By Krzysztof Patan

An unappealing attribute of all real-world platforms is the truth that they're at risk of faults, malfunctions and, extra in most cases, unforeseen modes of - haviour. This explains why there's a non-stop desire for trustworthy and common tracking structures in response to appropriate and e?ective fault analysis ideas. this can be very true for engineering systems,whose complexity is completely growing to be as a result of the inevitable improvement of recent in addition to the knowledge and verbal exchange expertise revolution. certainly, the layout and operation of engineering structures require an elevated consciousness with admire to availability, reliability, safeguard and fault tolerance. hence, it's usual that fault analysis performs a primary function in glossy keep an eye on thought and perform. this can be re?ected in lots of papers on fault analysis in lots of control-oriented c- ferencesand journals.Indeed, a largeamount of knowledgeon version basedfault prognosis has been gathered via scienti?c literature because the starting of the Seventies. for this reason, a large spectrum of fault analysis options were built. a massive type of fault analysis concepts is the version dependent one, the place an analytical version of the plant to be monitored is believed to be available.

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**Extra resources for Artificial Neural Networks for the Modelling and Fault Diagnosis of Technical Processes**

**Example text**

Un . . ym Fig. 7. Structure of the radial basis function network with n inputs and m outputs 20 2 Modelling Issue in Fault Diagnosis network. Hence, it is unsuitable to use the RBF network in problems where the input space has large sizes. To train such a network, hybrid techniques are used. First, the centres and the spreads of the basis functions are established heuristically. After that, the adjusting of the weights is performed. g. as values of the random distribution over the input space or by clustering algorithms [103, 104], which give statistically the best choice of the centre numbers and their positions as well.

In multivariate statistical data analysis techniques, fault signatures are extracted from process 24 2 Modelling Issue in Fault Diagnosis Faults f Disturbances d Input u(k) Output y(k) PROCESS Generation of diagnostic signals (Neural network) Diagnostic signals s Fig. 9. Model-free fault diagnosis using neural networks operational data through some multivariate statistical methods such as principal component analysis, projection to a latent structure or non-linear principal component analysis [111].

In many practical cases, there is no possibility to learn the order of the modelled process, and the number of suitable delays has to be selected experimentally by using the trial and error procedure [19]. Many papers show that the multi-layer perceptron is able to predict the outputs of various dynamic processes with high precision, but its inherent nonlinearity makes assuring stability a hard task, especially in the cases in which the output of the network is fed back to the network input as in the case of the parallel model [20, 19].