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Approximation closure method for Birkhoffian system under random excitations

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Abstract

A approximate method is proposed for Birkhoffian system subjected to Gaussian white noise excitation. The Itô equations of the system is proposed, and the corresponding Fokker–Planck–Kolmogorov (FPK) equation is derived. The probability density function (PDF) of the FPK is approximated with the exponential function of polynomial. The approximate probability density function is substituted into the FPK equation and the coefficients of polynomial are factored out. An illustrative example is given to illustrate the application of the proposed method, Monte Carlo simulation results show that the approximate method can provide a satisfactory PDF solution.

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Acknowledgements

This work was supported by the National Natural Science of China (Nos. 11302088 and 11502071).

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Authors and Affiliations

  1. School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Wen-An Jiang

  2. College of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Zhao-Wang Xia

  3. Department of Physics, Henan Institute of Education, Zhengzhou, 450046, China

    Li-Li Xia

Authors
  1. Wen-An Jiang
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  2. Zhao-Wang Xia
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  3. Li-Li Xia
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Correspondence to Wen-An Jiang.

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Jiang, WA., Xia, ZW. & Xia, LL. Approximation closure method for Birkhoffian system under random excitations. Int. J. Dynam. Control 6, 398–405 (2018). https://doi.org/10.1007/s40435-016-0282-6

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  • DOI: https://doi.org/10.1007/s40435-016-0282-6

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