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Optimization of water exchange based on RBF surrogate model and particle swarm optimization
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摘要: 良好的水交换对改善水环境、提高水域周边景观效果等具有十分重要的作用。而引水置换的方法对促进水交换效果显著，但利用数值模拟进行水交换研究耗时长、效率低，且人为改变参数的局限性大，不利于寻找最优的换水方案。为解决这一问题，基于径向基函数(简称RBF)代理模型建立水交换优化模型，并通过粒子群算法求最优解。以某人工岛游艇别墅区港池初拟方案为例，验证该方法的可行性和优越性。算例结果表明：（1）构建的基于RBF代理模型的水交换优化模型精度较高；（2）基于RBF代理模型的水交换优化模型计算1次所需时间量级为秒，而传统数值模拟计算的量级为小时；（3）通过粒子群算法，对建立的基于RBF代理模型的水交换优化模型求解，得到研究区域的最优换水方案。上述最优方案的结果与MIKE21水动力和对流扩散模型的计算结果相符。Abstract: Good water exchange is very essential, not only for improving the water environment, but also for enhancing the landscape effect around the water. The diversion replacement method is significant for promoting water exchange. However, the numerical simulation method used to carry out water exchange research operates at a high time cost with low calculation efficiency. Moreover, artificially changing parameters have numerous limitations and are not conducive for finding the optimal water exchange scheme. To solve this problem, we established the optimization model of water exchange based on the radial basis function (RBF) surrogate model and used the particle swarm optimization to find the optimal solution for the surrogate model. To verify the feasibility and superiority of the method, we established an RBF surrogate model based on the initial plan of the harbor pool of an artificial island yacht villa and solved it. This example showed that: (1) The water exchange optimization model based on the RBF surrogate model had high precision. (2) The order of time required by the water exchange optimization model based on the RBF surrogate model was in seconds, while the order of time required by the traditional numerical simulation was in hours. (3) The particle swarm optimization, used to solve the established water exchange optimization model based on the RBF surrogate model, obtained the optimal water exchange scheme for the study area. The results were compared with the optimal scheme results
obtained through the surrogate model where the difference between the two is negligible. -
图 5 测试集平均水位与预测结果相关性分析
Figure 5. Correlation analysis between average water level in test set and prediction results
图 7 初始方案引水结束46 h污染物浓度
Figure 7. Concentration of pollutants after the initial water diversion scheme for 46 h
图 8 最优方案引水结束46 h污染物浓度
Figure 8. Concentration of pollutants after the optimal water diversion scheme for 46 h
表 1 潮位资料
Table 1. Tidal level data
时刻 11:00 11:20 11:30 12:00 12:30 13:00 13:30 14:00 14:30 14:48 15:00 潮位/m −1.50 −1.00 −0.45 0.00 0.50 1.00 1.43 1.89 2.30 2.50 2.63 
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表 2 人工岛内河道各测点最大流速统计
Table 2. Maximum flow rate statistics of various measuring points in rivers in artificial islands
单位：m/s 测点 实测速度 模拟速度 测点 实测速度 模拟速度 d1 0.74 0.70 d4 0.39 0.35 d2 0.38 0.35 d5 0.90 0.86 d3 0.46 0.41 d6 0.99 1.00
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表 3 引水方案样本及数值模拟结果
Table 3. Water diversion scheme and numerical simulation results
样本 开闸时刻 引水时长/min 引水结束最高水位/m 引水结束最低水位/m 平均水位/m 46 h污染物平均浓度/% 1 13:00 20 1.285 1.251 1.279 98.476 2 13:00 40 1.589 1.558 1.573 93.695 3 13:00 60 1.890 1.839 1.884 88.827 4 13:00 80 2.179 2.153 2.171 84.787 $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 43 14:30 30 6.575 5.107 5.919 52.568 44 14:40 20 7.323 5.632 6.649 49.389 45 14:50 10 4.093 3.263 3.906 66.399 46 14:55 5 2.508 1.700 2.258 83.524
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