Abstract:
Dam structures are inherently dynamic systems affected by multiple time-varying factors. This behavior is particularly pronounced during the initial operation period or first impoundment, when concrete creep and shrinkage continue to develop, mechanical properties have not yet fully stabilized, and the dam foundation system undergoes structural adjustment and stress redistribution under high reservoir water levels. Consequently, dam deformation during this stage often exhibits marked time-varying and non-stationary characteristics. Conventional statistical monitoring models generally assume fixed regression coefficients and therefore have limited capability to represent such evolving structural behavior, which may lead to a gradual deterioration in prediction accuracy. To address this limitation, this study introduces the extended Kalman filter (EKF) into dam deformation monitoring and develops an adaptive dynamic monitoring model. In the proposed framework, the regression coefficients of the conventional statistical model are treated as time-varying state variables, while the monitoring model is formulated in a state-space form that explicitly considers both process noise and measurement noise. By recursively applying the prediction-update mechanism of the EKF, the model parameters and their uncertainties are updated online as new observations become available. A noise-adaptive mechanism is further incorporated to adjust the process-noise and measurement-noise covariances according to recent residuals and parameter variations, thereby improving adaptability to changing operating conditions and robustness against abnormal observations. The proposed model is applied to a concrete arch dam in Sichuan, China. Two representative deformation monitoring points, PL11-2 and PL11-4, are selected for verification. The training dataset covers the initial impoundment period from June 15, 2013, to February 28, 2015, and the test dataset extends from March 1, 2015, to October 1, 2015. For comparison, three methods are implemented: least squares (LS), recursive least squares (RLS), and forgetting factor recursive least squares (FFRLS) with a forgetting factor of 0.97. Model performance is evaluated using the coefficient of determination (
R2), mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results show that all four models achieve satisfactory fitting performance, with
R2 values greater than 0.99, MAE values below 0.5 mm, and RMSE values below 0.6 mm. However, clear differences emerge during prediction. The prediction accuracy of the LS model gradually decreases because its parameters remain fixed, while the dynamic adjustment capability of the RLS model weakens as the sample size increases and data saturation becomes more pronounced. The FFRLS model alleviates data saturation by assigning greater weight to recent observations and therefore maintains favorable dynamic prediction performance, but its parameter estimates are more sensitive to noise and may exhibit relatively large fluctuations. In contrast, the EKF model provides both favorable dynamic prediction performance and stronger noise robustness. For PL11-2 and PL11-4, the prediction-stage
R2 values reach 0.984 and 0.989, respectively, while the corresponding RMSE values are 0.751 mm and 0.542 mm. Compared with the FFRLS model, the EKF model increases
R2 by 0.018 and 0.025 at the two monitoring points and reduces MAE, MAPE, and RMSE by 49.9%—58.9%, 41.5%—53.5%, and 30.8%—44.6%, respectively. The parameter update process of the EKF is also more stable than that of the FFRLS model. Whereas FFRLS parameter estimates may fluctuate substantially because of their sensitivity to newly introduced observations, the EKF regulates parameter evolution through process-noise covariance, measurement-noise covariance, and the time-varying Kalman gain, enabling the estimated parameters to better reflect structural evolution while suppressing disturbances caused by abnormal data. The uncertainty estimates provided by the EKF further reflect the adaptation process of the monitoring model. When structural behavior is relatively stable and observations are consistent with model predictions, the parameter covariance gradually contracts and the estimated uncertainty decreases. When changes in external loads or structural behavior lead to increased prediction deviations, the Kalman gain increases, the model absorbs new information more rapidly, and the uncertainty may rise temporarily before converging again. Therefore, variations in parameter uncertainty can provide an intuitive indication of the model’s response to changing operating conditions and assist in identifying key turning points in structural behavior. The proposed EKF-based dynamic monitoring approach can provide methodological support for dam deformation prediction, structural behavior tracking, and safety assessment during operation.