PBDW: a non-intrusive Reduced Basis Data Assimilation Method and its application to outdoor Air Quality Models
PBDW: a non-intrusive Reduced Basis Data Assimilation Method and its application to outdoor Air Quality Models
复制标题
DOI：
--
复制
发表时间：
2017-06
期刊：
影响因子：
--
通讯作者：
J. K. Hammond;R. Chakir;F. Bourquin;Y. Maday
中科院分区：
文献类型：
--
作者：
J. K. Hammond;R. Chakir;F. Bourquin;Y. Maday
随着全球大规模城市化导致的污染物排放和暴露增加，空气质量测量活动和关于空气污染和健康影响的流行病学研究越来越普遍，以估计个人暴露并评估其与各种疾病的关系。由于空气污染浓度是高度异质性的，复杂的基于物理的空气质量模型（AQM），特别是基于计算流体动力学的模型，可以提供空间丰富的近似值，并能够更好地估计个人暴露。在这项工作中，我们研究了缩减基（RB）方法[1]，以减少为城市尺度的浓度评估而开发的先进AQM的分辨率成本。这些模型依赖于各种参数，包括气象条件和污染物排放，这些参数在微观尺度上往往是未知的。RB方法使用由参数化偏微分方程（PDE）支配的AQM的解的合适样本构成的近似空间，以快速构造精确且计算高效的近似。这种技术的关键是将计算工作分解为离线和在线阶段。用于构建近似空间的RB函数和所有昂贵的参数无关项都是“离线”计算并存储的，而便宜的参数相关量则是针对每个新的参数值“在线”计算的。然而，将矩阵分解成离线-在线片段需要修改计算代码，这是一个侵入性过程，在某些情况下是不切实际的。在这项工作中，我们将[2]中介绍的参数化背景数据弱（PBDW）方法扩展到基于物理的AQM。我们将从具有不同气象条件和污染排放的物理AQM生成解决方案的样本，以构建RB近似空间，并使用[3]中的方法将其与实验观察结合联合收割机，以改善污染物浓度估计，目标是与加州大学伯克利分校的流行病学暴露评估团队合作。目标是以非侵入性和计算效率高的方式使用现有的AQM，在微观尺度上快速估计感兴趣区域周围的“在线”污染物浓度。[1] Prud'homme，C.，Rovas，D.五、Veroy，K.，马谢尔湖Maday，Y.，Patera，A. T.，& Turinici，G.（2002年）的报告。“参数化偏微分方程的可靠实时解：减少基础输出界方法”。Journal of Fluids Engineering，124（1），70-80 [2] Y. Maday，A.T Patera，J.D. Penn和M. Yano，“变分数据同化的参数化背景数据弱方法：公式化，分析和应用于声学”，Int. J. Numer。Meth. Engng（2014年）。[3]伊冯·马代和奥尔加·穆拉。广义经验内插法：缩减基技术在资料同化中的应用。偏微分方程的分析和数值，第221-235页。施普林格，2013年。
With increased pollutant emissions and exposure due to mass urbanization worldwide, air quality measurement campaigns and epidemiology studies on air pollution and health effects have become increasingly common to estimate individual exposures and evaluate their association to various illnesses. As air pollution concentrations are known to be highly heterogeneous, sophisticated physically based air quality models (AQMs), in particular models based on Computational Fluid Dynamics, can provide spatially rich approximations and enable to better estimate individual exposure. In this work we investigate reduced basis (RB) methods [1] to diminish the resolution cost of advanced AQMs developed for concentration evaluation at urban scales. These models depend on varying parameters including meteorological conditions and pollutant emissions, often unknown at the micro scale. RB methods use approximation spaces made of suitable samples of solutions of AQMs governed by parameterized partial differential equations (PDEs), to rapidly construct accurate and computationally efficient approximations. A key to this technique is decomposing computational work into an offline and online stage. The RB functions used to build approximation spaces and all expensive parameter-independent terms, are computed 'offline' once and stored, whereas inexpensive parameter-dependent quantities are evaluated 'online' for each new value of the parameters. However, the decomposition of the matrices into offline-online pieces requires modifying the calculation code, an intrusive procedure, which in some situations is impractical. In this work, we extend the Parameterized-Background Data-Weak (PBDW) method introduced in [2] to physically based AQMs. We will generate a sample of solutions from physical AQMs with varying meteorological conditions and pollution emissions to build the RB approximation space and combine it with experimental observations, using the method in [3], to improve pollutant concentration estimations, with the goal of collaboration with an epidemiology exposure assessment team at the University of California-Berkeley. The goal is to rapidly estimate 'online' pollutant concentration(s) around an area of interest at micro scale, using available AQMs in a non-intrusive and computationally efficient manner. REFERENCES [1] Prud'homme, C., Rovas, D. V., Veroy, K., Machiels, L., Maday, Y., Patera, A. T., & Turinici, G. (2002). 'Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods'. Journal of Fluids Engineering, 124(1), 70-80 [2] Y. Maday, A.T Patera, J.D. Penn and M. Yano, 'A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics', Int. J. Numer. Meth. Engng (2014). [3] Yvon Maday and Olga Mula. A generalized empirical interpolation method: application of reduced basis techniques to data assimilation. In Analysis and numerics of partial differential equations, pages 221-235. Springer, 2013.