Robust optimisation of computationally expensive computational fluid dynamics models using multi-fidelity approaches

• Main Author: Ellison, Matthew
• Format: Dissertation
• Language: English
• Published: University of Liverpool 2021
• DOI: 10.17638/03139981

This dissertation explores the optimisation of computationally expensive models, whilst taking into account input uncertainty. The methods proposed are designed to be applicable to models used within the engineering industry, where a key aspect is the process of selecting a design that satisfies several constraints and performance objectives simultaneously. Modern engineering products often have to balance performance against factors such as profitability and environmental impact. There are often many feasible designs that satisfy these requirements. Locating such designs, and subsequently selecting an optimal choice, is often a challenging task. Moreover, any final design choice is subject to a variety of uncertainty that arises in both the manufacture and life cycle of the product. Selecting a design that is robust to such uncertainty, whilst still exhibiting near-optimal performance, is critical to the lifetime performance of a new product. Complex computer models are increasingly employed in the design process to provide information on the estimated performance of a potential design. Such models are typically computationally expensive, which often limits the number of evaluations available to perform tasks such as robust optimisation. Two novel approaches are presented in this work to address this problem. The first is a direct optimisation approach extending an algorithm known as subset simulation to factor in input uncertainty, alongside strategies to boost its computational efficiency. In general, this is the preferred approach as it introduces no further uncertainty into the problem, however in the case that computational constraints prohibits its application, another approach is necessary. This provided the motivation behind the second approach, which employs a surrogate modelling technique known as Gaussian process emulation to provide an inexpensive statistical approximation of the expensive computer model. This emulator is enhanced with a novel sampling scheme and multi-fidelity training data, and is optimised in place of the expensive computer model without the computational constraints. As such, the approaches are not in direct competition, but provide the means to perform robust optimisation across a range of computational budgets. The theoretical underpinnings of each of the proposed methods are discussed in detail, before they are applied to illustrative examples. Finally, each of the methods are applied to industrial case studies involving expensive computational fluid dynamics models provided by the industrial partner. The results showed that the two approaches were successful in performing efficient robust optimisation of computational expensive engineering models. In particular, the direct approach results showcased the considerable impact on the computational efficiency of the robust optimisation process, without compromising on performance. For the surrogate approach, the case studies highlight the ability to successfully perform robust optimisation even with stringent computational constraints.