Uncertainty propagation and quantification for digital twins

概率有一个不充分的无知模型，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加以推广，以处理认识上的不确定性，这种不确定性通常出现在不完善的测量、未研究的依赖性和不完整的科学理解中。目前的方法迫使科学家和工程师做出站不住脚的假设，以获得任何定量的答案，而不是开发技术来进行计算，只需要他们感到舒适的假设。这些方法可以导致随着样本量的增加而逐渐变得更可靠的测试，而无需参考任何金标准结果。它们也可能导致概率膨胀，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盒）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盒可以用于使用概率界限分析方法的计算中，并产生也承认这种置信度解释的结果。该项目将分析如何使用C盒来改进数字孪生决策方法。该项目还将研究如何将不确定性量化纳入计算机模拟，这是开发数字孪生模型的一个基本问题。不确定性分析是任何计算的一半。最好用我们知道的信息进行计算，而不是用无限精确的数字进行假装的计算。考虑这样一种情况：一位分析师有5万行“不确定性初始”的源代码，但由于数学复杂性或所需时间，他不愿意重写代码，以便充分考虑所涉及的不确定性。将开发一个编译器，处理规格的不确定性，无论是自动或最终用户的输入，并插入调用面向对象的库的'侵入式'不确定性量化（UQ）算法，包括概率分布，置信度盒，概率盒和间隔。ANTLR是一个解析器/词法分析器生成器，它将与Python一起沿着使用，将原始代码翻译成相同语言的UQ代码。理论上，这种方法可以适用于任何计算机语言。最初，编译器将为Python开发，但可能扩展到能够处理MATLAB，C和FORTRAN语言。辅助策略支持涉及重复变量的数学表达式的自动简化，将有助于减少不确定性。S.（2012）“信心结构理论的数学基础”，国际近似推理杂志，53（7），pp。1003-1019. doi：10.1016/j.ijar.2012.05.006。

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.