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Fig. 12.27 Approximation of the system's temperature output ( red line ) by a neural network with
Hermite polynomial basis functions ( blue-line )( a ) temperature's time variation—profile 3 ( b )
temperature's time variation—profile 4
The spectral components of the temperature signal for both the fault-free and
the under-fault operation of the system have been shown in Figs. 12.28 , 12.29 ,
12.30 , 12.31 . It can be noticed that after a fault has occurred the amplitude of the
aforementioned spectral components changes and this can be a strong indication
about failure of the monitored system.
Obviously, the proposed spectral decomposition of the monitored signal, with
series expansion in Gauss-Hermite basis functions can be used for fault detection
tasks. As it can be seen in Figs. 12.28 , 12.29 , 12.30 , 12.31 , in case of failure,
the spectral components of the monitored signal differ from the ones which are
obtained when the system is free of fault. Moreover, the fact that certain spectral
components exhibit greater sensitivity to the fault and change value in a more abrupt
manner is a feature which can be exploited for fault isolation. Specific failures can
be associated with variations of specific spectral components. Therefore, they can
provide indication about the appearance of specific types of failures and specific
malfunctioning components.
 
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