Damages such as cracks often have time-domain nonlinear characteristics of variable stiffness during vibration， and the data before damage is difficult to obtain. In response to the above problems， the acceleration time series of each position of the inspection structure are collected. The generalized autoregressive conditional heteroskedasticity in the mean （GARCH-M） model of the lay response data is established for the inspect and base layers. Furthermore， the Chebyshev distance between the two model coefficients is analyzed， and a combined index of normalized damage recognition based on GARCH-M model and Chebyshev distance is proposed. The simulation and experimental results show that based on the above combined indicators， only the acceleration response data after damage can be used for damage identification， that is， the location of the nonlinear damage layer can be effectively identified. Compared with the GARCH model， the GARCH-M model is nonlinear to the structure， and the damage acceleration response time series has better adaptability. Moreover， the calculation process of the above model is simple and accurate， and it has good engineering application value in the field of nonlinear damage identification of engineering structures such as transmission towers.