By Marcin Mrugalski
The current e-book is dedicated to difficulties of version of synthetic neural networks to strong fault analysis schemes. It provides neural networks-based modelling and estimation concepts used for designing strong fault analysis schemes for non-linear dynamic systems.
A a part of the booklet specializes in basic concerns equivalent to architectures of dynamic neural networks, equipment for designing of neural networks and fault analysis schemes in addition to the significance of robustness. The e-book is of an instructional worth and will be perceived as an exceptional place to begin for the new-comers to this box. The e-book can be dedicated to complex schemes of description of neural version uncertainty. specifically, the tools of computation of neural networks uncertainty with powerful parameter estimation are awarded. additionally, a unique strategy for process id with the state-space GMDH neural community is delivered.
All the ideas defined during this booklet are illustrated through either uncomplicated educational illustrative examples and functional applications.
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Extra resources for Advanced Neural Network-Based Computational Schemes for Robust Fault Diagnosis
Ns and: Aj (q −1 ) = 1 + . . + aj,l q −l + . . 63) Bi (q −1 ) = bi,0 + . . + bi,m q −m + . . 64) where: l = 1, . . , na , m = 1, . . , nb and pˆ = [a1,1 , . . , any ,na , b10 , . . , bnu ,nb ]T = [a, b]T , represents the vector of the parameters estimate. 66) where Aj (q −1 ) and Bi (q −1 ) denote polynomials in the delay operator q. The polynomial Aj (q −1 ) can be represented as follows: Aj (q −1 ) = na al q −l = l=0 na (1 − λl q −l ). 67) l=1 Coeﬃcients al are assumed to be real and the parameters λl , l = 1, .
5 Structures of Dynamic Neurons in GMDH Neural Networks ... z −1 b1,0 ... u1,k 35 b1,nb ... z −1 bnu ,0 y˜k f (·) ... unu ,k bnu ,nb ana ... z −1 z ... Filter module yˆk Activation module a1 −1 y˜k Fig. 12. Dynamic neuron model with the IIR ﬁlter The behaviour of the ﬁlter module is described by the following equation: y˜k = −a1 y˜k−1 − . . − ana y˜k−na + bT0 uk + bT1 uk−1 +, . . 57) or equivalently, ˆ. 58) where rk = [−˜ yk−1 , . . , −˜ yk−na , uk , uk−1 , . . , uk−nb ] represents the regresˆ = [a1 , .
2 Synthesis of MIMO GMDH Neural Network The assumptions of the GMDH approach presented in Sect. 1 lead to the formation of the neural network of a multi input u1,k , u2,k , . . 4 GMDH in Design of Neural Networks 29 single output yk . However, systems of the multi input u1,k , u2,k , . . , unu ,k and the multi output y1,k , . . , yr,k , . . , yny ,k are found in practical applications most often. The synthesis of the MIMO model  can be performed in a similar way as in the case of MISO models.