By Marcin Mrugalski
The current e-book is dedicated to difficulties of version of man-made neural networks to strong fault analysis schemes. It provides neural networks-based modelling and estimation innovations used for designing strong fault prognosis schemes for non-linear dynamic systems.
A a part of the ebook specializes in basic concerns resembling 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 instructional worth and will be perceived as an exceptional start line for the new-comers to this box. The e-book can be dedicated to complex schemes of description of neural version uncertainty. particularly, the tools of computation of neural networks uncertainty with strong parameter estimation are awarded. in addition, a singular procedure for process identity with the state-space GMDH neural community is delivered.
All the techniques defined during this e-book are illustrated by means of either uncomplicated educational illustrative examples and sensible applications.
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Extra resources for Advanced Neural Network-Based Computational Schemes for Robust Fault Diagnosis
The application of the GMDH approach to the model structure selection can improve the quality of the model but it can not eliminate the model uncertainty at all. , the model-reality mismatch . It is necessary to analyze each stage of the neural model synthesis process in order to identify each source of uncertainty. This knowledge makes it possible to reduce the model uncertainty or eventually calculate in the form which can be applied in the robust FDI schemes. 1 Neural Network Structure Errors The errors in the structure of the network are important sources of uncertainty of the GMDH neural model.
In this way the searching space is limited to a class of digraphs of N nodes. Any architecture of the neural network included in M is represented by the incidence matrix V inc . Each element equaled the Narch to Vi,j = 1 or Vi,j = 0 depends on the existing or no connection between i-th and j-th neurons in the network. On the beginning of the algorithm the initial set of the incidence matrixes is randomly generated. On the basis of the incidence matrixes the chromosomes are created, which are processed by the application of the mutation and crossover operators.
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.