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Calculation method of state transfer matrix in Markov chain model for airborne contaminant transport: Investigation and improvement

机译：机载污染物运输马尔可夫链模型状态转移矩阵的计算方法：调查与改进

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摘要

Rapid contaminant transport simulation is important in emergency scenarios, and Markov chain models have shown promise in this regard. The state transfer matrix (STM) is the core of the Markov chain model and determines the simulation accuracy and computing cost. However, existing methods to calculate the STM result in significant errors or large computing costs. Using set theory, the characteristic form of the STM was investigated according to the continuity equation for incompressible fluids. Based on this form, the calculation method of the STM when the initial contaminant is distributed uniformly was improved. The performances of the original and modified methods were compared via a case study. In addition, the influence of underlying airflow grid resolution on model performance was analyzed. Finally, sensitivity analysis was conducted to determine the dominant factor. The results revealed that the STM should be constructed as an approximate doubly stochastic matrix; however, this is problematic due to the discrete underlying airflow and the associated interpolation. As an alternative, a left stochastic matrix is appropriate, with higher accuracy when the initial contaminant is uniformly distributed over a large area. Increasing the underlying airflow grid resolution can improve the model accuracy; however, a minimum grid resolution with a credible velocity field is sufficient, especially considering the computing cost. Sensitivity analysis showed that the Markov state size is the dominant factor for the accuracy and computing cost, and it should be carefully selected. This study can aid the development of a Markov chain model for airborne contaminant transport.
机译：快速污染的运输模拟在紧急情况中很重要，马尔可夫链模型在这方面表现出承诺。状态转移矩阵（STM）是马尔可夫链模型的核心，并确定模拟精度和计算成本。但是，计算STM的现有方法导致显着的错误或大计算成本。使用设定理论，根据不可压缩流体的连续性方程来研究STM的特征形式。基于这种形式，改善了初始污染物均匀分布时STM的计算方法。通过案例研究比较了原始和改性方法的性能。此外，分析了潜在的气流网格分辨率对模型性能的影响。最后，进行了敏感性分析以确定显性因素。结果表明，STM应构造为近似双随机基质;然而，由于离散的底层气流和相关的插值，这是有问题的。作为替代方案，当初始污染物均匀地分布在大面积上时，左随机矩阵是合适的，具有更高的精度。增加潜在的气流网格分辨率可以提高模型精度;然而，具有可靠速度场的最小网格分辨率足够，特别是考虑计算成本。敏感性分析表明，马尔可夫状态大小是准确性和计算成本的主导因素，应该仔细选择它。本研究可以帮助开发Markov链模型的空气污染物运输。

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  • 来源
    《Building and Environment》 |2020年第11期|107295.1-107295.15|共15页
  • 作者

    Hu Mengqiang; Liu Lumeng; Liu Meng;

  • 作者单位

    Chongqing Univ Sch Civil Engn Chongqing 400044 Peoples R China|Chongqing Univ Joint Int Res Lab Green Bldg & Built Environm Minist Educ Chongqing 400044 Peoples R China|Chongqing Univ Natl Ctr Int Res Low Carbon & Green Bldg Chongqing 400044 Peoples R China;

    Chongqing Univ Sch Civil Engn Chongqing 400044 Peoples R China|Chongqing Univ Joint Int Res Lab Green Bldg & Built Environm Minist Educ Chongqing 400044 Peoples R China|Chongqing Univ Natl Ctr Int Res Low Carbon & Green Bldg Chongqing 400044 Peoples R China;

    Chongqing Univ Sch Civil Engn Chongqing 400044 Peoples R China|Chongqing Univ Joint Int Res Lab Green Bldg & Built Environm Minist Educ Chongqing 400044 Peoples R China|Chongqing Univ Natl Ctr Int Res Low Carbon & Green Bldg Chongqing 400044 Peoples R China;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Markov chain model; State transfer matrix; Contaminant transport; Sensitivity analysis;

    机译：马尔可夫链模型;国家转移矩阵;污染物;敏感性分析;

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