| 应用最优控制理论自动率定二维浅水方程的糙率参数 |
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| 引用本文： | 赖锡军,姜加虎,黄群.应用最优控制理论自动率定二维浅水方程的糙率参数[J].水科学进展,2008,19(3):383-388. |
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| 作者姓名： | 赖锡军 姜加虎 黄群 |
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| 作者单位： | 中国科学院南京地理与湖泊研究所湖泊与环境国家重点实验室, 江苏, 南京, 210008 |
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| 基金项目： | 国家自然科学基金
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江苏省高校自然科学基金 |
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| 摘 要： | 应用偏微分方程最优化控制理论,导出了二维浅水方程糙率自动率定的最优化系统,实现了二维水力学模型计算中分布式糙率参数的自动率定算法。结合实际应用的可操作性,按区块设定糙率,对恒定流和非恒定流两种流态分别进行了常数糙率和随水深变化的糙率自动率定实验。数值实验表明,在观测数据包含足够的信息时,该方法不仅能够准确地自动率定出相关的糙率参数,还能成功地将糙率随水深的变化关系式识别出来。但是,糙率水深变化关系识别迭代收敛速度显著变慢,因此,建议采用相应的实现对策来考虑变糙率的洪水预测问题。
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| 关 键 词： | 糙率 自动率定 参数识别 最优化控制 浅水方程 |
| 收稿时间： | 2007-06-15 |
Calibration of Manning roughness coefficients in two-dimensional shallow water flows using optimal control theory |
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| LAI Xi-jun,JIANG Jia-hu,HUANG Qun.Calibration of Manning roughness coefficients in two-dimensional shallow water flows using optimal control theory[J].Advances in Water Science,2008,19(3):383-388. |
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| Authors: | LAI Xi-jun JIANG Jia-hu HUANG Qun |
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| Affiliation: | State Key Laboratory of Lake Science and Environment, Nanjing Institute of Geography & Limnology, Chinese Academy of Sciences, Nanjing 210008, China |
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| Abstract: | The optimal Manning roughness coefficients(n)control system of two-dimensional shallow water equations are first derived by using the optimal control theory for the partial differential equations. Then,the algorithm for automatically calibrating distributed n is implemented based on the framework of the unstructured finite volume methods. Considering the operational application,the n is not defined in each cell,but in each land cover block. Two conditions are investigated in our calibration experiments. One is the time-independent n identification for steady flows,and the other is the time-dependent n, which has fixed reference value and varies with water depth as given empiric relationship for unsteady flows. In both groups experiments,it is found that the n can be successfully calibrated using enough observations. Also,the functional relationship between referencen and water depth can be identified. But,the iteration number for the identification of the functional relationship increases largely because of larger freedom of control variables. Finally,the strategy for calibration are suggested in the modeling flood event,in which varied n is required to be considered. |
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