https://doi.org/10.1140/epjs/s11734-024-01438-2
Regular Article
Deep learning-based stochastic averaging method for quasi-Hamiltonian system
Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, 310027, Hangzhou, China
Received:
31
July
2024
Accepted:
5
December
2024
Published online:
7
January
2025
The stochastic averaging method has great advantages in predicting the stationary response of MDOF (multi-degree-of-freedom) strongly nonlinear systems under random excitation. However, the challenge of applying this method is that the drift and diffusion coefficients of the averaged SDEs (stochastic differential equations) usually cannot be analytically obtained, making the analytical prediction for system response extremely difficult. This paper proposes a new strategy that combines the BPNN (back propagation neural network) with the stochastic averaging method for quasi-Hamiltonian system to predict system response. Firstly, the MDOF nonlinear system is transformed into a quasi-Hamiltonian system. Then, the stochastic averaging method is applied to obtain the averaged SDEs, where the drift and diffusion coefficients are obtained by BPNN. Finally, the system response is obtained by solving the FPK (Fokker Planck Kolmogorov) equations corresponding to the averaged SDEs. Two examples are carried out to demonstrate the effectiveness of this strategy.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
