基于骨架线和贝叶斯估计的单自由度非线性系统参数辨识

This paper proposcs a paramctcr idcntificaüon method for single-degree-of-freedom nonlinear Systems based on backbone and envelope curves. The method uses the System's backbone and envelope curves as observational data, combining them with their analytical expressions to obtain the posterior Joint distribution of physical Parameters through Bayesian estimation. Subscqucntly, the Markov Chain Monte Carlo method is employed to derive the marginal probability distributions of each physical Parameter. The proposed approach avoids the need for complex time-domain numerical integration, significant-ly improving computational efficiency. Furthermore, the effect of noise is considered, and the rcsults of the Hubert transform and the zero-crossing method for estimating the backbone and envelope curves arc compared. To validate the aecuraey of the proposed method, it is applied to identify the Duffing oscilla-tor with a discussion of the impact of noise at different levels. The results demonstrate that the proposed method is aecurate in identifying the physical parameters of singlc-dcgree-of-freedom nonlincar Systems under noisy environments.