一维不恒定流与卡尔曼滤波耦合的河道实时洪水预报模型

Real-time flood forecasting modeling coupling between 1D unsteady channel flow and Kalman filter

对一维不恒定流方程组进行简化,导出扩散波的一维不恒定流方程,用有限差分对其进行离散化。考虑实时洪水预报的特点,上边界拟采用入流已知,下边界对于自然河段拟采用水位流量关系,对有闸、坝控制的拟采用相应的出流计算公式。对离散化的方程和边界条件进行线性化,得到系统方程。由于实际河道中实测变量的个数总少于待求变量的个数,为此,根据滤波方面的理论提出了一维不恒定流与卡尔曼滤波耦合的半自适应滤波模型。在该模型中量测误差系列的协方差矩阵可以通过信息更新系列实时地估计出来,只有模型误差系列的协方差矩阵需要预先给出。最后用实例对模型进行了检验并与其他方法进行了比较。

This paper attempted to couple the 1D unsteady channel flow model with Kalman filter for realtime channel flood forecasting. Taking into account the realtime forecasting, the suitable upstream boundary condition is the Q(t) and the downstream boundary condition is the Z(Q rating curve). The system equation is formed by the linearization of the finitedifference equations of the mass conservation and momentum equations as well as the boundary conditions. In Kalman filter updating model, because the number of measurement variables are less than that of statespace variables, the measurement error covariance matrix can be estimated in realtime through the innovation sequence, and the system error covariance matrix needs to be estimated preliminarily. An example of the Huaihe River is given to explain how the method works. The results show that the model is reasonable and effective. 