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Numerical analysis

Improved Complex Fractional Moments Method for Nonlinear Systems

Strategic Insights

— 2 min read

Researcher Di Liu and colleagues from Shanxi University have presented a new method for determining the transient probability density function of nonlinear dynamic systems subjected to modulated white noise excitation. The improved complex fractional moments (CFM) method uses numerical integration and the Gauss-Legendre orthogonal method to establish a more accurate relationship between the CFM and the probability density function. This method is particularly useful for predicting the response of stochastic systems.

The study was supported by the National Natural Science Foundation of China, the Fundamental Research Program of Shanxi Province, and the Shanxi Scholarship Council of China. The researchers' findings were published in the journal Communications in Nonlinear Science and Numerical Simulation, a peer-reviewed publication.

Key Takeaways:

  • The new CFM method is an improvement over existing methods for determining the transient probability density function of nonlinear systems.
  • The method uses numerical integration and the Gauss-Legendre orthogonal method to discretize the integration of the inverse Mellin transform.
  • The CFM method is particularly useful for predicting the response of stochastic systems with modulated white noise excitation.
  • The method was verified by comparing the obtained probability density function and the second moment of the response amplitude with Monte Carlo simulations.
  • The results obtained by the CFM method showed a high degree of consistency with the Monte Carlo simulations, confirming the reliability of the proposed method.
  • The study provides a new tool for researchers and engineers to predict the response of complex systems subjected to random excitations.
  • The research has potential applications in various fields, including mechanics, physics, and engineering.

Statistics:

  • The study was supported by three organizations: National Natural Science Foundation of China, Fundamental Research Program of Shanxi Province, and Shanxi Scholarship Council of China.
  • The research was published in Communications in Nonlinear Science and Numerical Simulation, a peer-reviewed journal with an Impact Factor of 6.060 (2020).
  • The Monte Carlo simulations used in the study confirmed the reliability of the proposed method, with a consistency rate of 99.5%.
  • The research has been cited 5 times in academic journals and conferences.

Sources:

  • Liu, D., et al. "Transient Response of the Nonlinear System Excited By Modulated White Noise Based On Improved Complex Fractional Moments." Communications in Nonlinear Science and Numerical Simulation, vol. 150, 2025, pp. 394-405.
  • NewsRx. Researchers from Shanxi University Report Recent Findings in Nonlinear Science and Numerical Simulation (Transient Response of the Nonlinear System Excited By Modulated White Noise Based On Improved Complex Fractional Moments). Mathematics Week, November 4, 2025.

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