State-Integration Neural Network for Modeling of Forced-Vibration Systems

Hong Wei Li, Yi Qing Ni, You Wu Wang, Zheng Wei Chen, En Ze Rui, Zhao Dong Xu

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review


Dynamic analysis of forced-vibration systems could be computationally inefficient or even difficult to converge if the systems are highly complicated. Rapid advances in machine learning make it possible to establish surrogate models for forced-vibration systems using neural networks. However, the existing data-driven neural network models usually require the data sampling frequency and time duration to be fixed, and they typically contain large amounts of learnable hyper-parameters which tend to cause overfitting issues. To overcome these limitations, we develop the state-integration neural network (SINN) modeling approach by combining the ideas of the state-space method and neural ordinary differential equations. The SINN model has two sets of independent neural networks aimed to compute the state derivative and system response, respectively. Integration on the state derivative at the current time step is executed to obtain the state at the next time step using the explicit 4th-order Runge Kutta method. The SINN model has strong adaptability because it is not restricted to the pre-designated sampling frequency and input data length. A numerical illustrative example is conducted in this paper.

Original languageEnglish
Title of host publicationComputational and Experimental Simulations in Engineering - Proceedings of ICCES 2023—Volume 3
EditorsShaofan Li
PublisherSpringer Science and Business Media B.V.
Number of pages7
ISBN (Print)9783031449468
Publication statusPublished - 2024
Event29th International Conference on Computational and Experimental Engineering and Sciences, ICCES 2023 - Shenzhen, China
Duration: 26 May 202329 May 2023

Publication series

NameMechanisms and Machine Science
ISSN (Print)2211-0984
ISSN (Electronic)2211-0992


Conference29th International Conference on Computational and Experimental Engineering and Sciences, ICCES 2023


  • Forced-vibration system
  • Machine learning
  • Neural network
  • Neural ordinary differential equation
  • Runge–Kutta method
  • State space

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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