Anchor-Constrained Residual Stacking for Missing Data Reconstruction in Structural Health Monitoring

During long-term monitoring, data missing often happens due to environmental interference, sensor malfunction or transmission problems, which will threaten the effectiveness of structural health monitoring. This study proposes an anchor-constrained residual stacking method, which can improve data reconstruction performance relative to individual models across diverse missing patterns while reducing the risk of performance degradation associated with unconstrained ensemble learning. The method adopts a two-level stacking framework in which heterogeneous base learners generate candidate reconstructed data and grouped out-of-fold predictions are used to select an anchor learner for different missing patterns. A residual meta-learner then learns complementary residual information relative to the anchor learner, while validation-gated fusion regulates residual correction and final fusion based on reserved validation data, reducing unreliable fusion contributions. The effectiveness of the proposed method is verified using monitoring data with different missing patterns from a steel stringer bridge under multiple structural states. It achieves a coefficient of determination (R2) of 0.9020, together with the lowest relative root mean square error (RRMSE) and mean absolute error (MAE) among the compared methods. Operational modal analysis further confirms that the method preserves the main dynamic characteristics of structural responses, supporting reliable reconstruction across diverse missing patterns and multiple structural states.