Aiming at the problem of false alarms caused by environmental interference in structural damage early warning, a structural damage early warning method based on Reduced-order Variational Mode Decomposition Integrated with Cointegration and Extended Kalman Filtering (RVMD-CEKF) is proposed. RVMD is adopted to decompose structural vibration response signals and extract the central frequency of each mode, and the modal parameter sequences of the structure are obtained as cointegration variables to construct a cointegration equation and calculate the cointegration residuals. EKF is used to perform real-time optimal estimation of the cointegration residuals, and the X-bar control chart is adopted to determine the early warning threshold, so as to realize real-time early warning. Different damage test cases are designed based on the indoor offshore platform model, and both the traditional cointegration-based early warning method and the proposed RVMD-CEKF method are used for damage early warning verification. The results show that the traditional cointegration early warning method has a false alarm at 1800 s; while after optimizing the cointegration residuals via RVMD-CEKF, the amplitude of abnormal fluctuations is significantly reduced, which effectively eliminates false alarms, and the proposed damage early warning index can more truly reflect the actual state of the structure. Furthermore, the proposed method is applied to a real in-service offshore platform, and the results verify that it can adaptively improve the accuracy of structural damage early warning, and is applicable to real-time structural damage early warning under complex environmental interference.