基于骨架线和贝叶斯估计的二自由度非线性系统参数辨识

PARAMETER IDENTIFICATION OF A TWO-DEGREE-OF- FREEDOM NONLINEAR SYSTEM BASED ON BACKBONE CURVE AND BAYESIAN ESTIMATION

  • 摘要: 提出一种基于骨架线和贝叶斯估计的二自由度非线性系统参数辨识方法。该方法通过共振衰减法和希尔伯特变换提取骨架线作为观测数据,利用贝叶斯估计和马尔可夫蒙特卡罗抽样得到各物理参数的边缘概率分布。该方法避免了复杂的时域数值积分,从而提高了计算效率。为验证所提方法的有效性,将其应用于二自由度非线性振子系统的参数识别。结果表明,所提方法能够在噪声环境下识别二自由度非线性系统参数且具有较高精度。

     

    Abstract: This study proposes a parameter identification method for two-degree-of-freedom nonlinear vibration systems based on backbone curves and Bayesian estimation. The method first employs the resonance attenuation method and the Hilbert transform to extract the backbone curves, which are then used as observation data. By combining these data with their analytical expressions, the Bayesian estimation and the Markov Monte Carlo sampling method are employed to obtain the posterior joint distribution and the marginal probability distributions of the physical parameters. This approach avoids complex time-domain numerical integration, thereby improving computational efficiency. The effectiveness and accuracy of the proposed method is validated by applying it to the parameter identification of a two-degree-of-freedom nonlinear oscillator system. The results indicate that the proposed method can identify the parameters of a two-degree-of-freedom nonlinear system with high accuracy, even in a noisy environment.

     

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