Download Advanced Neural Network-Based Computational Schemes for by Marcin Mrugalski PDF

By Marcin Mrugalski

The current e-book is dedicated to difficulties of edition of man-made neural networks to powerful fault analysis schemes. It provides neural networks-based modelling and estimation innovations used for designing powerful fault analysis schemes for non-linear dynamic systems.

A a part of the publication specializes in basic matters resembling architectures of dynamic neural networks, equipment for designing of neural networks and fault prognosis schemes in addition to the significance of robustness. The ebook is of an instructional worth and will be perceived as a superb start line for the new-comers to this box. The booklet is usually dedicated to complicated schemes of description of neural version uncertainty. particularly, the tools of computation of neural networks uncertainty with powerful parameter estimation are awarded. in addition, a singular technique for method identity with the state-space GMDH neural community is delivered.

All the innovations defined during this booklet are illustrated by way of either easy educational illustrative examples and sensible applications.

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Np are estimated parameters. The neuron with the memory can be perceived as a special case of the generalized local output feedback architecture. It has a feedback transfer function only with one pole. The feed-forward structure of networks consisting of the dynamic neurons seems to make the training process easier in comparison to the global recurrent network presented in Sect. 2. On the other hand, the introduction of the dynamic neurons increases the parameter space significantly. This drawback together with the non-linear and multi-modal properties of the dynamic neuron implies that the parameters estimation still becomes complex.

32) f (ei ) = g(ei ) + h(ei ). 3 Methods for Designing of Neural Models 23 • A set of goal architectures G ⊂ Narch . • The expansion operator Ξ(Narch ) : Narch → 2Narch which enables the determination of the set of network architectures being successors of the architecture Narch . The operator Ξ(Narch ) can generate successor by adding a new hidden layer of neurons directly before the output layer or by adding a new neuron in the hidden layer. 33) g(Narch , Narch ) = ϑl (Narch ) − ϑl (Narch ) L−1 where ϑh (Narch ) = i=1 card(Vi ) denotes the number of neurons in ϑl = (l − 1) hidden layers.

The main disadvantage of such method relies on repeating of learning process after the pruning of the network structure. The improved version of the OBD algorithm is the Optimal Brain Surgeon p) (OBS) method [46]. In this approach, also the expansion of the function JV (ˆ ˆ is performed and the first into Taylor series around the current solution p order factor is removed. However, all components of the Hessian matrix are taken into account: 1 pˆ2i = . 13) where ei represents unitary vector with ones at i-th position.

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