document: The GFRFs of nonlinear systems can be determined by either a parametric-model-based method or a nonparametric-model-based method [8]. In the parametric approach, a nonlinear parametric model is first identified from the input–output data. The GFRFs are then obtained by mapping the resultant model into the frequency domain using the probing method [9]. The nonparametric approach is often referred to as frequency-domain Volterra system identification and is based on the observation that the Volterra model of nonlinear systems is linear in terms of the unknown Volterra kernels, which, in the frequency domain, corresponds to a linear relation between the output frequency response and linear, quadratic, and higher order GFRFs. This linear relationship allows the use of a least squares (LS) approach to solve for the GFRFs. Several researchers [10–12] have used this method to estimate the GFRFs. But they usually made the assumption that it is known a priori that the system under study can be represented by just two or three terms. However, such information is rarely available a priori.
doc_bio_tags: O B O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O B O O O O B I I I I I I I O O B I O O B I O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O B O B I O O O O O O O O O O O O O B O O O O O O O O O O B O O O B I I O O O O O O O B I O O O O O O O B I I I O O O O O O O O
extractive_keyphrases: a nonlinear parametric model corresponds to a linear relation gfrfs linear relationship made the assumption mapping the resultant model into the frequency domain nonparametric approach probing method the system two or three terms volterra model of nonlinear systems
abstractive_keyphrases: a least squares (ls) approach a nonparametric-model-based method a parametric-model-based method frequency-domain volterra system identification the gfrfs of nonlinear systems