Uncertainty and correlation propagation analysis of powertrain mounting systems based on multi-ellipsoid convex model

Abstract

In engineering practice, uncertainty and correlation may coexist in both input parameters and output responses of the powertrain mounting system (PMS) of a vehicle. A methodology is developed for the uncertainty and correlation propagation analysis of the inherent characteristics of PMSs in this research. In the proposed methodology, the multi-ellipsoid convex model is introduced to quantify multiple groups of uncertain parameters with correlation, where dependent and independent uncertain parameters are considered simultaneously. In the uncertainty propagation analysis, it aims to calculate the interval bounds of system responses. To perform uncertainty propagation analysis, the Monte Carlo uncertainty analysis (MCUA) method is firstly presented based on Monte Carlo simulation, and the first-order perturbation-central difference-Lagrange multiplier (FPCDLM) method and the second-order perturbation-central difference-Lagrange multiplier (SPCDLM) method are then derived to promote the computational efficiency. In the correlation propagation analysis, it aims to compute the correlation between different system responses. To conduct the correlation propagation analysis, the Monte Carlo correlation analysis (MCCA) method is firstly proposed and the second-order perturbation correlation analysis (SPCA) method are then developed to enhance the computational efficiency. Next, the whole procedures for uncertainty and correlation propagation analysis of PMS are established by combining the above uncertainty analysis and correlation analysis methods, and the elliptical domain of any two system responses can be obtained. Finally, numerical examples of the PMS of an electric vehicle are provided to demonstrate the effectiveness of the proposed methodology.