Zhang, B. orcid.org/0000-0001-7327-0923 and Billings, S.A. (2016) Volterra Series Truncation and Kernel Estimation of Nonlinear Systems in the Frequency Domain. Mechanical Systems and Signal Processing, 84 (A). pp. 39-57. ISSN 0888-3270
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | orthogonal least squares; Volterra series; generalised frequency response function; nonlinear systems |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Advanced Manufacturing Institute (Sheffield) > Nuclear Advanced Manufacturing Research Centre |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Jul 2016 11:36 |
Last Modified: | 01 Aug 2017 05:14 |
Published Version: | https://dx.doi.org/10.1016/j.ymssp.2016.07.008 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.ymssp.2016.07.008 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:102491 |
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