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Technical Brief

Fuzzy Approximation by a Novel Levenberg–Marquardt Method for Two-Degree-of-Freedom Hypersonic Flutter Model

[+] Author and Article Information
Y. H. Wang

College of Automation Engineering,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China;
Key Laboratory of Optical-Electrics Control Technology,
Luoyang 471009, China
e-mail: wangyh@nuaa.edu.cn

L. Zhu

Shanghai Aircraft Airworthiness,
Certification Center of CAAC,
Shanghai 200335, China
e-mail: zhuliang_zl@163.com

Q. X. Wu, C. S. Jiang

College of Automation Engineering,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 9, 2013; final manuscript received April 23, 2014; published online May 19, 2014. Assoc. Editor: Bogdan I. Epureanu.

J. Vib. Acoust 136(4), 044502 (May 19, 2014) (6 pages) Paper No: VIB-13-1103; doi: 10.1115/1.4027524 History: Received April 09, 2013; Revised April 23, 2014

The two-degree-of-freedom (2DOF) hypersonic flutter dynamical system has strong aeroelastic nonlinearities, and it is very difficult to obtain a more precise mathematical model. By considering varying learning rate and σ-modification factor, a novel Levenberg– Marquardt (L–M) method is proposed, based on which, an online fuzzy approximation scheme for 2DOF hypersonic flutter model is established without any human knowledge. Compared with the standard L–M method, the proposed method can obtain faster converge speed and avoid parameter drift. Numerical simulations approve the advantages of the proposed scheme.

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Figures

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Fig. 1

The online approximation scheme

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Fig. 2

The response curve of λ

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Fig. 3

The flow chart of the training process

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Fig. 4

The simulate graph after one iterations. (a) Fuzzy approximation of f3(x), (b) approximation error of f3(x), (c) fuzzy approximation of f4(x), and (d) approximation error of f4(x).

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Fig. 5

The simulate graph after four iterations. (a) Fuzzy approximation of f3(x), (b) approximation error of f3(x), (c) fuzzy approximation of f4(x), and (d) approximation error of f4(x).

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Fig. 6

The simulate graph after eight iterations. (a) Fuzzy approximation of f3(x), (b) approximation error of f3(x), (c) fuzzy approximation of f4(x), and (d) approximation error of f4(x).

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