhibited (zero). The goal is to ensure that the training set encompasses the test set. Following are issues that should be considered when designing and using back-propagation artificial neural networks.
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David C. Silverman, Ph.D. - Primary Consultant |