By Marcin Mrugalski

ISBN-10: 331901546X

ISBN-13: 9783319015460

ISBN-10: 3319015478

ISBN-13: 9783319015477

The current ebook is dedicated to difficulties of edition of synthetic neural networks to powerful fault prognosis schemes. It offers neural networks-based modelling and estimation concepts used for designing strong fault prognosis schemes for non-linear dynamic systems.

A a part of the booklet specializes in basic concerns 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 booklet is of an academic price and will be perceived as a great 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 tools of computation of neural networks uncertainty with strong parameter estimation are awarded. furthermore, a singular method for procedure id with the state-space GMDH neural community is delivered.

All the recommendations defined during this publication are illustrated by way of either uncomplicated educational illustrative examples and useful applications.

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P ˆ nu−1 ,nu are the estimates of the network parameters where p and should be obtained during the identification process. , the LMS [69, 70]. It follows from the facts that the parameters of each partial models are estimated separately and the neuron’s activation function f (·) fulfills the following conditions: 1. , ∀ x ∈ R : a < f (x) < b. 42) 2. , ∀ x, y ∈ R : x ≤ y iff f (x) ≤ f (y). 43) 3. , there exists f −1 (·). The advantage of this approach is a simple computation algorithm that gives good results even for small sets of measuring data.

During the selection, neurons which have too large value of the evaluation (l) criterion Q(ˆ yn,k ), are rejected. A few methods of performing the selection procedure can be applied [118]. One of the most often used is the constant population method. It is based (l) on a selection of g neurons, which evaluation criterion Q(ˆ yn,k ) reaches the smallest values. The constant g is chosen in an empirical way and the most important advantage of this method is its simplicity of implementation. Unfortunately, the constant population method has very restrictive structure evolution possibilities.

34) ˆ (Narch , p ˆ 0 )) represents a generalisation error for the where supu∈V JV (y, y optimal trained architecture of the network Narch0 for which the algorithm A was initialized. 32). The A algorithms consist of the following steps [48]: 1. Inclusion of the initial architecture Narch0 to the space of the network architectures Narch . 2. Calculation of the goal function f (Narch0 ). 3. Obtaining the network architecture Narch characterized by lower value of the goal function from the set Narch .

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Advanced Neural Network-Based Computational Schemes for Robust Fault Diagnosis by Marcin Mrugalski

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