基于扩展卡尔曼滤波算法的大坝变形动态监控模型

A dynamic monitoring model for dam deformation based on the extended Kalman filter

  • 摘要: 大坝结构本质上是一个由多种因素驱动的动态系统,特别是在运行初期,大坝结构呈现出典型的时变特征。然而,传统的大坝变形统计模型采用固定的回归系数,难以适应其在长期运行过程中的动态特性。为此,本文引入扩展卡尔曼滤波(Extended Kalman Filter, EKF)算法,在滤波过程中将回归系数作为状态向量,将监控模型本身作为观测方程,同时融入噪声自适应机制,实现了模型的自适应更新,从而使其始终保持较高的预测精度。以运行初期的某混凝土坝为例,研究结果表明传统最小二乘方法的预测效果随着时间的推移会越来越差;在数据饱和的情况下,递推最小二乘算法的动态调整能力会越来越弱;遗忘递推最小二乘(Forgetting Factor Recursive Least Squares, FFRLS)算法具有良好的动态预测效果,但参数更新易受噪声影响;而EKF具有良好的动态预测和抗噪声干扰能力,相较于FFRLS算法,EKF算法的参数更新过程更加稳健,预测性能最优,对应的平均绝对误差、平均绝对百分比误差和均方根误差指标分别降低了49.9%~58.9%、41.5%~53.5%和30.8%~44.6%。研究成果可为大坝运行期变形动态预测和结构性态评估提供理论支撑。

     

    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.

     

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