IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v256y2025ics0951832024007749.html

Non-stationary semi-analytical solution of vibro-impact system with multiplicative and external random stimulations

Author

Listed:
  • Luo, Jie
  • Er, Guo-Kang
  • Iu, Vai Pan

Abstract

This article aims to investigate the non-stationary semi-analytical solution of the vibro-impact (VI) system with multiplicative and external random stimulations. Firstly, the original VI system is replaced by an equivalent nonlinear system without collisional barriers in the new phase space using the Zhuravlev transformation. Afterward, the Fokker–Planck (FP) equation for the equivalent nonlinear system is formulated and solved using the evolutionary EPC method. The transitional probability density functions (TPDFs) of responses of the equivalent nonlinear system are then achieved. Subsequently, by using the variable relationships between the original VI system and the transformed nonlinear system, the TPDFs of responses of the original VI system are achieved at various time instants. Finally, three VI systems with various nonlinearity driven by both multiplicative and external random stimulations are investigated and studied by the presented procedure. The results show that the responses of the VI systems are strongly non-Gaussian due to the influence of the barrier, the nonlinear terms and the correlated random stimulations. Moreover, the accuracy of the obtained results and computational efficiency of the presented procedure are assessed by comparison with the simulated results.

Suggested Citation

  • Luo, Jie & Er, Guo-Kang & Iu, Vai Pan, 2025. "Non-stationary semi-analytical solution of vibro-impact system with multiplicative and external random stimulations," Reliability Engineering and System Safety, Elsevier, vol. 256(C).
    • Handle: RePEc:eee:reensy:v:256:y:2025:i:c:s0951832024007749
    DOI: 10.1016/j.ress.2024.110703
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832024007749
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2024.110703?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. Hu, Zhen & Mahadevan, Sankaran, 2019. "Probability models for data-Driven global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 40-57.
    2. Xu, Zidong & Wang, Hao & Zhao, Kaiyong & Zhang, Han & Liu, Yun & Lin, Yuxuan, 2024. "Evolutionary probability density reconstruction of stochastic dynamic responses based on physics-aided deep learning," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    3. Bao, Yuequan & Sun, Huabin & Guan, Xiaoshu & Tian, Yuxuan, 2024. "An active learning method using deep adversarial autoencoder-based sufficient dimension reduction neural network for high-dimensional reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    4. Das, Sourav & Tesfamariam, Solomon, 2024. "Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    5. Li, Yang & Xu, Jun, 2024. "Neural network-aided simulation of non-Gaussian stochastic processes," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    6. Zhou, Taotao & Zhang, Xiaoge & Droguett, Enrique Lopez & Mosleh, Ali, 2023. "A generic physics-informed neural network-based framework for reliability assessment of multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    7. Saraygord Afshari, Sajad & Enayatollahi, Fatemeh & Xu, Xiangyang & Liang, Xihui, 2022. "Machine learning-based methods in structural reliability analysis: A review," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    8. Guan, Yu & Li, Wei & Kozak, Drazan & Zhao, Junfeng, 2024. "Response and reliability analysis of a nonlinear VEH systems with FOPID controller by improved stochastic averaging method and LBFNN algorithm," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Yu & Chen, Hanshu & Yang, Dixiong, 2025. "Simultaneous determination of stochastic dynamic responses and reliabilities for bilateral vibro-impact systems under colored noise excitation," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).

