Propagating and visualising parametric uncertainties conditioned by modelling

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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