BinHuang

Innovation and Contributions

Under the supervision of Professor Bin Huang, master’s student Xiaolong Zhang made significant progress in the stochastic stability of nonlinear dynamical systems with random parameters. Part of this research was published in Volume 56, Issue 7 (2026) of SCIENTIA SINICA Physica, Mechanica & Astronomica. The paper extends the theory of stability of motion for general dynamical systems introduced by Lyapunov in 1892 from deterministic systems to systems with random parameters, establishing a theoretical foundation for analysing the stochastic stability of nonlinear systems with random parameters.

Building on the definition of stochastic stability, the paper develops a theory and methods for stability analysis in the Lyapunov sense. It formulates and proves a theorem giving sufficient conditions for stochastic asymptotic stability, establishes a theorem on stochastic boundedness, and formulates and proves a theorem on stochastic instability for dynamical systems with random parameters.

Innovation and Contributions

Under the supervision of Professor Bin Huang, master’s student Miancheng She applied the group’s stochastic perturbation–Galerkin method to random vibration response calculations for the first time. The study addresses the computation of random vibration responses of multi-degree-of-freedom structures whose random parameters follow different probability distributions. In particular, it uses an elementary algebraic approach to invert random matrices, providing a new approach to solving problems in mechanics involving random parameters.

Innovation and Contributions

Under the supervision of Professor Bin Huang, doctoral student Hui Chen proposed a new framework for stochastic model updating based on stochastic finite element methods. The framework comprises the formulation and solution of stochastic model updating equations. The paper solves these equations using the stochastic perturbation–Galerkin method developed by the group. Compared with Bayesian updating using Markov chain Monte Carlo sampling, the new method achieves high computational efficiency while maintaining updating accuracy.

Innovation and Contributions

Associate Professor Heng Zhang of Yangtze University, together with corresponding author Professor Bin Huang and their collaborators, advanced the determination of homotopy parameters in the homotopy stochastic finite element method from a sample-point approach to a stochastic residual approach. This work advances the development of the homotopy stochastic finite element method.