Novel algorithm for flexible multibody systems with hybrid uncertainties

In this paper, a sparse polynomial chaos-Legendre metamodel based on compressed sensing is proposed to quantify the hybrid uncertainties in flexible multibody systems. Based on the fully parameterized beam elements of absolute nodal coordinate formulation, the differential-algebraic equations of the multibody system with hybrid uncertain parameters are established firstly. Secondly, the dynamical response of the multibody system can be expanded by using the polynomial chaos-Legendre metamodel, and the matrix form of dynamical response can be transformed into vector form by Kronecker product. Then, the coefficients of the polynomial are sparsely reconstructed by using the subspace pursuit algorithm. Finally, the effectiveness of sparse polynomial chaos-Legendre metamodel based on compressed sensing is verified through numerical examples. Especially, compared with the traditional methods, the sampling size of the proposed method is less than the number of degrees of freedom of unknown coefficients in the polynomial surrogate model. Therefore, the proposed sparse polynomial chaos-Legendre metamodel based on compressed sensing can effectively alleviate the “curse of dimensionality”.