Comparison of polynomial chaos and Gaussian process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows
Comparison of polynomial chaos and Gaussian process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows
复制标题
空间分布明渠稳定流不确定性量化和相关性估计的多项式混沌与高斯过程代理的比较
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Rochoux
中科院分区：
文献类型：
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作者：
Pamphile T. Roy;N. El Moçayd;S. Ricci;J. Jouhaud;N. Goutal;Matthias De Lozzo;M. Rochoux
数据同化被广泛用于提高洪水预报能力，特别是通过参数推断，需要关于不确定输入参数（上游流量、摩擦系数）以及水位变化及其对输入的敏感性的统计信息。对于粒子滤波器或集合卡尔曼滤波器，随机估计概率密度函数和协方差矩阵从蒙特卡洛随机采样需要一个大的集合的模型评估，限制了它们在实时应用中的使用。为了解决这一问题，可以使用基于多项式混沌和高斯过程的快速代理模型来表示空间分布的水位，而不是求解浅水方程。本研究探讨使用这些替代估计概率密度函数和协方差矩阵，在降低计算成本，而不会损失的准确性，在整体数据同化的角度。本研究的重点是1-D稳态流模拟与MASCARET加龙河（法国西南部）。结果表明，这两个代理功能相似的性能，蒙特-卡罗随机抽样，但对于一个小得多的计算预算;几个MASCARET模拟（在10-100的顺序）是足以准确地检索协方差矩阵和概率密度函数的所有沿着河流，即使在流动动态更复杂，由于不均匀的测深。这为数据同化中适用于代表非定常明渠流的代理策略的设计铺平了道路。
Data assimilation is widely used to improve flood forecasting capability, especially through parameter inference requiring statistical information on the uncertain input parameters (upstream discharge, friction coefficient) as well as on the variability of the water level and its sensitivity with respect to the inputs. For particle filter or ensemble Kalman filter, stochastically estimating probability density function and covariance matrices from a Monte Carlo random sampling requires a large ensemble of model evaluations, limiting their use in real-time application. To tackle this issue, fast surrogate models based on polynomial chaos and Gaussian process can be used to represent the spatially distributed water level in place of solving the shallow water equations. This study investigates the use of these surrogates to estimate probability density functions and covariance matrices at a reduced computational cost and without the loss of accuracy, in the perspective of ensemble-based data assimilation. This study focuses on 1-D steady state flow simulated with MASCARET over the Garonne River (South-West France). Results show that both surrogates feature similar performance to the Monte-Carlo random sampling, but for a much smaller computational budget; a few MASCARET simulations (on the order of 10–100) are sufficient to accurately retrieve covariance matrices and probability density functions all along the river, even where the flow dynamic is more complex due to heterogeneous bathymetry. This paves the way for the design of surrogate strategies suitable for representing unsteady open-channel flows in data assimilation.
影响因子：
5.2
作者：
King, Matt A.;Watson, Christopher S.;Clarke, Peter J.
通讯作者：
Clarke, Peter J.