Impulse response function identification of linear mechanical systems based on Kautz basis expansion with multiple poles

ABSTRACT

The impulse response function (IRF) identification of linear mechanical systems is important in many engineering applications. This paper proposes a novel IRF identification method of linear systems based on Kautz basis expansion with multiple poles. In order to reduce the parameters to be identified, the IRF is expanded in terms of orthogonal Kautz functions with multiple poles, and the poles in Kautz functions should be optimised. This allows the identification of IRF for linear mechanical systems operated under more than one mode, such as systems under the white noise excitation or the swept frequency excitation with a wide range of frequency, and can improve the identification accuracy. Furthermore, based on the backpropagation through-time technique and the expectation maximisation algorithm, a pole optimisation algorithm is presented in this paper. The simulation studies verify the effectiveness of the proposed IRF identification method.

KEYWORDS:

• Impulse response function
• EM algorithm
• system identification
• Kautz function

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 11632011], [grant number 11702171], [grant number 51121063].

Notes on contributors

Changming Cheng

C.M. Cheng received the B.S. degree in mechanical engineering from Huaqiao University, Xiamen, China, in 2009, and M.S. and Ph.D. degree in mechanical engineering from Shanghai Jiao Tong University, Shanghai, China, in 2012 and 2015, respectively. He is currently a postdoctoral fellow with the State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, and a visiting scholar in the University of Iowa. His research interests include signal processing, nonlinear system identification, machine health diagnosis, and prognostics.

Zhike Peng

Z.K. Peng received the B.Sc. and Ph.D. degrees from Tsinghua University, Beijing, China, in 1998 and 2002, respectively. He was a Research Associate with the City University of Hong Kong, Hong Kong, from 2003 to 2004, and a Research Officer with Cranfield University, Cranfield, U.K. He was with The University of Sheffield, Sheffield, U.K., for four years. He is currently the Cheung Kong Chair Professor with the State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, China. His current research interests include nonlinear vibration, signal processing and condition monitoring, and fault diagnosis for machines and structures.

Xingjian Dong

Xingjian Dong received the B.S. degree in aircraft design engineering and the M.S. degree in solid mechanics from Northwestern Polytechnical University, Xi'an, China, in 1999 and 2002, respectively, and the Ph.D. degree in mechanical engineering from Shanghai Jiao Tong University, Shanghai, China, in 2006. He is currently an Associate Professor with the State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University. His current research interests include vibration analysis, smart structures, and fatigue analysis of structures. Wenming Zhang (M’10) received the B.S. degree in mechanical engineering and the M.S. degree in mechanical design and theories from Southern Yangtze University, Wuxi, China, in 2000 and 2003, respectively, and the Ph.D. degree in mechanical engineering from Shanghai Jiao Tong University, Shanghai, China, in 2006. He is currently a Professor with the State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University. His current research interests include nonlinear dynamics and the reliability analysis and assessment for MEMS/NEMS applications.

Wenming Zhang

Wenming Zhang (M’10) received the B.S. degree in mechanical engineering and the M.S. degree in mechanical design and theories from Southern Yangtze University, Wuxi, China, in 2000 and 2003, respectively, and the Ph.D. degree in mechanical engineering from Shanghai Jiao Tong University, Shanghai, China, in 2006. He is currently a Professor with the State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University. His current research interests include nonlinear dynamics and the reliability analysis and assessment for MEMS/NEMS applications.

Guang Meng

Guang Meng received the Ph.D. degree from Northwestern Polytechnical University, Xi'an, China, in 1988. In 1993, he was a Professor and the Director of the Vibration Engineering Institute, Northwestern Polytechnical University. From 1989 to 1993, he was also a Research Assistant with Texas A&M University, College Station, an Alexander von Humboldt Fellow with Technical University Berlin, Berlin, Germany, and a Research Fellow with New South Wales University, Sydney, Australia. From 2000 to 2008, he was with Shanghai Jiao Tong University, Shanghai, China, as the Cheung Kong Chair Professor, the Associate Dean, and the Dean of the School of Mechanical Engineering. He is currently a Professor with the State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University. His research interests include dynamics and vibration control of mechanical systems, nonlinear vibration, and microelectromechanical systems.