Propagating and visualising parametric uncertainties conditioned by modelling

通过多尺度模型传播不确定性的问题在许多领域都遇到过，包括在飞机设计中，需要根据来自联片试验的有限数据估计机翼等完整部件的可靠性。本博士的目标之一是开发一种方法，以一种计算效率高的方式将模型最小尺度输入的不确定性传播到最大尺度的输出。这将允许设计师在多尺度模型上执行不确定性量化，这将有助于通过减少对物理测试的需求来加快设计过程。图1说明了这一点。所开发的方法也应该适用于所谓的反问题，其中需要给出某种输出的材料的性质（以分布形式）可以反计算。这个博士学位的另一个目标是开发工具来帮助设计师预测所谓的“不确定性锥体”。随着在设计过程中做出更多的设计决策，潜在产品设计所占的空间就会减少；因此，在性能范围内实现的产品也减少。随着时间的推移，设计性能中减少不确定性的包络被称为不确定性锥。将开发一种工具，其中将应用机器学习技术，这将帮助设计师估计他们可能希望在不确定性锥体上做出的设计决策的后果。这在多学科设计中特别有用，因为它可以让每个学科的团队了解在不与其他团队协商的情况下对初步设计进行更改的后果。例如，在飞机设计的背景下，这样的工具可以让空气动力学家了解拟议的设计变更如何影响机翼的内力，而无需咨询结构团队。博士课程的最后一个方面涉及参数不确定性的可视化。换句话说，不确定性分析的结果如何最好地呈现并传达给可能没有强大统计背景的决策者。实现这一目标将需要识别不确定性分析的最重要方面，并应用数据科学中常见的表示方法，例如在平行坐标中绘图，以可视化不确定性分析的结果。总之，博士学位有以下目标：-在多尺度模型中通过尺度传播不确定性-预测设计的“不确定性锥”-考虑沟通和表示不确定性分析结果的策略

The problem of propagating uncertainty through multiscale models is one encountered in many fields, including in aircraft design where it is necessary to estimate the reliability of a complete part such as a wing based on limited data from coupon tests. One aim of this PhD is to develop methods of propagating uncertainties in the inputs of the smallest scales of a model through to the outputs of the largest scales in a computationally efficient way. This will allow designers to perform uncertainty quantification on multiscale models which will help to speed up the design process by reducing the need for physical tests. This is illustrated in Figure 1. The methods developed should also be applicable to the so called inverse problem, where the properties of the materials (in distribution form) needed to give a certain output may be back calculated.Another aim of this PhD is to develop tools to assist designers by forecasting the so called 'cone of uncertainty'. As more design decisions are made over the course of the design process the space occupied by potential product designs is reduced; hence the range in performance achieved by the product also decreases. The envelope of the reducing uncertainty in the performance of the design over time is referred to as the cone of uncertainty. A tool will be developed, in which machine learning techniques will be applied, that will assist designers by estimating the consequences of design decisions they may wish to make on the cone of uncertainty. This would be particularly useful in multi-disciplinary design as it would give teams in each discipline an idea of the consequences of making changes to preliminary designs without having to consult with other teams. For instance in the context of aircraft design, such a tool could give an aerodynamicist an idea of how a proposed design change could affect the internal forces in the wing, without having to consult with the structures team. The final aspect of the PhD concerns the visualisation of parametric uncertainties. In other words, how the results of uncertainty analyses may be best represented and communicated to decision makers who may not have a strong background in statistics. Meeting this aim will require identification of the most important aspects of an uncertainty analyses and application of methods of representation common in data science, such as plotting in parallel coordinates, to visualising the results of uncertainty analyses. In summary, the PhD has the following goals: - To propagate uncertainty through scales in multiscale models - To forecast the 'cone of uncertainty' of a design- To consider strategies for communicating and representing the results of uncertainty analyses