IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v202y2026ip1s0960077925015036.html

Transient response analysis of nonlinear systems under combined nonstationary and stationary noise excitations: An improved complex fractional moment method

Author

Listed:
  • Li, Jing
  • Wang, Yongchun
  • Liu, Di

Abstract

This study presents a computational framework for modelling transient responses in nonlinear systems under combined nonstationary and stationary excitations, developing a solution strategy based on the improved complex fractional moment (CFM) method. The investigated single-degree-of-freedom nonlinear stochastic system incorporates nonstationary excitations exhibiting time-evolving statistical characteristics, where temporal variations in power spectral density (PSD) and frequency induce explicit time-dependence in system responses, leading to a nonautonomous Fokker-Planck-Kolmogorov (FPK) equation. The proposed methodology first transforms the original displacement-velocity response formulation into a reduced-order representation of the slow-varying amplitude process through equivalent linearization and stochastic averaging, establishing a nonautonomous amplitude FPK equation. Subsequently, an improved CFM method based on the fifth-order Gauss-Legendre quadrature is introduced to obtain the CFM of the system amplitude and reconstruct the transient probability density function (PDF) through the inverse Mellin transform. Finally, the displacement-velocity response domain of the original system is obtained using the Jacobian mapping, thereby achieving a complete characterization of the system's transient response characteristics. Numerical examples confirm the applicability of the method for various types of nonlinear systems with combined nonstationary and stationary excitations, revealing the coupled effects of structural parameters and excitation characteristics on the statistical behavior of the response. The results demonstrate the method's superior performance in computational accuracy, numerical robustness, and practical engineering applicability, while successfully capturing both the nonstationary characteristics and non-Gaussian statistical properties of the system response.

Suggested Citation

  • Li, Jing & Wang, Yongchun & Liu, Di, 2026. "Transient response analysis of nonlinear systems under combined nonstationary and stationary noise excitations: An improved complex fractional moment method," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925015036
    DOI: 10.1016/j.chaos.2025.117490
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925015036
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117490?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Alotta, G. & Di Paola, M., 2015. "Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 265-276.
    2. Yue Zhao & Jijian Lian & Chong Lian & Xiaofeng Dong & Haijun Wang & Chunxi Liu & Qi Jiang & Pengwen Wang, 2019. "Stochastic Dynamic Analysis of an Offshore Wind Turbine Structure by the Path Integration Method," Energies, MDPI, vol. 12(16), pages 1-18, August.
    3. Kuznetsov, Sergey V., 2025. "Forced harmonic vibrations of duffing oscillator with cubic-quintic spring nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    4. D. M. Nachane, 2018. "Time-varying spectral analysis: theory and applications," Indian Economic Review, Springer, vol. 53(1), pages 3-27, December.
    5. Dilip M. Nachane, 2018. "Time – Varying Spectral Analysis: Theory and Applications," Working Papers id:12956, eSocialSciences.
    6. Liu, Li & Xu, Wei & Yue, Xiaole & Qiao, Yan, 2020. "Reliability of elastic impact system with Coulomb friction excited by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    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. Padha, Vimarsh & Chaubal, Aditi, 2025. "Multiscale foreign exchange dynamics in India: A wavelet approach," International Economics, Elsevier, vol. 184(C).
    2. Ramezani, Mahyar & Choe, Do-Eun & Heydarpour, Khashayar & Koo, Bonjun, 2023. "Uncertainty models for the structural design of floating offshore wind turbines: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 185(C).
    3. Hyun-Gi Kim & Bum-Joon Kim, 2020. "Design Optimization of Conical Concrete Support Structure for Offshore Wind Turbine," Energies, MDPI, vol. 13(18), pages 1-21, September.
    4. Jia, Wantao & Guo, Qinyu & Lyu, Mengze & Zan, Wanrong, 2026. "Dynamic reliability analysis of systems under combined Gaussian and Poisson white noise by time-varying extreme value process," Reliability Engineering and System Safety, Elsevier, vol. 265(PB).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:chsofr:v:202:y:2026:i:p1:s0960077925015036. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.