    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. Zhang, Yang & Lyu, Meng-Ze & Xu, Jun & Luo, Yi, 2026. "A sampling-variability-free dimension-reduced probability density evolution equation method for high-dimensional nonlinear stochastic dynamic analysis," Reliability Engineering and System Safety, Elsevier, vol. 266(PB).
    2. Bai, Guo-Peng & Er, Guo-Kang & Iu, Vai Pan, 2024. "A novel stochastic approach to investigate the probabilistic characteristics of the ship roll system with sinusoidal restoring force," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    3. van Essen, Sanne M. & Seyffert, Harleigh C., 2025. "Designing for dangerous waves – a new ‘Adaptive Screening’ method to predict extreme values of non-linear marine and coastal structure responses to waves," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).
    4. Zhang, Yu & Chen, Hanshu & Yang, Dixiong, 2025. "Simultaneous determination of stochastic dynamic responses and reliabilities for bilateral vibro-impact systems under colored noise excitation," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).
    5. Mei, Fabin & Chen, Hao & Yang, Wenying & Zhai, Guofu, 2024. "A hybrid physics-informed machine learning approach for time-dependent reliability assessment of electromagnetic relays," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    6. Wang, Ziqi & Song, Junho & Broccardo, Marco, 2024. "Probabilistic Performance-Pattern Decomposition (PPPD): Analysis framework and applications to stochastic mechanical systems," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    7. Ni, Fei & Fan, Lin & Zheng, Qinghua & Jia, Wantao, 2026. "Probabilistic density evolution of maglev train levitation systems using residual-augmented physics-informed neural networks," Reliability Engineering and System Safety, Elsevier, vol. 269(C).
    8. He, Yuxuan & Zio, Enrico & Yang, Zhaoming & Xiang, Qi & Fan, Lin & He, Qian & Peng, Shiliang & Zhang, Zongjie & Su, Huai & Zhang, Jinjun, 2025. "A systematic resilience assessment framework for multi-state systems based on physics-informed neural network," Reliability Engineering and System Safety, Elsevier, vol. 257(PB).
    9. Cai, Xiaopei & Wang, Yuqi & Tang, Xueyang & Wang, Yi & Wang, Tao, 2026. "PEDRA-VTB: A precision-efficient framework for dynamic reliability assessment of vehicle-track-bridge system under extreme disasters," Reliability Engineering and System Safety, Elsevier, vol. 267(PB).
    10. Wei, Pengfei & Zheng, Yu & Fu, Jiangfeng & Xu, Yuannan & Gao, Weikai, 2023. "An expected integrated error reduction function for accelerating Bayesian active learning of failure probability," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    11. Hao, Donghui & Zhang, Jian & Yue, Xinxin & Chen, Lei, 2025. "Combined dimensionality reduction based adaptive polynomial chaos expansion for high-dimensional reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 264(PA).
    12. Shang, Xiaobing & Wang, Lipeng & Fang, Hai & Lu, Lingyun & Zhang, Zhi, 2024. "Active Learning of Ensemble Polynomial Chaos Expansion Method for Global Sensitivity Analysis," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    13. Zhou, Gaoyang & Zhu, Zhihui & Zheng, Weiqi & Biondini, Fabio, 2026. "Seismic traffic risk assessment method for high-speed railway bridge networks based on multi-level running reliability," Reliability Engineering and System Safety, Elsevier, vol. 267(PB).
    14. Pan, Yongjun & Sun, Yu & Li, Zhixiong & Gardoni, Paolo, 2023. "Machine learning approaches to estimate suspension parameters for performance degradation assessment using accurate dynamic simulations," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    15. Chen, Jun-Yu & Feng, Yun-Wen & Teng, Da & Lu, Cheng & Fei, Cheng-Wei, 2022. "Support vector machine-based similarity selection method for structural transient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    16. Zhang, Tianyu & Zhang, Jize, 2025. "iCE-NGM: Improved cross-entropy importance sampling with non-parametric adaptive Gaussian mixtures and budget-informed stopping criterion," Reliability Engineering and System Safety, Elsevier, vol. 264(PA).
    17. Phan, Hieu Chi & Dhar, Ashutosh Sutra & Bui, Nang Duc, 2023. "Reliability assessment of pipelines crossing strike-slip faults considering modeling uncertainties using ANN models," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    18. Dhulipala, Somayajulu L.N. & Shields, Michael D. & Chakroborty, Promit & Jiang, Wen & Spencer, Benjamin W. & Hales, Jason D. & Labouré, Vincent M. & Prince, Zachary M. & Bolisetti, Chandrakanth & Che, 2022. "Reliability estimation of an advanced nuclear fuel using coupled active learning, multifidelity modeling, and subset simulation," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    19. Kim, Gyeongho & Choi, Jae Gyeong & Jeon, Sujin & Park, Soyeon & Lim, Sunghoon, 2026. "Towards efficient data-driven fault diagnosis under low-budget scenarios via hybrid deep active learning," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
    20. Luo, Changqi & Zhu, Shun-Peng & Keshtegar, Behrooz & Niu, Xiaopeng & Taylan, Osman, 2023. "An enhanced uniform simulation approach coupled with SVR for efficient structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 237(C).

    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:reensy:v:256:y:2025:i:c:s0951832024007749. 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/reliability-engineering-and-system-safety .

    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.