基于粒子滤波的一维非恒定流模拟多变量校正方法

为减少数值模型的不确定性,将粒子滤波方法引入一维非恒定流水量计算,建立了一维水量模拟的多变量校正方法。该方法通过对水流状态粒子进行统计估值,实现模型状态变量的最优估计。以单一河道洪水演进过程为例,探讨了多变量校正方法在一维非恒定流计算中的性能,分析了粒子数量、状态变量扰动误差和边界条件的不确定性对滤波效果的影响,从准确性、稳定性和高效性三方面对粒子滤波和集合卡尔曼滤波的性能进行了比较。结果表明:粒子数量为100时可兼顾滤波效果和模拟效率;水位、流量扰动误差标准差均取实际值的10%,边界条件相对误差在20%以内时,模拟精度可达94%以上;粒子滤波虽然在准确性和稳定性上较集合卡尔曼滤波稍弱,但是计算效率约是集合卡尔曼滤波的2.3倍。太湖流域河网水量校正证实,粒子滤波可显著改善模拟精度。

Multivariable correction method for one-dimensional unsteady flow simulation based on particle filter

In order to reduce the uncertainty of the numerical model, the particle filter method is introduced into the calculation of one-dimensional unsteady flow to establish a multivariable correction method for water quantity simulation. The optimal estimation of the state variables is realized by statistically estimating the water state particles. Taking the flood process of a single channel as an example, the performance of the proposed method was discussed and the influence of particle number, state variable disturbance and uncertainty of the boundary condition on the filtering effect was analyzed. The performance of particle filter and ensemble Kalman filter was compared in terms of accuracy, stability and efficiency. The results show that 100 particles can guarantee both the filtering effect and computational efficiency. The best filtering effect can be obtained when the water level disturbance variance and the flow disturbance variance are both 10 percent of the actual value. When the relative error of the boundary condition is within 20%, the simulated precision can be over 94%. The particle filter is slightly less accurate and stable than the ensemble Kalman filter, but its computational efficiency is about 2. 3 times higher than that of the Kalman filter. Application to the river network water quantity correction in the Taihu Basin shows that particle filter can significantly improve the simulation accuracy.