<p>Vortex-induced vibration (VIV) of bluff body sections presents significant challenges in wind engineering, particularly for double-layer sections where aerodynamic interference complicates the motion characteristics. A framework based on unscented Kalman filter (UKF) is developed to systematically identify nonlinear aerodynamic damping utilizing free vibration response histories, which enables comprehensive characterization of damping evolution throughout the whole VIV process. The amplitude-dependent aerodynamic damping is mathematically formulated as a fourth-order polynomial function within an augmented state-space model, enabling simultaneous estimation of motion states, nonlinear damping parameters, and stochastic excitation. Methodological validation demonstrates robust predictive capability through accurate reconstruction of steady-state vertical amplitudes under varying mechanical damping conditions, accompanied by parametric sensitivity analysis of key identification variables. The variation of aerodynamic damping and the contribution of nonlinear damping terms are investigated for different aerodynamic shape configurations. The results reveal identical evolution patterns: Linear damping components maintain substantial influence across all VIV ranges, while the contributions of high-order nonlinear terms peak at the extreme amplitude point, with the cubic term being particularly critical. A progressive intensification of corresponding negative aerodynamic damping at low amplitude with increasing wind speed indicates heightened VIV susceptibility. Notably, double-layer systems demonstrate accelerated convergence rate accompanied by enhanced positive aerodynamic damping at large amplitudes and elevated negative damping predictions at low amplitudes when compared to single-layer rectangular configuration.</p>