Hybrid uncertainty propagation for mechanical dynamics problems via polynomial chaos expansion and Legendre interval inclusion function

• Published in: Mechanical systems and signal processing Vol. 223; p. 111826
• Main Authors: Wang, Liqun, Guo, Chengyuan, Xu, Fengjie, Xiao, Hui
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.01.2025
• Subjects: Hybrid stochastic and interval uncertainty; Legendre inclusion function; Mechanical dynamics; Polynomial chaos expansion; Uncertainty propagation; Uncertainty propagation; Mechanical dynamics; Hybrid stochastic and interval uncertainty; Polynomial chaos expansion; Legendre inclusion function
• ISSN: 0888-3270
• DOI: 10.1016/j.ymssp.2024.111826

•A hybrid uncertainty propagation method for mechanical dynamics is accomplished.•Legendre polynomial inclusion technique is applied to interval uncertainty analysis.•This method improves the computational efficiency while satisfying the precision.•The non-intrusive method is generally applicable for various mechanical dynamics.•The effectiveness of the presented method is verified by three numerical examples. This paper investigates a non-intrusive hybrid uncertainty propagation framework in mechanical dynamic systems, utilizing polynomial chaos expansion (PCE) and Legendre inclusion function. Uncertainties with substantial knowledge and information are conceptualized as stochastic parameters and described using PCE, while Legendre polynomials are employed to represent uncertain, bounded parameters, specifically interval uncertainties. During the computation, the PCE model for each time step is developed through Galerkin projection and sparse grid numerical integration. Consequently, the statistical moments of the dynamic responses relative to the stochastic parameters are derived from the orthogonality of the PCE and transformed into functions reflecting the interval parameters. The interval bounds for these statistical moments are further determined using the Legendre inclusion function, which is obtained through optimal Latin hypercube sampling and collocation methods. Three dynamics examples, respectively, modeled by differential–algebraic equations, finite element method, and commercial software proves its applicability and superiority. Detailed assessment demonstrates that this method offers high computational efficiency and accuracy. As a non-intrusive approach, it poses no particular limitations on numerical methods for solving differential equations, making it universally applicable.