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39) where: p - the number of pattern, i-the number of output neuron. b) Sum Squared Error, cf. 41) d) Root Mean Squared Error: RMSE= oJ MSE . 42) The above listed errors can be easily computed at the end of each epoch or they can be used as a network error introduced to the BP algorithm. 27) should be formulated adequately. 3. Generalization, cross-validation and testing. Let us assume that in the behaviour space X we can separate a subspace 1( in which the input and output variables obey a set of rules (relations).

70) P=! g. a = 1IN in order to simplify the mathematical description of information retrieval, cf. [2). In what follows the binary digits are used. Fundamentals of ANNs 43 In the retrieval phase a probe is presented to the network and the activation potential of the i-th neuron Vi (s) and output Yi (s) is computed: Vi(S) N = LWi/Yj(s)+bi =Ui -Oi ~ Yi(s)=F(vi(s)). 72) < 0i . the iteration procedure is performed for a randomly selected neuron i. : Yi(s+l)=Yj(s) forall i. (1. 73) corresponds to the stable state of the network.

Eds): Artificial Neural Networks - An Introduction to ANN Theory and Practice, Springer, Berlin/ Heidelberg 1995. 28. Adeli, H. , 121 (1995), 1205-1212. 29. P. : Neural network approximation in a simulated annealing based optimal structural design, Structural Optimization, 5 (1993), 159-165. 30. P. : Damage detection in structures based on featuresensitive neural networks, J. , 8 (1993),163-178. 31. Kortesis, S. : Neural networks for computing in structural analysis - methods and prospects of applications, Int.

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