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Predictive simulation and model based hazard maps of geophysical mass flows.

机译：预测模拟和基于模型的地球物理质量流危害图。

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摘要

The purpose of this work is to improve the predictive capabilities of geophysical flow computer models and in particular the Titan2D depth-averaged granular flow simulator. Within this broad scope, there are three interrelated themes. The first is to improve the accuracy of Titan2D's physical and numerical modeling capabilities. The second is to quantify the uncertainty in geophysical ow simulation output. The third is to develop a systematic methodology to aid volcanologists in incorporating simulator output into the production of hazard maps. The motivating challenge often is the need to analyze hazards over a jurisdiction in a short period of time (e.g. less than 24 hours) following a specified premonitory event. The need requires advances in all of the above themes. We note that new ideas that we introduce will potentially impact areas beyond the application at hand. In pursuit of the first theme, contributions of this work to Titan2D include (1) The capability to accept spatially varying material properties (2) A physics-based criteria to determine if the ow should be stopped, and techniques to bring the flow to rest (3) A new flow initiation mechanism modeling a flux of material effusing from the ground (4) A multi-faceted approach that mitigates the "thin-layer problem" common to "depth-averaged" flow solvers.;Toward the second theme, we developed two different classes of uncertainty representation approaches. The first is Polynomial Chaos Quadrature (PCQ) which is similar to Non-Intrusive Spectral Projection (NISP) but with a few numerical advantages. It is general enough to be considered a superset of NISP and Point Estimate Methods (PEM). The second class involves Bayesian Emulation, in particular the Bayes Linear Method (BLM). Some of its advantages include: it provides an estimate of the discrepancy between the statistical model and the simulator, which can also be used to drive adaptive sampling;;and this class can reuse existing data, rather than requiring that it be known at very specific locations in sample space. Notable contributions in this field include (1) A positive-definite error model with a different set of roughness parameters for each of the multiple outputs (2) A new formula to compute the unadjusted variance given a set of data and roughness parameters that has favorable properties compared to what is found in the literature (3) A set of guidelines that significantly reduces the region of roughness parameter space that must be searched in order to find good values without requiring specification of a prior by an expert user (4) A way to construct a Bayes Linear emulator that accounts for known measurement noise without requiring specification of a prior by an expert user (5) Adaptive selection of global polynomial basis functions for the least squares fit used as the unadjusted mean of a Bayes Linear emulator (6) A new PieceWise linear ensemble of EMulators (PWEM) approach which is equally applicable to fully Bayesian and Bayes Linear emulation, and appears to be more accurate than adaptively selected global polynomial basis functions. Of even greater importance, these computations can be parallelized easily, enabling the use of modern supercomputers.;For the third theme, this dissertation introduces new approaches to constructing maps of probability-of-hazard through PCQ and PWEM fast surrogates. The PWEM approach correlates through physical space as well as uncertainty space, i.e. it produces a single macro-emulator that can be evaluated at all points on an East-North map. We produced a "probability within a specified time period" of hazard map for the island of Montserrat by drawing sample volumes from a Pareto distribution that was provided by collaborators at SAMSI (Statistical and Applied Mathematical Sciences Institute). With the distributions in hand and utilizing roughly 1000 processors of a supercomputer cluster, we created a probability-of-hazard map in less than 9 hours from start to finish. The original goal was to generate a model based hazard map in under 24 hours.;The ideas described above under themes two and three are of general applicability for many related areas and our current work is focused on such generalizations. Limited application of the PCQ method for the simulation of other complex systems, e.g. child restraint systems, has been successful.
机译：这项工作的目的是提高地球物理流量计算机模型的预测能力，尤其是Titan2D深度平均颗粒流量模拟器的预测能力。在这个广泛的范围内，存在三个相互关联的主题。首先是提高Titan2D物理和数值建模功能的准确性。第二个是量化地球物理流模拟输出的不确定性。第三是开发一种系统的方法，以帮助火山学家将模拟器的输出整合到危险图的制作中。激励性挑战通常是需要在特定的监控事件发生后的短时间内（例如少于24小时）分析辖区内的危害。需要在上述所有主题上取得进步。我们注意到，我们引入的新想法可能会影响当前应用程序以外的领域。为了追求第一个主题，这项工作对Titan2D的贡献包括（1）接受空间变化的材料属性的能力（2）基于物理的标准来确定是否应停止流动以及使流动停止的技术（3）一种新的流动启动机制，用于模拟从地面流出的物质通量（4）一种多方面的方法，可以减轻“深度平均”流动求解器常见的“薄层问题”。我们开发了两种不同类别的不确定性表示方法。第一个是多项式混沌正交（PCQ），它与非介入式光谱投影（NISP）相似，但具有一些数值上的优势。它足以被视为NISP和点估计方法（PEM）的超集。第二类涉及贝叶斯仿真，尤其是贝叶斯线性方法（BLM）。它的一些优点包括：它提供了统计模型与仿真器之间的差异的估计，也可以用于驱动自适应采样；并且此类可以重用现有数据，而不是要求非常具体地知道它样本空间中的位置。该领域的显着贡献包括（1）对于多个输出中的每个输出，具有一组不同粗糙度参数的正定误差模型（2）给定一组数据和粗糙度参数，它们具有有利的条件，用于计算未调整方差的新公式与文献中所发现的相比具有更好的特性（3）一组准则，可显着减少必须寻找的粗糙度参数空间区域，才能找到良好的值，而无需专家用户事先指定（4）构造贝叶斯线性仿真器，以解决已知的测量噪声，而无需专业用户指定先验条件（5）自适应选择全局多项式基函数，以最小二乘拟合作为贝叶斯线性仿真器的未调整均值（6）一种新的PieceWise模拟器线性集成（PWEM）方法，同样适用于完全贝叶斯和贝叶斯线性仿真，并且比自适应选择的全局多项式基函数。更为重要的是，这些计算可以很容易地并行化，从而可以使用现代超级计算机。对于第三个主题，本论文介绍了通过PCQ和PWEM快速替代方法构建危险概率图的新方法。 PWEM方法通过物理空间以及不确定性空间进行关联，即它产生了一个可以在东西向地图上的所有点进行评估的单个宏仿真器。我们通过从SAMSI（统计和应用数学科学研究所）的合作伙伴提供的帕累托分布中抽取样本量，得出了蒙特塞拉特岛的“特定时间范围内”的风险图。掌握了这些分布，并利用了大约1000个超级计算机集群的处理器，我们从头到尾都在不到9小时的时间内创建了危险概率图。最初的目标是在24小时之内生成基于模型的危害图。上面在主题2和主题3下描述的思想在许多相关领域具有普遍适用性，我们目前的工作集中在这种概括上。 PCQ方法在模拟其他复杂系统方面的应用有限儿童约束系统，已经成功。

著录项

  • 作者

    Dalbey, Keith R.;

  • 作者单位

    State University of New York at Buffalo.;

  • 授予单位 State University of New York at Buffalo.;
  • 学科 Engineering Civil.;Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 316 p.
  • 总页数 316
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 建筑科学;机械、仪表工业;
  • 关键词

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