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. First, the method extracts the backbone curves from the system response using the resonance attenuation method and the Hilbert transform, which are then treated as observational data. By combining these data with their analytical expressions, the Bayesian estimation integrated with Markov Chain Monte Carlo sampling is employed to obtain the posterior joint distribution and the marginal probability distributions of the physical parameters. This approach circumvents complex time-domain numerical integration, thereby improving computational efficiency. The effectiveness and accuracy of the proposed method are validated through its application 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.