Higher-order Frequency Response Functions for Nonlinear Systems from Neural Networks

algorithm [3]. A method is presented for calculating the Higher-order In this paper, the method of Way and Green [2] will Frequency Response Functions (HFRFs) of NARX neural be extended to the frequency-domain. By harmonically networks. HFRFs are the Fourier transforms of Volterra probing the network equation, the HFRFs of the network kernels and can be viewed as multi-dimensional equivawill be calculated. Using the more general NARX class lents of the famil&r Frequency Response Function. If a of network in which the network training data consists of network can be trained to model some nonlinear dynomithe system’s past input and past output data, a nonlinear cal system then the obtained network HFRFs may cow~esystem will be modelled and t,he HFRFs of the network spond closely to that system’s HFRFs. extracted. It is argued that if the network is an accurate model of the system, then the calculated HFRFs of