Abstract
The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.
Highlights
Volterra series[1] have been used for the modelling and analysis of nonlinear systems in many industries such as marine[2], automotive[3], structural[4], biological[5], and communication systems[6]
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 Generalised Frequency Response Functions (GFRFs)
Billings and Lang[13] proposed an algorithm to truncate Volterra series representations, the algorithm makes an assumption that the GFRFs are known a priori or they can be obtained from the time-domain model, which is, not practical in many cases
Summary
Volterra series[1] have been used for the modelling and analysis of nonlinear systems in many industries such as marine[2], automotive[3], structural[4], biological[5], and communication systems[6]. The GFRFs have received much more research interest over the time-domain Volterra kernels This is because important nonlinear phenomena such as harmonics, intermodulation and gain expansion/depression can be explained by the interactions between different frequency components and orders of these GFRFs[7]. Even for a weakly nonlinear system, the order of the Volterra series expansion to achieve an approximation accuracy may still be very high. Billings and Lang[13] proposed an algorithm to truncate Volterra series representations, the algorithm makes an assumption that the GFRFs are known a priori or they can be obtained from the time-domain model, which is, not practical in many cases. A novel approach utilising a complex-valued orthogonal least squares (OLS) algorithm regularised by an adjustable prediction error sum of squares (APRESS) criterion will be developed for both the truncation of the Volterra series expansion and the estimation of the GFRFs
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
