Abstract: Early-stage damage of practical engineering structures often exhibits nonlinear characteristics, such as breathing crack damage and bolt looseness damage. One of the most commonly used methods for structural damage identification is comparing the response information between the undamaged (baseline) state and the test state to determine the location of structural damage. It is often difficult to accurately obtain the structural baseline state response information in practical engineering. To address this issue, this paper proposes a baseline-free nonlinear damage localization method by integrating the AR-GARCH (autoregressive-generalized autoregressive conditional heteroskedasticity) model with bispectral theory, which features theoretical simplicity and strong interpretability. This paper describes the fundamental theories of the AR-GARCH model and bispectral analysis. The bispectral analysis is performed on the conditional variance series derived from the AR-GARCH model, and a damage indicator based on the flatness of the bispectral image is constructed to localize nonlinear structural damage. The proposed method is experimentally validated through nonlinear damage experiments conducted on both a three-story frame model and a relay tower model. The results demonstrate that the proposed structural nonlinear damage identification method performs effectively in identifying nonlinear damage in both the frame and the relay tower structure. The damage indicators calculated by the proposed method for damaged floor are significantly greater than those of undamaged floors. It can accurately identify nonlinear damage caused by breathing cracks and bolt looseness, and efficiently determine the locations of structural nonlinear damage sources.