FREQUENCY DOMAIN ANALYSIS OF NARX NEURAL NETWORKS

✍ Scribed by J.E. Chance; K. Worden; G.R. Tomlinson

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 378 KB
• Volume: 213
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1539

✦ Synopsis

A method is proposed for interpreting the behaviour of NARX neural networks. The correspondence between time-delay neural networks and Volterra series is extended to the NARX class of networks. The Volterra kernels, or rather, their Fourier transforms, are obtained via harmonic probing. In the same way that the Volterra kernels generalize the impulse response to non-linear systems, the Volterra kernel transforms can be viewed as higher-order analogues of the Frequency Response Functions commonly used in Engineering dynamics; they can be interpreted in much the same way. 7 1998 Academic Press Limited * The distinction between the two processes is important; the process of validation establishes if the model conforms to requirements, the process of verification is the procedure by which correct operation is assured [9]. * Note that the expressions can be made symmetrical at the expense of introducing a delta-function and an extra integration i.e., Y2(v) = 1 2p g +a -a g +a -a dv1 dv2 d(v -v1 -v2)H2(v1, v2)X(v1)X(v2).