Learning-based frequency response function estimation for nonlinear systems

ABSTRACT

In this paper, we perform the nonlinear frequency response function (FRF) estimation for a class of nonlinear systems. Two non-parametric estimation techniques are considered: radial basis function neural network (RBF-NN)-based estimation and support vector machine (SVM)-based estimation. Based on the system's available observations, the proposed estimation models are used to predict its frequency response. Simulation results are provided to demonstrate the model implementation. Finally, a comparative study is carried out to evaluate the effectiveness of the RBF-NN and SVM schemes, which has demonstrated that the SVM outperformed RBF-NN in the FRF estimation.

KEYWORDS:

• Neural network
• nonlinear frequency response
• non-parametric modelling
• RBF
• support vector machines

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Suresh Thenozhi http://orcid.org/0000-0002-0288-9953

Notes

1. If the system's Jacobian matrix is uniformly negative-semidefinite, then the system is uniformly convergent or semi-contracting, which implies the asymptotic convergence of solutions.

Additional information

Funding

The first author would like to thank DGAPA of UNAM, Mexico for the Post-Doctoral fellowship. Part of this work was supported by SEP-CONACyT [grant number 253677] and PAPIIT-UNAM [grant number IN113418].

Notes on contributors

Suresh Thenozhi

Suresh Thenozhi received the Ph.D. degree in automatic control from the Department of Automatic Control, Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico City, Mexico, in 2014. From 2014 to 2016, he was a Post-Doctoral Researcher with the Faculty of Engineering, National Autonomous University of Mexico, Mexico. Since 2016, he has been a Research Associate and a Lecturer with the Faculty of Engineering, Autonomous University of Queretaro, Queretaro, Mexico. His current research focuses on intelligent control, structural vibration control, nonlinear vibrations and contraction analysis. He is a member of the National System of Researchers (SNI) in Mexico.

Yu Tang

Yu Tang received his Ph.D. degree in electrical engineering from the National Autonomous University of Mexico, Mexico City, in 1988. He joined the same university in 1988 and is currently a Full Professor at the Faculty of Engineering. He held a research position with the University of California, Berkeley from January to December 1996 and with the Mexican Petroleum Institute from March 2002 to February 2003. His research interests include nonlinear system control and their applications in a variety of engineering fields. Prof. Tang is a Regular Member of the Mexican Academy of Sciences and a member of the National System of Researchers (SNI). He received the Weizmann Prize from the Mexican Academy of Sciences in 1991, the ‘National University Distinction for Young Academics’ in 1995 and the ‘National University Recognized Professor’ in 1997, both from the National Autonomous University of Mexico.