IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v373y2020ics0096300320300059.html
   My bibliography  Save this article

An improved path integration method for nonlinear systems under Poisson white noise excitation

Author

Listed:
  • Ren, Zhicong
  • Xu, Wei

Abstract

In order to overcome some unsatisfactory trends and limitations of the traditional path integration (PI) method for Poisson white noise, a novel PI method is proposed in this paper, which includes two improved schemes. The first one is a new Transition Probability Density Function (TPDF) approximation which considers the randomness of the impulse happening time during each time intervals. The second one is a transformation of Chapman–Kolmogorov (CK) equation by a variable substitution instead of directly using it, whose numerical calculation is based on the back stepping Runge–Kutta scheme and the triangulation-based interpolation. Monte Carlo Simulations (MCS) are utilized to measure the accuracy of the improved algorithm with three illustrative nonlinear systems. The results show that compared with the traditional PI method, the improved PI method can give a more accurate description of the TPDF values, and provide more precise stationary Probability Density Function (PDF) results whenever the mean arrival rate is large or small. The improved algorithm has a wider range of choices in time interval values to maintain the accuracy of stationary PDF results. Besides, it is discovered that cubic interpolation deserves to be applied in the improved PI method more than linear and natural interpolations.

Suggested Citation

  • Ren, Zhicong & Xu, Wei, 2020. "An improved path integration method for nonlinear systems under Poisson white noise excitation," Applied Mathematics and Computation, Elsevier, vol. 373(C).
  • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300320300059
    DOI: 10.1016/j.amc.2020.125036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320300059
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2020.125036?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ren, Zhicong & Xu, Wei & Qiao, Yan, 2019. "Local averaged path integration method approach for nonlinear dynamic systems," Applied Mathematics and Computation, Elsevier, vol. 344, pages 68-77.
    2. Yue, Xiaole & Xu, Wei & Jia, Wantao & Wang, Liang, 2013. "Stochastic response of a ϕ6 oscillator subjected to combined harmonic and Poisson white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 2988-2998.
    3. Qiao, Yan & Xu, Wei & Jia, Wantao & Han, Qun, 2017. "Stochastic stationary response of a variable-mass system with mass disturbance described by Poisson white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 122-134.
    4. Jia, Wantao & Zhu, Weiqiu, 2014. "Stochastic averaging of quasi-partially integrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 125-144.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han, Ping & Xu, Wei & Wang, Liang & Ma, Shichao, 2020. "The most probable response of some prototypical stochastic nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Han, Qun & Xu, Wei & Sun, Jian-Qiao, 2016. "Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 115-125.
    3. Ma, Shichao & Wang, Liang & Ning, Xin & Yue, Xiaole & Xu, Wei, 2019. "Probabilistic responses of three-dimensional stochastic vibro-impact systems," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 308-314.
    4. Han, Qun & Xu, Wei & Hu, Bing & Huang, Dongmei & Sun, Jian-Qiao, 2018. "Extinction time of a stochastic predator–prey model by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 351-366.
    5. Li, Chao, 2019. "Stochastic response of a vibro-impact system with variable mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 151-160.
    6. Yue, Xiaole & Xu, Yong & Xu, Wei & Sun, Jian-Qiao, 2019. "Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 509-519.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300320300059. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.