Uncertainty propagation and quantification for digital twins

数字孪生的不确定性传播和量化

• 批准号: 2120256
• 金额: --
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2120256
• 关键词: Uncertainty; propagation; quantification; digital; twins

Probability has an inadequate model of ignorance, which creates practical problems in risk analysis. The mathematics used in risk assessments must be generalised to handle the epistemic uncertainty that commonly arises in imperfect measurements, unstudied dependencies, and incomplete scientific understanding generally. Current methods force scientists and engineers to make untenable assumptions in order to get any quantitative answer at all, rather than developing technologies for making calculations that require only the assumptions they feel comfortable making. These methods can result in tests that get asymptotically more reliable with increasing sample size, without referencing any gold standard results. They can also result in probability dilation were, counterintuitively, more information can necessarily lead to higher uncertainty.Confidence structures (c-boxes) generalise confidence distributions and provide an interpretation by which confidence intervals at any confidence level can be specified for a parameter of interest (Balch, 2012). C-boxes can be used in calculations using the methods of probability bounds analysis and yield results that also admit this confidence interpretation. The project will analyse ways in which c-boxes can be used to improve digital twin decision making methodology. Similar problems, including satellite conjunction analysis and medical diagnosis will be examined.The project will also look at ways in which uncertainty quantification can be included in computer simulations, a fundamental problem in the development of digital twins. Uncertainty analysis is half the story in any computation. It is better to compute with information that we do know rather than making pretend calculations with infinitely precise numbers. Consider the situation where an analyst has fifty thousand lines of 'uncertainty-naïve' source code but is unwilling, either due to mathematical complexity or the time required, to rewrite their code so that it contains full account of the uncertainty involved. A compiler will be developed that handles the specifications of uncertainties, either automatically or with end-user input, and inserts calls to an object-oriented library of 'intrusive' uncertainty quantification (UQ) algorithms, including probability distributions, confidence boxes, probability boxes and intervals. ANTLR, a parser/lexer generator, will be used along with Python to translate original code into UQ code in the same language. In theory, the approach could work with any computer language. Initially the compiler will be developed for Python but possibly extended to be able to handle MATLAB, C and FORTRAN languages. Ancillary strategies supporting automated simplification of mathematical expressions involving repeated variables will be developed to help reduce uncertainty.Balch, M. S. (2012) 'Mathematical foundations for a theory of confidence structures', International Journal of Approximate Reasoning, 53(7), pp. 1003-1019. doi: 10.1016/j.ijar.2012.05.006.

概率的无知模型不充分，这在风险分析中产生了实际问题。风险评估中使用的数学必须得到推广，以处理通常在不完美的测量、未经研究的依赖性和不完整的科学理解中常见的认知不确定性。当前的方法迫使科学家和工程师做出站不住脚的假设，以获得任何定量答案，而不是开发只需要他们觉得舒服的假设进行计算的技术。这些方法可以使测试随着样本量的增加而逐渐变得更加可靠，而无需参考任何金标准结果。它们还可能导致概率膨胀，与直觉相反，更多的信息必然会导致更高的不确定性。置信结构（c-box）概括了置信分布，并提供了一种解释，通过这种解释可以为感兴趣的参数指定任何置信水平的置信区间（Balch，2012）。 C 盒可用于使用概率界限分析方法进行的计算，并产生也承认这种置信度解释的结果。该项目将分析使用 c-box 改进数字孪生决策方法的方法。类似的问题，包括卫星结合分析和医学诊断，也将得到研究。该项目还将研究如何将不确定性量化纳入计算机模拟中，这是数字孪生发展中的一个基本问题。不确定性分析只是任何计算的一半。最好使用我们已知的信息进行计算，而不是使用无限精确的数字进行假装计算。考虑这样一种情况：分析师拥有五万行“不确定性朴素”源代码，但由于数学复杂性或所需时间而不愿意重写其代码，以使其包含所涉及的不确定性的完整考虑。将开发一个编译器，自动或通过最终用户输入处理不确定性规范，并插入对“侵入式”不确定性量化（UQ）算法的面向对象库的调用，包括概率分布、置信框、概率框和区间。 ANTLR 是一个解析器/词法分析器生成器，将与 Python 一起使用，将原始代码翻译为相同语言的 UQ 代码。理论上，该方法可以适用于任何计算机语言。最初，编译器将针对 Python 开发，但可能会扩展为能够处理 MATLAB、C 和 FORTRAN 语言。将开发支持自动简化涉及重复变量的数学表达式的辅助策略，以帮助减少不确定性。Balch, M. S. (2012)“置信结构理论的数学基础”，国际近似推理杂志，53(7)，第 1003-1019 页。 doi：10.1016/j.ijar.2012.05.006。