By Krzysztof Patan
An unappealing attribute of all real-world platforms is the truth that they're susceptible to faults, malfunctions and, extra normally, unforeseen modes of - haviour. This explains why there's a non-stop want for trustworthy and common tracking structures in accordance with appropriate and e?ective fault analysis options. this can be very true for engineering systems,whose complexity is completely becoming end result of the inevitable improvement of contemporary in addition to the knowledge and verbal exchange know-how revolution. certainly, the layout and operation of engineering platforms require an elevated cognizance with admire to availability, reliability, security and fault tolerance. hence, it truly is usual that fault analysis performs a primary function in sleek regulate 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 collected via scienti?c literature because the starting of the Seventies. hence, a large spectrum of fault prognosis suggestions were built. a tremendous classification of fault prognosis thoughts is the version established one, the place an analytical version of the plant to be monitored is thought to be available.
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Additional info for Artificial Neural Networks for the Modelling and Fault Diagnosis of Technical Processes
6) Faults that inﬂuence the input or output of the process result in changes of the residual e (t) with diﬀerent transients. The polynomials of GM (s) can also be used to form a polynomial error : e(s) = AM (s)y(s) − BM (s)u(s) = Ap (s)fy (s) + Bp (s)fu (s). 7) are known as parity equations (parity relations) . Parity relations can also be derived from the state-space representation; then they oﬀer more freedom in the design of parity relations . The fault isolation strategy can be relatively easily realised for sensor faults.
G. deriving training algorithms, investigating approximation abilities and stability problems, and selecting optimal training sequences. These problems are presented in the forthcoming chapters. Neural network based algorithms for residual evaluation are also considered. 3 Locally Recurrent Neural Networks Artiﬁcial neural networks provide an excellent mathematical tool for dealing with non-linear problems [18, 23, 77]. They have an important property according to which any continuous non-linear relation can be approximated with arbitrary accuracy using a neural network with a suitable architecture and weight parameters.
The feedforward part of the network still maintains the well-known curve-ﬁtting properties of the multi-layer perceptron, while the feedback part provides its dynamic character. Moreover, the usage of the past process observations is not necessary, because their eﬀect is captured by internal network states. The RMLP network has been successfully used as a model for dynamic system identiﬁcation . However, a drawback of this dynamic structure is increased network complexity strictly dependent on the number of hidden neurons and the resulting long training time.