By Marcin Mrugalski
The current booklet is dedicated to difficulties of edition of synthetic neural networks to strong fault prognosis schemes. It offers neural networks-based modelling and estimation strategies used for designing strong fault prognosis schemes for non-linear dynamic systems.
A a part of the ebook makes a speciality of basic concerns similar to architectures of dynamic neural networks, tools for designing of neural networks and fault analysis schemes in addition to the significance of robustness. The e-book is of an educational worth and will be perceived as a superb place to begin for the new-comers to this box. The booklet can also be dedicated to complicated schemes of description of neural version uncertainty. specifically, the tools of computation of neural networks uncertainty with strong parameter estimation are offered. additionally, a unique method for method id with the state-space GMDH neural community is delivered.
All the suggestions defined during this publication are illustrated through either basic educational illustrative examples and useful applications.
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Fig. 9). (1) yˆ1,1,k Neuron removed (1) yˆ1,nN ,k (1) u2,k ... Q ny ... Q ny ... (1) u1,k Q1 Q2 Q1 Q2 ... ... (1) u3,k (1) ... (1) unu ,k Q1 Q2 ... Q ny ... Q ny ... yˆny ,1,k (1) unu −1,k (1) yˆny ,nN ,k Q1 Q2 Neurons selection Fig. 9. Selection in the MIMO GMDH model The eﬀectiveness of a neuron in processing at least one output signal is suﬃcient to leave the neuron in the network. Based on all selected neurons, a new layer is created. The parameters of the neurons in a newly created layer are ,,frozen” during further network synthesis.
Conduct a series of ny competitions between each n-th neuron in the layer and nj randomly selected neurons (the so-called opponent) from the same layer. The n-th neuron is the so-called winner neuron when: (l) (l) Q(ˆ yn,k ) ≤ Q(ˆ yj,k ), j = 1, . . , nj , (l) where yˆj,k denotes a signal generated by the opponent neuron; 3. Select the neurons for the (l + 1)-th layer with the number of winnings bigger than nw (the remaining neurons are removed). The property of soft selection follows from the speciﬁc series of competitions.
2 Bottom-Up Methods The concept of the Bottom-up methods relies on gradually increase of a small neural network until it achieves a suﬃcient complexity to identify the considered system. Among numerous Bottom-up methods a wide class of methods for the selection of the feed-forward network consists of neurons with a step activation function exists. Between these algorithms the Machands , Tiling  and Upstart  algorithms can be distinguished. Moreover, a limited number of methods for the feed-forward neural networks with a monotonic activation function in neurons can be found.