Presented in this thesis are novel methods for uncertainty quantification and management (UQ&M) in computational engineering design. The research has been motivated by the industrial need for improved UQ&M techniques, particularly in response to the rapid development of the model-based approach and its application to the (early) design of complex products such as aircraft. Existing work has already addressed a number of theoretical and computational challenges, especially regarding uncertainty propagation. In this research, the contributions to knowledge are within the wider UQ&M area.
The first contribution is related to requirements for an improved margin management policy, extracted from the FP7 European project, TOICA (Thermal Overall Integrated Conception of Aircraft). Margins are traditional means to mitigate the effect of uncertainty. They are relatively better understood and less intrusive in current design practice, compared with statistical approaches. The challenge tackled in this research has been to integrate uncertainty analysis with deterministic margin allocations, and to provide a method for exploration and trade-off studies. The proposed method incorporates sensitivity analysis, uncertainty propagation, and the set-based design paradigm. The resulting framework enables the designer to conduct systematic and interactive trade-offs between margins, performances and risks. Design case studies have been used to demonstrate the proposed method, which was partially evaluated in the TOICA project.
The second contribution addresses the industrial need to properly ‘allocate’ uncertainty during the design process. The problem is to estimate how much uncertainty could be tolerated from different sources, given the acceptable level of uncertainty associated with the system outputs. Accordingly, a method for inverse uncertainty propagation has been developed. It is enabled by a fast forward propagation technique and a workflow reversal capability. This part of the research also forms a contribution to the TOICA project, where the proposed method was applied on several test-cases. Its usefulness was evaluated and confirmed through the project review process.
The third contribution relates to the reduction of UQ&M computational cost, which has always been a burden in practice. To address this problem, an efficient sensitivity analysis method is proposed. It is based on the reformulation and approximation of Sobol’s indices with a quadrature technique. The objective is to reduce the number of model evaluations. The usefulness of the proposed method has been demonstrated by means of analytical and practical test-cases. Despite some limitations for several specific highly non-linear cases, the tests confirmed significant improvement in computational efficiency for high dimensional problems, compared with traditional methods.
In conclusion, this research has led to novel UQ&M tools and techniques, for improved decision making in computational engineering design. The usefulness of these methods with regard to efficiency and interactivity has been demonstrated through relevant test-cases and qualitative evaluation by (industrial) experts.
Finally, it is argued that future work in this field should involve research and development of a comprehensive framework, which is able to accommodate uncertainty, not only with regard to computation, but also from the perspective of (expert) knowledge and assumptions
