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Decision Support for Flow in Porous Media: Optimal Sampling for Data Assimilation

多孔介质流动的决策支持：数据同化的最佳采样

基本信息

批准号：
9870005
负责人：
Roger Ghanem
金额：
$ 18.21万
依托单位：
Johns Hopkins University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1998
资助国家：
美国
起止时间：
1998-09-01 至 2002-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870005&HistoricalAwards=false
关键词：
Decision Support Flow Porous Media

项目摘要

This research features a novel concept for addressing environmental engineering problems that takes into account the heterogeneous nature of the soil medium. The emphasis of the research is on developing and implementing new simulation techniques the output of which can be readily utilized in decision making as related to ensuring a sustainable environment. In particular, the output will permit a very efficient simulation of statistically consistent realizations of fate of pollutants in the ground. Additionally, the simulation technique will provide the optimal location for the sampling of hydraulic properties in a heterogeneous porous medium. Optimality, in this case, is construed to imply good predictive capability of the mathematical model under incomplete information. The concept hinges upon representing uncertain material properties as a combination of their various scales multiplied by random coefficients. This will be achieved by relying on the Karhunen-Loeve expansion that takes into account the probabilistic structure of the field, as well as the finite extent of the domain over which the problem is defined. The solution process is represented as a nonlinear functional expansion with respect to these scales of heterogeneity. The coefficients in this expansion are calculated by solving a linear system of algebraic equations. Once this expansion is obtained, the sensitivity of the predicted solution will be analytically evaluated. The sensitivity of the solution with respect to the values of the random hydraulic parameters at various spatial locations can be readily evaluated, and the optimal location of samples identified. This formulation affords a theoretical rigor which is believed to be essential to progress in the field of stochastic hydrology and reliability of ground-water flow systems. It permits an optimal representation of the random processes involved using a minimum number of random variables. The research will complement current work by the Principal Investigator on stochastic model development for ground water flow and extend its applicability to decision support.

这项研究的特点是一个新的概念，解决环境工程问题，考虑到土壤介质的异质性。研究的重点是开发和实施新的模拟技术，其输出可以很容易地用于决策，以确保可持续的环境。特别是，输出将允许一个非常有效的模拟统计一致的实现污染物在地面上的命运。此外，模拟技术将提供最佳的位置，在非均质多孔介质中的水力特性的采样。在这种情况下，最优性被解释为在不完全信息下数学模型具有良好的预测能力。这个概念取决于将不确定的材料属性表示为它们的各种尺度乘以随机系数的组合。这将通过依赖于Karhunen-Loeve展开来实现，该展开考虑了场的概率结构以及定义问题的域的有限范围。的解决方案的过程表示为一个非线性的功能扩展这些尺度的异质性。这种展开式中的系数是通过求解线性代数方程组来计算的。一旦获得该展开，将分析评估预测解的灵敏度。可以很容易地评估在不同的空间位置的随机水力参数的值的解决方案的灵敏度，并确定样本的最佳位置。这个公式提供了一个理论上的严谨性，这被认为是必不可少的随机水文学和地下水流系统的可靠性领域的进展。它允许使用最少数量的随机变量的随机过程的最佳表示。这项研究将补充首席研究员目前在地下水流随机模型开发方面的工作，并将其适用性扩展到决策支持。