Data-driven model order reduction with proper symplectic decomposition for flexible multibody system

Flexible multibody system plays an important role for the simulation of mechanism system. Due to the requirement of precision or high complexity of the model, the number of the finite elements of flexible multibody system will increase rapidly, which will lead to the decrease in the computational efficiency. In order to save the computational cost for simulating flexible multibody system, a novel model order reduction strategy based on the idea of data-driven model is proposed. In addition, the proposed method which is called symplectic model order reduction is in light of proper symplectic decomposition and symplectic Galerkin projection. At first, the snapshot matrix is obtained by an empirical data ensemble of the full-order model, and the transfer symplectic matrix of high dimension to low dimension is obtained by reduced-order bases using the method of cotangent lift. Then, the discrete governing equations of reduced-order model (ROM) are derived by symplectic discretization. Furthermore, a systematic study of model order reduction in system level and component level is provided in the paper. In addition, for adaption of ROM to parameter variation, a parameter interpolation method is offered to obtain the ROM. Eventually, several examples are used to verify the effectiveness of the proposed method, and the results show that the proposed method has better numerical accuracy and higher computational efficiency with respect to classic proper orthogonal decomposition-based ROM.

Automated summary

This paper introduces a novel model order reduction strategy for simulating flexible multibody systems based on the idea of data-driven models, known as the symplectic model order reduction. By obtaining snapshot matrices and converting them to symplectic matrices using cotangent lift, as well as conducting a systematic study on model order reduction at both system and component levels, the proposed method is validated to have better numerical accuracy and computational efficiency compared to classic POD-based models.