An Improved Polynomial Chaos-Legendre Metamodel Method for Hybrid Uncertainty Analysis of Flexible Multibody Systems

Uncertainty quantification is of great significance to enhance the reliability and robustness of flexible multibody systems. The Polynomial chaos-Legendre metamodel (PCLM) method is commonly employed for hybrid uncertainty analysis of multibody systems; however, the fitting accuracy deteriorates over time when dealing with periodic time domain problems. To solve this problem, the Polynomial chaos-Legendre metamodel based on the local mean decomposition (PCLM-LMD), which combines the local mean decomposition technique (LMD) with the PCLM method, is proposed. Firstly, the LMD is utilized to decompose the multi-component responses of multibody systems into several mono-components and a trend component. Subsequently, the instantaneous amplitude (IA), instantaneous phase (IP), and the trend component are approximated using their respective surrogate models based on the PCLM method. The entire surrogate model of the system response can be established using the surrogate models of IA, IP, trend. Evaluation indices of the long-period dynamical response with hybrid uncertain parameters are obtained. Finally, the efficacy of the PCLM-LMD method is validated through two typical multibody dynamical models. Numerical results demonstrate that the PCLM-LMD method effectively solve the fitting accuracy issue at later time instants and present high-accuracy results in long-period dynamical response analysis compared to the PCLM method.