Advanced Neural Network-Based Computational Schemes for by Marcin Mrugalski

By Marcin Mrugalski

The current booklet is dedicated to difficulties of edition of synthetic neural networks to powerful fault prognosis schemes. It provides neural networks-based modelling and estimation strategies used for designing powerful fault analysis schemes for non-linear dynamic systems.

A a part of the booklet specializes in primary matters reminiscent of architectures of dynamic neural networks, equipment for designing of neural networks and fault prognosis schemes in addition to the significance of robustness. The publication is of an educational price and will be perceived as a very good place to begin for the new-comers to this box. The e-book is additionally dedicated to complex schemes of description of neural version uncertainty. particularly, the equipment of computation of neural networks uncertainty with powerful parameter estimation are awarded. additionally, a singular method for procedure id with the state-space GMDH neural community is delivered.

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

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This relatively simple network architecture is designed for real time signals processing and this is a reason why this network is called the RTRN. The fundamental advantage of such networks is the possibility of approximating of a wide class of dynamic systems. Unfortunately, training of the RTRN network is usually complex and slowly convergent [87]. Moreover, there are problems with keeping network stability. The Elman neural network [89] also belongs to the class of global recurrent networks.

1) unu −1,k unu ,k (L ) 2 yˆ2,opt,k ... (1) u3,k yˆ1,k ... (1) u2,k ... (1) u1,k yˆny ,k ... Fig. 11. 1 Dynamic Neuron with IIR Filter The GMDH approach allows much freedom in defining the partial model structure. 40). As it was already mentioned in Sect. 40) allows to use the techniques for the parameters estimation of linear-in-parameter models. 40) can be relatively easily transformed into a linear-in-parameter one. Such neuron can be used for the identification of the non-linear static systems.

The proposed dynamic neuron consists of the linear state-space module and activation module [61, 77] (cf. Fig. 15). 84) 2 Designing of Dynamic Neural Networks ... rnr ,k s˜1,k s˜2,k Linear Activation state-space module module s˜ns ,k ... r1,k r2,k sˆ1,k sˆ2,k ... 40 sˆns ,k Fig. 15. Dynamic neuron model in the state-space representation ˜i,j,k ∈ Rns are the inputs and outputs of the linear where ri,k ∈ Rnr and s state-space submodule of the dynamic neuron. A ∈ Rnz ×nz , B ∈ Rnz ×nr , C ∈ Rns ×nz , z k ∈ Rnz , where nz represents the order of the dynamics.

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