Download Neural Networks in the Analysis and Design of Structures by Zenon Waszczyszyn (eds.) PDF

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By Zenon Waszczyszyn (eds.)

Neural Networks are a brand new, interdisciplinary instrument for info processing. Neurocomputing being effectively brought to structural difficulties that are tricky or maybe most unlikely to be analysed through general desktops (hard computing). The booklet is dedicated to foundations and functions of NNs within the structural mechanics and layout of structures.

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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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