Propagating and visualising parametric uncertainties conditioned by modelling
Lead Research Organisation:
Imperial College London
Department Name: Aeronautics
Abstract
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
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
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R511961/1 | 01/10/2017 | 31/03/2023 | |||
| 2091447 | Studentship | EP/R511961/1 | 01/10/2017 | 30/09/2021 | Nicholas Pepper |
| Description | Designs of new engineering products must yield good performance in a wide variety of operating conditions. The performance of these designs are stochastic due to irreducible uncertainties present in the system. To address this, Uncertainty Quantification (UQ) techniques are used to evaluate the performance of candidate designs. As part of this award we developed several methods for assisting engineers with decision making in the early stages of the design process. At this stage, the performance of candidate designs are assessed using computational models and experimental data is typically scarce or unavailable. In particular, we address three early design challenges: how to efficiently propagate uncertainty through computational models at multiple scales; how to infer missing data from scarce experimental data using computational models; and how scarce experimental measurements of a quantity can be leveraged using computational simulations (a problem referred to as data fusion). The methods combine non-intrusive Polynomial Chaos (NIPC), probabilistic equivalence and the Maximum Entropy Principle and are applied to several test cases involving missing data in turbomachinery and composite structures. In addition to developing methods based on polynomial chaos, we have also researched how machine learning techniques may be applied to make these algorithms more scalable. For instance, we have developed a knowledge based neural network (KBaNN) method as an alternative formulation for data fusion problems. KBaNNs share the advantages of other neural networks, having good approximation properties; they can also handle scarce training sets efficiently. Finally, we are collaborating with NASA on an adaptive method for reliability analysis that uses machine learning to learn the boundary between the regions of a design space where a design is feasible and where it will suffer failure. While still in the early stages of development, our algorithm shows promising results when compared to existing methods in the literature. |
| Exploitation Route | There are several ways in which the novel methods developed as part of this award may be taken forward. The first task is to raise awareness of the outcomes of the award. From an academic standpoint, 5 papers have been published or accepted for publishing in journals and conferences, with a further 2 journal papers under review. We plan to present the results of our current collaboration with NASA at the ESREL conference in September. The second task is to apply the methods that have been developed as part of this award to more challenging industrial test cases, that can demonstrate the benefits of the algorithms to a wider audience that is perhaps not expert in Uncertainty Quantification. To this end, the results of the PhD have been presented to an internal audience at Airbus in two seminars, with discussions scheduled about possible test cases. |
| Sectors | Aerospace, Defence and Marine,Manufacturing, including Industrial Biotechology,Transport |