An approach to fault diagnosis of nonlinear systems using neural networks with invariance to Fourier transform

作者：Rigatos Gerasimos^*; Siano Pierluigi; Zervos Nikolaos

来源：Journal of Ambient Intelligence and Humanized Computing, 2013, 4(6): 621-639.

DOI：10.1007/s12652-012-0173-4

• Feed-forward neural networks
• Orthogonal basis functions
• Gauss-Hermite polynomials
• Fourier transform invariance
• Spectral decomposition
• Fault detection and isolation

A neural network with Gauss-Hermite polynomial activation functions is used for approximating the nonlinear system%26apos;s dynamics out of a set of input-output data. Thus the output of the neural network provides a series expansion that takes the form of a weighted sum of Gauss-Hermite basis functions. Knowing that the GaussHermite basis functions satisfy the orthogonality property and remain unchanged under the Fourier transform, subjected only to a change of scale, one has that the considered neural network provides the spectral analysis of the output of the monitored system. Actually, the squares of the weights of the output layer of the neural network denote the distribution of energy into the associated spectral components for the output signal of the monitored nonlinear system. By observing changes in the amplitude of the aforementioned spectral components one can have also an indication about malfunctioning of the monitored system and can detect the existence of failures. Moreover, since specific faults are associated with amplitude changes of specific spectral components of the system fault isolation can be also performed.

• 出版日期2013-12