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

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.