Correlation propagation for dynamic analysis of a multibody system with multiple interval parameters

Abstract

Interval uncertainty analysis plays a fundamental role in performance evaluation, reliability design, and parameter optimization of a multibody system. In this work, the method for correlation propagation of a multibody system considering multiple interval parameters is investigated. To this end, a method of bivariate Chebyshev-polynomials difference combining with the Lagrangian-multiplier method (BCDLM) is proposed. First, the multiple-ellipsoid model is employed to quantify simultaneously the correlated and independent interval parameters examined in this work. The bivariate Chebyshev difference method is developed to calculate the partial derivatives of the relevant responses with respect to the uncertain parameters subsequently. To obtain the response bounds the Lagrangian-multiplier method is incorporated with the Taylor-series expansion. Additionally, the uncertain domain of the uncertain output responses is constructed by the developed BCDLM. Several examples are illustrated to verify the effectiveness of the proposed method to propagate correlations for the multibody system considering independent and correlated interval parameters. Results show that the BCDLM is more suitable for correlation propagation of a high-dimensional interval problem with relatively small uncertainty levels.